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Subject

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waec model questions vol1 2021 mathematics | Objective

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Question 1 View Details

Express the repeating decimal 0.\overline{27} as a fraction in lowest terms.

A. 5/17

B. 7/18

C. 6/19

Correct D. 5/18

Correct Answer: D

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Question 2 View Details

A positive integer n leaves a remainder of 5 when divided by 8 and a remainder of 7 when divided by 9. If n is less than 200, what is n?

A. 69

Correct B. 61

C. 85

D. 53

Correct Answer: B

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Question 3 View Details

Solve for the acute angle \(\theta\) (in degrees) that satisfies \(2\sin\theta = \sqrt{3}\,\cos(\theta-30^{\circ})\). Give your answer correct to one decimal place.

A. 60.0°

Correct B. 52.8°

C. 45.0°

D. 30.0°

Correct Answer: B

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Question 4 View Details

The graph of a function \(f\) consists of a straight line from \((0,2)\) to \((4,10)\) and then a parabolic segment from \((4,10)\) to \((8,10)\) whose vertex is at \((6,14)\). Find the average value of \(f(x)\) on the interval \([0,8]\).

A. 30/3

B. 32/3

Correct C. 28/3

D. 24/3

Correct Answer: C

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Question 5 View Details

A class of 30 students took a test. Their mean score was 68 and the standard deviation was 6. Later, 5 absent students took a make‑up test and scored 80, 85, 78, 90 and 82. Assuming the original 30 scores remain unchanged, what are the new mean and the new standard deviation of the 35 scores? Give the mean to two decimal places and the standard deviation to two decimal places.

A. Mean = 70.14, SD = 8.12

Correct B. Mean = 70.14, SD = 7.80

C. Mean = 69.85, SD = 7.55

D. Mean = 71.23, SD = 7.80

Correct Answer: B

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Question 6 View Details

If three‑quarters of a number equals 45% of the same number plus 6, what is the number?

A. 30

Correct B. 20

C. 15

D. 25

Correct Answer: B

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Question 7 View Details

The sum of the first three terms of an arithmetic sequence is 45 and the sum of the next three terms is 81. Find the 10th term of the sequence.

Correct A. 47

B. 45

C. 49

D. 52

Correct Answer: A

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Question 8 View Details

A shop sells pens at a price p naira each and notebooks at n naira each. Three pens and two notebooks cost 560 naira, while five pens and four notebooks cost 960 naira. What is the price of one pen?

Correct A. 160

B. 140

C. 200

D. 120

Correct Answer: A

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Question 9 View Details

In a class of 70 students, 40 study Mathematics, 30 study Physics, and 20 study Chemistry. Fifteen study both Mathematics and Physics, ten study both Mathematics and Chemistry, eight study both Physics and Chemistry, and five study all three subjects. How many students study none of these subjects?

A. 10

B. 12

C. 5

Correct D. 8

Correct Answer: D

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Question 10 View Details

In triangle ABC, AB = 12 cm, AC = 9 cm and ∠BAC = 60°. The internal bisector of ∠BAC meets BC at D. Find the length of BD (in simplest surd form).

Correct A. (12\sqrt{13})/7 cm

B. (8\sqrt{13})\/7 cm

C. (12\sqrt{7})\/7 cm

D. (12\sqrt{13})\/5 cm

Correct Answer: A

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Question 11 View Details

In a school of 120 students, let A be the set of students who study Mathematics and B the set of students who study Physics. It is known that |A| = 72, the number of students who study neither subject is 20, and the number of students who study both subjects is twice the number who study Mathematics only. How many students study Physics only?

A. 36

B. 24

Correct C. 28

D. 32

Correct Answer: C

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Question 12 View Details

In the five‑digit number 23X45, the digit X is unknown. If the number is divisible by 9, what is the value of X?

A. 7

B. 1

C. 9

Correct D. 4

Correct Answer: D

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Question 13 View Details

A shop sells Item A for ₦1,200 and Item B for ₦850. A customer buys 3 of Item A and 5 of Item B and receives a discount of 12.5 % on the total bill. How much does the customer pay (in naira)?

A. 6908.00

B. 7400.00

C. 7850.00

Correct D. 6868.75

Correct Answer: D

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Question 14 View Details

The quadratic equation \(x^{2}-(n+7)x+(2n+6)=0\) has integer roots. Find the sum of all integer values of \(n\) for which this occurs.

A. -8

B. -10

Correct C. -9

D. 0

Correct Answer: C

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Question 15 View Details

In the coordinate plane shown, points A(2, -1) and C(8, 5) are marked. Point B lies on line AC such that AB : BC = 2 : 3. Determine the coordinates of B.

A. (28/5, 13/5)

B. (-2/5, -17/5)

C. (25/5, 10/5)

Correct D. (22/5, 7/5)

Correct Answer: D

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Question 16 View Details

A quantity y varies directly as the square of x and inversely as (x+2). When x = 4, y = 48. Find the value of x when y = 108. Give your answer in simplest exact form.

A. 5+\sqrt{21}

B. 3+\sqrt{20}

Correct C. 3+\sqrt{21}

D. 3-\sqrt{21}

Correct Answer: C

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Question 17 View Details

A smooth curve on the Cartesian plane passes through the points (0,2), (2,6) and (4,14). Assuming the curve is a quadratic of the form y = ax^2 + bx + c, determine the equation of the curve and then find the value of y when x = 3.

A. 8.5

B. 9

C. 10.5

Correct D. 9.5

Correct Answer: D

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Question 18 View Details

The following frequency distribution gives the scores of 38 students in a test. Score : 40 45 50 55 60 65 70 75 80 Frequency : 2 5 8 7 6 4 3 2 1 (a) Calculate the mean score (to 2 decimal places). (b) Calculate the standard deviation of the scores (population standard deviation, to 2 decimal places). (c) If one additional student scores 90, what will be the new mean (to 2 decimal places)?

A. Mean = 55.32, SD = 10.12, New mean = 56.78

B. Mean = 56.00, SD = 9.88, New mean = 57.00

C. Mean = 57.10, SD = 9.45, New mean = 58.02

Correct D. Mean = 56.58, SD = 9.88, New mean = 57.44

Correct Answer: D

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Question 19 View Details

Given the vectors \(\mathbf{a}=3\mathbf{i}-4\mathbf{j}+\mathbf{k}\) and \(\mathbf{b}=-\mathbf{i}+2\mathbf{j}+2\mathbf{k}\): (i) Find the magnitude of \(\mathbf{a}\). (ii) Determine the angle between \(\mathbf{a}\) and \(\mathbf{b}\) (to the nearest degree). (iii) Find a vector \(\mathbf{c}\) that is perpendicular to both \(\mathbf{a}\) and \(\mathbf{b}\) and has magnitude 5. Express \(\mathbf{c}\) in unit‑vector form.

A. -\frac{55}{\sqrt{153}}\mathbf{i} -\frac{40}{\sqrt{153}}\mathbf{j}+\frac{5}{\sqrt{153}}\mathbf{k}

B. -\frac{45}{\sqrt{153}}\mathbf{i} -\frac{30}{\sqrt{153}}\mathbf{j}+\frac{15}{\sqrt{153}}\mathbf{k}

Correct C. -\frac{50}{\sqrt{153}}\mathbf{i} -\frac{35}{\sqrt{153}}\mathbf{j}+\frac{10}{\sqrt{153}}\mathbf{k}

D. -\frac{50}{\sqrt{152}}\mathbf{i} -\frac{35}{\sqrt{152}}\mathbf{j}+\frac{10}{\sqrt{152}}\mathbf{k}

Correct Answer: C

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Question 20 View Details

Simplify the expression \(\displaystyle \frac{x^{2}-4y^{2}}{x-2y}+ (2x+4y)\). Then, given that \(x = 3y + 1\), find the value of the simplified expression in terms of \(y\) and evaluate it for \(y = 2\).

A. 30

Correct B. 33

C. 31

D. 35

Correct Answer: B

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Question 21 View Details

A solid consists of a right circular cylinder of radius r cm and height h cm, with a right circular cone of the same radius placed on top of the cylinder. The height of the cone equals the radius r. The total volume of the solid is 500π cm³. Find the total curved (lateral) surface area of the solid, expressed in terms of π.

A. (560\/3 + 25\\sqrt{2})\\pi cm^2

B. (550\/3 + 25\\sqrt{3})\\pi cm^2

C. (550\/3 + 30\\sqrt{2})\\pi cm^2

Correct D. (550/3 + 25\sqrt{2})\pi cm^2

Correct Answer: D

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Question 22 View Details

The system of linear equations \[(a+1)x + 2y = 7\]\n\[3x - (a-2) y = a\] is known to have a solution in which the two variables satisfy the relation \(x = y + 1\). Determine the value of \(x\).

A. 11\/7

B. 13\/8

Correct C. 11/8

D. 9\/8

Correct Answer: C

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Question 23 View Details

In a box there are red, blue and green balls. The probability of drawing a green ball is 0.2. The probability of drawing a red ball is three times the probability of drawing a blue ball. Two balls are drawn successively without replacement. The probability that the two balls are of different colours is 0.7. How many green balls are in the box if the total number of balls is 5?

Correct A. 1

B. 3

C. 2

D. 0

Correct Answer: A

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Question 24 View Details

In a plane, vectors \(\mathbf{a}\) and \(\mathbf{b}\) satisfy \(|\mathbf{a}| = 5\) and \(|\mathbf{b}| = 8\). A third vector is defined by \(\mathbf{c} = 2\mathbf{a} - \mathbf{b}\). If \(|\mathbf{c}| = 7\), find the angle between \(\mathbf{a}\) and \(\mathbf{b}\) in degrees (to the nearest tenth).

A. 60.0°

B. 30.0°

C. 90.0°

Correct D. 44.0°

Correct Answer: D

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Question 25 View Details

In a school of 120 students, three subjects are offered: Mathematics (set A), Physics (set B) and Chemistry (set C). The Venn diagram shows the following data: \(|A\cap B| = 30\), \(|A\cap C| = 25\), \(|B\cap C| = 20\), \(|A\cap B\cap C| = 10\), 15 students study none of the three subjects, and the total number of students studying Mathematics is 70. If the total number of students studying Physics is 60, how many students study **only** Physics?

Correct A. 20

B. 10

C. 30

D. 40

Correct Answer: A

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