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neco model questions vol1 2018 mathematics | Objective

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Question 1 View Details

The sum of the first 5 terms of an arithmetic progression is \(S_5 = 70\) and the sum of the first 8 terms is \(S_8 = 136\). Find the 12th term of the progression.

A. 30

B. 28

Correct C. 32

D. 34

Correct Answer: C

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Question 2 View Details

The cost of type A candy is \(\,\text{₦}125\) per kilogram and type B candy is \(\,\text{₦}180\) per kilogram. If a customer buys \(\frac{3}{4}\) kg of type A and \(\frac{2}{5}\) kg of type B, what is the total amount paid (in Naira)?

A. 166.25

Correct B. 165.75

C. 164.75

D. 160.50

Correct Answer: B

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Question 3 View Details

If \(2^{x}=8\) and \(3^{y}=27\), find the value of \(x+y\).

A. 8

Correct B. 6

C. 7

D. 5

Correct Answer: B

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Question 4 View Details

The graph of a quadratic function passes through the points \((1,2)\) and \((2,5)\) and its vertex lies on the y‑axis. Determine the equation of the function in the form \(y = ax^{2}+bx+c\) and state its y‑intercept.

A. y = 2x^2 + 1; y‑intercept = 1

Correct B. y = x^2 + 1; y‑intercept = 1

C. y = x^2 - 1; y‑intercept = -1

D. y = x^2 + 2; y‑intercept = 2

Correct Answer: B

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Question 5 View Details

In triangle \(ABC\) the side lengths are \(AB = 13\) cm, \(AC = 15\) cm and \(BC = 14\) cm. The incircle touches side \(BC\) at point \(D\) such that \(BD = 6\) cm. (i) Find the radius \(r\) of the incircle. (ii) Determine the distance from the incenter \(I\) to vertex \(A\).

Correct A. r = 4 cm; IA = \sqrt{65} cm

B. r = 5 cm; IA = \sqrt{61} cm

C. r = 3 cm; IA = \sqrt{73} cm

D. r = 4 cm; IA = \sqrt{70} cm

Correct Answer: A

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Question 6 View Details

An arithmetic sequence has the property that the sum of its first five terms is \(70\) and the sum of its first eight terms is \(154\). Find the sum of the terms from the ninth to the twelfth inclusive.

A. 165

Correct B. 161

C. 159

D. 170

Correct Answer: B

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Question 7 View Details

A real number \(x\) satisfies both \(|2x-7| < x+4\) and \(x^{2} - 5x + 6 \ge 0\). Find the product of all distinct integer values of \(x\) that satisfy the two inequalities.

A. 362880

Correct B. 3628800

C. 7257600

D. 39916800

Correct Answer: B

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Question 8 View Details

Points \(A(2,k)\) and \(B(5,8)\) are such that the perpendicular bisector of segment \(AB\) passes through the point \(C(4,1)\). Determine the possible values of \(k\).

A. 1 \pm 2\sqrt{46}

Correct B. 1 \pm \sqrt{46}

C. 1 \pm \sqrt{42}

D. 1 \pm \sqrt{45}

Correct Answer: B

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Question 9 View Details

In a school of 120 students, 70 study Mathematics, 65 study Physics, and 50 study Chemistry. The number of students studying both Mathematics and Physics is twice the number studying both Physics and Chemistry, and exactly 30 students study both Mathematics and Chemistry. Moreover, 20 students study none of these subjects. How many students study all three subjects?

A. 20

Correct B. 10

C. 5

D. 15

Correct Answer: B

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Question 10 View Details

The Venn diagram below represents the numbers of students who study Mathematics (set \(A\)), Physics (set \(B\)), and Chemistry (set \(C\)). The diagram shows: only \(A\): 20, only \(B\): 15, only \(C\): 10, \(A\cap B\) only: 8, \(B\cap C\) only: 5, \(A\cap C\) only: 7. It is known that 85 students take at least one of the three subjects, and the total number of students surveyed is 100. Find the number of students who study all three subjects.

A. 10

Correct B. 20

C. 25

D. 15

Correct Answer: B

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Question 11 View Details

A quadratic curve opens downwards. Its vertex is at \((2,8)\) and the curve passes through the point \((0,4)\). Find the two x‑coordinates at which the curve has a y‑value of \(6\).

A. 2 \pm \sqrt{5}

Correct B. 2 \pm \sqrt{2}

C. 2 \pm \sqrt{3}

D. 2 \pm \sqrt{6}

Correct Answer: B

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Question 12 View Details

Simplify the expression \(\displaystyle \frac{27^{\frac{2}{3}}\times \sqrt[3]{8}}{\sqrt{9}}\) and give your answer as an integer.

Correct A. 6

B. 9

C. 8

D. 4

Correct Answer: A

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Question 13 View Details

The distance \(s\) (in km) travelled by a car varies directly as the square of its speed \(v\) (km/h) and inversely as its fuel consumption rate \(f\) (L/h). When the car travels at \(v=60\) km/h with a fuel consumption of \(f=5\) L/h it covers \(s=180\) km. (a) Find the constant of variation \(k\). (b) Using this constant, determine the distance the car will travel if its speed is increased to \(80\) km/h and its fuel consumption rises to \(8\) L/h. (c) By what percentage does this new distance exceed the original 180 km? Give your answer to the nearest whole percent.

A. k = 0.30; distance = 210 km; percentage increase ≈ 17%

B. k = 0.25; distance = 180 km; percentage increase ≈ 0%

Correct C. k = 0.25; distance = 200 km; percentage increase ≈ 11%

D. k = 0.20; distance = 160 km; percentage increase ≈ -11%

Correct Answer: C

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Question 14 View Details

For the quadratic equation \(2x^{2} - 5x + 3 = 0\) let \(\alpha\) and \(\beta\) be its roots. Evaluate \(\displaystyle \frac{\alpha^{3} + \beta^{3}}{\alpha + \beta}\) and express your answer as a fraction in lowest terms.

A. \frac{3}{2}

B. \frac{5}{2}

Correct C. \frac{7}{4}

D. \frac{9}{4}

Correct Answer: C

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Question 15 View Details

Points \(A(1,2)\) and \(B(5,k)\) are the endpoints of a diameter of a circle. The circle also passes through point \(C(3,4)\). (i) Determine the value of \(k\). (ii) Write the equation of the circle in standard form. (iii) Find the area of triangle \(ABC\). Give your answer as a decimal to one place.

A. k = 0; equation: (x-3)^2 + (y-1)^2 = 5; area = 6.0

Correct B. k = 2; equation: (x-3)^2 + (y-2)^2 = 4; area = 4.0

C. k = 2; equation: (x-3)^2 + (y-2)^2 = 9; area = 5.0

D. k = 6; equation: (x-3)^2 + (y-4)^2 = 8; area = 0.0

Correct Answer: B

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Question 16 View Details

The expression \(E = \frac{3x^{2} - kx + 12}{x - 2}\) yields an integer value for every integer \(x\neq 2\). Determine the smallest positive integer value of the parameter \(k\).

A. 10

B. 16

Correct C. 12

D. 14

Correct Answer: C

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Question 17 View Details

Four different even digits 2, 4, 6 and 8 are to be used without repetition to form a three‑digit number. How many such numbers are divisible by 4?

A. 8

Correct B. 6

C. 4

D. 12

Correct Answer: B

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Question 18 View Details

In a plane, vectors \(\mathbf{a}\) and \(\mathbf{b}\) satisfy \(|\mathbf{a}| = 5\) and \(|\mathbf{b}| = 7\). The vector \(\mathbf{c}=2\mathbf{a}-\mathbf{b}\) is perpendicular to \(\mathbf{a}+3\mathbf{b}\). Find, to the nearest degree, the acute angle between \(\mathbf{a}\) and \(\mathbf{b}\).

Correct A. 56

B. 30

C. 90

D. 70

Correct Answer: A

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Question 19 View Details

Solve for \(x\) in degrees, with \(0^{\circ}<x<180^{\circ}\), the equation \(\sin 2x = \sqrt{3}\cos x\). List all solutions.

A. 45°, 75°, 135°

Correct B. 60°, 90°, 120°

C. 30°, 45°, 150°

D. 30°, 60°, 150°

Correct Answer: B

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Question 20 View Details

A bag contains red, blue and green balls. The number of red balls is twice the number of blue balls. The number of green balls is five less than the total number of red and blue balls combined. A ball is drawn at random, its colour noted and it is not replaced. A second ball is then drawn. What is the probability that the two balls are of different colours? Express your answer as a reduced fraction.

A. 3/4

B. 5/6

C. 1/2

Correct D. 2/3

Correct Answer: D

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Question 21 View Details

The expression \(E = \frac{2x^{2} - 5x - 3}{x+2} - (x-3)\) is defined for \(x \neq -2\). Simplify \(E\) and then find the sum of all real values of \(x\) for which \(E = 7\).

A. 9

B. 13

C. 15

Correct D. 11

Correct Answer: D

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Question 22 View Details

Solve for \(x\) (with \(x>0\) and \(x\neq 1\)) such that \(\log_{x}\bigl(2\sqrt{x}\bigr)=2\). Express your answer in simplest radical form.

A. \sqrt[3]{8}

Correct B. \sqrt[3]{4}

C. \sqrt[3]{2}

D. \sqrt[3]{16}

Correct Answer: B

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Question 23 View Details

A quadratic equation \(x^{2}-(k+3)x+(k+2)=0\) has two distinct real roots that satisfy the relation \(r_{1}=2r_{2}+1\). Find the sum of all possible values of the parameter \(k\).

A. -2

B. 1

C. 0

Correct D. -1

Correct Answer: D

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Question 24 View Details

A closed rectangular box is made of thin sheet metal. Its length and width are both equal to the diameter of a right circular cylindrical tank that fits exactly inside the box, and its height equals the height of the tank. The cost of the sheet metal for the box is ₦12 per cm\(^2\) and the cost of the metal for the tank (including its curved surface and two circular ends) is ₦20 per cm\(^2\). If the total cost of the box and the tank together is ₦30 000, and the volume of the cylindrical tank is 1800 cm\(^3\), determine the radius of the tank (in cm) correct to two decimal places.

A. 6.84

Correct B. 7.95

C. 9.10

D. 8.23

Correct Answer: B

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Question 25 View Details

The time \(t\) (in seconds) required for a particle to travel a distance \(s\) (in metres) under a certain force varies directly as \(\sqrt{s}\) and inversely as the cube of its speed \(v\) (in m\,s\(^{-1}\)). If it takes 8 s to travel 200 m at a speed of 4 m s\(^{-1}\), how long will it take to travel 450 m at a speed of 6 m s\(^{-1}\)? Give your answer to two decimal places.

Correct A. 3.56

B. 4.12

C. 2.89

D. 5.03

Correct Answer: A

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