ATAR Calculation Fundamentals 4

Question 1

If 5 workers can complete a job in 8 days, how many days will 10 workers take to complete the same job?

Accepted Answer

4 days

Answer

Inverse proportion: 5×8 = 10×d, so d = 40÷10 = 4 days.

Question 2

What is the value of (−3)^4?

Accepted Answer

81

Answer

(−3)^4 = (−3)×(−3)×(−3)×(−3) = 9×9 = 81 (even exponent gives positive result).

Question 3

A tank holds 500 litres. If 35% is already filled, how many litres are still needed to fill it?

Accepted Answer

325 L

Answer

35% filled = 0.35×500 = 175 L; remaining = 500 − 175 = 325 L.

Question 4

Which expression equals 64^(1/3)?

Accepted Answer

4

Answer

64^(1/3) is the cube root of 64; since 4³ = 64, the answer is 4.

Question 5

Solve: 2(3x + 4) = 5x + 14

Accepted Answer

x = 6

Answer

Expand: 6x + 8 = 5x + 14; subtract 5x and 8 from both sides: x = 6.

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