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waec model questions vol1 2017 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 2017 mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

A quadratic equation is given by the expression x^2 - 5x + k = 0, where k is a constant. If the equation has equal roots, find the value of k.

A. 5.25

B. 7.75

C. 8.00

Correct D. 6.25

Correct Answer: D

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Question 2

In triangle ABC, angle A is 30 degrees and angle B is 45 degrees. If side a (opposite angle A) measures 10 cm, calculate the length of side b (opposite angle B) using the sine rule.

A. 5√2

B. 20√2

C. 15√2

Correct D. 10√2

Correct Answer: D

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Question 3

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

A. x = 10/3, y = 8/5

Correct B. x = 27/14, y = 19/7

C. x = 15/7, y = 9/4

D. x = 5/2, y = 11/6

Correct Answer: B

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Question 4

A cylindrical tank has a radius of 3 m and a height of 5 m. Calculate the volume of the tank and the surface area, then determine how much water is needed to fill the tank to three-quarters of its capacity.

A. 40π

Correct B. 33.75π

C. 30π

D. 25π

Correct Answer: B

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Question 5

A shop sells two types of shirts: type A for ₦1,200 each and type B for ₦1,500 each. If a customer buys a total of 10 shirts for ₦13,500, how many of each type did the customer buy?

A. 3 type A shirts and 7 type B shirts

B. 6 type A shirts and 4 type B shirts

Correct C. 5 type A shirts and 5 type B shirts

D. 4 type A shirts and 6 type B shirts

Correct Answer: C

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Question 6

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. 12/45

B. 10/45

C. 8/45

Correct D. 14/45

Correct Answer: D

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Question 7

The graph of the function f(x) = 2x^2 - 4x + 1 intersects the x-axis at points A and B. Calculate the coordinates of points A and B.

A. (1 - √4/2, 0) and (1 + √4/2, 0)

B. (1 - √3/2, 0) and (1 + √3/2, 0)

Correct C. (1 - √2/2, 0) and (1 + √2/2, 0)

D. (1 - √1/2, 0) and (1 + √1/2, 0)

Correct Answer: C

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Question 8

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

Correct A. 30

B. 40

C. 35

D. 25

Correct Answer: A

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Question 9

In a survey of 100 students, 60 like Mathematics, 50 like English, and 30 like both subjects. How many students like only Mathematics?

A. 50

Correct B. 30

C. 40

D. 20

Correct Answer: B

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Question 10

Simplify the expression: (3^2 * 3^4) / 3^5.

A. 27

B. 9

Correct C. 3

D. 1

Correct Answer: C

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Question 11

A company produces two types of products, A and B. The cost to produce one unit of product A is ₦150, while the cost to produce one unit of product B is ₦200. If the company has a budget of ₦10,000 for production and wants to produce at least twice as many units of product A as product B, how many units of each product can the company produce while staying within budget?

A. 30 units of product A and 15 units of product B

Correct B. 40 units of product A and 20 units of product B

C. 20 units of product A and 10 units of product B

D. 50 units of product A and 25 units of product B

Correct Answer: B

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Question 12

The graph below represents the relationship between the number of hours studied and the score obtained in a mathematics test. If the line passes through the points (2, 50) and (6, 90), determine the equation of the line in the form y = mx + c, and find the score when 4 hours are studied.

Correct A. 70

B. 75

C. 80

D. 60

Correct Answer: A

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Question 13

In triangle ABC, angle A measures 40 degrees, and angle B measures 70 degrees. If side AB is 10 cm, calculate the length of side AC using the Law of Sines.

A. 8.10 cm

B. 5.67 cm

C. 7.25 cm

Correct D. 6.84 cm

Correct Answer: D

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Question 14

A student scored 75% in Mathematics, 60% in English, and 85% in Science. If the total marks for each subject are 100, what is the student's overall percentage across the three subjects?

A. 80%

Correct B. 73.33%

C. 75.5%

D. 70%

Correct Answer: B

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Question 15

In a coordinate plane, the points A(2, 3), B(4, 7), and C(x, y) form a right triangle at point B. If the length of side AB is 5 units, find the coordinates of point C.

A. C can be any point on the line y = 2x - 3 that satisfies the right triangle condition.

B. C can be any point on the line y = -3x + 6 that satisfies the right triangle condition.

Correct C. C can be any point on the line y = -1/2x + 9 that satisfies the right triangle condition.

D. C can be any point on the line y = x + 5 that satisfies the right triangle condition.

Correct Answer: C

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Question 16

Two vectors, \( \mathbf{a} = 3\mathbf{i} + 4\mathbf{j} \) and \( \mathbf{b} = -2\mathbf{i} + \mathbf{j} \), are given. Calculate the magnitude of the vector \( \mathbf{c} = \mathbf{a} + 2\mathbf{b} \) and determine the angle between \( \mathbf{a} \) and \( \mathbf{c} \).

A. Magnitude of \( \mathbf{c} \) is \( \sqrt{50} \) and angle \( \theta = \cos^{-1}\left(\frac{20}{5\sqrt{50}}\right) \).

B. Magnitude of \( \mathbf{c} \) is \( \sqrt{29} \) and angle \( \theta = \cos^{-1}\left(\frac{15}{4\sqrt{29}}\right) \).

Correct C. Magnitude of \( \mathbf{c} \) is \( \sqrt{37} \) and angle \( \theta = \cos^{-1}\left(\frac{21}{5\sqrt{37}}\right) \).

D. Magnitude of \( \mathbf{c} \) is \( \sqrt{45} \) and angle \( \theta = \cos^{-1}\left(\frac{18}{5\sqrt{45}}\right) \).

Correct Answer: C

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Question 17

Simplify the expression \( 4^{x+1} \cdot 16^{2-x} \) and express the result in terms of \( 2^x \).

A. The expression simplifies to \( 2^{6 - 2x} \).

B. The expression simplifies to \( 2^{8 - 2x} \).

Correct C. The expression simplifies to \( 2^{10 - 2x} \).

D. The expression simplifies to \( 2^{12 - 2x} \).

Correct Answer: C

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Question 18

Given the points A(2, 3), B(4, 7), and C(6, y) are collinear. Find the value of y.

Correct A. The value of y is 11.

B. The value of y is 13.

C. The value of y is 9.

D. The value of y is 7.

Correct Answer: A

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Question 19

A shopkeeper sells a shirt for ₦1,200 after applying a discount of 20%. What was the original price of the shirt before the discount?

A. The original price of the shirt was ₦1,000.

B. The original price of the shirt was ₦1,200.

C. The original price of the shirt was ₦1,800.

Correct D. The original price of the shirt was ₦1,500.

Correct Answer: D

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Question 20

Solve the quadratic equation \( x^2 - 5x + 6 = 0 \) by factoring and find the roots.

A. The roots of the equation are x = -2 and x = -3.

B. The roots of the equation are x = 1 and x = 6.

C. The roots of the equation are x = 0 and x = 5.

Correct D. The roots of the equation are x = 2 and x = 3.

Correct Answer: D

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Question 21

A quadratic equation is given by the expression x^2 - 5x + k = 0. If the roots of the equation are equal, find the value of k.

A. 8.50

B. 5.25

C. 7.00

Correct D. 6.25

Correct Answer: D

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Question 22

Solve the inequality 3x - 7 < 2x + 5 and express the solution in interval notation.

A. (-∞, 15)

Correct B. (-∞, 12)

C. (-∞, 8)

D. (-∞, 10)

Correct Answer: B

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Question 23

Simplify the expression (2x^2 - 3x + 4) - (x^2 - 5x + 2) and state the resulting polynomial in standard form.

Correct A. x^2 + 2x + 2

B. x^2 - 2x + 6

C. 2x^2 + 2x + 2

D. x^2 + 3x + 1

Correct Answer: A

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Question 24

If a number is increased by 15% and the result is 69, what was the original number?

A. 80

B. 50

Correct C. 60

D. 75

Correct Answer: C

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Question 25

Two vectors A and B are given as A = 3i + 4j and B = 2i - j. Calculate the magnitude of the resultant vector R = A + B.

A. √38

Correct B. √34

C. √25

D. √29

Correct Answer: B

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