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neco 2017 mathematics | Objective

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Question 1 View Details

A certain number is first increased by \(12.5\%\) and then decreased by \(10\%\), resulting in 108. Find the original number.

A. \frac{96}{1}

B. \frac{215}{2}

Correct C. \frac{320}{3}

D. \frac{211}{2}

Correct Answer: C

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Question 2 View Details

A cylindrical water tank is to be painted only on its curved surface. The tank must hold at least \(5\) m\(^3\) of water. The radius \(r\) and height \(h\) of the tank are required to be whole numbers of metres. Paint costs \(2500\) Naira per square metre. Determine the minimum possible cost of painting the curved surface of the tank.

A. 9000\pi

B. 8000\pi

Correct C. 10000\pi

D. 12500\pi

Correct Answer: C

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Question 3 View Details

Find all integer values of \(x\) satisfying \(\frac{2x-5}{x+3}<1\) with \(-10\le x\le 10\).

A. -3,-2,-1,0,1,2,3,4,5,6,7

B. -2,-1,0,1,2,3,4,5,6

Correct C. -2,-1,0,1,2,3,4,5,6,7

D. -2,-1,0,1,2,3,4,5,6,7,8

Correct Answer: C

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Question 4 View Details

A box contains white, black and red balls. The probability of drawing a white ball is \(\frac12\). The probability of drawing a red ball is one‑third of the probability of drawing a black ball. Two balls are drawn successively without replacement and both are observed not to be white. What is the probability that both drawn balls are red?

A. \frac{3}{44}

Correct B. \frac{1}{22}

C. \frac{2}{33}

D. \frac{1}{24}

Correct Answer: B

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Question 5 View Details

A straight line passes through the point \((2,3)\) and meets the coordinate axes at points \(A\) and \(B\). If the triangle formed by the origin \(O\) and the intercepts \(A\) and \(B\) has area \(12\) square units, determine the coordinates of point \(B\) (the x‑intercept).

A. (8,0)

B. (3,0)

C. (6,0)

Correct D. (4,0)

Correct Answer: D

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Question 6 View Details

In the expression \( \log_{2}(\sqrt{32}) - \log_{4} 8 \), evaluate the value.

A. -1

Correct B. 1

C. 2

D. 0

Correct Answer: B

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Question 7 View Details

Two vectors \(\mathbf{a}\) and \(\mathbf{b}\) in a plane satisfy \(|\mathbf{a}| = 5\), \(|\mathbf{b}| = 7\) and the vector \(\mathbf{c}=2\mathbf{a}-3\mathbf{b}\) has magnitude \(13\). Determine the angle \(\theta\) between \(\mathbf{a}\) and \(\mathbf{b}\) (give your answer as \(\cos^{-1}\left(\frac{31}{35}\right)\) or to one decimal place in degrees).

A. \cos^{-1}\left(\frac{31}{34}\right)

B. \cos^{-1}\left(\frac{33}{35}\right)

Correct C. \cos^{-1}\left(\frac{31}{35}\right)

D. \cos^{-1}\left(\frac{29}{35}\right)

Correct Answer: C

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Question 8 View Details

A rectangular box has length \(L\), width \(W\) and height \(H\) such that \(L = 2W\) and \(H = W + 3\). If the total surface area of the box is \(94\ \text{cm}^2\), find the volume of the box in cubic centimetres (give your answer in simplest exact form).

A. (1191-181\\sqrt{1021})\/125

B. (1191+181\\sqrt{1020})\/125

C. (1191+181\\sqrt{1021})\/124

Correct D. (1191+181\sqrt{1021})/125

Correct Answer: D

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Question 9 View Details

A bag contains only red and blue balls. The probability that a ball drawn at random is red is greater than \(0.3\). Two balls are drawn successively without replacement and the probability that both are red is \(0.12\). Determine the total number of balls in the bag.

A. 30

Correct B. 25

C. 20

D. 35

Correct Answer: B

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Question 10 View Details

In triangle \(ABC\) the side \(c = AB\) measures \(13\ \text{cm}\) and the altitude from \(C\) to \(AB\) meets \(AB\) at \(D\) such that \(AD = 5\ \text{cm}\). If \(\angle C = 60^{\circ}\), find the lengths of sides \(a = BC\) and \(b = AC\) and the area of the triangle (express the area in simplest radical form).

A. a \\approx 14.2\\,cm,\\ b \\approx 11.5\\,cm,\\ \\text{area} \\approx 73.5\\,cm^{2}

B. a \\approx 12.5\\,cm,\\ b \\approx 13.0\\,cm,\\ \\text{area} \\approx 70.0\\,cm^{2}

C. a \\approx 13.0\\,cm,\\ b \\approx 12.5\\,cm,\\ \\text{area} \\approx 71.2\\,cm^{2}

Correct D. a \approx 13.68\,cm,\ b \approx 12.18\,cm,\ \text{area} \approx 72.1\,cm^{2}

Correct Answer: D

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Question 11 View Details

The line graph shows the distance travelled (km) by a car over time (h). The plotted points are \((0,0)\), \((2,30)\), \((4,70)\) and \((6,120)\), joined by straight segments. Using the graph, determine the average speed of the car between \(t = 2\) h and \(t = 5\) h. Express your answer as a fraction of km per hour.

A. \frac{65}{2}

Correct B. \frac{65}{3}

C. \frac{85}{3}

D. \frac{70}{3}

Correct Answer: B

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Question 12 View Details

Express the decimal \(0.375\) as a fraction in its lowest terms.

A. \frac{3}{7}

B. \frac{5}{8}

C. \frac{2}{5}

Correct D. \frac{3}{8}

Correct Answer: D

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Question 13 View Details

A quantity \(y\) varies directly as the square of \(x\) and inversely as \(x+2\). When \(x = 2\) the value of \(y\) is \(48\). Find the value of \(y\) when \(x = 4\).

Correct A. 128

B. 96

C. 192

D. 384

Correct Answer: A

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Question 14 View Details

Find the least common multiple (LCM) of \(12\) and \(18\).

A. 48

B. 30

Correct C. 36

D. 24

Correct Answer: C

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Question 15 View Details

A three‑digit number is formed using the digits \(2, 5, 7\) without repetition. How many such numbers are greater than \(500\)?

A. 3

B. 6

Correct C. 4

D. 5

Correct Answer: C

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Question 16 View Details

An urn contains red, blue and green balls. The total number of balls is 30. The probability that a randomly selected ball is red is \(\frac{1}{3}\). If two balls are drawn successively without replacement, the probability that both are blue is \(\frac{1}{29}\). How many green balls are in the urn?

A. 16

B. 15

C. 12

Correct D. 14

Correct Answer: D

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Question 17 View Details

Find the value of \(k\) such that the quadratic equation \(x^{2}-kx+(k-6)=0\) has two distinct real roots whose sum is twice their product. Then determine the two roots.

A. k = 10; roots are 5 \pm \sqrt{20}

B. k = 14; roots are 7 \pm \sqrt{30}

C. k = 12; roots are 6 \pm \sqrt{24}

Correct D. k = 12; roots are 6 \pm \sqrt{30}

Correct Answer: D

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Question 18 View Details

The quadratic function \(f(x)=ax^{2}+bx+c\) has its vertex at the point \((1,-2)\) and passes through the point \((3,6)\). Find the value of \(a+b+c\).

Correct A. -2

B. 2

C. 0

D. -4

Correct Answer: A

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Question 19 View Details

Based on the Venn diagram of three clubs—Drama (D), Music (M) and Sports (S)—the following numbers are shown: total in D is 70, total in M is 55, total in S is 65; the numbers of students who belong to exactly two clubs are: D\cap M only = 20, D\cap S only = 15, M\cap S only = 25; and 10 students belong to none of the clubs. How many students belong to all three clubs?

A. 5

Correct B. 10

C. 20

D. 15

Correct Answer: B

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Question 20 View Details

The graph of a function \(f\) consists of straight line segments joining the points \(A(0,2)\), \(B(4,10)\) and \(C(6,8)\). Find the value of \(x\) for which \(f(x)=9\).

A. 4.0

B. 2.5

C. 5.5

Correct D. 3.5

Correct Answer: D

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Question 21 View Details

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

A. 71 + 30\sqrt{5}

Correct B. 71 - 30\sqrt{5}

C. 41 - 30\sqrt{5}

D. 71 - 25\sqrt{5}

Correct Answer: B

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Question 22 View Details

In a school, 45% of students study Mathematics (M), 35% study Physics (P), and 25% study Chemistry (C). 15% study both Mathematics and Physics, 10% study both Mathematics and Chemistry, 8% study both Physics and Chemistry, and 5% study all three subjects. If a student is known to study Chemistry, what is the probability that the student studies neither Mathematics nor Physics? Express your answer as a decimal.

A. 0.60

Correct B. 0.48

C. 0.40

D. 0.52

Correct Answer: B

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Question 23 View Details

Two numbers have a sum of 12 and the sum of their squares is 84. Find the product of the two numbers.

A. 42

B. 24

C. 36

Correct D. 30

Correct Answer: D

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Question 24 View Details

If three quarters of a number is increased by 20%, the result is 180. Find the original number.

Correct A. 200

B. 213.33

C. 240

D. 190

Correct Answer: A

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Question 25 View Details

A cylindrical tank has a total surface area (including top and bottom) of 5000 cm\(^2\). The tank must hold a volume of at least 20000 cm\(^3\). Find the minimum possible radius \(r\) (in cm) of the tank, rounded to two decimal places.

Correct A. 8.90

B. 8.70

C. 9.45

D. 9.10

Correct Answer: A

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