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waec model questions vol1 2024 mathematics | Objective

Are you preparing for waec model questions vol1 exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2024 mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

In the coordinate plane, point A is located at (2, 3) and point B is at (8, 7). A line segment is drawn between points A and B. Determine the midpoint of the line segment AB and the slope of the line. What is the equation of the line in slope-intercept form?

A. y = (1/2)x + 4

B. y = (3/2)x + 2

C. y = (4/3)x + 1

Correct D. y = (2/3)x + 5/3

Correct Answer: D

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Question 2

A student scored 75 out of 100 in Mathematics and 60 out of 80 in English. What is the student's overall percentage score across both subjects?

A. 65%

B. 80%

C. 70%

Correct D. 75%

Correct Answer: D

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Question 3

In a Venn diagram, set A contains 15 elements, set B contains 10 elements, and the intersection of sets A and B contains 5 elements. How many elements are in the union of sets A and B?

A. 15

B. 22

C. 18

Correct D. 20

Correct Answer: D

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Question 4

A box contains 12 red balls, 8 blue balls, and 5 green balls. If one ball is drawn at random, what is the probability that it is either red or green?

A. 3/5

B. 8/25

C. 1/2

Correct D. 17/25

Correct Answer: D

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Question 5

The relationship between the variables x and y is given by the equation y = kx^2, where k is a constant. If y = 50 when x = 5, what is the value of k? If x is doubled, what will be the new value of y?

A. 150

Correct B. 200

C. 100

D. 250

Correct Answer: B

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Question 6

Two vectors, A and B, are represented as A = 3i + 4j and B = 2i - j. Calculate the magnitude of the vector C, where C = A + 2B. Then, determine the angle between vector C and the positive x-axis.

Correct A. √53 and tan^(-1)(2/7)

B. √60 and tan^(-1)(4/9)

C. √50 and tan^(-1)(1/6)

D. √55 and tan^(-1)(3/8)

Correct Answer: A

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Question 7

A cylindrical tank has a radius of 3 meters and a height of 5 meters. Water is being poured into the tank at a rate of 2 cubic meters per hour. Determine how long it will take to fill the tank completely. Then, calculate the surface area of the tank when it is full.

A. 25π hours and 50π m²

B. 30π hours and 45π m²

C. 20π hours and 40π m²

Correct D. 22.5π hours and 48π m²

Correct Answer: D

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Question 8

In triangle ABC, angle A is 40 degrees, angle B is 60 degrees, and side a (opposite angle A) is 10 cm. Calculate the length of side b (opposite angle B) using the Law of Sines. Then, find the length of side c (opposite angle C) using the same law.

A. 15.00 cm and 12.50 cm

B. 12.50 cm and 14.20 cm

Correct C. 13.45 cm and 15.33 cm

D. 11.75 cm and 16.00 cm

Correct Answer: C

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Question 9

The graph of a linear function passes through the points (2, 3) and (4, 7). Determine the equation of the line in slope-intercept form. Then, find the y-intercept of the line.

A. y = 3x - 1 and -1

Correct B. y = 2x - 1 and -1

C. y = x + 2 and 2

D. y = 2x + 1 and 1

Correct Answer: B

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Question 10

If y varies directly with x and inversely with z, and y = 12 when x = 4 and z = 3, find the constant of variation k. Then, express y in terms of x and z.

A. k = 6 and y = 6(x/z)

B. k = 8 and y = 8(x/z)

Correct C. k = 9 and y = 9(x/z)

D. k = 10 and y = 10(x/z)

Correct Answer: C

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Question 11

A cylindrical tank has a radius of 3 meters and a height of 5 meters. If the tank is filled with water to a height of 4 meters, calculate the volume of the water in the tank. Then, if the tank is emptied and filled with sand, what would be the height of the sand if the volume of sand is equal to the volume of water previously in the tank?

Correct A. 4

B. 7

C. 5

D. 3

Correct Answer: A

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Question 12

Solve the following system of equations: 2x + 3y = 12 and 4x - y = 5. Determine the values of x and y, and then find the value of 3x + 2y.

Correct A. 6

B. 8

C. 4

D. 10

Correct Answer: A

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Question 13

A student scored 75% in Mathematics, 60% in English, and 90% in Science. If the maximum marks for each subject are 100, calculate the total percentage of marks obtained by the student across all three subjects.

Correct A. 75

B. 80

C. 65

D. 70

Correct Answer: A

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Question 14

In a class of 30 students, the mean score in a test is 70. If one student scored 90, what is the new mean score if that student is removed from the class?

A. 68.25

B. 71.00

C. 70.50

Correct D. 69.31

Correct Answer: D

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Question 15

Solve the inequality 3x - 5 < 2x + 4. Then, determine the range of values for x that satisfy this inequality.

A. x ≥ 8

Correct B. x < 9

C. x > 7

D. x ≤ 10

Correct Answer: B

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Question 16

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 are of different colors?

A. 15/45

B. 35/45

Correct C. 31/45

D. 25/45

Correct Answer: C

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Question 17

Solve the inequality 3x - 5 < 2x + 4 and express the solution in interval notation.

A. (-∞, 7)

Correct B. (-∞, 9)

C. (-∞, 10)

D. (-∞, 8)

Correct Answer: B

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Question 18

If y varies directly as x and y = 12 when x = 4, find the value of y when x = 10.

A. 36

Correct B. 30

C. 24

D. 40

Correct Answer: B

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Question 19

The first term of an arithmetic sequence is 5, and the common difference is 3. What is the 10th term of the sequence?

A. 38

Correct B. 32

C. 25

D. 29

Correct Answer: B

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Question 20

The graph of the function f(x) = 2x^2 - 8x + 6 is shown. Determine the coordinates of the vertex of the parabola.

A. (1, -1)

Correct B. (2, -2)

C. (4, 0)

D. (3, -3)

Correct Answer: B

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Question 21

A quadratic equation is given by the expression x^2 - 5x + k = 0. If the equation has one repeated root, find the value of k.

A. 7.50

B. 5.00

Correct C. 6.25

D. 8.00

Correct Answer: C

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Question 22

Solve the system of linear equations: 2x + 3y = 12 and 4x - y = 5. Find the value of x + y.

A. 3.50

Correct B. 4.64

C. 6.20

D. 5.00

Correct Answer: B

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Question 23

Simplify the expression: (2^3 * 4^2) / (8 * 16).

A. 5

Correct B. 1

C. 2

D. 3

Correct Answer: B

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Question 24

If 3^x = 81, find the value of x.

A. 3

B. 2

C. 5

Correct D. 4

Correct Answer: D

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Question 25

Convert the decimal number 156 to binary.

A. 10100100

B. 11001100

C. 10011010

Correct D. 10011100

Correct Answer: D

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