waec model questions vol1 2022 mathematics | Objective

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Question 1 View Details
If \\((2^x\) = 64\), what is the value of x?
A. 8
B. 7
Correct C. 6
D. 5

Correct Answer: C

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Question 2 View Details
The first term of an arithmetic sequence is 5 and the common difference is 3. What is the 10th term of the sequence?
A. 25
Correct B. 32
C. 29
D. 36

Correct Answer: B

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Question 3 View Details
A student scored 75 out of 100 in Mathematics and 60 out of 80 in English. What is the student's overall percentage score?
Correct A. 75
B. 70
C. 65
D. 80

Correct Answer: A

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Question 4 View Details
If y varies directly as x and \(y = 12\) when \(x = 4\), what is the value of y when \(x = 10\)?
A. 15
B. 40
Correct C. 30
D. 24

Correct Answer: C

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Question 5 View Details
Simplify the expression: \((3^4 * 3^\)\(2) / 3\\()^5\).
Correct A. 3
B. 9
C. 1
D. 27

Correct Answer: A

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Question 6 View Details
A company produces two types of products, A and B. The total cost (in Naira) of producing x units of product A and y units of product B is given by the equation \(C = 200x + 150y\). If the company wants to minimize the cost while producing a total of 100 units of products A and B combined, how many units of each product should be produced if the production of product A must be at least twice that of product B?
A. 70 units of product A and 30 units of product B
B. 60 units of product A and 40 units of product B
C. 50 units of product A and 50 units of product B
Correct D. 67 units of product A and 33 units of product B

Correct Answer: D

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Question 7 View Details
Solve the quadratic equation \\((3x^2 - 12x + 9\) = 0\) using the quadratic formula. What are the roots of the equation?
A. \(x = 2\) and \(x = 2\)
B. \(x = 5\) and x = -1
C. \(x = 4\) and \(x = 0\)
Correct D. \(x = 3\) and \(x = 1\)

Correct Answer: D

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Question 8 View Details
A rectangle has a length that is 4 meters longer than its width. If the perimeter of the rectangle is 40 meters, what are the dimensions of the rectangle?
A. \(Length = 14\) meters, \(Width = 10\) meters
Correct B. \(Length = 12\) meters, \(Width = 8\) meters
C. \(Length = 16\) meters, \(Width = 12\) meters
D. \(Length = 10\) meters, \(Width = 6\) meters

Correct Answer: B

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Question 9 View Details
A student scored 75% in Mathematics, 85% in English, and 90% in Science. If the total marks for each subject are 100, what is the student's overall percentage across the three subjects?
A. 75%
B. 90%
Correct C. 83.33%
D. 80%

Correct Answer: C

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Question 10 View Details
In a coordinate plane, the points A(2, 3) and B(8, 15) are the endpoints of a line segment. Find the midpoint of the line segment AB.
Correct A. (5, 9)
B. (6, 10)
C. (3, 7)
D. (4, 8)

Correct Answer: A

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Question 11 View Details
A triangle has two sides measuring 8 cm and 6 cm. The angle between these two sides is 60 degrees. Calculate the area of the triangle and then determine the length of the third side.
A. \(8√3\) cm² for area and \(5√13\) cm for the length of the third side.
B. \(14√3\) cm² for area and \(4√13\) cm for the length of the third side.
Correct C. \(12√3\) cm² for area and \(2√13\) cm for the length of the third side.
D. \(10√3\) cm² for area and \(3√13\) cm for the length of the third side.

Correct Answer: C

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Question 12 View Details
The graph of the function f(x) = \(2x^2 - 4x + 1\) intersects the x-axis at two points. Determine the coordinates of these points and the vertex of the parabola.
A. (1 + \(√2\), 0) and (1 - \(√2\), 0) for x-intercepts; (0, -1) for the vertex.
B. (2 + \(√2\), 0) and (2 - \(√2\), 0) for x-intercepts; (2, -1) for the vertex.
C. (1 + \(√3\), 0) and (1 - \(√3\), 0) for x-intercepts; (1, -2) for the vertex.
Correct D. (1 + \(√2\), 0) and (1 - \(√2\), 0) for x-intercepts; (1, -1) for the vertex.

Correct Answer: D

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Question 13 View Details
In a vector space, vector A is represented as 3i + 4j and vector B is represented as -2i + 5j. Calculate the resultant vector \(R = A + B\) and find its magnitude.
A. Resultant vector \(R = 3i + 5j\) and its magnitude is \(√34\).
B. Resultant vector \(R = 5i + 9j\) and its magnitude is \(√82\).
Correct C. Resultant vector \(R = i + 9j\) and its magnitude is \(√82\).
D. Resultant vector \(R = i + 7j\) and its magnitude is \(√50\).

Correct Answer: C

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Question 14 View Details
If a student scored 75% in Mathematics and 60% in English, and the total marks for each subject are 100, calculate the total marks obtained by the student and the average percentage score across both subjects.
A. Total \(marks = 150\) and average percentage \(score = 75\)%.
B. Total \(marks = 145\) and average percentage \(score = 72.5\)%.
C. Total \(marks = 120\) and average percentage \(score = 60\)%.
Correct D. Total \(marks = 135\) and average percentage \(score = 67.5\)%.

Correct Answer: D

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Question 15 View Details
The graph of the linear equation \(y = 3x + 2\) intersects the y-axis at which point? Also, find the x-intercept of the line.
A. Y-intercept is (0, 1) and x-intercept is (-1, 0).
B. Y-intercept is (0, 3) and x-intercept is \((-3/2\), 0).
Correct C. Y-intercept is (0, 2) and x-intercept is \((-2/3\), 0).
D. Y-intercept is (0, 4) and x-intercept is \((-4/3\), 0).

Correct Answer: C

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Question 16 View Details
A box contains 5 red balls, 3 blue balls, and 2 green balls. If two balls are drawn at random without replacement, what is the probability that both balls drawn are of the same color?
A. \(10/45\)
Correct B. \(14/45\)
C. \(8/45\)
D. \(12/45\)

Correct Answer: B

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Question 17 View Details
In a class of 30 students, 18 study Mathematics, 15 study Physics, and 10 study both subjects. How many students study only Mathematics?
Correct A. 8
B. 5
C. 12
D. 10

Correct Answer: A

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Question 18 View Details
The first term of an arithmetic sequence is 5 and the common difference is 3. What is the 10th term of the sequence?
A. 25
B. 35
Correct C. 32
D. 29

Correct Answer: C

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Question 19 View Details
The coordinates of points A and B are (2, 3) and (8, 7) respectively. Find the midpoint of the line segment AB.
Correct A. (5, 5)
B. (6, 6)
C. (4, 4)
D. (3, 4)

Correct Answer: A

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Question 20 View Details
In a coordinate plane, points A(2, 3) and B(8, k) lie on a straight line with a slope of 2. Determine the value of k.
A. 18
B. 10
C. 12
Correct D. 15

Correct Answer: D

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Question 21 View Details
A survey was conducted among 200 students to determine their preferred mode of transportation to school. The results showed that 60 students preferred walking, 80 preferred cycling, and the rest preferred using public transport. If the students who preferred public transport were further divided into those who used buses and those who used taxis in the ratio of 3:2, how many students preferred public transport?
A. 80
B. 50
C. 70
Correct D. 60

Correct Answer: D

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Question 22 View Details
A cylindrical water tank has a radius of 3 meters and a height of 5 meters. If the tank is filled to 80% of its capacity, how much water (in cubic meters) is in the tank? Use π = 3.14.
A. 130.00
B. 120.48
C. 100.56
Correct D. 113.04

Correct Answer: D

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Question 23 View Details
What is the least common multiple (LCM) of 12 and 15?
Correct A. 60
B. 30
C. 45
D. 75

Correct Answer: A

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Question 24 View Details
A rectangular garden measures 10 meters in length and 6 meters in width. If a path of uniform width is to be built around the garden, increasing the total area to 120 square meters, what is the width of the path?
A. 1
B. 4
C. 3
Correct D. 2

Correct Answer: D

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Question 25 View Details
If the sum of three consecutive integers is 72, what is the smallest of these integers?
A. 21
B. 24
Correct C. 23
D. 22

Correct Answer: C

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