ATAR Calculation Fundamentals 5

Question 1

What is the greatest common factor (GCF) of 84 and 126?

Accepted Answer

42

Answer

84 = 2²×3×7 and 126 = 2×3²×7; GCF = 2×3×7 = 42.

Question 2

If a/b = 3/5 and b = 35, what is the value of a?

Accepted Answer

21

Answer

a/35 = 3/5, so a = 35×3/5 = 105/5 = 21.

Question 3

A cylinder has radius 5 cm and height 10 cm. What is its volume? (Use π ≈ 3.14)

Accepted Answer

785 cm³

Answer

Volume = πr²h = 3.14 × 25 × 10 = 785 cm³.

Question 4

What is 7/9 − 2/3 expressed as a fraction in lowest terms?

Accepted Answer

1/9

Answer

Convert 2/3 to 6/9; then 7/9 − 6/9 = 1/9.

Question 5

A store marks up goods by 40% then offers a 20% sale. What is the net effect on the original price?

Accepted Answer

12% increase

Answer

1.40 × 0.80 = 1.12, so the final price is 12% above the original.

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