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Core mathematics

Written by Hassan Raza (Mathematics)

IBA · Mathematics · 50 questions

Name: ____________________ Date: ____________

The highest common factor of 36 and 48 is:
- A 12
- B 144
- C 24
- D 6
The lowest common multiple of 6, 8 and 12 is:
- A 72
- B 24
- C 12
- D 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?
- A 25
- B 13
- C 17
- D 21
If f(x) = 7x − 9, then f(3) is:
- A −6
- B 12
- C 21
- D 30
If f(x) = 7x − 9, the inverse function is:
- A (x − 9) ÷ 7
- B 7x + 9
- C (x + 9) ÷ 7
- D 1 ÷ (7x − 9)
The cube root of 343 is:
- A 7
- B 17
- C 9
- D 49
The decimal 0.35 as a percentage is:
- A 350%
- B 0.35%
- C 35%
- D 3.5%
The number 4.8764 rounded to 2 decimal places is:
- A 4.87
- B 4.80
- C 4.90
- D 4.88
Rs 5000 is divided in the ratio 3 : 7. The smaller share is:
- A Rs 2000
- B Rs 3500
- C Rs 1500
- D Rs 1250
A car uses 8 litres of fuel for every 100 km. How much fuel does it use for 250 km?
- A 25 litres
- B 18 litres
- C 16 litres
- D 20 litres
A price rises from Rs 80 to Rs 100. The percentage increase is:
- A 125%
- B 25%
- C 20%
- D 80%
The value of log₁₀ 0.01 is:
- A −2
- B 2
- C 0.01
- D −1
If 2ˣ = 64, then x is:
- A 8
- B 5
- C 32
- D 6
The length 2.5 km in metres is:
- A 25000 m
- B 2500 m
- C 250 m
- D 25 m
The simple interest on Rs 12,000 at 6% a year for 3 years is:
- A Rs 2000
- B Rs 720
- C Rs 2160
- D Rs 1800
Rs 10,000 is invested at 10% compound interest for 2 years. The amount at the end is:
- A Rs 12,200
- B Rs 12,000
- C Rs 11,000
- D Rs 12,100
The gradient of the line y = 3x − 5 is:
- A −5
- B −3
- C 5
- D 3
The gradient of the line through (1, 2) and (3, 8) is:
- A 4
- B 2
- C 6
- D 3
Expand (x + 3)(x − 2).
- A x² − x − 6
- B x² + x − 6
- C x² + x + 6
- D x² + 5x − 6
The value of (2³ × 2⁴) ÷ 2⁵ is:
- A 8
- B 2
- C 4
- D 32
Solve 3x − 7 > 11.
- A x < 6
- B x > 18
- C x > 6
- D x > 4
The larger solution of x² − 5x + 6 = 0 is:
- A 3
- B 6
- C 5
- D 2
The sum of the interior angles of a pentagon is:
- A 450°
- B 360°
- C 540°
- D 720°
The area of a circle of radius 6 cm is:
- A 72π cm²
- B 6π cm²
- C 12π cm²
- D 36π cm²
In a right triangle the hypotenuse is 10 and the side opposite angle θ is 6. Then cos θ is:
- A 3/5
- B 3/4
- C 5/3
- D 4/5
The mean of 4, 8, 9, 11 and 13 is:
- A 10
- B 9
- C 8
- D 11
Two fair dice are thrown. The probability that the sum is 12 is:
- A 1/12
- B 1/6
- C 1/36
- D 2/36
The sum of the matrices with rows (1, 2) and (3, 4), and with rows (0, 1) and (2, 1), has rows:
- A (0, 2) and (6, 4)
- B (1, 2) and (5, 4)
- C (1, 3) and (6, 5)
- D (1, 3) and (5, 5)
The magnitude of the vector (3, 4) is:
- A 12
- B 25
- C 7
- D 5
The volume of a cylinder of radius 3 cm and height 10 cm is:
- A 300π cm³
- B 60π cm³
- C 30π cm³
- D 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)?
- A 5
- B 4
- C 1
- D 2
If 2 ÷ (x − 1) = 3, then x is:
- A 3/2
- B 5/3
- C 7/3
- D 1/3
If 3x + 2y = 16 and x − y = 2, then x + y is:
- A 8
- B 10
- C 6
- D 4
The larger solution of x² − 4x − 5 = 0 is:
- A 5
- B 4
- C −1
- D −5
The solution of −2x + 5 ≥ 1 is:
- A x ≥ 2
- B x ≥ 3
- C x ≤ −2
- D x ≤ 2
A number is increased by 20% and the result is then decreased by 20%. The net change is:
- A An increase of 4%
- B A decrease of 2%
- C A decrease of 4%
- D No change
Rs 5000 is invested at 8% compound interest for 2 years. The amount at the end is:
- A Rs 5832
- B Rs 5640
- C Rs 5800
- D Rs 5864
A shop gives a 15% discount and then a further 10% off the reduced price. The single equivalent discount is:
- A 22.5%
- B 25%
- C 23.5%
- D 24%
A mixture of 20 litres has milk and water in the ratio 3 : 2. How much water is there?
- A 6 litres
- B 12 litres
- C 8 litres
- D 10 litres
The number 0.004567 rounded to 2 significant figures is:
- A 0.00457
- B 0.0045
- C 0.0050
- D 0.0046
The number 45000 in standard form is:
- A 0.45 × 10⁴
- B 4.5 × 10⁴
- C 4.5 × 10³
- D 45 × 10³
The value of 8^(2/3) is:
- A 6
- B 4
- C 16
- D 2
The value of log₂ 40 − log₂ 5 is:
- A 5
- B 8
- C 35
- D 3
In a group of 60 people, 35 like tea, 30 like coffee and 10 like both. How many like neither?
- A 5
- B 15
- C 10
- D 0
A bag has 4 red and 6 blue marbles. Two are drawn without replacement. The probability that both are red is:
- A 3/10
- B 2/15
- C 1/5
- D 4/25
The mean of 5 numbers is 12. When one number, 10, is removed, the mean of the other 4 is:
- A 12
- B 12.5
- C 13
- D 11.5
The median of 3, 9, 4, 7, 1 and 8 is:
- A 4
- B 6
- C 7
- D 5.5
Each exterior angle of a regular hexagon is:
- A 30°
- B 60°
- C 72°
- D 120°
The total surface area of a cube of side 4 cm is:
- A 64 cm²
- B 48 cm²
- C 16 cm²
- D 96 cm²
If tan θ = 3/4 and θ is an acute angle, then sin θ is:
- A 5/3
- B 4/5
- C 3/5
- D 3/4

Answer key

1. A, 2. B, 3. C, 4. B, 5. C, 6. A, 7. C, 8. D, 9. C, 10. D, 11. B, 12. A, 13. D, 14. B, 15. C, 16. D, 17. D, 18. D, 19. B, 20. C, 21. C, 22. A, 23. C, 24. D, 25. D, 26. B, 27. C, 28. D, 29. D, 30. D, 31. D, 32. B, 33. C, 34. A, 35. D, 36. C, 37. A, 38. C, 39. C, 40. D, 41. B, 42. B, 43. D, 44. A, 45. B, 46. B, 47. D, 48. B, 49. D, 50. C

36 = 2² × 3² and 48 = 2⁴ × 3, so the HCF is 2² × 3 = 12.
The LCM is the smallest number that all three divide: 24.
The number is 12 + 9 − 4 = 17.
f(3) = 21 − 9 = 12.
Solve y = 7x − 9 for x to get x = (y + 9) ÷ 7.
7 × 7 × 7 = 343.
Multiply by 100.
The third decimal place is 6, so round up.
One part is 500, so the smaller share is 1500.
The fuel is 8 × 2.5 = 20 litres.
The rise of 20 is 25% of 80.
10⁻² = 0.01.
2⁶ = 64.
One kilometre is 1000 metres.
Interest = 12000 × 6 × 3 ÷ 100 = 2160.
The amount is 10000 × 1.1 × 1.1 = 12100.
In y = mx + c the gradient is m.
Gradient = (8 − 2) ÷ (3 − 1) = 3.
x² − 2x + 3x − 6 = x² + x − 6.
The indices combine to 2⁷⁻⁵ = 2².
3x > 18, so x > 6.
The solutions are 2 and 3.
The sum is (n − 2) × 180° = 540°.
Area = πr².
The adjacent side is 8, so cos θ = 8 ÷ 10.
The sum is 45 and 45 ÷ 5 = 9.
Only 6 and 6 give a sum of 12.
Add the matching entries.
The magnitude is √(9 + 16) = 5.
Volume = πr²h = π × 9 × 10.
Setting the functions equal gives a² − 5a + 6 = 0, so a = 2 or a = 3.
x − 1 = 2/3, so x = 5/3.
Solving gives x = 4 and y = 2.
The equation factors as (x − 5)(x + 1) = 0.
−2x ≥ −4, and dividing by −2 turns the sign around.
1.2 × 0.8 = 0.96.
The amount is 5000 × 1.08 × 1.08.
0.85 × 0.90 = 0.765, so the discount is 23.5%.
The water is 2/5 of 20 litres.
The first two significant figures are 4 and 5, and the next digit 6 rounds up.
Move the decimal point four places.
The cube root of 8 is 2, and 2² = 4.
The difference is log₂ 8 = 3.
The number who like at least one is 35 + 30 − 10 = 55.
The probability is 4/10 × 3/9 = 2/15.
The total is 60, and 50 ÷ 4 = 12.5.
In order the numbers are 1, 3, 4, 7, 8, 9, and the middle two are 4 and 7.
The exterior angles add up to 360°, and 360 ÷ 6 = 60.
There are 6 faces of area 16 cm².
The triangle has sides 3, 4 and 5, so sin θ = 3/5.