waec model questions vol1 2020 mathematics | Objective

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Question 1 View Details
A bag contains red, blue and green balls. The probability that a ball drawn at random is red is 1/3. If it is known that the first ball drawn is red, the probability that the second ball drawn (without replacement) is blue is 2/7. The bag originally contains a total of 36 balls. How many green balls are in the bag?
Correct A. 14
B. 18
C. 12
D. 16

Correct Answer: A

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Question 2 View Details
Two numbers satisfy that when the larger number is increased by 8 and the smaller number is decreased by 5, the sum of the resulting numbers equals twice the difference of the original numbers. If the sum of the original two numbers is 39, find the two numbers.
A. 27 and 12
B. 31 and 8
C. 28 and 11
Correct D. 30 and 9

Correct Answer: D

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Question 3 View Details
Simplify the expression \[ \frac{\frac{2x}{x+1}+\frac{3}{x-2}}{\frac{x-1}{x+1}} \] and then evaluate the simplified expression for x = 3.
A. 12
B. 10
C. 8
Correct D. 9

Correct Answer: D

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Question 4 View Details
Evaluate \[ (2^{3}\times2^{-5})\times\frac{\sqrt{16}}{2} \].
A. 3\/4
B. 1\/4
Correct C. 1/2
D. 2\/3

Correct Answer: C

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Question 5 View Details
The quadratic equation \[ x^{2}-(k+2)x+(k-3)=0 \] has two distinct real roots whose product is 6. Find the value of k and then give the sum of the roots.
A. k = 10; sum = 12
B. k = 7; sum = 9
Correct C. k = 9; sum = 11
D. k = 8; sum = 10

Correct Answer: C

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Question 6 View Details
In a class of 150 students, the following information is known about the subjects Mathematics (M), Physics (P) and Chemistry (C): - The number of students who study Mathematics is twice the number who study Physics. - 30 students study both Mathematics and Chemistry. - 20 students study Physics but not Chemistry. - 40 students study both Mathematics and Physics. - 70 students study Chemistry. No student studies a subject outside these three. How many students study Chemistry only?
A. 40
B. 45
C. 30
Correct D. 35

Correct Answer: D

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Question 7 View Details
Find all integer values of $k$ for which the inequality $|2x-5|<k$ has exactly five integer solutions for $x$.
A. k = 6
B. k = 5
C. All integer values of k
Correct D. No integer values of k satisfy the condition

Correct Answer: D

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Question 8 View Details
A right circular cone and a right circular cylinder have the same base radius $r$ and the same height $h$. The total surface area of the cone (including its base) equals the lateral surface area of the cylinder. Determine the ratio of the cone's slant height to its height. Express your answer as a fraction in lowest terms.
A. 3/2
Correct B. 5/4
C. 6/5
D. 7/5

Correct Answer: B

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Question 9 View Details
The Venn diagram shows three sets A, B and C within a universal set of 55 elements, with the region counts as given in the diagram. What is the probability that a randomly selected element from the universal set belongs to exactly two of the sets A, B and C? Give your answer as a fraction in lowest terms.
Correct A. 17/55
B. 18/55
C. 19/55
D. 16/55

Correct Answer: A

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Question 10 View Details
Solve for $x$: \[\frac{2x-5}{x+3}=\frac{x-1}{2x+7}.\]
A. (1+√97)\/3, (1-√97)\/3
B. (-1+√97)\/2, (-1-√97)\/2
Correct C. (-1+√97)/3, (-1-√97)/3
D. (-1+√101)\/3, (-1-√101)\/3

Correct Answer: C

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Question 11 View Details
Find the least common multiple (LCM) of the integers 12, 15 and 20.
A. 30
Correct B. 60
C. 90
D. 120

Correct Answer: B

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Question 12 View Details
In the plane, let vector \(\mathbf{a}\) have magnitude 5 and lie along the positive x‑axis. Vector \(\mathbf{b}\) has magnitude 8 and makes an angle of 60° with \(\mathbf{a}\). A third vector \(\mathbf{c}\) has magnitude 7 and satisfies \((\mathbf{a}+\mathbf{c})\) \(\perp\) \(\mathbf{b}\). Find the greatest possible magnitude of \(\mathbf{a}+\mathbf{b}+\mathbf{c}\). Give your answer to one decimal place.
A. 12.8
Correct B. 13.5
C. 14.2
D. 11.9

Correct Answer: B

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Question 13 View Details
The quadratic equation \(x^{2}-(k+2)x+(k-3)=0\) has two real roots whose difference is 4. Find the value of \(k\).
A. -4
Correct B. 0
C. 4
D. 2

Correct Answer: B

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Question 14 View Details
The quadratic equation \(2x^{2}-(p+5)x+(p-2)=0\) has roots that are reciprocals of each other. Find \(p\) and then compute the sum of the squares of the two roots. Express the final answer as an improper fraction.
A. 69/4
Correct B. 73/4
C. 73/2
D. 71/4

Correct Answer: B

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Question 15 View Details
In triangle \(ABC\), side \(AB=7\) cm and side \(AC=9\) cm. The altitude from \(A\) meets \(BC\) at \(D\) such that \(BD:DC=1:2\). Determine the measure of angle \(BAC\) correct to one decimal place.
Correct A. 74.3
B. 68.5
C. 73.0
D. 81.2

Correct Answer: A

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Question 16 View Details
The sum of the first n terms of an arithmetic progression is given by \(S_n = 5n^{2} + 3n\), where \(n\) is a positive integer. Find the 10th term of the progression.
A. 108
B. 95
C. 100
Correct D. 98

Correct Answer: D

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Question 17 View Details
In triangle \(ABC\) the angle \(C\) is a right angle. The side opposite \(C\) has length \(c=\sqrt{39}\) and the other two sides are \(a=7\) and \(b=5\). Find the exact value of \(\cos(A-B)\).
A. 9/13
B. 11/12
Correct C. 11/13
D. 12/13

Correct Answer: C

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Question 18 View Details
A shop sold \(\frac{3}{8}\) of its stock of 240 items. What percentage of the original stock was sold?
Correct A. 37.5
B. 45
C. 35
D. 40

Correct Answer: A

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Question 19 View Details
In triangle \(ABC\) the angles are \(\angle A = 40^{\circ}, \angle B = 70^{\circ}, \angle C = 70^{\circ}\) and side \(AB = 12\) cm. Point \(D\) lies on side \(BC\) such that \(BD:DC = 1:2\). Find the length of \(AD\) correct to two decimal places.
Correct A. 11.36
B. 12.50
C. 9.87
D. 10.24

Correct Answer: A

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Question 20 View Details
The time \(t\) (in seconds) taken for a particle to travel a distance \(s\) (in metres) under a constant force \(F\) (in newtons) varies directly with \(\sqrt{s}\) and inversely with \(F\). If it takes 8 s to travel 16 m when the force is 4 N, how long will it take to travel 25 m when the force is 9 N? Give your answer as a fraction in simplest form.
A. 45/8
B. 40/7
C. 35/9
Correct D. 40/9

Correct Answer: D

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Question 21 View Details
The amount of fuel (in litres) used by a car varies directly as the distance travelled (km) and inversely as the square of its average speed (km/h). A car travelling at 60 km/h for 150 km uses 12 litres of fuel. How many litres will the car use to travel 200 km at an average speed of 80 km/h?
A. 8
B. 10
C. 12
Correct D. 9

Correct Answer: D

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Question 22 View Details
Solve for x in the equation 2^x = 5^{x-2}. Then, using the value of x, find the numerical value of 2^x (rounded to two decimal places).
A. 10.58
B. 12.73
C. 9.95
Correct D. 11.42

Correct Answer: D

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Question 23 View Details
In the coordinate plane the points O(0,0), A(2,3), B(8,3) and C(8,-1) are joined in order O‑A‑B‑C‑O to form a quadrilateral. Find the area of this quadrilateral (in square units).
A. 30
B. 26
C. 24
Correct D. 25

Correct Answer: D

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Question 24 View Details
In right‑angled triangle ABC, the right angle is at B, AB = 6 cm and BC = 8 cm. Point D lies on hypotenuse AC such that AD : DC = 1 : 2. Find the length of BD, expressed in simplest surd form.
A. 4\sqrt{10}\/3
B. 5\sqrt{13}\/3
Correct C. 4\sqrt{13}/3
D. 4\sqrt{13}\/5

Correct Answer: C

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Question 25 View Details
The total cost of 4 pens and 5 notebooks is ₦2,280. Each pen costs ₦80 less than twice the cost of a notebook. What is the cost of one pen (in naira)?
A. 280
B. 300
C. 340
Correct D. 320

Correct Answer: D

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