ATAR Mathematical Reasoning 2

Question 1

A rectangle has a perimeter of 54 cm and a length that is twice its width. What is the area of the rectangle?

Accepted Answer

108 cm²

Answer

Width = 9 cm, length = 18 cm, so area = 9 × 18 = 162 cm².

Question 2

If the probability of rain on any given day is 0.3, what is the probability that it does NOT rain on exactly 2 consecutive days?

Accepted Answer

0.49

Answer

P(no rain on 2 consecutive days) = 0.7 × 0.7 = 0.49.

Question 3

A car travels 120 km at 60 km/h, then 80 km at 40 km/h. What is the average speed for the whole journey?

Accepted Answer

48 km/h

Answer

Total distance = 200 km, total time = 2 + 2 = 4 hours, so average speed = 200/4 = 50 km/h.

Question 4

What is the value of x if log₂(x) + log₂(x − 2) = 3?

Accepted Answer

x = 4

Answer

log₂(x(x−2)) = 3 means x(x−2) = 8, giving x² − 2x − 8 = 0, so (x−4)(x+2) = 0; x = 4 (x must be positive).

Question 5

A sequence is defined by aₙ = 3n − 1. What is the sum of the first 10 terms?

Accepted Answer

155

Answer

Sum = Σ(3n−1) for n=1 to 10 = 3(55) − 10 = 165 − 10 = 155.

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