Core mathematics

The highest common factor of 36 and 48 is:

• 1 12
• 2 144
• 3 24
• 4 6

The lowest common multiple of 6, 8 and 12 is:

• 1 72
• 2 24
• 3 12
• 4 48

In a class, 12 students play cricket, 9 play football and 4 play both. How many play at least one of the two games?

• 1 25
• 2 13
• 3 17
• 4 21

If f(x) = 7x − 9, then f(3) is:

• 1 −6
• 2 12
• 3 21
• 4 30

If f(x) = 7x − 9, the inverse function is:

• 1 (x − 9) ÷ 7
• 2 7x + 9
• 3 (x + 9) ÷ 7
• 4 1 ÷ (7x − 9)

The cube root of 343 is:

• 1 7
• 2 17
• 3 9
• 4 49

The decimal 0.35 as a percentage is:

• 1 350%
• 2 0.35%
• 3 35%
• 4 3.5%

The number 4.8764 rounded to 2 decimal places is:

• 1 4.87
• 2 4.80
• 3 4.90
• 4 4.88

Rs 5000 is divided in the ratio 3 : 7. The smaller share is:

• 1 Rs 2000
• 2 Rs 3500
• 3 Rs 1500
• 4 Rs 1250

A car uses 8 litres of fuel for every 100 km. How much fuel does it use for 250 km?

• 1 25 litres
• 2 18 litres
• 3 16 litres
• 4 20 litres

A price rises from Rs 80 to Rs 100. The percentage increase is:

• 1 125%
• 2 25%
• 3 20%
• 4 80%

The value of log₁₀ 0.01 is:

• 1 −2
• 2 2
• 3 0.01
• 4 −1

If 2ˣ = 64, then x is:

• 1 8
• 2 5
• 3 32
• 4 6

The length 2.5 km in metres is:

• 1 25000 m
• 2 2500 m
• 3 250 m
• 4 25 m

The simple interest on Rs 12,000 at 6% a year for 3 years is:

• 1 Rs 2000
• 2 Rs 720
• 3 Rs 2160
• 4 Rs 1800

Rs 10,000 is invested at 10% compound interest for 2 years. The amount at the end is:

• 1 Rs 12,200
• 2 Rs 12,000
• 3 Rs 11,000
• 4 Rs 12,100

The gradient of the line y = 3x − 5 is:

• 1 −5
• 2 −3
• 3 5
• 4 3

The gradient of the line through (1, 2) and (3, 8) is:

• 1 4
• 2 2
• 3 6
• 4 3

Expand (x + 3)(x − 2).

• 1 x² − x − 6
• 2 x² + x − 6
• 3 x² + x + 6
• 4 x² + 5x − 6

The value of (2³ × 2⁴) ÷ 2⁵ is:

• 1 8
• 2 2
• 3 4
• 4 32

Solve 3x − 7 > 11.

• 1 x < 6
• 2 x > 18
• 3 x > 6
• 4 x > 4

The larger solution of x² − 5x + 6 = 0 is:

• 1 3
• 2 6
• 3 5
• 4 2

The sum of the interior angles of a pentagon is:

• 1 450°
• 2 360°
• 3 540°
• 4 720°

The area of a circle of radius 6 cm is:

• 1 72π cm²
• 2 6π cm²
• 3 12π cm²
• 4 36π cm²

In a right triangle the hypotenuse is 10 and the side opposite angle θ is 6. Then cos θ is:

• 1 3/5
• 2 3/4
• 3 5/3
• 4 4/5

The mean of 4, 8, 9, 11 and 13 is:

• 1 10
• 2 9
• 3 8
• 4 11

Two fair dice are thrown. The probability that the sum is 12 is:

• 1 1/12
• 2 1/6
• 3 1/36
• 4 2/36

The sum of the matrices with rows (1, 2) and (3, 4), and with rows (0, 1) and (2, 1), has rows:

• 1 (0, 2) and (6, 4)
• 2 (1, 2) and (5, 4)
• 3 (1, 3) and (6, 5)
• 4 (1, 3) and (5, 5)

The magnitude of the vector (3, 4) is:

• 1 12
• 2 25
• 3 7
• 4 5

The volume of a cylinder of radius 3 cm and height 10 cm is:

• 1 300π cm³
• 2 60π cm³
• 3 30π cm³
• 4 90π cm³

Two functions are defined by f(x) = 4 − (x − 2)² and g(x) = 6 − x. What is one possible value of a such that f(a) = g(a)?

• 1 5
• 2 4
• 3 1
• 4 2

If 2 ÷ (x − 1) = 3, then x is:

• 1 3/2
• 2 5/3
• 3 7/3
• 4 1/3

If 3x + 2y = 16 and x − y = 2, then x + y is:

• 1 8
• 2 10
• 3 6
• 4 4

The larger solution of x² − 4x − 5 = 0 is:

• 1 5
• 2 4
• 3 −1
• 4 −5

The solution of −2x + 5 ≥ 1 is:

• 1 x ≥ 2
• 2 x ≥ 3
• 3 x ≤ −2
• 4 x ≤ 2

A number is increased by 20% and the result is then decreased by 20%. The net change is:

• 1 An increase of 4%
• 2 A decrease of 2%
• 3 A decrease of 4%
• 4 No change

Rs 5000 is invested at 8% compound interest for 2 years. The amount at the end is:

• 1 Rs 5832
• 2 Rs 5640
• 3 Rs 5800
• 4 Rs 5864

A shop gives a 15% discount and then a further 10% off the reduced price. The single equivalent discount is:

• 1 22.5%
• 2 25%
• 3 23.5%
• 4 24%

A mixture of 20 litres has milk and water in the ratio 3 : 2. How much water is there?

• 1 6 litres
• 2 12 litres
• 3 8 litres
• 4 10 litres

The number 0.004567 rounded to 2 significant figures is:

• 1 0.00457
• 2 0.0045
• 3 0.0050
• 4 0.0046

The number 45000 in standard form is:

• 1 0.45 × 10⁴
• 2 4.5 × 10⁴
• 3 4.5 × 10³
• 4 45 × 10³

The value of 8^(2/3) is:

• 1 6
• 2 4
• 3 16
• 4 2

The value of log₂ 40 − log₂ 5 is:

• 1 5
• 2 8
• 3 35
• 4 3

In a group of 60 people, 35 like tea, 30 like coffee and 10 like both. How many like neither?

• 1 5
• 2 15
• 3 10
• 4 0

A bag has 4 red and 6 blue marbles. Two are drawn without replacement. The probability that both are red is:

• 1 3/10
• 2 2/15
• 3 1/5
• 4 4/25

The mean of 5 numbers is 12. When one number, 10, is removed, the mean of the other 4 is:

• 1 12
• 2 12.5
• 3 13
• 4 11.5

The median of 3, 9, 4, 7, 1 and 8 is:

• 1 4
• 2 6
• 3 7
• 4 5.5

Each exterior angle of a regular hexagon is:

• 1 30°
• 2 60°
• 3 72°
• 4 120°

The total surface area of a cube of side 4 cm is:

• 1 64 cm²
• 2 48 cm²
• 3 16 cm²
• 4 96 cm²

If tan θ = 3/4 and θ is an acute angle, then sin θ is:

• 1 5/3
• 2 4/5
• 3 3/5
• 4 3/4