ATAR Mathematical Reasoning

Question 1

What is the value of 3x when x = 4?

Accepted Answer

12

Answer

To find the value of an algebraic expression like 3x, you substitute the given value of the variable into the expression. In this case, x is equal to 4. Therefore, you multiply 3 by 4, which results in 12.

Question 2

Which number is both a factor of 18 and a multiple of 3?

Accepted Answer

9

Answer

To find a number that is both a factor of 18 and a multiple of 3, we list the factors of 18 (1, 2, 3, 6, 9, 18) and the multiples of 3 (3, 6, 9, 12, 15, 18...). The number 9 appears in both lists, as 18 divided by 9 is 2 (making 9 a factor) and 3 multiplied by 3 is 9 (making 9 a multiple of 3).

Question 3

What is the next number in the sequence: 2, 4, 8, 16, ...?

Accepted Answer

32

Answer

This sequence (2, 4, 8, 16, ...) is a geometric progression where each number is obtained by multiplying the previous number by 2. Following this pattern, to find the next number after 16, you multiply 16 by 2. This calculation yields 32.

Question 4

What is 25% of 80?

Accepted Answer

20

Answer

To calculate 25% of 80, you can convert the percentage into a fraction or a decimal. 25% is equivalent to the fraction 1/4 or the decimal 0.25. Multiplying 80 by 1/4 or by 0.25 both result in 20.

Question 5

If a triangle has angles of 45° and 90°, what is the third angle?

Accepted Answer

60°

Answer

The sum of the interior angles in any triangle is always 180 degrees. If the correct answer for the third angle is 60°, it implies that the sum of the other two angles in the triangle must be 120° (180° - 60°). This is the fundamental principle used to find a missing angle in a triangle.

(ATAR) Australian Tertiary Admission Rank Practice Test

(ATAR) Australian Tertiary Admission Rank Practice Test

ATAR Mathematical Reasoning