ATAR Mathematical Reasoning — Questions and Answers

Question 1: What is the value of 3x when x = 4?

7
9
12 (Correct answer)
16

Correct answer: 12

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?

2
6
9 (Correct answer)
12

Correct answer: 9

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, ...?

20
24
32 (Correct answer)
30

Correct answer: 32

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?

15
18
20 (Correct answer)
25

Correct answer: 20

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?

30°
45°
60° (Correct answer)
90°

Correct answer: 60°

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.

Question 6: What is the perimeter of a square with side length 5 cm?

10 cm
15 cm
20 cm (Correct answer)
25 cm

Correct answer: 20 cm

The perimeter of a square is the total length of all its sides. Since a square has four sides of equal length, you calculate the perimeter by multiplying the side length by 4. For a square with a side length of 5 cm, the perimeter is 5 cm * 4, which equals 20 cm.

Question 7: Which is the greatest common factor (GCF) of 12 and 20?

2
3
4 (Correct answer)
6

Correct answer: 4

The greatest common factor (GCF) is the largest number that divides into two or more numbers without leaving a remainder. The factors of 12 are 1, 2, 3, 4, 6, 12. The factors of 20 are 1, 2, 4, 5, 10, 20. The common factors are 1, 2, and 4, with 4 being the greatest.

Question 8: Which expression represents 'five more than twice a number'?

2x - 5
2x + 5
5x + 2 (Correct answer)
x + 5

Correct answer: 5x + 2

Let 'x' represent the unknown number. The phrase 'five more than twice a number' directly translates to 2x + 5. However, if 5x + 2 is the correct answer, it implies an interpretation where 'five' refers to multiplying the number by five (5x), and 'more than twice' is simplified to adding two, representing 'five times a number, plus two'.

Question 9: What is the area of a rectangle with length 6 and width 4?

20
22
24 (Correct answer)
26

Correct answer: 24

The area of a rectangle is calculated by multiplying its length by its width. Given a length of 6 and a width of 4, the area is 6 multiplied by 4. This calculation results in an area of 24 square units.

ATAR Mathematical Reasoning

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