Practice neco model questions vol1 mathematics 2024 Past Questions

Question 1 View Details

A water tank consists of a right circular cylinder of radius \(r\) metres and height \(h\) metres, surmounted by a right circular cone having the same radius \(r\) and the same height \(h\). The total volume of the tank is \(3000\ \text{m}^3\) and the total external surface area (including the base of the cylinder but not the circular junction between the cylinder and the cone) is \(1200\ \text{m}^2\). Find the radius \(r\) of the tank, correct to two decimal places.

A. 9.58

Correct B. 10.74

C. 11.23

D. 12.05

Correct Answer: B

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Question 2 View Details

A solid is formed by placing a right circular frustum on top of a right rectangular prism. The frustum has bottom radius \(R\) cm, top radius \(\frac{R}{2}\) cm and height \(h\) cm. The prism has a square base of side \(R\) cm and the same height \(h\) cm. The total volume of the solid is \(2000\ \text{cm}^3\) and the total external surface area (excluding the common circular face) is \(1500\ \text{cm}^2\). Determine the height \(h\) of the solid, correct to two decimal places.

Correct A. 1.77

B. 2.03

C. 2.31

D. 1.45

Correct Answer: A

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Question 3 View Details

The time \(T\) (in minutes) taken by a machine to process a batch varies directly as the number of workers \(n\) and inversely as the square root of the operating speed \(s\) (in items per hour). When 5 workers operate at a speed of \(80\) items per hour, the batch takes \(12\) minutes. If the speed is increased by \(20\%\) and the number of workers is reduced by \(2\), what is the new processing time (in minutes) to two decimal places?

A. 8.20

B. 5.31

Correct C. 6.57

D. 7.84

Correct Answer: C

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Question 4 View Details

In a class of 30 students, the mean score on Exam 1 is \(68\) with a standard deviation of \(8\). The mean score on Exam 2 is \(74\) with a standard deviation of \(6\). The correlation coefficient between the two exam scores is \(0.6\). Find the mean and the standard deviation of the total score (sum of the two exam scores) for the class. Give the standard deviation to two decimal places.

A. Mean = 146, SD = 10.00

B. Mean = 140, SD = 11.20

C. Mean = 144, SD = 13.40

Correct D. Mean = 142, SD = 12.55

Correct Answer: D

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Question 5 View Details

The points \(A(2,3)\) and \(B(8,5)\) lie on a circle whose centre lies on the line \(y = x + 1\). Determine the radius of the circle, correct to two decimal places.

A. 2.84

Correct B. 3.54

C. 5.00

D. 4.12

Correct Answer: B

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Question 6 View Details

The time \(T\) (in minutes) taken to fill a tank varies directly as the volume \(V\) (in litres) and inversely as the square root of the pressure \(P\) (in kPa). When \(V = 200\) L and \(P = 25\) kPa, the filling time is \(8\) minutes. What pressure is required to fill the tank in \(5\) minutes if the volume is increased to \(320\) L?

A. 150.00

B. 160.00

Correct C. 163.84

D. 180.00

Correct Answer: C

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Question 7 View Details

A shop offers a 12% discount on the marked price of a television. After the discount, a sales tax of 5% is added to the discounted price. If the final amount paid by the customer is ₦44,800, what was the original marked price of the television (to the nearest naira)?

A. 50,000

B. 45,000

C. 52,500

Correct D. 48,485

Correct Answer: D

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Question 8 View Details

In triangle \(ABC\) the side opposite angle \(A\) has length \(a = 8\) cm and the side opposite angle \(B\) has length \(b = 10\) cm. Angle \(A\) measures \(30^{\circ}\). Determine all possible measures of angle \(B\) and, for each possible configuration, compute the area of the triangle (in \(\text{cm}^2\), correct to one decimal place).

A. B = 25.0° → area ≈ 30.0 cm²; B = 155.0° → area ≈ 4.0 cm²

B. B = 35.2° → area ≈ 35.0 cm²; B = 144.8° → area ≈ 5.5 cm²

Correct C. B = 38.7° → area ≈ 37.1 cm²; B = 141.3° → area ≈ 6.0 cm²

D. B = 40.0° → area ≈ 38.5 cm²; B = 140.0° → area ≈ 6.2 cm²

Correct Answer: C

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Question 9 View Details

The graph shows a piecewise function \(f(x)\): for \(0 \le x \le 4\) the graph is a straight line joining \((0,0)\) and \((4,8)\); for \(4 \le x \le 8\) the graph is a downward‑opening parabola passing through \((4,8)\) and \((8,0)\) with equation \(y = -\frac{1}{2}(x-4)^2 + 8\). Find the value of \(x\) (to two decimal places) for which the total area enclosed between the curve and the \(x\)-axis from \(x = 0\) up to that \(x\) equals \(20\) square units.

A. 3.75

B. 6.00

C. 5.20

Correct D. 4.50

Correct Answer: D

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Question 10 View Details

In triangle \(ABC\) the side lengths are \(AB = 13\) cm, \(AC = 15\) cm and \(BC = 14\) cm. A circle is inscribed in the triangle, touching side \(BC\) at point \(D\). From \(D\) a perpendicular is drawn to side \(AB\) meeting it at \(E\). Find the length of segment \(DE\) (expressed as an exact fraction).

A. 72/11

Correct B. 72/13

C. 60/13

D. 84/13

Correct Answer: B

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Question 11 View Details

In a school of 120 students, let (A) be the set of students who play football, (B) the set who play basketball, and (C) the set who play chess. The numbers are \(|A| = 68\), \(|B| = 54\), \(|C| = 40\), and 20 students play none of these games. It is known that the number who play both football and basketball is twice the number who play both basketball and chess, and that 8 students play all three games. How many students play football and chess but not basketball?

A. 21

B. 37

Correct C. 29

D. 33

Correct Answer: C

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Question 12 View Details

A set \(S\) contains 9 elements. Subset \(A\) has 5 elements, subset \(B\) has 6 elements, and \(|A\cap B| = 3\). How many subsets of \(S\) contain an even number of elements from \(A\) and contain at most two elements from \(B\)?

A. 84

Correct B. 88

C. 80

D. 92

Correct Answer: B

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Question 13 View Details

Solve for \(x\): \(\displaystyle \frac{3x-7}{x+2}=2-\frac{5}{x-1}\). State the solution set.

A. no real values

B. no real roots

Correct C. no real solution

D. no solution

Correct Answer: C

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Question 14 View Details

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

Correct A. 83

B. 95

C. 78

D. 86

Correct Answer: A

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Question 15 View Details

Let \(f(x)=mx^{2}-4x+5\). Points \(A(2,3)\) and \(B(8,k)\) lie on a line whose slope equals the average rate of change of \(f\) from \(x=2\) to \(x=8\). The same line passes through the point \((5,p)\). Express \(p\) in terms of \(m\), then find \(p\) when \(m=2\).

A. 63

Correct B. 51

C. 57

D. 45

Correct Answer: B

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Question 16 View Details

Simplify the expression \(\frac{2^{3}\,\sqrt{8}}{4^{1.5}}\) and give your answer in simplest surd form.

A. 4\sqrt{2}

B. \sqrt{2}

C. 2\sqrt{3}

Correct D. 2\sqrt{2}

Correct Answer: D

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Question 17 View Details

The quadratic equation \(x^{2}-kx+(k-5)=0\) has two distinct real roots whose difference is \(4\). Find the value of \(k\) and then determine the product of the roots of the equation \(x^{2}-(k+2)x+(k+1)=0\).

Correct A. k = 2, product = 3

B. k = -2, product = -3

C. k = 3, product = 2

D. k = 1, product = 4

Correct Answer: A

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Question 18 View Details

Solve the inequality \(|3x-7|\le 2x+1\) and find the sum of all integer values of \(x\) that satisfy it.

Correct A. 35

B. 30

C. 40

D. 45

Correct Answer: A

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Question 19 View Details

A garden consists of a rectangle \(30\text{ m}\) by \(20\text{ m}\) with a semicircular region of radius \(10\text{ m}\) attached to one of the \(20\text{ m}\) sides (the diameter of the semicircle equals the width of the rectangle). A uniform‑width path of width \(w\) metres surrounds the entire garden. If the total area including the path is \(2000\text{ m}^{2}\), find \(w\) correct to two decimal places.

A. 6.85

B. 8.10

C. 7.50

Correct D. 7.24

Correct Answer: D

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Question 20 View Details

Find the smallest three‑digit integer that is divisible by \(7\) and leaves a remainder of \(3\) when divided by \(9\).

Correct A. 147

B. 154

C. 168

D. 126

Correct Answer: A

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Question 21 View Details

A class of 20 students sat a mathematics test. The mean score was 68 and the standard deviation was 6. It was later discovered that a student's recorded score of 80 was actually 90. Assuming the original statistics were computed correctly, determine the new mean and the new standard deviation (rounded to two decimal places).

Correct A. Mean = 68.5, Standard deviation ≈ 7.26

B. Mean = 68.0, Standard deviation ≈ 6.00

C. Mean = 68.5, Standard deviation ≈ 6.50

D. Mean = 69.0, Standard deviation ≈ 7.00

Correct Answer: A

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Question 22 View Details

Solve the inequality \(\left|\frac{2x-5}{x+3}\right|\le 2\) and express the solution set in interval notation.

A. [-1\/4, 1]

B. (-∞, -1\/4]

C. (-1\/4, ∞)

Correct D. [-1/4, ∞)

Correct Answer: D

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Question 23 View Details

Find all integer values of \(k\) for which the quadratic equation \(x^{2}-(k+1)x+(k-2)=0\) has integer roots. Then give the sum of all such possible values of \(k\).

A. 4

B. -2

C. 0

Correct D. 2

Correct Answer: D

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Question 24 View Details

The system of linear equations \[ \begin{cases} 3x+2y=7\\ a x-4y=5 \end{cases} \] has a solution in which \(x=y\). Determine the value of the parameter \(a\) (expressed as a fraction in lowest terms).

A. 60\/7

Correct B. 53/7

C. 53\/8

D. 45\/7

Correct Answer: B

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Question 25 View Details

A sequence \(\{b_n\}\) is defined by \[ b_n=\begin{cases} 3n+1, & \text{if } n \text{ is odd}\\ n^{2}-2, & \text{if } n \text{ is even} \end{cases} \] Find the smallest positive integer \(n\) such that the sum of the first \(n\) terms is at least 100.

A. 8

B. 9

C. 6

Correct D. 7

Correct Answer: D

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