ISAT Mathematical Problem-Solving 5

Question 1

A cylinder has a radius of 4 cm and a height of 10 cm. What is its volume?

Accepted Answer

160π cm³

Answer

V = πr²h = π(4²)(10) = 160π cm³.

Question 2

If the system of equations 2x + y = 7 and x − y = 2 is solved, what is the value of x + y?

Accepted Answer

5

Answer

Adding the equations: 3x = 9 → x = 3; then y = 1; so x + y = 4... wait: 2(3)+1=7 ✓, 3−1=2 ✓, x+y=4.

Question 3

An investment grows by 8% per year compounded annually. Approximately how many years will it take to double?

Accepted Answer

9 years

Answer

Using the Rule of 72: 72 ÷ 8 = 9 years.

Question 4

The ratio of boys to girls in a class is 3:4. If there are 28 girls, how many students are in the class total?

Accepted Answer

49

Answer

If 4 parts = 28, then 1 part = 7; boys = 21; total = 21 + 28 = 49.

Question 5

What is the slope of the line perpendicular to 4x − 2y = 8?

Accepted Answer

−1/2

Answer

Rewrite as y = 2x − 4, so slope = 2; perpendicular slope = −1/2.

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