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Key Stage 3 (KS3) Math Models and Geometry — practice questions

Explore 18 free Math Models and Geometry questions in Key Stage 3 (KS3) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Math Models and Geometry questions and exercises with answers

Showing questions 1–18 of 18.

The difference of a number and six is 13. What is the number?Read the answer and worked solution →The sum of twice a number and seven is 15. What is the number?Read the answer and worked solution →One number is five more than another. The sum of the two numbers is twenty-one. What are the two numbers?Read the answer and worked solution →The sum of two consecutive integers is 47. What are the two integers?Read the answer and worked solution →A pile contains 17 dimes, each worth $0.10. What is the total value of the pile of dimes?Read the answer and worked solution →Adalberto has $2.25 in dimes and nickels. He has nine more nickels than dimes. Solving 0.10d + 0.05(d + 9) = 2.25 gives which number of dimes?Read the answer and worked solution →If the sum of the measures of two angles is 180 degrees, what are the two angles called?Read the answer and worked solution →The three angles of a triangle measure 55 degrees, 82 degrees, and x degrees. What is the value of x?Read the answer and worked solution →One angle of a right triangle measures 28 degrees. What is the measure of the third angle?Read the answer and worked solution →The Pythagorean Theorem relates the two legs of a right triangle to its hypotenuse. Which equation states this relationship?Read the answer and worked solution →A right triangle has legs measuring 3 units and 4 units. What is the length of the hypotenuse?Read the answer and worked solution →A right triangle has a hypotenuse of 13 units and one leg of 5 units. What is the length of the other leg?Read the answer and worked solution →If two triangles are similar, what must be true about their corresponding side lengths?Read the answer and worked solution →A rectangle has a length of 32 meters and a width of 20 meters. What is its perimeter?Read the answer and worked solution →A rectangle has a length of 32 meters and a width of 20 meters. What is its area?Read the answer and worked solution →A rectangle has a perimeter of 50 inches and a width of 10 inches. What is its length?Read the answer and worked solution →A triangle has a base of 10 centimeters and a height of 6 centimeters. Using the triangle area formula, what is its area?Read the answer and worked solution →Pick the pile worth moreRead the answer and worked solution →

Worked practice questions

The difference of a number and six is 13. What is the number?

  1. n = 7
  2. n = 13
  3. n = 6
  4. n = 19
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Correct answer: D. n = 19

1. Let n represent the unknown number and translate the sentence into an equation: n minus 6 equals 13. 2. Add 6 to both sides to isolate n: n minus 6 plus 6 equals 13 plus 6. 3. Simplify: n equals 19. 4. Checking, the difference of 19 and 6 is 13, so the number is 19. _Source: OpenStax Prealgebra (CC BY 4.0), Ch 9 "Math Models and Geometry", section 9.1 Use a Problem Solving Strategy_

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The sum of twice a number and seven is 15. What is the number?

  1. n = 4
  2. n = 8
  3. n = 11
  4. n = 22
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Correct answer: A. n = 4

1. Let n represent the unknown number and translate the sentence: 2n plus 7 equals 15. 2. Subtract 7 from each side: 2n equals 8. 3. Divide each side by 2: n equals 4. 4. Checking, twice 4 is 8, and 8 plus 7 equals 15, so the number is 4. 5. Dividing 15 by 2 first without subtracting the 7 would give the wrong starting point for isolating n. _Source: OpenStax Prealgebra (CC BY 4.0), Ch 9 "Math Models and Geometry", section 9.1 Use a Problem Solving Strategy_

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One number is five more than another. The sum of the two numbers is twenty-one. What are the two numbers?

  1. 7 and 12
  2. 8 and 13
  3. 9 and 14
  4. 10 and 15
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Correct answer: B. 8 and 13

1. Let n represent the first number, so n plus 5 represents the second number, which is five more. 2. The sum of the two numbers is twenty-one: n plus (n plus 5) equals 21. 3. Combine like terms: 2n plus 5 equals 21. 4. Subtract 5 and then divide by 2: 2n equals 16, so n equals 8. 5. The second number is n plus 5, which is 8 plus 5, or 13, so the numbers are 8 and 13. 6. Choosing 7 and 12 keeps the five-more relationship but their sum is only 19, not 21, so that pair fails the second condition. 7. Choosing 9 and 14 also differs by five, but 9 plus 14 equals 23, overshooting the required sum of 21. _Source: OpenStax Prealgebra (CC BY 4.0), Ch 9 "Math Models and Geometry", section 9.1 Use a Problem Solving Strategy_

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More Mathematics topics

IntegersThe Language of AlgebraGraphsAbsolute ValueExponential NotationIntroduction to IntegersOrder of OperationsPerimeter and Area