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Basic math word problemsYou encounter and solve basic math word problems on a daily basis without thinking about it. Knowing how to tackle and solve word problems is an important skill in school. You may find it useful to review some math problem solving strategies . Whole number word problemsFractions word problems, ratio and proportion word problems . Ratio word problems Six carefully selected ratio word problems with solutions to help you master ratios. Proportion word problems Four carefully selected proportion word problems with solutions. Convert square feet to acres See how you can use proportion to convert square feet to acres Percentage word problemsAverage word problems. Average word problems Word problems about finding the average from easy to challenging Comparison word problemsComparison word problems A variety of comparison word problems from easy to challenging Venn diagram word problemsVenn diagram word problems A variety of word problems from easy to challenging Have A Great Basic Math Word Problem?Share it here with a very detailed solution! Enter Your Title Entering your basic math word problem is easy to do. Just type!...
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Breadcrumbs ![basic maths problem solving questions Math Workbooks](https://www.k5learning.com/docs/k-5-math-workbooks-pr.png) Download & Print From only $2.20 Free Math WorksheetsPrintable math worksheets from k5 learning. Our free math worksheets cover the full range of elementary school math skills from numbers and counting through fractions, decimals, word problems and more. All worksheets are printable files with answers on the 2nd page. Math worksheets by grade:Math worksheets by topic:![basic maths problem solving questions basic maths problem solving questions](https://www.k5learning.com/themes/custom/k5_b/images/pinit-20.png) Sample Math Worksheet What is K5? K5 Learning offers free worksheets , flashcards and inexpensive workbooks for kids in kindergarten to grade 5. Become a member to access additional content and skip ads. ![basic maths problem solving questions basic maths problem solving questions](https://www.k5learning.com/themes/custom/k5_b/images/k5-member-logo-100px.png) Our members helped us give away millions of worksheets last year. We provide free educational materials to parents and teachers in over 100 countries. If you can, please consider purchasing a membership ($24/year) to support our efforts. Members skip ads and access exclusive features. Learn about member benefits This content is available to members only. Join K5 to save time, skip ads and access more content. Learn More Mastery-Aligned Maths Tutoring “The best thing has been the increase in confidence and tutors being there to deal with any misunderstandings straight away." FREE daily maths challenges A new KS2 maths challenge every day. Perfect as lesson starters - no prep required! ![basic maths problem solving questions FREE daily maths challenges](https://thirdspacelearning.com/wp-content/uploads/2024/02/Daily-maths-challenge-3.png) 30 Problem Solving Maths Questions And Answers For GCSESophie Bessemer Problem solving maths questions can be challenging for GCSE students as there is no ‘one size fits all’ approach. In this article, we’ve compiled tips for problem solving, example questions, solutions and problem solving strategies for GCSE students. Since the current GCSE specification began, there have been many maths problem solving exam questions which take elements of different areas of maths and combine them to form new maths problems which haven’t been seen before. While learners can be taught to approach simply structured problems by following a process, questions often require students to make sense of lots of new information before they even move on to trying to solve the problem. This is where many learners get stuck. GCSE MATHS 2024: STAY UP TO DATE Join our email list to stay up to date with the latest news, revision lists and resources for GCSE maths 2024. We’re analysing each paper during the course of the 2024 GCSEs in order to identify the key topic areas to focus on for your revision. Thursday 16th May 2024: GCSE Maths Paper 1 2024 Analysis & Revision Topic List Monday 3rd June 2024: GCSE Maths Paper 2 2024 Analysis & Revision Topic List Monday 10th June 2024: GCSE Maths Paper 3 2024 Analysis GCSE 2024 dates GCSE 2024 results (when published) GCSE results 2023 How to teach problem solvingIn the Ofsted maths review , published in May 2021, Ofsted set out their findings from the research literature regarding the sort of curriculum and teaching that best supports all pupils to make good progress in maths throughout their time in school. Regarding the teaching of problem solving skills, these were their recommendations: - Teachers could use a curricular approach that better engineers success in problem-solving by teaching the useful combinations of facts and methods, how to recognise the problem types and the deep structures that these strategies pair to.
- Strategies for problem-solving should be topic specific and can therefore be planned into the sequence of lessons as part of the wider curriculum. Pupils who are already confident with the foundational skills may benefit from a more generalised process involving identifying relationships and weighing up features of the problem to process the information.
- Worked examples, careful questioning and constructing visual representations can help pupils to convert information embedded in a problem into mathematical notation.
- Open-ended problem solving tasks do not necessarily mean that the activity is the ‘ideal means of acquiring proficiency’. While enjoyable, open ended problem-solving activities may not necessarily lead to improved results.
If you’re a KS2 teacher needing more support and CPD around teaching reasoning, problem solving & planning for depth we have a whole series of word problems and strategies to teach them available for you. ![basic maths problem solving questions 30 Problem Solving Maths Questions, Solutions & Strategies](https://thirdspacelearning.com/wp-content/uploads/2023/04/30-Problem-solving-maths-listing-image.png) 30 Problem Solving Maths Questions, Solutions & Strategies Help your students prepare for their math GCSE with these free problem solving maths questions, solutions and strategies. 6 tips to tackling problem solving maths questionsThere is no ‘one size fits all’ approach to successfully tackling problem solving maths questions however, here are 6 general tips for students facing a problem solving question: - Read the whole question, underline important mathematical words, phrases or values.
- Annotate any diagrams, graphs or charts with any missing information that is easy to fill in.
- Think of what a sensible answer may look like. E.g. Will the angle be acute or obtuse? Is £30,000 likely to be the price of a coat?
- Tick off information as you use it.
- Draw extra diagrams if needed.
- Look at the final sentence of the question. Make sure you refer back to that at the end to ensure you have answered the question fully.
There are many online sources of mathematical puzzles and questions that can help learners improve their problem-solving skills. Websites such as NRICH and our blog on SSDD problems have some great examples of KS2, KS3 and KS4 mathematical problems. Read more: KS2 problem solving and KS3 maths problem solving In this article, we’ve focussed on GCSE questions and compiled 30 problem solving maths questions and solutions suitable for Foundation and Higher tier students. Additionally, we have provided problem solving strategies to support your students for some questions to encourage critical mathematical thinking . For the full set of questions, solutions and strategies in a printable format, please download our 30 Problem Solving Maths Questions, Solutions & Strategies. Looking for additional support and resources at KS3? You are welcome to download any of the secondary maths resources from Third Space Learning’s resource library for free. There is a section devoted to GCSE maths revision with plenty of maths worksheets and GCSE maths questions . There are also maths tests for KS3, including a Year 7 maths test , a Year 8 maths test and a Year 9 maths test For children who need more support, our maths intervention programmes for KS3 achieve outstanding results through a personalised one to one tuition approach. 10 problem solving maths questions (Foundation tier)These first 10 questions and solutions are similar to Foundation questions. For the first three, we’ve provided some additional strategies. In our downloadable resource, you can find strategies for all 10 Foundation questions . 1) L-shape perimeter Here is a shape: ![basic maths problem solving questions l-shape perimeter](https://thirdspacelearning.com/wp-content/uploads/2023/04/problem_solving_foundation_1.jpg) Sarah says, “There is not enough information to find the perimeter.” Is she correct? What about finding the area? - Try adding more information – giving some missing sides measurements that are valid.
- Change these measurements to see if the answer changes.
- Imagine walking around the shape if the edges were paths. Could any of those paths be moved to another position but still give the same total distance?
The perimeter of the shape does not depend on the lengths of the unlabelled edges. ![basic maths problem solving questions solution to finding perimeter of l-shape](https://thirdspacelearning.com/wp-content/uploads/2023/04/problem-solving-questions-2.jpg) Edge A and edge B can be moved to form a rectangle, meaning the perimeter will be 22 cm. Therefore, Sarah is wrong. The area, however, will depend on those missing side length measurements, so we would need more information to be able to calculate it. 2) Find the missing pointHere is a coordinate grid with three points plotted. A fourth point is to be plotted to form a parallelogram. Find all possible coordinates of the fourth point. ![basic maths problem solving questions coordinate grid](https://thirdspacelearning.com/wp-content/uploads/2023/04/problem_solving_foundation_2.jpg) - What are the properties of a parallelogram?
- Can we count squares to see how we can get from one vertex of the parallelogram to another? Can we use this to find the fourth vertex?
There are 3 possible positions. ![basic maths problem solving questions coordinate grid](https://thirdspacelearning.com/wp-content/uploads/2023/04/problem-solving-questions-1.jpg) 3) That rating was a bit mean!The vertical line graph shows the ratings a product received on an online shopping website. The vertical line for 4 stars is missing. ![basic maths problem solving questions vertical graph](https://thirdspacelearning.com/wp-content/uploads/2023/04/problem_solving_foundation_3.jpg) If the mean rating is 2.65, use the information to complete the vertical line graph. Strategies - Can the information be put into a different format, either a list or a table?
- Would it help to give the missing frequency an algebraic label, x ?
- If we had the data in a frequency table, how would we calculate the mean?
- Is there an equation we could form?
Letting the frequency of 4 star ratings be x , we can form the equation \frac{45+4x}{18+x} =2.65 Giving x=2 ![basic maths problem solving questions vertical graph](https://thirdspacelearning.com/wp-content/uploads/2023/04/problem-solving-questions-4.jpg) 4) Changing anglesThe diagram shows two angles around a point. The sum of the two angles around a point is 360°. ![basic maths problem solving questions two angles around a point diagram](https://thirdspacelearning.com/wp-content/uploads/2023/04/problem_solving_foundation_4.jpg) Peter says “If we increase the small angle by 10% and decrease the reflex angle by 10%, they will still add to 360°.” Explain why Peter might be wrong. Are there two angles where he would be correct? Peter is wrong, for example, if the two angles are 40° and 320°, increasing 40° by 10% gives 44°, decreasing 320° by 10% gives 288°. These sum to 332°. 10% of the larger angle will be more than 10% of the smaller angle so the sum will only ever be 360° if the two original angles are the same, therefore, 180°. 5) Base and powerThe integers 1, 2, 3, 4, 5, 6, 7, 8 and 9 can be used to fill in the boxes. ![basic maths problem solving questions base and power empty boxes](https://thirdspacelearning.com/wp-content/uploads/2023/04/problem_solving_foundation_5.jpg) How many different solutions can be found so that no digit is used more than once? There are 8 solutions. 6) Just an average problem Place six single digit numbers into the boxes to satisfy the rules. ![basic maths problem solving questions boxes](https://thirdspacelearning.com/wp-content/uploads/2023/04/problem_solving_foundation_6.jpg) The mean in maths is 5 \frac{1}{3} The median is 5 The mode is 3. How many different solutions are possible? There are 4 solutions. 2, 3, 3, 7, 8, 9 3, 3, 4, 6, 7, 9 3, 3, 3, 7, 7, 9 3, 3, 3, 7, 8, 8 7) Square and rectangle The square has an area of 81 cm 2 . The rectangle has the same perimeter as the square. Its length and width are in the ratio 2:1. ![basic maths problem solving questions square and rectangle areas](https://thirdspacelearning.com/wp-content/uploads/2023/04/problem_solving_foundation_7.jpg) Find the area of the rectangle. The sides of the square are 9 cm giving a perimeter of 36 cm. We can then either form an equation using a length 2x and width x . Or, we could use the fact that the length and width add to half of the perimeter and share 18 in the ratio 2:1. The length is 12 cm and the width is 6 cm, giving an area of 72 cm 2 . 8) It’s all prime The sum of three prime numbers is equal to another prime number. ![basic maths problem solving questions empty number sequence](https://thirdspacelearning.com/wp-content/uploads/2023/04/problem_solving_foundation_8.jpg) If the sum is less than 30, how many different solutions are possible? There are 6 solutions. 2 can never be used as it would force two more odd primes into the sum to make the total even. 9) Unequal shareBob and Jane have £10 altogether. Jane has £1.60 more than Bob. Bob spends one third of his money. How much money have Bob and Jane now got in total? Initially Bob has £4.20 and Jane has £5.80. Bob spends £1.40, meaning the total £10 has been reduced by £1.40, leaving £8.60 after the subtraction. 10) Somewhere betweenFred says, “An easy way to find any fraction which is between two other fractions is to just add the numerators and add the denominators.” Is Fred correct? Solution Fred is correct. His method does work and can be shown algebraically which could be a good problem for higher tier learners to try. If we use these two fractions \frac{3}{8} and \frac{5}{12} , Fred’s method gives us \frac{8}{20} = \frac{2}{5} \frac{3}{8} = \frac{45}{120} , \frac{2}{5} = \frac{48}{120} , \frac{5}{12} = \frac{50}{120} . So \frac{3}{8} < \frac{2}{5} < \frac{5}{12} 10 problem solving maths questions (Foundation & Higher tier crossover)The next 10 questions are crossover questions which could appear on both Foundation and Higher tier exam papers. We have provided solutions for each and, for the first three questions, problem solving strategies to support learners. 11) What’s the difference?An arithmetic sequence has an nth term in the form an+b . 4 is in the sequence. 16 is in the sequence. 8 is not in the sequence. -2 is the first term of the sequence. What are the possible values of a and b ? - We know that the first number in the sequence is -2 and 4 is in the sequence. Can we try making a sequence to fit? Would using a number line help?
- Try looking at the difference between the numbers we know are in the sequence.
If we try forming a sequence from the information, we get this: ![basic maths problem solving questions Sequence](https://thirdspacelearning.com/wp-content/uploads/2023/04/problem-solving-questions-5.jpg) We can now try to fill in the missing numbers, making sure 8 is not in the sequence. Going up by 2 would give us 8, so that won’t work. ![basic maths problem solving questions Number sequence](https://thirdspacelearning.com/wp-content/uploads/2023/04/problem-solving-questions-6.jpg) The only solutions are 6 n -8 and 3 n -5. 12) Equation of the hypotenuse The diagram shows a straight line passing through the axes at point P and Q . Q has coordinate (8, 0). M is the midpoint of PQ and MQ has a length of 5 units. ![basic maths problem solving questions diagram with points p m and q](https://thirdspacelearning.com/wp-content/uploads/2023/04/problem_solving_crossover_12.jpg) Find the equation of the line PQ . - We know MQ is 5 units, what is PQ and OQ ?
- What type of triangle is OPQ ?
- Can we find OP if we know PQ and OQ ?
- A line has an equation in the form y=mx+c . How can we find m ? Do we already know c ?
PQ is 10 units. Using Pythagoras’ Theorem OP = 6 The gradient of the line will be \frac{-6}{8} = -\frac{3}{4} and P gives the intercept as 6. ![](//theknowledge.site/777/templates/cheerup1/res/banner1.gif) 13) What a wasteHarry wants to cut a sector of radius 30 cm from a piece of paper measuring 30 cm by 20 cm. ![basic maths problem solving questions section of a radius](https://thirdspacelearning.com/wp-content/uploads/2023/04/problem_solving_crossover_13.jpg) What percentage of the paper will be wasted? - What information do we need to calculate the area of a sector? Do we have it all?
- Would drawing another line on the diagram help find the angle of the sector?
The angle of the sector can be found using right angle triangle trigonometry. The angle is 41.81°. This gives us the area of the sector as 328.37 cm 2 . The area of the paper is 600 cm 2 . The area of paper wasted would be 600 – 328.37 = 271.62 cm 2 . The wasted area is 45.27% of the paper. 14) Tri-polygonometryThe diagram shows part of a regular polygon and a right angled triangle. ABC is a straight line. Find the sum of the interior angles of the polygon. ![basic maths problem solving questions Part of a regular polygon diagram](https://thirdspacelearning.com/wp-content/uploads/2023/04/problem_solving_crossover_14.jpg) Finding the angle in the triangle at point B gives 30°. This is the exterior angle of the polygon. Dividing 360° by 30° tells us the polygon has 12 sides. Therefore, the sum of the interior angles is 1800°. 15) That’s a lot of PiA block of ready made pastry is a cuboid measuring 3 cm by 10 cm by 15 cm. ![basic maths problem solving questions cuboid with measurements](https://thirdspacelearning.com/wp-content/uploads/2023/04/problem_solving_crossover_15.jpg) Anne is making 12 pies for a charity event. For each pie, she needs to cut a circle of pastry with a diameter of 18 cm from a sheet of pastry 0.5 cm thick. How many blocks of pastry will Anne need to buy? The volume of one block of pastry is 450 cm 3 . The volume of one cylinder of pastry is 127.23 cm 3 . 12 pies will require 1526.81 cm 3 . Dividing the volume needed by 450 gives 3.39(…). Rounding this up tells us that 4 pastry blocks will be needed. 16) Is it right?A triangle has sides of (x+4) cm, (2x+6) cm and (3x-2) cm. Its perimeter is 80 cm. Show that the triangle is right angled and find its area. Forming an equation gives 6x+8=80 This gives us x=12 and side lengths of 16 cm, 30 cm and 34 cm. Using Pythagoras’ Theorem 16 2 +30 2 =1156 Therefore, the triangle is right angled. The area of the triangle is (16 x 30) ÷ 2 = 240 cm 2 . 17) Pie chart ratioThe pie chart shows sectors for red, blue and green. ![basic maths problem solving questions pie chart](https://thirdspacelearning.com/wp-content/uploads/2023/04/problem_solving_crossover_17.jpg) The ratio of the angles of the red sector to the blue sector is 2:7. The ratio of the angles of the red sector to the green sector is 1:3. Find the angles of each sector of the pie chart. Multiplying the ratio of red : green by 2, it can be written as 2:6. Now the colour each ratio has in common, red, has equal parts in each ratio. The ratio of red:blue is 2:7, this means red:blue:green = 2:7:6. Sharing 360° in this ratio gives red:blue:green = 48°:168°:144°. 18) DIY SimultaneouslyMr Jones buys 5 tins of paint and 4 rolls of decorating tape. The total cost was £167. The next day he returns 1 unused tin of paint and 1 unused roll of tape. The refund amount is exactly the amount needed to buy a fan heater that has been reduced by 10% in a sale. The fan heater normally costs £37.50. Find the cost of 1 tin of paint. The sale price of the fan heater is £33.75. This gives the simultaneous equations p+t = 33.75 and 5 p +4 t = 167. We only need the price of a tin of paint so multiplying the first equation by 4 and then subtracting from the second equation gives p =32. Therefore, 1 tin of paint costs £32. 19) Triathlon paceJodie is competing in a Triathlon. A triathlon consists of a 5 km swim, a 40 km cycle and a 10 km run. Jodie wants to complete the triathlon in 5 hours. She knows she can swim at an average speed of 2.5 km/h and cycle at an average speed of 25 km/h. There are also two transition stages, in between events, which normally take 4 minutes each. What speed must Jodie average on the final run to finish the triathlon in 5 hours? Dividing the distances by the average speeds for each section gives times of 2 hours for the swim and 1.6 hours for the cycle, 216 minutes in total. Adding 8 minutes for the transition stages gives 224 minutes. To complete the triathlon in 5 hours, that would be 300 minutes. 300 – 224 = 76 minutes. Jodie needs to complete her 10 km run in 76 minutes, or \frac{19}{15} hours. This gives an average speed of 7.89 km/h. 20) Indices a 2x × a y =a 3 (a 3 ) x ÷ a 4y =a 32 Find x and y . Forming the simultaneous equations Solving these gives 10 problem solving maths questions (Higher tier)This final set of 10 questions would appear on the Higher tier only. Here we have just provided the solutions. Try asking your learners to discuss their strategies for each question. 21) Angles in a polygonThe diagram shows part of a regular polygon. ![basic maths problem solving questions part of a polygon diagram](https://thirdspacelearning.com/wp-content/uploads/2023/04/problem_solving_higher_21.png) A , B and C are vertices of the polygon. The size of the reflex angle ABC is 360° minus the interior angle. Show that the sum of all of these reflex angles of the polygon will be 720° more than the sum of its interior angles. Each of the reflex angles is 180 degrees more than the exterior angle: 180 + \frac{360}{n} The sum of all of these angles is n (180 + \frac{360}{n} ). This simplifies to 180 n + 360 The sum of the interior angles is 180( n – 2) = 180 n – 360 The difference is 180 n + 360 – (180 n -360) = 720° 22) Prism and force (Non-calculator)The diagram shows a prism with an equilateral triangle cross-section. ![basic maths problem solving questions Prism](https://thirdspacelearning.com/wp-content/uploads/2023/04/problem_solving_higher_22.png) When the prism is placed so that its triangular face touches the surface, the prism applies a force of 12 Newtons resulting in a pressure of \frac{ \sqrt{3} }{4} N/m^{2} Given that the prism has a volume of 384 m 3 , find the length of the prism. Pressure = \frac{Force}{Area} Area = 12÷ \frac{ \sqrt{3} }{4} = 16\sqrt{3} m 2 Therefore, the length of the prism is 384 ÷ 16\sqrt{3} = 8\sqrt{3} m 23) Geometric sequences (Non-calculator)A geometric sequence has a third term of 6 and a sixth term of 14 \frac{2}{9} Find the first term of the sequence. The third term is ar 2 = 6 The sixth term is ar 5 = \frac{128}{9} Diving these terms gives r 3 = \frac{64}{27} Giving r = \frac{4}{3} Dividing the third term twice by \frac{4}{3} gives the first term a = \frac{27}{8} 24) Printing factoryA printing factory is producing exam papers. When all 10 of its printers are working, it can produce all of the exam papers in 12 days. For the first two days of printing, 3 of the printers are broken. At the beginning of the third day it is discovered that 2 more printers have broken down, so the factory continues to print with the reduced amount of printers for 3 days. The broken printers are repaired and now all printers are available to print the remaining exams. How many days in total does it take the factory to produce all of the exam papers? If we assume one printer prints 1 exam paper per day, 10 printers would print 120 exam papers in 12 days. Listing the number printed each day for the first 5 days gives: Day 5: 5 This is a total of 29 exam papers. 91 exam papers are remaining with 10 printers now able to produce a total of 10 exam papers each day. 10 more days would be required to complete the job. Therefore, 15 days in total are required. 25) CirclesThe diagram shows a circle with equation x^{2}+{y}^{2}=13 . ![basic maths problem solving questions tangent and circle](https://thirdspacelearning.com/wp-content/uploads/2023/04/problem_solving_higher_25.png) A tangent touches the circle at point P when x=3 and y is negative. The tangent intercepts the coordinate axes at A and B . Find the length AB . Using the equation x^{2}+y^{2}=13 to find the y value for P gives y=-2 . The gradient of the radius at this point is - \frac{2}{3} , giving a tangent gradient of \frac{3}{2} . Using the point (3,-2) in y = \frac {3}{2} x+c gives the equation of the tangent as y = \frac {3}{2} x – \frac{13}{2} Substituting x=0 and y=0 gives A and B as (0 , -\frac {13}{2}) and ( \frac{13}{3} , 0) Using Pythagoras’ Theorem gives the length of AB as ( \frac{ 13\sqrt{13} }{6} ) = 7.812. ![basic maths problem solving questions tangent and circle diagram](https://thirdspacelearning.com/wp-content/uploads/2023/04/problem_solving_higher_26.png) 26) Circle theoremsThe diagram shows a circle with centre O . Points A, B, C and D are on the circumference of the circle. EF is a tangent to the circle at A . Angle EAD = 46° Angle FAB = 48° Angle ADC = 78° Find the area of ABCD to the nearest integer. The Alternate Segment Theorem gives angle ACD as 46° and angle ACB as 48°. Opposite angles in a cyclic quadrilateral summing to 180° gives angle ABC as 102°. Using the sine rule to find AC will give a length of 5.899. Using the sine rule again to find BC will give a length of 3.016cm. We can now use the area of a triangle formula to find the area of both triangles. 0.5 × 5 × 5.899 × sin (46) + 0.5 × 3.016 × 5.899 × sin (48) = 17 units 2 (to the nearest integer). 27) Quadratic functionThe quadratic function f(x) = -2x^{2} + 8x +11 has a turning point at P . Find the coordinate of the turning point after the transformation -f(x-3) . There are two methods that could be used. We could apply the transformation to the function and then complete the square, or, we could complete the square and then apply the transformation. Here we will do the latter. This gives a turning point for f(x) as (2,19). Applying -f(x-3) gives the new turning point as (5,-19). 28) Probability with fruitA fruit bowl contains only 5 grapes and n strawberries. A fruit is taken, eaten and then another is selected. The probability of taking two strawberries is \frac{7}{22} . Find the probability of taking one of each fruit. There are n+5 fruits altogether. P(Strawberry then strawberry)= \frac{n}{n+5} × \frac{n-1}{n+4} = \frac{7}{22} This gives the quadratic equation 15n^{2} - 85n - 140 = 0 This can be divided through by 5 to give 3n^{2} - 17n- 28 = 0 This factorises to (n-7)(3n + 4) = 0 n must be positive so n = 7. The probability of taking one of each fruit is therefore, \frac{5}{12} × \frac{7}{11} + \frac {7}{12} × \frac {5}{11} = \frac {70}{132} 29) Ice cream tub volumeAn ice cream tub in the shape of a prism with a trapezium cross-section has the dimensions shown. These measurements are accurate to the nearest cm. ![basic maths problem solving questions prism with a trapezium cross-section image](https://thirdspacelearning.com/wp-content/uploads/2023/04/problem_solving_higher_29.png) An ice cream scoop has a diameter of 4.5 cm to the nearest millimetre and will be used to scoop out spheres of ice cream from the tub. Using bounds find a suitable approximation to the number of ice cream scoops that can be removed from a tub that is full. We need to find the upper and lower bounds of the two volumes. Upper bound tub volume = 5665.625 cm 3 Lower bound tub volume = 4729.375 cm 3 Upper bound scoop volume = 49.32 cm 3 Lower bound scoop volume = 46.14 cm 3 We can divide the upper bound of the ice cream tub by the lower bound of the scoop to get the maximum possible number of scoops. Maximum number of scoops = 122.79 Then divide the lower bound of the ice cream tub by the upper bound of the scoop to get the minimum possible number of scoops. Minimum number of scoops = 95.89 These both round to 100 to 1 significant figure, Therefore, 100 scoops is a suitable approximation the the number of scoops. 30) Translating graphs The diagram shows the graph of y = a+tan(x-b ). The graph goes through the points (75, 3) and Q (60, q). Find exact values of a , b and q . ![basic maths problem solving questions graph of y= a + tan (x-b)](https://thirdspacelearning.com/wp-content/uploads/2023/04/problem_solving_higher_30.png) The asymptote has been translated to the right by 30°. Therefore, b=30 So the point (45,1) has been translated to the point (75,3). Therefore, a=2 We hope these problem solving maths questions will support your GCSE teaching. To get all the solutions and strategies in a printable form, please download the complete resource . DO YOU HAVE STUDENTS WHO NEED MORE SUPPORT IN MATHS?Every week Third Space Learning’s specialist online maths tutors support thousands of students across hundreds of schools with weekly online 1 to 1 maths lessons designed to plug gaps and boost progress. Since 2013 these personalised one to 1 lessons have helped over 150,000 primary and secondary students become more confident, able mathematicians. 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Convert the following readings of pressureto kPa absolute, assuming that the barometer reads 760mm Hg:... Show that an element and its inverse have the same order in any group. A cubic block of wood, 10.0 cm on each side, floats at the interface between... An ice cube tray of negligible mass contains 0.315 kg of water at17.7∘. How much... An open tank has a vertical partition and on one side contains gasoline with a... A 100g cube of ice at 0C is dropped into 1.0kg of water thatwas originally... Complete the equation of the line through (2, 1) and (5, -8). Use exact numbers. Write a function based on the given parent function and transformations in the given order.... How many solutions does the equationx1+x2+x3=13have wherex1,x2,andx3are non negative integers less than 6. Determine whether f : Z×Z→Z is onto if a) f(m,n)=2m−nb) b) f(m,n)=m2−n2 c) f(m,n)=m+n+1 d)... The base of S is an elliptical region with boundary curve 9x2+4y2=36. Cross-sections perpendicular to... Create a graph of y=2x−6. Construct a graph corresponding to the linear equation y=2x−6. Use the graphs of f and g to graph h(x) = (f + g)(x). (Graph... find expressions for the quadratic functions whose graphs are shown. f(x)=? g(x)=? Find the volume V of the described solid S. A cap of a sphere with... Find a counterexample to show that each statement is false. The sum of any three... Read the numbers and decide what the next number should be. 5 15 6 18... In how many different orders can five runners finish a race if no ties are... A farmer plants corn and wheat on a 180 acre farm. He wants to plant... Find the distance between (0, 0) and (-3, 4) pair of points. If needed, show... Whether each of these functions is a bijection from R to R.a)f(x)=−3x+4b)f(x)=−3x2+7c)f(x)=x+1x+2d)f(x)=x5+1 Find two numbers whose difference is 100 and whose product is a minimum. Find an expression for the function whose graph is the given curve. The line segment... Prove or disprove that if a and b are rational numbers, then ab is also... How to find a rational number halfway between any two rational numbers given infraction form... Fill in the blank with a number to make the expression a perfect square x2−6x+? Look at this table: x y 1–2 2–4 3–8 4–16 5–32 Write a linear (y=mx+b),... Part a: Assume that the height of your cylinder is 8 inches. Think of A... The graph of a function f is shown. Which graph is an antiderivative of f? A rectangle has area 16m2 . Express the perimeter of the rectangle as a function... Find the equation of the quadratic function f whose graph is shown below. (5, −2) Use the discriminant, b2−4ac, to determine the number of solutions of the following quadratic equation.... How many solutions does the equation ||2x-3|-m|=m have if m>0? If a system of linear equations has infinitely many solutions, then the system is called... A bacteria population is growing exponentially with a growth factor of 16 each hour.By what... A system of linear equations with more equations than unknowns is sometimes called an overdetermined... Express the distance between the numbers 2 and 17 using absolute value. Then find the... Find the Laplace transform of f(t)=(sint–cost)2 Express the interval in terms of an inequality involving absolute value. (0,4) A function is a ratio of quadratic functions and has a vertical asymptote x =4... how do you graph y > -2 Find the weighted average of a data set where 10 has a weight of 5,... The population of California was 29.76 million in 1990 and 33.87 million in 2000. Assume... The population of a region is growing exponentially. There were 10 million people in 1980... Two cables BG and BH are attached to the frame ACD as shown.Knowing that the... A bird flies in the xy-plane with a position vector given by r→=(αt−βt3)i^+γt2j^, with α=2.4... A movie stuntman (mass 80.0kg) stands on a window ledge 5.0 mabove the floor. Grabbing... Solve the following linear congruence, 25x≡15(bmod29) For the equation, a. Write the value or values of the variable that make a... Which of the following statements is/are correct about logistic regression? (There may be more than... Compute 4.659×104−2.14×104. Round the answer appropriately. Express your answer as an integer using the proper... Find the 52nd term of the arithmetic sequence -24,-7, 10 Find the 97th term of the arithmetic sequence 17, 26, 35, An equation that expresses a relationship between two or more variables, such as H=910(220−a), is... The football field is rectangular. a. Write a polynomial that represents the area of the... The equation 1.5r+15=2.25r represents the number r of movies you must rent to spend the... While standing on a ladder, you drop a paintbrush. The function represents the height y... When does data modeling use the idea of a weak entity? Give definitions for the... Write an equation of the line passing through (-2, 5) and parallel to the line... Find a polar equation for the curve represented by the given Cartesian equation. y =... Find c such that fave=f(c) List five integers that are congruent to 4 modulo 12. A rectangular package to be sent by a postal service can have a maximum combined... A juggler throws a bowling pin straight up with an initial speed of 8.20 m/s.... The One-to-One Property of natural logarithms states that if ln x = ln y, then... Find an equation of a parabola that has curvature 4 at the origin. Find a parametric representation of the solution set of the linear equation. 3x − 1/2y... Find the product of the complex number and its conjugate. 2-3i Find the prime factorization of 10!. Find a polynomial f(x) of degree 5 that has the following zeros. -3, -7, 5... True or False. The domain of every rational function is the set of all real... What would be the most efficient step to suggest to a student attempting to complete... 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Use vectors to decide whether the triangle with vertices P(1, -3, -2), Q(2, 0, -4),... Find a path that traces the circle in the plane y=5 with radius r=2 and... a. Find an upper bound for the remainder in terms of n.b. Find how many... Find two unit vectors orthogonal to both j−k and i+j. Obtain the Differential equations: parabolas with vertex and focus on the x-axis. The amount of time, in minutes, for an airplane to obtain clearance for take off... Use the row of numbers shown below to generate 12 random numbers between 01 and... Here’s an interesting challenge you can give to a friend. Hold a $1 (or larger!)... A random sample of 1200 U.S. college students was asked, "What is your perception of... The two intervals (114.4, 115.6) and (114.1, 115.9) are confidence intervals (The same sample data... How many different 10 letter words (real or imaginary) can be formed from the following... Assume that σ is unknown, the lower 100(1−α)% confidence bound on μ is: a) μ≤x―+tα,n−1sn... A simple random sample of 60 items resulted in a sample mean of 80. The... Decresing the sample size, while holding the confidence level and the variance the same, will... A privately owned liquor store operates both a drive-n facility and a walk-in facility. On... Show that the equation represents a sphere, and find its center and radius. x2+y2+z2+8x−6y+2z+17=0 Describe in words the region of R3 represented by the equation(s) or inequality. x=5 Suppose that the height, in inches, of a 25-year-old man is a normal random variable... Find the value and interest earned if $8906.54 is invested for 9 years at %... Which of the following statements about the sampling distribution of the sample mean is incorrect?... The random variable x stands for the number of girls in a family of four... The product of the ages, in years, of three (3) teenagers os 4590. None of... A simple random sample size of 100 is selected from a population with p=0.40 What... Which of the following statistics are unbiased estimators of population parameters? Choose the correct answer... The probability distribution of the random variable X represents the number of hits a baseball... Let X be a random variable with probability density function.f(x)={c(1−x2)−1<x<10otherwise(a) What is the value of... A survey of 4826 randomly selected young adults (aged 19 to 25) asked, "What do... The monthly worldwide average number of airplane crashes of commercial airlines is 2.2. What is... Given that z is a standard normal random variable, compute the following probabilities.a.P(z≤−1.0)b.P(z≥−1)c.P(z≥−1.5)d.P(−2.5≤z)e.P(−3<z≤0) Given a standard normal distribution, find the area under the curve that lies(a) to the... Chi-square tests are best used for which type of dependent variable? nominal, ordinal ordinal interval... True or False 1.The goal of descriptive statistics is to simplify, summarize, and organize data.... What is the difference between probability distribution and sampling distribution? A weather forecaster predicts that the temperature in Antarctica will decrease 8∘F each hour for... The tallest person who ever lived was approximately 8 feet 11 inches tall. a) Write... An in-ground pond has the shape of a rectangular prism. The pond has a depth... The average zinc concentration recovered from a sample of measurements taken in 36 different locations... Why is it important that a sample be random and representative when conducting hypothesis testing?... Which of the following is true about the sampling distribution of means? A. Shape of... Give an example of a commutative ring without zero-divisors that is not an integral domain. List all zero-divisors in Z20. Can you see relationship between the zero-divisors of Z20 and... Find the integer a such that a≡−15(mod27) and −26≤a≤0 Explain why the function is discontinuous at the given number a. Sketch the graph of... Two runners start a race at the same time and finish in a tie. Prove... Which of the following graphs represent functions that have inverse functions? find the Laplace transform of f (t). f(t)=tsin3t Find Laplace transforms of sinh3t cos22t find the Laplace transform of f (t). f(t)=t2cos2t The Laplace transform of the product of two functions is the product of the Laplace... The Laplace transform of u(t−2) is (a) 1s+2 (b) 1s−2 (c) e2ss(d)e−2ss Find the Laplace Transform of the function f(t)=eat Explain First Shift Theorem & its properties? Solve f(t)=etcost Find Laplace transform of the given function te−4tsin3t Reduce to first order and solve:x2y″−5xy′+9y=0 y1=x3 (D3−14D+8)y=0 A thermometer is taken from an inside room to the outside ,where the air temperature... Find that solution of y′=2(2x−y) which passes through the point (0, 1). Radium decomposes at a rate proportional to the amount present. In 100 years, 100 mg... Let A, B, and C be sets. 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A proton is released in a uniform electric field, and it experiences an electric force... A potters wheel having a radius of 0.50 m and a moment of inertia of12kg⋅m2is... Two spherical objects are separated by a distance of 1.80×10−3m. The objects are initially electrically... An airplane pilot sets a compass course due west and maintainsan airspeed of 220 km/h.... Resolve the force F2 into components acting along the u and v axes and determine... A conducting sphere of radius 0.01m has a charge of1.0×10−9Cdeposited on it. The magnitude of... Starting with an initial speed of 5.00 m/s at a height of 0.300 m, a... In the figure a worker lifts a weightωby pulling down on a rope with a... A stream of water strikes a stationary turbine bladehorizontally, as the drawing illustrates. The incident... Until he was in his seventies, Henri LaMothe excited audiences by belly-flopping from a height... A radar station, located at the origin of xz plane, as shown in the figure... 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A coffee connoisseur claims that he can distinguish between a cup of instant coffee and... Two firms V and W consider bidding on a road-building job, which may or may... Two cards are drawn without replacement from an ordinary deck, find the probability that the... In August 2012, tropical storm Isaac formed in the Caribbean and was headed for the... A local bank reviewed its credit card policy with the intention of recalling some of... The accompanying table gives information on the type of coffee selected by someone purchasing a... A batch of 500 containers for frozen orange juice contains 5 that are defective. Two... The probability that an automobile being filled with gasoline also needs an oil change is... Let the random variable X follow a normal distribution with μ=80 and σ2=100. a. Find... A card is drawn randomly from a standard 52-card deck. Find the probability of the... The next number in the series 38, 36, 30, 28, 22 is ? What is the coefficient of x8y9 in the expansion of (3x+2y)17? A boat on the ocean is 4 mi from the nearest point on a straight... How many different ways can you make change for a quarter? (Different arrangements of the... Seven balls are randomly withdrawn from an urn that contains 12 red, 16 blue, and... Approximately 80,000 marriages took place in the state of New York last year. Estimate the... The probability that a student passes the Probability and Statistics exam is 0.7. (i)Find the... Customers at a gas station pay with a credit card (A), debit card (B), or... It is conjectured that an impurity exists in 30% of all drinking wells in a... Assume that the duration of human pregnancies can be described by a Normal model with... According to a renowned expert, heavy smokers make up 70% of lung cancer patients. If... Two cards are drawn successively and without replacement from an ordinary deck of playing cards... 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The number of hours per week that the television is turned on is determined for... Data was collected for 259 randomly selected 10 minute intervals. For each ten-minute interval, the... Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in... A normal distribution has a mean of 80 and a standard deviation of 14. Determine... True or false: a. All normal distributions are symmetrical b. All normal distributions have a... Would you expect distributions of these variables to be uniform, unimodal, or bimodal? Symmetric or... Annual sales, in millions of dollars, for 21 pharmaceutical companies follow. 8408 1374 1872 8879... The velocity function (in meters per second) is given for a particle moving along a... Find the area of the parallelogram with vertices A(-3,0) , B(-1,6) , C(8,5) and D(6,-1) What is the area of the parallelogram with vertices A(-3, 0), B(-1, 5), C(7, 4),... The integral represents the volume of a solid. Describe the solid. π∫01(y4−y8)dy a) The integral... Two components of a minicomputer have the following joint pdf for their useful lifetimes X... Use the table of values of f(x,y) to estimate the values of fx(3,2), fx(3,2.2), and... Calculate net price factor and net price. Dollars list price −435.20$ Trade discount rate −26%,15%,5%. Represent the line segment from P to Q by a vector-valued function and by a... (x2+2xy−4y2)dx−(x2−8xy−4y2)dy=0 If f is continuous and integral 0 to 9 f(x)dx=4, find integral 0 to 3... Find the parametric equation of the line through a parallel to ba=[3−4],b=[−78] Find the velocity and position vectors of a particle that has the given acceleration and... If we know that the f is continuous and integral 0 to 4f(x)dx=10, compute the... Integration of (y⋅tanxy) For the matrix A below, find a nonzero vector in the null space of A... Find a nonzero vector orthogonal to the plane through the points P, Q, and R.... Suppose that the augmented matrix for a system of linear equations has been reduced by... Find two unit vectors orthogonal to both (3 , 2, 1) and (- 1, 1,... What is the area of the parallelogram whose vertices are listed? (0,0), (5,2), (6,4), (11,6) Using T defined by T(x)=Ax, find a vector x whose image under T is b,... Use the definition of Ax to write the matrix equation as a vector equation, or... We need to find the volume of the parallelepiped with only one vertex at the... List five vectors in Span {v1,v2}. For each vector, show the weights on v1 and... (1) find the projection of u onto v and (2) find the vector component of... Find the area of the parallelogram determined by the given vectors u and v. u... (a) Find the point at which the given lines intersect. r = 2,... (a) find the transition matrix from B toB′,(b) find the transition matrix fromB′to B,(c) verify... A box contains 5 red and 5 blue marbles. Two marbles are withdrawn randomly. If... Given the following vector X, find anon zero square marix A such that AX=0; You... Construct a matrix whose column space contains (1, 1, 5) and (0, 3.1) and whose... At what point on the paraboloid y=x2+z2 is the tangent plane parallel to the plane... Label the following statements as being true or false. (a) If V is a vector... Find the Euclidean distance between u and v and the cosine of the angle between... Write an equation of the line that passes through (3, 1) and (0, 10) There are 100 two-bedroom apartments in the apartment building Lynbrook West.. The montly profit (in... State and prove the linearity property of the Laplace transform by using the definition of... The analysis of shafts for a compressor is summarized by conformance to specifications. Suppose that... The Munchies Cereal Company combines a number of components to create a cereal. Oats and... Movement of a Pendulum A pendulum swings through an angle of 20∘ each second. If... If sinx+siny=aandcosx+cosy=b then find tan(x−y2) Find the values of x such that the angle between the vectors (2, 1, -1),... Find the dimensions of the isosceles triangle of largest area that can be inscribed in... Suppose that you are headed toward a plateau 50 meters high. If the angle of... Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport.... Find an equation of the plane. The plane through the points (2, 1, 2), (3,... Match each of the trigonometric expressions below with the equivalent non-trigonometric function from the following... two small spheres spaced 20.0cm apart have equal charges. How many extra electrons must be... The base of a pyramid covers an area of 13.0 acres (1 acre =43,560 ft2)... Find out these functions' domain and range. To find the domain in each scenario, identify... Your bank account pays an interest rate of 8 percent. You are considering buying a... Whether f is a function from Z to R ifa)f(n)=±n.b)f(n)=n2+1.c)f(n)=1n2−4. The probability density function of X, the lifetime of a certain type of electronic device... A sandbag is released by a balloon that is rising vertically at a speed of... A proton is located in a uniform electric field of2.75×103NCFind:a) the magnitude of the electric... A rectangular plot of farmland are finite on one facet by a watercourse and on... A solenoid is designed to produce a magnetic field of 0.0270 T at its center.... I want to find the volume of the solid enclosed by the paraboloidz=2+x2+(y−2)2and the planesz=1,x=−1y=0,andy=4 Let W be the subspace spanned by the u’s, and write y as the sum... Can u find the point on the planex+2y+3z=13that is closest to the point (1,1,1). You... A spring of negligible mass stretches 3.00 cm from its relaxed length when a force... A force of 250 Newtons is applied to a hydraulic jack piston that is 0.01... Three identical blocks connected by ideal strings are being pulled along a horizontal frictionless surface... A credit card contains 16 digits between 0 and 9. However, only 100 million numbers... Every real number is also a complex number? True of false? Let F be a fixed 3x2 matrix, and let H be the set of all... Find a vector a with representation given by the directed line segment AB. Draw AB... Find A such that the given set is Col A. {[2s+3tr+s−2t4r+s3r−s−t]:r,s,t real} Find the vector that has the same direction as (6, 2, -3) but is four... For the matrices (a) find k such that Nul A is a subspace of Rk,... How many subsets with an odd number of elements does a set with 10 elements... In how many ways can a set of five letters be selected from the English... Suppose that f(x) = x/8 for 3 < x < 5. Determine the following probabilities:... Describe all solutions of Ax=0 in parametric vector form, where A is row equivalent to... Find two vectors parallel to v of the given length. v=PQ→ with P(1,7,1) and Q(0,2,5);... A dog in an open field runs 12.0 m east and then 28.0 m in... Can two events with nonzero probabilities be both independent and mutually exclusive? Explain your reasoning. Use the Intermediate Value Theorem to show that there is a root of the given... In a fuel economy study, each of 3 race cars is tested using 5 different... A company has 34 salespeople. A board member at the company asks for a list... A dresser drawer contains one pair of socks with each of the following colors: blue,... A restaurant offers a $12 dinner special with seven appetizer options, 12 choices for an... A professor writes 40 discrete mathematics true/false questions. Of the statements in these questions, 17... Suppose E(X)=5 and E[X(X–1)]=27.5, find ∈(x2) and the variance. A Major League baseball diamond has four bases forming a square whose sides measure 90... Express f(x)=4x3+6x2+7x+2 in term of Legendre Polynomials. Find a basis for the space of 2×2 diagonal matrices. Basis ={[],[]} Which of the following expressions are meaningful? Which are meaningless? Explain. a) (a⋅b)⋅c (a⋅b)⋅c has... Vectors V1 and V2 are different vectors with lengths V1 and V2 respectively. Find the... Find an equation for the plane containing the two (parallel) lines v1=(0,1,−2)+t(2,3,−1) and v2=(2,−1,0)+t(2,3,−1). Find, correct to the nearest degree, the three angles of the triangle with the given... Find the vector, not with determinants, but by using properties of cross products. (i+j)×(i−j) Find the curve’s unit tangent vector. Also, find the length of the indicated portion of... Construct a 4×3 matrix with rank 1 Find x such that the matrix is equal to its inverse.A=[7x−8−7] Find a polynomial with integer coefficients that satisfies the given conditions. Q has degree 3... Write in words how to read each of the following out loud.a.{x∈R′∣0<x<1}b.{x∈R∣x≤0orx⇒1}c.{n∈Z∣nisafactorof6}d.{n∈Z⋅∣nisafactorof6} Pets Plus and Pet Planet are having a sale on the same aquarium. At Pets... Find the average value of F(x, y, z) over the given region. F(x,y,z)=x2+9 over the... Find the trace of the plane in the given coordinate plane. 3x−9y+4z=5,yz Determine the level of measurement of the variable. Favorite color Choose the correct level of... How wide is the chasm between what men and women earn in the workplace? According... Write an algebraic expression for: 6 more than a number c. Please, can u convert 3.16 (6 repeating) to a fraction. Evaluate the expression. P(8, 3) In a poker hand consisting of 5 cards, find the probability of holding 3 aces. Give an expression that generates all angles coterminal with each angle. Let n represent any... An ideal Otto cycle has a compression ratio of 10.5, takes in air at 90... A piece of wire 10 m long is cut into two pieces. One piece is... Put the following equation of a line into slope intercept form, simplifying all fractions 3x+3y=24 Find the point on the hyperbola xy = 8 that is closest to the point... Water is pumped from a lower reservoir to a higher reservoir by a pump that... A piston–cylinder device initially contains 0.07m3 of nitrogen gas at 130 kPa and 180∘. The... Write an algebraic expression for each word phrase. 4 more than p A club has 25 members. a) How many ways are there to choose four members... For each of the sets below, determine whether {2} is an element of that set.... Which expression has both 8 and n as factors? If repetitions are not permitted (a) how many 3 digit number can be formed from... To determine the sum of all multiples of 3 between 1 and 1000 On average, there are 3 accidents per month at one intersection. We need to find... One number is 2 more than 3 times another. Their sum is 22. Find the... The PMF for a flash drive with X (GB) of memory that was purchased is... An airplane needs to reach a velocity of 203.0 km/h to takeoff. On a 2000... A racquetball strikes a wall with a speed of 30 m/s and rebounds with a... Assuming that the random variable x has a cumulative distribution function,F(x)={0,x<00.25x,0≤x<51,5≤xDetermine the following:a)p(x<2.8)b)p(x>1.5)c)p(x<−z)d)p(x>b) At t = 0 a grinding wheel has an angular velocity of 24.0 rad/s. It... How many 3/4's are in 1? You’re driving down the highway late one night at 20 m/s when a deer steps... Table salt contains 39.33 g of sodium per 100 g of salt. The U.S. Food... The constant-pressure heat capacity of a sample of a perfect gas was found to vary... Coffee is draining from a conical filter into a cylindrical coffepot at the rate of... Cart is driven by a large propeller or fan, which can accelerate or decelerate the... A vending machine dispenses coffee into an eight-ounce cup. The amounts of coffee dispensed into... On an essentially frictionless, horizontal ice rink, a skater moving at 3.0 m/s encounters a... The gage pressure in a liquid at a depth of 3 m is read to... Consider a cylindrical specimen of a steel alloy 8.5 mm (0.33 in.) in diameter and... Calculate the total kinetic energy, in Btu, of an object with a mass of 10... A 0.500-kg mass on a spring has velocity as a function of time given by... An Australian emu is running due north in a straight line at a speed of... Another pitfall cited is expecting to improve the overall performance of a computer by improving... You throw a glob of putty straight up toward the ceiling, which is 3.60 m... A 0.150-kg frame, when suspended from a coil spring, stretches the spring 0.070 m. A... A batch of 140 semiconductor chips is inspected by choosing a sample of 5 chips.... A rock climber stands on top of a 50-m-high cliff overhanging a pool of water.... A tank whose bottom is a mirror is filled with water to a depth of... Two sites are being considered for wind power generation. In the first site, the wind... 0.250 kilogram of water at75.0∘Care contained in a tiny, inert beaker. How much ice, at... Two boats start together and race across a 60-km-wide lake and back. Boat A goes... A roller coaster moves 200 ft horizontally and the rises 135 ft at an angle... A tow truck drags a stalled car along a road. The chain makes an angle... Consider the curve created by2x2+3y2–4xy=36(a) Show thatdydx=2y−2x3y−2x(b) Calculate the slope of the line perpendicular to... The current entering the positive terminal of a device is i(t)=6e−2t mA and the voltage... The fastest measured pitched baseball left the pitcher’s hand at a speed of 45.0 m/s.... Calculate the total potential energy, in Btu, of an object that is 20 ft below... A chemist in an imaginary universe, where electrons have a different charge than they do... When jumping, a flea reaches a takeoff speed of 1.0 m/s over a distance of... Determine the energy required to accelerate a 1300-kg car from 10 to 60 km/h on... The deepest point in the ocean is 11 km below sea level, deeper than MT.... A golfer imparts a speed of 30.3 m/s to a ball, and it travels the... Calculate the frequency of each of the following wavelengths of electromagnetic radiation. A) 632.8 nm... Prove that there is a positive integer that equals the sum of the positive integers... A hurricane wind blows across a 6.00 m×15.0 m flat roof at a speed of... If an electron and a proton are expelled at the same time,2.0×10−10mapart (a typical atomic... The speed of sound in air at 20 C is 344 m/s. (a) What is... Which of the following functions f has a removable discontinuity at a? If the discontinuity... A uniform steel bar swings from a pivot at one end with a period of... A wind farm generator uses a two-bladed propellermounted on a pylon at a height of... A copper calorimeter can with mass 0.100 kg contains 0.160 kgof water and 0.018 kg... Jones figures that the total number of thousands of miles that a used auto can... Assign a binary code in some orderly manner to the 52 playingcards. Use the minimum... A copper pot with mass 0.500 kg contains 0.170 kg of water ata temperature of... Ea for a certain biological reaction is 50 kJ/mol, by what factor ( how many... When a person stands on tiptoe (a strenuous position), the position of the foot is... A solution was prepared by dissolving 1210 mg of K3Fe(CN)6 (329.2 g/mol) in sufficient waterto... A 58-kg skier is going down a slope oriented 35 degree abovethe horizontal. The area... The mechanics at lincoln automotive are reboring a 6-in deepcylinder to fit a new piston.... A 0.48 kg piece of wood floats in water but is found to sinkin alcohol... A 50-g ice cube at 0oC is heated until 45-g hasbecome water at 100oC and... A solution containing 6.23 ppm of KMnO4 had a transmittance of 0.195 in a 1.00-cm... A black body at 7500K consists of an opening of diameter 0.0500mm, looking into an... A new absolute temperature scale is proposed. On thisscale the ice point of water is... A 65.0 mm focal length converging lens is 78.0 mm away from a sharp image.... A crate of fruit with mass 35.0 kg and specific heat capacity 3650 J/Kg .... A freezer has a thermal efficiency of 2.40. Thefreezer is to convert 1.80 kg of... A horizontal force of 210N is exerted on a 2.0 kg discus as it rotates... Lead has a specific heat of 0.030 cal/gC. In an insulated container, 300 grams of... A parachutist relies on air resistance mainly on her parachute to decrease her downward velocity.... The distance between a carbon atom (m=12 u) and an oxygen atom (m + 16... A car heading north collides at an intersection with a truckheading east. If they lock... Water stands at a depth H in a large, open tank whose sidewalls are vertical.... The heaviest invertebrate is the giant squid, which is estimated to have a weight of... Which of the following is a correct comment? */ Comments */ ** Comment ** /*... The concentrated sulfuric acid we use in the laboratory is 98% H2SO4 by mass. Calculate... Consider the reaction N2(g)+3H2(g)→2NH3(g) suppose that a particular moment during the reaction molecular hydrogen on... use Green’s Theorem to find the counterclockwise circulation and outward flux for the field F... - High School Questions
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Connect with us Get Plainmath App ![basic maths problem solving questions Plainmath Logo](https://plainmath.org/build/images/pm_logo_w.png) E-mail us: [email protected] Our Service is useful for: Plainmath is a platform aimed to help users to understand how to solve math problems by providing accumulated knowledge on different topics and accessible examples. 2023 Plainmath. All rights reserved ![basic maths problem solving questions no-js-running-man-logo](https://www.wolframalpha.com/_next/static/images/running-man_2cHgyknz.png) Unlimited AI-generated practice problems and answers With Wolfram Problem Generator, each question is generated instantly, just for you. Get integrated Step-by-step solutions with a subscription to Wolfram|Alpha Pro. Pro subscribers can also create printable worksheets for study sessions and quizzes. ![basic maths problem solving questions [object Object]](https://www.wolframalpha.com/_next/static/images/step-by-step-need-hint_2fEuIFM8.png) The most amazing part of Wolfram Problem Generator is something you can't even see.Instead of pulling problems out of a database, Wolfram Problem Generator makes them on the fly, so you can have new practice problems and worksheets each time. Each practice session provides new challenges. ![basic maths problem solving questions [object Object]](https://www.wolframalpha.com/_next/static/images/arithmetic_1O6isb1P.png) Practice for all agesWolfram Problem Generator offers beginner, intermediate, and advanced difficulty levels for a number of topics including algebra, calculus, statistics, number theory, and more. ![basic maths problem solving questions [object Object]](https://www.wolframalpha.com/_next/static/images/wa-sbs-solution_2dmwSaz1.png) Work with Step-by-step Solutions!Only Wolfram Problem Generator directly integrates the popular and powerful Step-by-step Solutions from Wolfram|Alpha. You can use a single hint to get unstuck, or explore the entire math problem from beginning to end. Maths Quiz Questions![basic maths problem solving questions Class Registration Banner](https://cdn1.byjus.com/wp-content/uploads/2023/06/Dark-BG-mobile-top.webp) We are providing here maths quiz questions for children to help them increase their knowledge of the subject. These questions are prepared based on fundamental mathematical concepts. The problems here are provided with four multiple answers and students have to choose the right answer. The questions here could be solved by students of all the classes from 6 to 10, as they are based on basic arithmetic operations and geometrical concepts. Thus, on solving them they can also participate in quiz competitions conducted in schools. Solving these quizzes will help students to gain more knowledge and boost their problem-solving skills. These questions are very easy to solve and will not take much time. Hence, it is recommended to all the children to solve each one of them and test their abilities. Maths Quiz Questions with Answers (MCQs)Let us answer here some of the quizzes which are based on simple arithmetic concepts. These problems are based on fundamental concepts, which students can easily answer without picking up a pen and paper. Q.1. What is the sum of 130+125+191? Q.2: If we minus 712 from 1500, how much do we get? Q.3: 50 times of 8 is equal to: Q.4: 110 divided by 10 is: D. None of these Q.5: 20+(90÷2) is equal to: Q.6: The product of 82 and 5 is: Q.7: Find the missing terms in multiple of 3: 3, 6, 9, __, 15 Q.8: Solve 24÷8+2. Q.9: Solve: 300 – (150×2) Q.10: The product of 121 x 0 x 200 x 25 is Q.11: What is the next prime number after 5? Also, read: - Class 8 Maths MCQs
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Maths Quizzes and AnswersHere are some quiz questions which children should be able to answer quickly. Q.12: The circumference of the circle is also sometimes called: Answer: Perimeter of a circle Q.13: 90 – 35 is equal to: Q.14: 72 divided by 8 is equal to: Q.15: How many sides does a decagon have? Answer: Ten Q.16: Is -5 an integer? Yes or No. Answer: Yes Q.17: The value of pi is equal to: Answer: 22/7 or 3.14 Q.18: 9 x 7 is equal to: Q.19: Is triangle a two-dimensional or three-dimensional shape? Answer: A two-dimensional shape Q.20: An equilateral triangle has two of its sides equal. True or false? Answer: False All the sides of the equilateral triangle are equal. Q.21: 10 is a natural number. True or false? Answer: True Q.22: -10 is a whole number. True or false? Q.23: 8 raised to the power 0 is equal to: Q.24: The largest 4 digit number is: Answer: 9999 Q.25: The smallest 4-digit number is: Answer: 1000 Q.26: The square of 8 is equal to: 8 2 = 8 x 8 = 64 Q.27: The square root of 5 is: Answer: 2.23 Q.28: 3 is a perfect square. True or False? Answer: False. Q.29: Cube of 5 is equal to: Answer: 125 5 3 = 5 x 5 x 5 = 125 Q.30: Cube root of 1331 is: 1331 = 11 x 11 x 11 = 11 3 Q.31: 27 is a perfect cube. True or False? 27 = 3 x 3 x 3= 3 3 Q.32: A square has all its angles equal to: Answer: 90 degrees Q.33: The area of rectangle is equal to: Answer: Length x Breadth Q.34: If a is the side of cube, then the volume of the cube is: Answer: a 3 Q.35: A regular polygon has all its sides: Answer: Equal Leave a Comment Cancel replyYour Mobile number and Email id will not be published. Required fields are marked * Request OTP on Voice Call Post My Comment ![basic maths problem solving questions](https://cdn1.byjus.com/wp-content/uploads/2023/03/avatar.png) Great thank you I am a student Great work keep it up thanks byjus because tommorow is my mental maths exam and this quiz increase my confidence to solve the mental maths exam [thanks a lot] . Best of studying It was a very nice quiz. I enjoyed answering. ![basic maths problem solving questions basic maths problem solving questions](https://cdn1.byjus.com/wp-content/uploads/2022/12/Vector-2219-2.png) Register with BYJU'S & Download Free PDFsRegister with byju's & watch live videos. Want Better Math Grades?✅ Unlimited Solutions ✅ Step-by-Step Answers ✅ Available 24/7 ➕ Free Bonuses ($1085 value!) On this page - Search IntMath
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- Data Measurement and Statistics
- Points and Line Segments
Math Word Problem SolutionsMath word problems require interpreting what is being asked and simplifying that into a basic math equation. Once you have the equation you can then enter that into the problem solver as a basic math or algebra question to be correctly solved. Below are math word problem examples and their simplified forms. Word Problem: Rachel has 17 apples. She gives some to Sarah. Sarah now has 8 apples. How many apples did Rachel give her? Simplified Equation: 17 - x = 8 Word Problem: Rhonda has 12 marbles more than Douglas. Douglas has 6 marbles more than Bertha. Rhonda has twice as many marbles as Bertha has. How many marbles does Douglas have? Variables: Rhonda's marbles is represented by (r), Douglas' marbles is represented by (d) and Bertha's marbles is represented by (b) Simplified Equation: {r = d + 12, d = b + 6, r = 2 �� b} Word Problem: if there are 40 cookies all together and Angela takes 10 and Brett takes 5 how many are left? Simplified: 40 - 10 - 5 Pre-Algebra SolutionsBelow are examples of Pre-Algebra math problems that can be solved. - Variables, Expressions, and Integers
- Simplifying and Evaluating Expressions
- Solving Equations
- Multi-Step Equations and Inequalities
- Ratios, Proportions, and Percents
- Linear Equations and Inequalities
Algebra SolutionsBelow are examples of Algebra math problems that can be solved. - Algebra Concepts and Expressions
- Points, Lines, and Line Segments
- Simplifying Polynomials
- Factoring Polynomials
- Linear Equations
- Absolute Value Expressions and Equations
- Radical Expressions and Equations
- Systems of Equations
- Quadratic Equations
- Inequalities
- Complex Numbers and Vector Analysis
- Logarithmic Expressions and Equations
- Exponential Expressions and Equations
- Conic Sections
- Vector Spaces
- 3d Coordinate System
- Eigenvalues and Eigenvectors
- Linear Transformations
- Number Sets
- Analytic Geometry
Trigonometry SolutionsBelow are examples of Trigonometry math problems that can be solved. - Algebra Concepts and Expressions Review
- Right Triangle Trigonometry
- Radian Measure and Circular Functions
- Graphing Trigonometric Functions
- Simplifying Trigonometric Expressions
- Verifying Trigonometric Identities
- Solving Trigonometric Equations
- Complex Numbers
- Analytic Geometry in Polar Coordinates
- Exponential and Logarithmic Functions
- Vector Arithmetic
Precalculus SolutionsBelow are examples of Precalculus math problems that can be solved. - Operations on Functions
- Rational Expressions and Equations
- Polynomial and Rational Functions
- Analytic Trigonometry
- Sequences and Series
- Analytic Geometry in Rectangular Coordinates
- Limits and an Introduction to Calculus
Calculus SolutionsBelow are examples of Calculus math problems that can be solved. - Evaluating Limits
- Derivatives
- Applications of Differentiation
- Applications of Integration
- Techniques of Integration
- Parametric Equations and Polar Coordinates
- Differential Equations
Statistics SolutionsBelow are examples of Statistics problems that can be solved. - Algebra Review
- Average Descriptive Statistics
- Dispersion Statistics
- Probability
- Probability Distributions
- Frequency Distribution
- Normal Distributions
- t-Distributions
- Hypothesis Testing
- Estimation and Sample Size
- Correlation and Regression
Finite Math SolutionsBelow are examples of Finite Math problems that can be solved. - Polynomials and Expressions
- Equations and Inequalities
- Linear Functions and Points
- Systems of Linear Equations
- Mathematics of Finance
- Statistical Distributions
Linear Algebra SolutionsBelow are examples of Linear Algebra math problems that can be solved. - Introduction to Matrices
- Linear Independence and Combinations
Chemistry SolutionsBelow are examples of Chemistry problems that can be solved. - Unit Conversion
- Atomic Structure
- Molecules and Compounds
- Chemical Equations and Reactions
- Behavior of Gases
- Solutions and Concentrations
Physics SolutionsBelow are examples of Physics math problems that can be solved. - Static Equilibrium
- Dynamic Equilibrium
- Kinematics Equations
- Electricity
- Thermodymanics
Geometry Graphing SolutionsBelow are examples of Geometry and graphing math problems that can be solved. - Step By Step Graphing
- Linear Equations and Functions
- Polar Equations
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A recent study by Ei, an EdTech company, revealed that nearly 80% of in-service math teachers in India and the Middle East lack basic conceptual understanding in areas such as ratio, proportional reasoning, algebraic reasoning, estimation, and logical reasoning. The study assessed 1,357 teachers from grades 3 to 6 across 152 schools in India, UAE, Oman, and Saudi Arabia over two years.
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