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waec model questions vol1 2019 mathematics | Objective

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Question 1 View Details

The quantity y varies directly as x and inversely as (x + 2). If y = 12 when x = 3, find the value of x when y = 8.

A. 2/3

Correct B. 4/3

C. 5/3

D. 3/2

Correct Answer: B

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Question 2 View Details

The sum of the first n terms of a series is given by \(S_n = n(2n+5)\). Find the smallest positive integer n for which the nth term of the series exceeds 100.

A. 24

B. 30

C. 26

Correct D. 25

Correct Answer: D

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Question 3 View Details

Solve for x: \(\dfrac{x-2}{x+3} > \dfrac{1}{2}\).

Correct A. x < -3 or x > 7

B. x < -3 and x > 7

C. x \le -3 or x \ge 7

D. -3 < x < 7

Correct Answer: A

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Question 4 View Details

A class of 20 students obtained the following test scores: - 45 (2 students) - 55 (3 students) - 65 (5 students) - 75 (6 students) - 85 (3 students) - 95 (1 student) The original mean score is calculated. Afterwards, each score is increased by 5 % of the difference between 100 and the original score (i.e., new_score = original + 0.05 × (100 - original)). Find the increase in the mean score after this adjustment, giving your answer to two decimal places.

A. 1.50

B. 1.45

Correct C. 1.55

D. 1.65

Correct Answer: C

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Question 5 View Details

Let a and b be real numbers such that a + b = 6 and a² + b² = 20. Find the value of a³ + b³.

Correct A. 72

B. 84

C. 96

D. 48

Correct Answer: A

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Question 6 View Details

Simplify the expression \(\dfrac{2^{3}\times5^{2}}{10^{2}}\times\sqrt{50}\).

A. 10\sqrt{5}

Correct B. 10\sqrt{2}

C. 5\sqrt{2}

D. 20\sqrt{2}

Correct Answer: B

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Question 7 View Details

Solve for \(x\): \(\dfrac{3x-7}{2}+\dfrac{x+5}{3}=10\).

A. 70/11

B. 69/11

C. 71/12

Correct D. 71/11

Correct Answer: D

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Question 8 View Details

If \(5-(2x-3)=3x+1\), find the value of \(4x-5\).

Correct A. 3/5

B. 2/5

C. 4/5

D. 3/4

Correct Answer: A

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Question 9 View Details

An item is first discounted by 10% and then by 20% on the reduced price. If the final price is \(\text{₦}1080\), what was the original price?

Correct A. 1500

B. 1200

C. 1800

D. 1350

Correct Answer: A

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Question 10 View Details

An arithmetic progression has first term \(a\) and common difference \(d\). The sum of the first 5 terms is 70 and the sum of the first 8 terms is 140. Find the 10th term of the progression.

A. 91/2

Correct B. 91/3

C. 95/3

D. 30/1

Correct Answer: B

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Question 11 View Details

In a plane, vectors **a** and **b** have magnitudes |a| = 7 cm and |b| = 5 cm respectively. If the vector **a** - 2**b** is perpendicular to the vector **a** + **b**, find the value of cos θ, where θ is the angle between **a** and **b**.

A. 1/35

B. 5/35

C. -1/7

Correct D. -1/35

Correct Answer: D

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Question 12 View Details

Find the least common multiple (LCM) of 12, 15 and 20.

A. 120

B. 90

C. 30

Correct D. 60

Correct Answer: D

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Question 13 View Details

Two real numbers a and b satisfy a + b = 6 and a² + b² = 20. Compute the value of (a³ + b³)/(a + b).

Correct A. 12

B. 10

C. 8

D. 14

Correct Answer: A

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Question 14 View Details

The time T (in hours) required for a job varies directly as the square of the number of workers w and inversely as the efficiency e of each worker. If 4 workers each having efficiency 5 complete the job in 10 hours, how many hours will be required if 6 workers each have efficiency 4?

Correct A. 225/8

B. 225/6

C. 225/10

D. 225/7

Correct Answer: A

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Question 15 View Details

The lines L₁: 2x - y + 3 = 0 and L₂: x + 2y - 5 = 0 intersect at point P. A line through P is perpendicular to the line joining the points (1, -2) and (4, k) and also passes through the point (7, 1). Determine the value of k.

Correct A. 23/2

B. 21/2

C. 23/3

D. 25/2

Correct Answer: A

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Question 16 View Details

The sum of the first n terms of an arithmetic sequence is given by S_n = 3n^2 + 5n. The sum of the first 2n terms is S_{2n} = 12n^2 + 10n. Find the expression for the nth term a_n of the sequence.

A. 5n + 2

B. 6n - 2

Correct C. 6n + 2

D. 6n + 3

Correct Answer: C

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Question 17 View Details

A parabola opening upwards passes through the points (0,4), (2,0) and (4,4). Determine its equation in the form y = ax^2 + bx + c.

A. y = x^2 - 2x + 4

Correct B. y = x^2 - 4x + 4

C. y = x^2 + 4x + 4

D. y = x^2 - 4x - 4

Correct Answer: B

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Question 18 View Details

In a plane, vectors \(\mathbf{a}\) and \(\mathbf{b}\) have magnitudes |a| = 5 and |b| = 7 respectively. If the vector (a + 2b) is perpendicular to (3a - b), find the angle between a and b (in degrees, correct to one decimal place).

A. 90.0°

B. 67.5°

Correct C. 82.4°

D. 45.0°

Correct Answer: C

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Question 19 View Details

In a class of 120 students, 68 study Mathematics, 55 study Physics and 48 study Chemistry. 30 study both Mathematics and Physics, 25 study both Mathematics and Chemistry, 20 study both Physics and Chemistry, and 10 study all three subjects. How many students study none of the three subjects?

Correct A. 14

B. 10

C. 20

D. 0

Correct Answer: A

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Question 20 View Details

A data set of 8 numbers has a mean of 14 and a standard deviation of 3. After adding one more number, the new data set of 9 numbers has a mean of 15 and a standard deviation of 4. What is the value of the added number?

A. 25

B. 21

Correct C. 23

D. 27

Correct Answer: C

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Question 21 View Details

In triangle ABC the side lengths are AB = 13 cm, AC = 15 cm and BC = 14 cm. Let M be the midpoint of BC and let N be the foot of the perpendicular from A to BC. Find the length of MN in centimetres.

Correct A. 2

B. 3

C. 1

D. 4

Correct Answer: A

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Question 22 View Details

A student obtained 45% in Mathematics (total marks 80), 60% in English (total marks 100) and 75% in Science (total marks 120). What is the student's overall percentage across the three subjects?

Correct A. 62

B. 60

C. 64

D. 58

Correct Answer: A

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Question 23 View Details

A cylindrical water tank has its height equal to twice its radius. The tank is to be painted on its curved surface and both circular ends. The cost of painting is ₦150 per square metre and the total painting cost is ₦126,000. When the tank is filled to 80% of its capacity, how many cubic metres of water does it hold? Give your answer to the nearest whole number.

A. 1480

B. 1520

C. 1605

Correct D. 1495

Correct Answer: D

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Question 24 View Details

A right circular cone has a height three times its base radius. A sphere is inscribed in the cone, touching the base and the lateral surface. Find the ratio of the volume of the sphere to the volume of the cone, expressed in simplest radical form.

Correct A. (52√10 -124)/81

B. (52√10 -124)\/72

C. (48√10 -124)\/81

D. (52√10 -112)\/81

Correct Answer: A

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Question 25 View Details

The time T (in minutes) taken by a machine to process a batch of items varies directly as the number of items N and inversely as the square root of the power P (in kilowatts) supplied to the machine. If 120 items are processed in 30 minutes when the machine is supplied with 25 kW, how long will it take to process 200 items when the power is increased to 40 kW? Give your answer to one decimal place.

A. 39.1

B. 38.0

Correct C. 39.5

D. 39.7

Correct Answer: C

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