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BC Graduation Assessments Math Models and Geometry — practice questions

Explore 6 free Math Models and Geometry questions in BC Graduation Assessments 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 1–6 of 6.

Pete bought a shirt on sale for $18, which is one-half the original price. What was the original price of the shirt?Read the answer and worked solution →Nga's car insurance premium increased by $60, which was 8% of the original cost. What was the original cost of the premium?Read the answer and worked solution →Alicia bought a package of 8 peaches for $3.20. To compare the deal with loose fruit, she wants the cost of each peach. What is it?Read the answer and worked solution →A fence must go around a rectangular swimming pool whose perimeter is 150 feet. The pool's length is 15 feet more than its width. What are the pool's dimensions?Read the answer and worked solution →A rectangular room has an area of 168 square feet, and carpet is sold by the foot of width. The room's length is 14 feet. How wide is the room?Read the answer and worked solution →Pick the pile worth moreRead the answer and worked solution →

Worked practice questions

Pete bought a shirt on sale for $18, which is one-half the original price. What was the original price of the shirt?

  1. $9
  2. $36
  3. $27
  4. $54
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Correct answer: B. $36

1. Let p stand for the original price, so 18 is one-half of p, which translates to 18 equals one-half times p. 2. Multiply both sides by 2 to undo the one-half: 2 times 18 equals p. 3. Simplify: p equals 36, so the original price was $36. 4. Check: half of $36 is $18, which matches the sale price. _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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Nga's car insurance premium increased by $60, which was 8% of the original cost. What was the original cost of the premium?

  1. $480
  2. $7,500
  3. $750
  4. $675
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Correct answer: C. $750

1. Let c stand for the original cost, so 60 is 8% of c, which translates to 60 equals 0.08 times c. 2. Divide both sides by 0.08 to isolate c: c equals 60 divided by 0.08. 3. Simplify: c equals 750, so the original premium was $750. 4. Check: 8% of 750 is 0.08 times 750, which equals 60, matching the increase. 5. $480 multiplies 60 by 8 instead of dividing by 0.08, running the percent relationship backwards. _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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Alicia bought a package of 8 peaches for $3.20. To compare the deal with loose fruit, she wants the cost of each peach. What is it?

  1. $0.32
  2. $0.80
  3. $0.25
  4. $0.40
Show answer and solution

Correct answer: D. $0.40

1. The cost of one peach is the package price divided by the number of peaches. 2. Divide: 3.20 divided by 8 equals 0.40. 3. Each peach costs $0.40, which is the number to compare against the loose-fruit price. _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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