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neco 2018 mathematics | Objective

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Question 1 View Details

The time \(T\) (in minutes) taken by a machine to process a batch varies directly as the number of items \(N\) and inversely as the square root of the power \(P\) (in watts) supplied to it. When 200 items are processed in 30 minutes with a power of 400 W, what time will be required to process 500 items if the power is increased to 900 W?

A. 75

B. 33

C. 45

Correct D. 50

Correct Answer: D

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Question 2 View Details

A cylindrical water tank has radius \(r\) and height \(h\) and is closed at both ends. Inside the cylinder a solid right circular cone of the same radius \(r\) and height \(\frac{h}{3}\) is placed with its base coinciding with the bottom of the cylinder. The tank is then filled with water to a depth of \(\frac{h}{2}\) measured from the bottom (including the cone). Find the volume of water in the tank in terms of \(r\) and \(h\), and then give the ratio of this water volume to the total volume of the cylinder, expressed in simplest fractional form.

Correct A. 7/18

B. 3/8

C. 5/12

D. 2/5

Correct Answer: A

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Question 3 View Details

The resistance \(R\) (in ohms) of a wire varies directly as its length \(L\) (in metres) and inversely as the square of its cross‑sectional area \(A\) (in \(\text{mm}^2\)). A wire of length \(2.0\) m and area \(1.0\) mm\(^2\) has resistance \(8\ \Omega\). What will be the resistance of a wire of length \(3.5\) m and area \(1.5\) mm\(^2\)?

A. 64/9

B. 28/9

Correct C. 56/9

D. 56/8

Correct Answer: C

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Question 4 View Details

A box contains red, blue, and yellow marbles. The number of red marbles is three times the number of blue marbles. The number of yellow marbles exceeds the number of blue marbles by 5. The total number of marbles in the box is 15. Three marbles are drawn at random without replacement. What is the probability that exactly one marble of each colour is drawn?

A. 13/65

B. 12/66

Correct C. 12/65

D. 11/65

Correct Answer: C

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Question 5 View Details

Let \(a\) and \(b\) be positive integers such that \(a+b=7\) and \(a^{2}-b=5\). Find the value of the expression \(E = a^{3}+b^{3}-3ab\).

Correct A. 55

B. 50

C. 65

D. 45

Correct Answer: A

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Question 6 View Details

A quadratic equation has two real roots that are reciprocals of each other and their sum is 5. Find the equation in standard form and give the value of the larger root. Use the relationship \(r + \frac{1}{r} = 5\) and express the larger root as \(\frac{5 + \sqrt{21}}{2}\).

A. \(\frac{5 + \sqrt{20}}{2}\)

B. \(\frac{5 + \sqrt{21}}{3}\)

C. \(\frac{5 - \sqrt{21}}{2}\)

Correct D. \(\frac{5 + \sqrt{21}}{2}\)

Correct Answer: D

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Question 7 View Details

A quadratic function \(f(x)=kx^{2}+mx+n\) has zeros at \(x=1\) and \(x=4\) and attains a maximum value of \(9\). Determine the coefficients \(k,m,n\) and state the y‑intercept of the graph.

A. -12

B. 0

C. -20

Correct D. -16

Correct Answer: D

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Question 8 View Details

If \(\frac{7}{8}\) litre of juice costs \(\text{₦}560\), what is the cost of \(1\) litre of juice?

A. 560

Correct B. 640

C. 490

D. 720

Correct Answer: B

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Question 9 View Details

In triangle \(ABC\), \(AB = 13\) cm, \(AC = 15\) cm and \(\angle BAC = 60^{\circ}\). The internal angle bisector of \(\angle BAC\) meets side \(BC\) at \(D\). If \(BD = 7\) cm, find (i) the length of \(CD\) and (ii) the length of the bisector \(AD\).

Correct A. CD = \(\frac{105}{13}\) cm, AD = \(\frac{195\sqrt{3}}{28}\) cm

B. CD = \(\frac{105}{13}\) cm, AD = \(\frac{195}{28}\) cm

C. CD = \(\frac{91}{15}\) cm, AD = \(\frac{195\sqrt{3}}{28}\) cm

D. CD = \(\frac{91}{15}\) cm, AD = \(\frac{195}{28}\) cm

Correct Answer: A

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Question 10 View Details

In a circle with radius \(5\) cm, a chord \(AB\) is \(8\) cm long. The tangents to the circle at \(A\) and \(B\) intersect at point \(P\). Find (i) the distance \(OP\) from the centre \(O\) to \(P\), and (ii) the area of triangle \(PAB\) (in \(\text{cm}^{2}\)).

A. OP = 6 cm, area = 7.5 cm^2

B. OP = 7 cm, area = 5 cm^2

C. OP = 5 cm, area = 8 cm^2

Correct D. OP = 6.25 cm, area = 6.75 cm^2

Correct Answer: D

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Question 11 View Details

In a universal set \(U\) containing 20 elements, two subsets \(A\) and \(B\) satisfy \(|A| = 12\), \(|B| = 9\), and the number of elements that belong to neither \(A\) nor \(B\) is 3. Find \(|A \cap B|\).

A. 7

Correct B. 4

C. 5

D. 3

Correct Answer: B

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Question 12 View Details

A shop sells \(\frac{3}{5}\) kg of rice for ₦2,400. What is the price per kilogram in naira?

A. 3000

Correct B. 4000

C. 4800

D. 5000

Correct Answer: B

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Question 13 View Details

In triangle \(ABC\) the angles are \(\angle A = 40^{\circ}\), \(\angle B = 70^{\circ}\), \(\angle C = 70^{\circ}\) and side \(AB = 10\) cm. Point \(D\) lies on side \(BC\) such that \(BD:DC = 1:2\). Find the length of \(AD\) (in cm) correct to two decimal places.

A. 7.58

B. 8.93

C. 10.12

Correct D. 9.47

Correct Answer: D

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Question 14 View Details

A straight line passes through the points \((0,-3)\) and \((2,5)\). The same line also passes through the point \((8,k)\). Find the value of \(k\) and then determine the \(x\)-coordinate at which the line has \(y = 7\).

A. k = 35, x = 2.5

Correct B. k = 29, x = 2.5

C. k = 29, x = 3

D. k = 25, x = 2.5

Correct Answer: B

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Question 15 View Details

A. 20

Correct B. 15

C. 10

D. 25

Correct Answer: B

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Question 16 View Details

A factory uses two machines, A and B, to produce items. Machine A produces 60% of the total output and has a defect rate of 2%; machine B produces the remaining 40% and has a defect rate of 5%. An item is selected at random and is found to be defective. A second item is then selected from the same machine that produced the first item (the machine is unknown). What is the probability that the second item is also defective? Express your answer as a fraction in lowest terms.

Correct A. \frac{31}{800}

B. \frac{31}{400}

C. \frac{33}{800}

D. \frac{4}{125}

Correct Answer: A

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Question 17 View Details

The time \(T\) (in seconds) taken by a car to travel a distance \(d\) (in kilometres) varies directly with \(d\) and inversely with the square root of its engine power \(P\) (in kilowatts). When \(d=120\) km and \(P=90\) kW the car takes exactly 30 minutes. How many seconds will the car take to travel \(d=180\) km if its power is increased to \(P=160\) kW? Give your answer as an integer number of seconds.

A. 2024

Correct B. 2025

C. 3600

D. 2700

Correct Answer: B

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Question 18 View Details

In a plane, two vectors \(\mathbf{A}\) and \(\mathbf{B}\) have magnitudes \(|\mathbf{A}|=5\) and \(|\mathbf{B}|=7\) respectively. The vector \(\mathbf{C}=2\mathbf{A}-3\mathbf{B}\) is known to have magnitude \(10\). Find the acute angle \(\theta\) between \(\mathbf{A}\) and \(\mathbf{B}\). Give your answer in degrees rounded to one decimal place.

Correct A. 70.4

B. 63.9

C. 82.7

D. 55.3

Correct Answer: A

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Question 19 View Details

A class of 20 students has a mean score of 68 and a standard deviation of 5. After 5 new students join the class, the overall mean becomes 70 and the new standard deviation becomes 6. Assuming that all five new students obtained the same score, determine that common score.

A. 80

Correct B. 78

C. 76

D. 74

Correct Answer: B

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Question 20 View Details

Solve the inequality \(\dfrac{|2x-5|}{x-3}<2\) and express the solution set in interval notation.

A. (-\infty, 2)

B. (-\infty, 4)

Correct C. (-\infty, 3)

D. (3, \infty)

Correct Answer: C

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Question 21 View Details

The sum of the first \(5\) terms of an arithmetic progression is \(70\) and the sum of the first \(9\) terms is \(210\). Find the \(12\)th term of the progression.

A. 64

B. 70

C. 48

Correct D. 56

Correct Answer: D

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Question 22 View Details

In triangle \(ABC\), angle \(B\) is twice angle \(A\). The side opposite \(A\) is \(10\) cm and the side opposite \(C\) is \(8\) cm. Find the measure of angle \(C\) in degrees, correct to the nearest integer.

Correct A. 37

B. 50

C. 30

D. 45

Correct Answer: A

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Question 23 View Details

In the Venn diagram shown, the universal set contains \(50\) elements. The numbers of elements are: \(|A| = 20\), \(|B| = 25\), \(|C| = 18\); \(|A \cap B| = 12\), \(|B \cap C| = 8\), \(|A \cap C| = 5\), and \(|A \cap B \cap C| = 3\). How many elements are in none of the three sets?

A. 10

Correct B. 9

C. 8

D. 12

Correct Answer: B

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Question 24 View Details

Let \(x\) satisfy \(x^{2} - 5x + 6 = 0\). Evaluate \(\frac{x^{3} - 6x^{2} + 11x - 6}{x^{2} - 5x + 6}\).

A. 1 or 3

B. 1 and 2

Correct C. 1 or 2

D. 0 or 3

Correct Answer: C

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Question 25 View Details

A shop sells pens and notebooks. The total cost of 4 pens and 3 notebooks is \(\text{₦}780\). If the cost of a pen is \(\frac{1}{2}\) the cost of a notebook minus \(\text{₦}30\), find the cost of one notebook in naira.

A. 210

Correct B. 180

C. 240

D. 150

Correct Answer: B

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