neco model questions vol1 2025 mathematics | Objective

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Question 1 View Details
Points \(A(2,-1)\) and \(B(5,3)\) are given. Let line \(L\) be the line through \(C(1,4)\) that is perpendicular to \(AB\). Let line \(N\) be the line through the intersection of \(L\) with the line \(y = x\) that is parallel to \(AB\). Find the y‑coordinate of the point where \(N\) meets the y‑axis.
A. -19/20
B. -20/21
Correct C. -19/21
D. -18/21

Correct Answer: C

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Question 2 View Details
A sequence \(\{a_n\}\) is defined by \(a_1 = 2\) and for \(n \ge 1\), \(a_{n+1} = 3a_n + 2(-1)^n\). Find the sum of the first five terms.
A. 176
Correct B. 182
C. 184
D. 180

Correct Answer: B

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Question 3 View Details
The time \(t\) (in hours) required to finish a job varies directly as the number of workers \(w\) and inversely as the square of the efficiency factor \(e\). If 6 workers each with efficiency factor \(1\) complete the job in 9 hours, how many workers each with efficiency factor \(2\) are needed to complete the same job in 6 hours?
A. 12
B. 18
C. 24
Correct D. 16

Correct Answer: D

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Question 4 View Details
In a plane, vectors \(\mathbf{a}\) and \(\mathbf{b}\) satisfy \(|\mathbf{a}| = 5\), \(|\mathbf{b}| = 8\), and the vector \(\mathbf{c} = 2\mathbf{a} - \mathbf{b}\) is perpendicular to \(\mathbf{a} + 3\mathbf{b}\). Find the acute angle between \(\mathbf{a}\) and \(\mathbf{b}\) in degrees, rounded to the nearest integer.
A. 30
Correct B. 45
C. 60
D. 75

Correct Answer: B

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Question 5 View Details
The total cost \(C\) (in dollars) of producing \(x\) units of a product varies directly as the square of the number of machines \(m\) used and inversely as the number of workers \(w\) employed. If using 4 machines and 8 workers produces 200 units at a total cost of $5000, what will be the cost to produce 300 units using 6 machines and the same number of workers?
A. 22500
Correct B. 16875
C. 8438
D. 7500

Correct Answer: B

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Question 6 View Details
In a school, 80 students study Mathematics, 70 study Physics and 60 study Chemistry. The numbers of students studying each pair of subjects are: \(|M\cap P| = 12\), \(|M\cap C| = 13\), \(|P\cap C| = 10\). It is known that the number of students studying all three subjects is twice the number studying exactly two subjects. If 15 students study none of the three subjects, how many students study exactly one subject?
Correct A. 170
B. 185
C. 155
D. 200

Correct Answer: A

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Question 7 View Details
The time \(T\) (in hours) required to complete a certain job varies directly as the number of workers \(W\) and inversely as the square of the speed \(S\) (in rpm) of a machine, i.e. \(T = k\,\frac{W}{S^{2}}\). When 5 workers operate the machine at 120 rpm, the job takes 8 hours. If the number of workers is increased to 8 and the job now takes 5 hours, what speed (in rpm) must the machine be set to?
A. 85
Correct B. 75
C. 90
D. 65

Correct Answer: B

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Question 8 View Details
The diagram shows three clubs in a school: Drama (D), Music (M) and Sports (S). The numbers in the three pairwise overlap regions (excluding the triple overlap) are 14, 9 and 11 respectively, and the triple‑overlap region contains 6 students. The total number of students in the school is 150, and 20 students belong to none of the clubs. The total memberships are: \(|D| = 60\), \(|M| = 58\), \(|S| = 58\). How many students are members of exactly one club?
Correct A. 90
B. 96
C. 102
D. 84

Correct Answer: A

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Question 9 View Details
A straight line on a graph of fuel consumption \(C\) (litres per hour) versus speed \(v\) (km h\(^{-1}\)) passes through the points \((40,5)\) and \((80,9)\). (i) Find the speed at which the consumption is \(7\) L h\(^{-1}\). (ii) If the car travels 300 km at that speed, how many litres of fuel are used in total?
A. 45
Correct B. 35
C. 30
D. 40

Correct Answer: B

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Question 10 View Details
Solve the inequality \(\displaystyle \frac{x^{2}-4x-5}{x-3}\le 2\). Then find the sum of all positive integer values of \(x\) that satisfy the inequality.
A. 8
B. 12
C. 10
Correct D. 9

Correct Answer: D

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Question 11 View Details
Two numbers have a sum of 30. When the larger number is increased by 4 and the smaller number is decreased by 2, the resulting numbers are in the ratio (3:2). Find the larger number.
Correct A. 76/5
B. 73/5
C. 77/5
D. 78/5

Correct Answer: A

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Question 12 View Details
For which integer values of \(n\) does the inequality \(|2x - 5| < n\) have solutions that include \(x = 3\) but exclude \(x = 6\)? List all such integers \(n\).
Correct A. 2,3,4,5,6,7
B. 1,2,3,4,5,6
C. 2,3,4,5,6,8
D. 3,4,5,6,7,8

Correct Answer: A

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Question 13 View Details
Simplify the expression \(\frac{2^{5}\cdot 4^{3}}{8^{2}}\) and give your answer as an integer.
A. 8
Correct B. 32
C. 256
D. 16

Correct Answer: B

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Question 14 View Details
Evaluate the expression \(\frac{2^{3/2}\times 8^{1/3}}{\sqrt{2}}\). Express your answer as an integer.
A. 16
B. 8
Correct C. 4
D. 2

Correct Answer: C

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Question 15 View Details
A contractor employs senior and junior workers. The total number of workers is 25 and the total daily wages paid amount to ₦18,500. Each senior worker earns ₦800 more per day than a junior worker, and the daily wage of a junior worker is a multiple of ₦100. Determine the number of senior workers and the daily wage of a junior worker.
A. Senior workers = 15, junior wage = ₦300
Correct B. Senior workers = 20, junior wage = ₦100
C. Senior workers = 18, junior wage = ₦200
D. Senior workers = 22, junior wage = ₦150

Correct Answer: B

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Question 16 View Details
In a recipe, the amount of sugar required is in the ratio \(\frac{2}{3}\) cup for every \(5\) cups of flour. If a baker uses \(12\) cups of flour, how many cups of sugar are needed?
Correct A. \frac{8}{5}
B. \frac{16}{5}
C. \frac{4}{5}
D. \frac{12}{5}

Correct Answer: A

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Question 17 View Details
In the plane, vectors \(\mathbf{a}\) and \(\mathbf{b}\) satisfy \(|\mathbf{a}| = 5\), \(|\mathbf{b}| = 8\) and the angle between them is \(60^{\circ}\). A third vector \(\mathbf{c}\) is defined by \(\mathbf{c}=\mathbf{a}+k\mathbf{b}\) for some real number \(k\). If the magnitude of \(\mathbf{c}\) equals the area of the parallelogram formed by \(\mathbf{a}\) and \(\mathbf{b}\), find the possible value(s) of \(k\).
A. \frac{-5+15\sqrt{20}}{16}\text{ or }\frac{-5-15\sqrt{20}}{16}
B. \frac{-5+10\sqrt{21}}{16}\text{ or }\frac{-5-10\sqrt{21}}{16}
C. \frac{-5+15\sqrt{21}}{8}\text{ or }\frac{-5-15\sqrt{21}}{8}
Correct D. \frac{-5+15\sqrt{21}}{16}\text{ or }\frac{-5-15\sqrt{21}}{16}

Correct Answer: D

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Question 18 View Details
The quadratic equation \(x^{2}-(2p+5)x+(p^{2}-1)=0\) has two real roots whose difference is \(5\). Find the value of \(p\) and then give the product of the two roots.
A. p = \\frac{1}{5}, \\; product = -\\frac{24}{25}
B. p = -\\frac{1}{5}, \\; product = \\frac{24}{25}
C. p = -\\frac{2}{5}, \\; product = -\\frac{24}{25}
Correct D. p = -\frac{1}{5}, \; product = -\frac{24}{25}

Correct Answer: D

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Question 19 View Details
A three‑digit integer in base ten has its digits in an arithmetic progression and is divisible by \(9\). If the first digit is \(2\), what is the integer?
A. 240
B. 258
C. 216
Correct D. 234

Correct Answer: D

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Question 20 View Details
In a school of 120 students, 70 study Mathematics (M), 65 study Physics (P) and 55 study Chemistry (C). The number studying both Mathematics and Physics is twice the number studying both Physics and Chemistry. Twenty students study all three subjects and fifteen study none of the three. Additionally, the number of students studying both Mathematics and Chemistry equals the number studying only Mathematics. How many students study exactly Mathematics and Chemistry but not Physics?
A. 12
B. 8
C. 14
Correct D. 10

Correct Answer: D

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Question 21 View Details
Simplify the expression \(2^{3}\times 2^{-5}\times \sqrt{2^{4}}\) and give your answer as an integer.
A. -1
Correct B. 1
C. 0
D. 2

Correct Answer: B

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Question 22 View Details
If \(x+\frac{1}{x}=3\), find the value of \(x^{3}+\frac{1}{x^{3}}\).
A. 27
B. 9
Correct C. 18
D. 12

Correct Answer: C

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Question 23 View Details
A three‑digit integer \(N\) leaves a remainder of 4 when divided by 7 and a remainder of 2 when divided by 9. What is the smallest such three‑digit integer?
A. 148
Correct B. 137
C. 124
D. 163

Correct Answer: B

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Question 24 View Details
In the coordinate plane, points \(A(2,3)\) and \(B(8,k)\) are endpoints of a line segment. The midpoint of \(AB\) is point \(C\), and point \(D\) has coordinates \((5,y)\). If the line through \(A\) and \(B\) has slope \(\frac{2}{3}\) and point \(D\) lies on this line, determine the values of \(k\) and \(y\).
A. k = 7, y = 7
B. k = 5, y = 7
C. k = 9, y = 5
Correct D. k = 7, y = 5

Correct Answer: D

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Question 25 View Details
In triangle \(ABC\), \(AB = 12\) cm, \(AC = 9\) cm and \(\angle BAC = 60^{\circ}\). The internal bisector of \(\angle BAC\) meets side \(BC\) at \(D\) and \(BD = 5\) cm. (i) Find the length of \(DC\). (ii) Find the radius of the circumcircle of \(\triangle ABC\). Give your answer for the radius correct to two decimal places.
A. DC = 3.20 cm, R ≈ 6.50 cm
B. DC = 4.00 cm, R ≈ 6.00 cm
C. DC = 4.25 cm, R ≈ 5.80 cm
Correct D. DC = 3.75 cm, R ≈ 6.24 cm

Correct Answer: D

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