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JAMB Mathematics 2011 past questions and answers

40 questions. Try each one, then open the answer to check yourself and read the explanation.

Question 2

Number Bases

If 2q35 = 778, find q.

  1. A.2
  2. B.1
  3. C.4
  4. D.0
Show the answer and explanation

Answer: A (2)

Explanation

2q35 = 50 + 5q + 3 and 778 = 63. So 5q = 10 and q = 2.

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Question 3

Fractions, Decimals and Approximation

Simplify (3⅔ × 5/6 × ⅔)/(11/15 × ¾ × 2/27)

  1. A.6⅔
  2. B.30
  3. C.4⅓
  4. D.50
Show the answer and explanation

Answer: D (50)

Explanation

The top is 11/3 × 5/6 × 2/3 = 55/27 and the bottom is 11/15 × 3/4 × 2/27 = 11/270. Dividing: 55/27 × 270/11 = 50.

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Question 4

Commercial Arithmetic

A man invested N5,000 for 9 months at 4%. What is the simple interest?

  1. A.N150
  2. B.N220
  3. C.N130
  4. D.N250
Show the answer and explanation

Answer: A (N150)

Explanation

I = PRT/100 = 5000 × 4 × (9/12)/100 = N150.

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Question 5

Ratio, Percentages and Rates

If the numbers M, N, Q are in the ratio 5:4:3, find the value of (2N − Q)/M.

  1. A.2
  2. B.3
  3. C.1
  4. D.4
Show the answer and explanation

Answer: C (1)

Explanation

Take M = 5, N = 4, Q = 3: (8 − 3)/5 = 1.

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Question 6

Indices

Simplify (16/81)¼ ÷ (9/16)−½.

  1. A.2/3
  2. B.1/2
  3. C.8/9
  4. D.1/3
Show the answer and explanation

Answer: B (1/2)

Explanation

(16/81)¼ = 2/3 and (9/16)−½ = 4/3. So 2/3 ÷ 4/3 = 1/2.

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Question 7

Logarithms

If log318 + log33 − log3x = 3, find x.

  1. A.1
  2. B.2
  3. C.0
  4. D.3
Show the answer and explanation

Answer: B (2)

Explanation

log3(54/x) = 3, so 54/x = 27 and x = 2.

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Question 8

Surds

Rationalize (2 − √5)/(3 − √5).

  1. A.(1 − √5)/2
  2. B.(1 − √5)/4
  3. C.(√5 − 1)/2
  4. D.(1 + √5)/4
Show the answer and explanation

Answer: B ((1 − √5)/4)

Explanation

Multiply by (3 + √5)/(3 + √5): (6 + 2√5 − 3√5 − 5)/(9 − 5) = (1 − √5)/4.

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Question 10

Sets

From the Venn diagram above, the complement of the set P∩Q is given by

Diagram for this question
  1. A.{a, b, d, e}
  2. B.{b, d}
  3. C.{a, e}
  4. D.{c}
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Answer: A ({a, b, d, e})

Explanation

P ∩ Q = {c}. Its complement is every other element of U: {a, b, d, e}.

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Question 11

Permutation and Combination

Raila has 7 different posters to be hung in her bedroom, living room and kitchen. Assuming she has plans to place, at least, a poster in each of the 3 rooms, how many choices does she have?

  1. A.49
  2. B.170
  3. C.21
  4. D.210
Show the answer and explanation

Answer: D (210)

Explanation

Choosing a different poster for each of the 3 rooms, in order, gives 7P3 = 7 × 6 × 5 = 210 choices.

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Question 13

Polynomials

Find the remainder when x3 − 2x2 + 3x − 3 is divided by x2 + 1.

  1. A.2x − 1
  2. B.x + 3
  3. C.2x + 1
  4. D.x − 3
Show the answer and explanation

Answer: A (2x − 1)

Explanation

x3 − 2x2 + 3x − 3 = (x − 2)(x2 + 1) + (2x − 1), so the remainder is 2x − 1.

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Question 14

Algebraic Expressions

Factorize completely 9y2 − 16x2.

  1. A.(3y − 2x)(3y + 4x)
  2. B.(3y + 4x)(3y + 4x)
  3. C.(3y + 2x)(3y − 4x)
  4. D.(3y + 4x)(3y − 4x)
Show the answer and explanation

Answer: D ((3y + 4x)(3y − 4x))

Explanation

Difference of two squares: (3y)2 − (4x)2 = (3y + 4x)(3y − 4x).

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Question 15

Linear and Simultaneous Equations

Solve for x and y respectively in the simultaneous equations −2x − 5y = 3, x + 3y = 0

  1. A.−3, −9
  2. B.9, −3
  3. C.−9, 3
  4. D.3, −9
Show the answer and explanation

Answer: C (−9, 3)

Explanation

x = −3y. Then 6y − 5y = 3, so y = 3 and x = −9.

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Question 16

Variation

If x varies directly as square root of y and x = 81 when y = 9, find x when y = 1 7/9.

  1. A.20¼
  2. B.27
  3. C.2¼
  4. D.36
Show the answer and explanation

Answer: D (36)

Explanation

x = k√y: 81 = 3k, so k = 27. y = 16/9 gives √y = 4/3, so x = 27 × 4/3 = 36.

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Question 17

Variation

T varies inversely as the cube of R. When R = 3, T = 2/81, find T when R = 2.

  1. A.1/18
  2. B.1/12
  3. C.1/24
  4. D.1/6
Show the answer and explanation

Answer: B (1/12)

Explanation

T = k/R3: k = 2/81 × 27 = 2/3. When R = 2, T = (2/3)/8 = 1/12.

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Question 18

Inequalities

Which of the following diagrams represents the solution of the inequalities y ≤ x − 2 and y ≥ x2 − 4?

Diagram for this question
  1. A.Diagram A
  2. B.Diagram B
  3. C.Diagram C
  4. D.Diagram D
Show the answer and explanation

Answer: A (Diagram A)

Explanation

The points must be on or below the line y = x − 2 and on or above the parabola y = x2 − 4. That is the region inside the parabola's bowl and under the line, between x = −1 and x = 2, which is shaded in A.

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Question 20

Inequalities

Solve the inequalities x2 + 2x > 15.

  1. A.x < −3 or x > 5
  2. B.−5 < x < 3
  3. C.x < 3 or x > 5
  4. D.x > 3 or x < −5
Show the answer and explanation

Answer: D (x > 3 or x < −5)

Explanation

x2 + 2x − 15 = (x + 5)(x − 3) > 0 when both factors have the same sign: x > 3 or x < −5.

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Question 21

Progressions

Find the sum of the first 18 terms of the series 3, 6, 9, ..., 36.

  1. A.505
  2. B.513
  3. C.433
  4. D.635
Show the answer and explanation

Answer: B (513)

Explanation

a = 3, d = 3: S18 = 18/2 × (6 + 17 × 3) = 9 × 57 = 513.

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Question 22

Progressions

The second term of a geometric series is 4 while the fourth term is 16. Find the sum of the first five terms.

  1. A.60
  2. B.62
  3. C.54
  4. D.64
Show the answer and explanation

Answer: B (62)

Explanation

ar = 4 and ar3 = 16 give r2 = 4, so r = 2 and a = 2. S5 = 2(25 − 1)/(2 − 1) = 62.

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Question 24

Matrices and Determinants

If |2 3; 5 3x| = |4 1; 3 2x|, find the value of x. (Determinants written row by row.)

  1. A.−6
  2. B.6
  3. C.−12
  4. D.12
Show the answer and explanation

Answer: A (−6)

Explanation

6x − 15 = 8x − 3, so −2x = 12 and x = −6.

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Question 25

Matrices and Determinants

Evaluate |4 2 −1; 2 3 −1; −1 1 3| (determinant written row by row)

  1. A.25
  2. B.45
  3. C.15
  4. D.55
Show the answer and explanation

Answer: A (25)

Explanation

4(9 + 1) − 2(6 − 1) + (−1)(2 + 3) = 40 − 10 − 5 = 25.

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Question 27

Angles and Polygons

What is the size of each interior angle of a 12-sided regular polygon?

  1. A.120°
  2. B.150°
  3. C.30°
  4. D.180°
Show the answer and explanation

Answer: B (150°)

Explanation

Each exterior angle is 360° ÷ 12 = 30°, so each interior angle is 180° − 30° = 150°.

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Question 28

Mensuration of Plane Shapes

A circle of perimeter 28 cm is opened to form a square. What is the maximum possible area of the square?

  1. A.56 cm2
  2. B.49 cm2
  3. C.98 cm2
  4. D.28 cm2
Show the answer and explanation

Answer: B (49 cm2)

Explanation

The wire of length 28 cm makes a square of side 7 cm, with area 49 cm2.

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Question 29

Circle Theorems

A chord of a circle of radius 7 cm is 5 cm from the centre of the circle. What is the length of the chord?

  1. A.4√6 cm
  2. B.3√6 cm
  3. C.6√6 cm
  4. D.2√6 cm
Show the answer and explanation

Answer: A (4√6 cm)

Explanation

Half the chord = √(72 − 52) = √24 = 2√6, so the chord is 4√6 cm.

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Question 30

Mensuration of Solids

A solid metal cube of side 3 cm is placed in a rectangular tank of dimensions 3, 4 and 5 cm. What volume of water can the tank now hold?

  1. A.48 cm3
  2. B.33 cm3
  3. C.60 cm3
  4. D.27 cm3
Show the answer and explanation

Answer: B (33 cm3)

Explanation

The tank holds 3 × 4 × 5 = 60 cm3, and the cube takes up 27 cm3, leaving 33 cm3.

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Question 31

Loci

The perpendicular bisector of a line XY is the locus of a point

  1. A.whose distance from X is always twice its distance from Y
  2. B.whose distance from Y is always twice its distance from X
  3. C.which moves on the line XY
  4. D.which is equidistant from the points X and Y.
Show the answer and explanation

Answer: D (which is equidistant from the points X and Y.)

Explanation

Every point on the perpendicular bisector of XY is the same distance from X as from Y.

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Question 32

Coordinate Geometry

The midpoint of P(x, y) and Q (8,6) is (5,8). Find x and y.

  1. A.(2,10)
  2. B.(2,8)
  3. C.(2,12)
  4. D.(2,6)
Show the answer and explanation

Answer: A ((2,10))

Explanation

(x + 8)/2 = 5 gives x = 2, and (y + 6)/2 = 8 gives y = 10.

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Question 33

Coordinate Geometry

Find the equation of a line perpendicular to line 2y = 5x + 4 which passes through (4,2).

  1. A.5y − 2x − 18 = 0
  2. B.5y + 2x − 18 = 0
  3. C.5y − 2x + 18 = 0
  4. D.5y + 2x − 2 = 0
Show the answer and explanation

Answer: B (5y + 2x − 18 = 0)

Explanation

The line has gradient 5/2, so the perpendicular has gradient −2/5: y − 2 = −2/5 (x − 4), i.e. 5y + 2x − 18 = 0.

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Question 34

Trigonometry

In a right angled triangle, if tanθ = 3/4. What is cosθ − sinθ?

  1. A.2/5
  2. B.3/5
  3. C.1/5
  4. D.4/5
Show the answer and explanation

Answer: C (1/5)

Explanation

A 3-4-5 triangle gives sin θ = 3/5 and cos θ = 4/5, so cos θ − sin θ = 1/5.

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Question 35

Bearings

A man walks 100 m due West from a point X to Y, he then walks 100 m due North to a point Z. Find the bearing of X from Z.

  1. A.195°
  2. B.135°
  3. C.225°
  4. D.045°
Show the answer and explanation

Answer: B (135°)

Explanation

From Z, X is 100 m east and 100 m south, so it lies exactly south-east: a bearing of 135°.

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Question 36

Differentiation

The derivative of (2x + 1)(3x + 1) is

  1. A.12x + 1
  2. B.6x + 5
  3. C.6x + 1
  4. D.12x + 5
Show the answer and explanation

Answer: D (12x + 5)

Explanation

Expanding gives 6x2 + 5x + 1, whose derivative is 12x + 5.

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Question 37

Differentiation

Find the derivative of sinθ/cosθ.

  1. A.sec2θ
  2. B.tanθ cosecθ
  3. C.cosecθ secθ
  4. D.cosec2θ
Show the answer and explanation

Answer: A (sec2θ)

Explanation

sin θ/cos θ = tan θ, and the derivative of tan θ is sec2θ.

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Question 38

Differentiation

Find the value of x at the minimum point of the curve y = x3 + x2 − x + 1.

  1. A.1/3
  2. B.−1/3
  3. C.1
  4. D.−1
Show the answer and explanation

Answer: A (1/3)

Explanation

dy/dx = 3x2 + 2x − 1 = (3x − 1)(x + 1) = 0 at x = 1/3 or −1. The second derivative 6x + 2 is positive at x = 1/3, so that is the minimum.

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Question 40

Integration

Find ∫cos 4x dx.

  1. A.¾ sin 4x + k
  2. B.−¼ sin 4x + k
  3. C.−¾ sin 4x + k
  4. D.¼ sin 4x + k
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Answer: D (¼ sin 4x + k)

Explanation

The derivative of sin 4x is 4 cos 4x, so ∫cos 4x dx = ¼ sin 4x + k.

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Question 42

Data Presentation

The bar chart above shows the distribution of SS2 students in a school. Find the total number of students.

Diagram for this question
  1. A.180
  2. B.135
  3. C.210
  4. D.105
Show the answer and explanation

Answer: A (180)

Explanation

Reading the bars: about 45 + 60 + 30 + 45 = 180 students.

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Question 43

Linear and Simultaneous Equations

The sum of four consecutive integers is 34. Find the least of these numbers.

  1. A.7
  2. B.6
  3. C.8
  4. D.5
Show the answer and explanation

Answer: A (7)

Explanation

n + (n + 1) + (n + 2) + (n + 3) = 34 gives 4n + 6 = 34, so n = 7.

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Question 44

Measures of Central Tendency

No.: 0, 1, 2, 3, 4, 5
Frequency: 1, 4, 3, 8, 2, 6
From the table above, find the median and range of the data respectively.

  1. A.(8,5)
  2. B.(3,5)
  3. C.(5,8)
  4. D.(5,3)
Show the answer and explanation

Answer: B ((3,5))

Explanation

There are 24 values. The 12th and 13th values are both 3 (cumulative frequencies 1, 5, 8, 16, ...), so the median is 3. Range = 5 − 0 = 5.

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Question 45

Measures of Central Tendency

Class Interval: 0-2, 3-5, 6-8, 9-11
Frequency: 3, 2, 5, 3
Find the mode of the above distribution.

  1. A.9
  2. B.8
  3. C.10
  4. D.7
Show the answer and explanation

Answer: D (7)

Explanation

The modal class is 6-8 (boundaries 5.5–8.5). Mode = 5.5 + (5 − 2)/((5 − 2) + (5 − 3)) × 3 = 5.5 + 1.8 = 7.3 ≈ 7.

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Question 47

Permutation and Combination

In how many ways can the letters of the word FLATION be arranged?

  1. A.6!
  2. B.7!
  3. C.5!
  4. D.8!
Show the answer and explanation

Answer: B (7!)

Explanation

FLATION has 7 different letters, so they can be arranged in 7! ways.

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Question 48

Permutation and Combination

In how many ways can five people sit round a circular table?

  1. A.24
  2. B.60
  3. C.12
  4. D.120
Show the answer and explanation

Answer: A (24)

Explanation

Around a circle, n people can sit in (n − 1)! ways: 4! = 24.

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Question 49

Probability

Find the probability that a number picked at random from the set {43, 44, 45, ..., 60} is a prime number.

  1. A.2/3
  2. B.1/3
  3. C.2/9
  4. D.7/9
Show the answer and explanation

Answer: C (2/9)

Explanation

The set has 18 numbers, and the primes are 43, 47, 53 and 59. So P = 4/18 = 2/9.

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