Practice neco model questions vol1 mathematics 2017 Past Questions

Question 1 View Details

Find the set of real numbers \(x\) that satisfy \(\left|\frac{2x-5}{x+3}\right|\le 2\).

Correct A. \( x \ge -\frac{1}{4} \)

B. \( x > -\frac{1}{4} \)

C. \( x \ge \frac{1}{4} \)

D. \( x \le -\frac{1}{4} \)

Correct Answer: A

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Question 2 View Details

The roots of a quadratic equation are reciprocals of each other and their sum is \(\frac{5}{2}\). Determine the quadratic equation in the form \(ax^{2}+bx+c=0\) with integer coefficients and the smallest possible positive leading coefficient.

A. \( 2x^{2} \) -5x -2 =0

B. \( 2x^{2} \) +5x +2 =0

Correct C. \( 2x^{2} \) -5x +2 =0

D. \( x^{2} \) -5x +2 =0

Correct Answer: C

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Question 3 View Details

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

A. 8.23 cm

B. 10.12 cm

C. 7.95 cm

Correct D. 9.47 cm

Correct Answer: D

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Question 4 View Details

Find the least integer value of \(k\) for which the quadratic equation \(x^{2}-(k-3)x+(k+2)=0\) has two distinct real roots, each greater than 2.

A. 8

Correct B. 10

C. 11

D. 9

Correct Answer: B

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Question 5 View Details

An arithmetic progression has positive integer first term \(a\) and common difference \(d\). The sum of the first 5 terms is 70 and the sum of the first 9 terms is 180. Determine the 12th term of the progression.

Correct A. 41

B. 50

C. 38

D. 44

Correct Answer: A

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Question 6 View Details

The following table shows the distribution of scores in a mathematics test: Score interval (marks) | Frequency \( 40\text{-}49 | 5 \\ \) \( 50\text{-}59 | 12 \\ \) \( 60\text{-}69 | 20 \\ \) \( 70\text{-}79 | 8 \\ \) \( 80\text{-}89 | 3 \\ \) (a) Assuming the scores are uniformly distributed within each interval, determine the lower quartile \(Q_{1}\) of the data (give your answer to one decimal place). (b) Using the same uniform‑distribution assumption, estimate how many students scored more than 65 marks.

A. 58.5, 18

B. 54.0, 20

C. 60.0, 17

Correct D. 56.0, 19

Correct Answer: D

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Question 7 View Details

A shop sells pens, notebooks and erasers. Let the price of a pen be \(p\) naira, a notebook \(n\) naira and an eraser \(e\) naira. The following information is given: \(4p + 2n + e = 3\,250\) \(2p + 5n + 3e = 4\,560\) A pen costs ₦50 more than an eraser. Find the price of a pen.

A. 452

Correct B. 472

C. 492

D. 430

Correct Answer: B

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Question 8 View Details

In triangle \(ABC\) the side lengths opposite the angles \(A, B, C\) are \(a = 12\text{ cm},\; b = 9\text{ cm}\) respectively, and \(\angle C = 60^{\circ}\). (a) Determine the length of side \(c\) (to two decimal places). (b) Find the area of the triangle (to two decimal places).

A. 10.45, 45.90

Correct B. 10.85, 46.76

C. 9.87, 44.21

D. 11.23, 48.12

Correct Answer: B

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Question 9 View Details

Two vectors \(\mathbf{a}\) and \(\mathbf{b}\) lie in the same plane. Their magnitudes are \(|\mathbf{a}| = 5\) and \(|\mathbf{b}| = 8\). The magnitude of the vector \(\mathbf{a} + 2\mathbf{b}\) is 13. (i) Find the angle \(\theta\) between \(\mathbf{a}\) and \(\mathbf{b}\) in degrees, correct to the nearest whole number. (ii) Determine the magnitude of the projection of \(\mathbf{a}\) onto \(\mathbf{b}\).

A. 100°, 5.0

Correct B. 134°, 3.5

C. 150°, 2.5

D. 120°, 4.0

Correct Answer: B

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Question 10 View Details

If real numbers \(x\) and \(y\) satisfy \(x + y = 6\) and \(xy = 5\), evaluate \(\displaystyle \frac{x^{3} + y^{3}}{x^{2} + y^{2}}\).

A. 62/13

B. 126/13

Correct C. 63/13

D. 63/14

Correct Answer: C

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Question 11 View Details

The two roots of a quadratic equation are reciprocals of each other and their sum is 5. Find the value of \(r^{3}+\left(\frac{1}{r}\right)^{3}\), where \(r\) is one root.

Correct A. 110

B. 95

C. 125

D. 85

Correct Answer: A

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Question 12 View Details

A cylindrical water tank has radius \(r\) cm and height \(h\) cm. A right circular cone of the same radius sits on top of the cylinder, its height being half the cylinder's height. The total exterior surface area (excluding the base of the cylinder) is \(600\pi\ \text{cm}^2\). If the cylinder's height is three times its radius, determine the total volume of the tank (cylinder plus cone) in cubic centimetres, correct to the nearest whole number.

A. 7600

B. 7200

Correct C. 7415

D. 8000

Correct Answer: C

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Question 13 View Details

The cost \(C\) (in naira) of producing \(x\) units of a product varies directly as the square of the number of units and inversely as the number of machines \(m\) used. When 5 machines produce 200 units, the cost is ₦8000. How much will it cost to produce 300 units using 8 machines? Also, state the percentage increase in cost compared with the original ₦8000.

Correct A. ₦11250, 40.6%

B. ₦9500, 18.8%

C. ₦10000, 25%

D. ₦12500, 56.3%

Correct Answer: A

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Question 14 View Details

A shop sells pens and notebooks. The number of pens sold is twice the number of notebooks sold, and each pen costs ₦200 more than each notebook. A total of 30 items were sold, and the total revenue from the sales is ₦5600. Find the price of one notebook (in naira).

A. 200/3

Correct B. 160/3

C. 180/3

D. 140/3

Correct Answer: B

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Question 15 View Details

A student scored 78% in Mathematics, 85% in English and 92% in Science. If each subject is weighted equally, what is the student's overall percentage?

A. 80

Correct B. 85

C. 84

D. 86

Correct Answer: B

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Question 16 View Details

The system of inequalities \(\frac{2x-5}{x+3}<a\) and \(x^{2}-6x+5<0\) is considered, where \(a\) is an integer. Determine the smallest integer value of \(a\) for which the system has exactly three integer solutions for \(x\).

Correct A. 1

B. 2

C. 0

D. -2

Correct Answer: A

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Question 17 View Details

For real parameter \(p\), consider the simultaneous equations \(\begin{cases}3x+py=12\\ px-4y=p\end{cases}\). Find the value of \(p\) for which the solution \((x,y)\) satisfies \(x>y\) and the sum \(x+y\) equals \(2\).

Correct A. -\frac{1}{2}

B. -\frac{2}{5}

C. \frac{1}{2}

D. -\frac{1}{3}

Correct Answer: A

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Question 18 View Details

A solid consists of a right circular cylinder of radius \(r\) cm and height \(h\) cm, surmounted by a hemisphere of the same radius. The height of the cylinder is twice its radius (\(h=2r\)). The total exterior surface area (excluding the base of the cylinder) is \(600\ \text{cm}^{2}\). Determine the total volume of the solid, giving your answer in exact form and to the nearest whole cubic centimetre.

A. \( \frac{7200}{3\sqrt{\pi}}\ \text{cm}^{3}\ \text{(approximately }1355\text{ cm}^{3}) \)

Correct B. \( \frac{8000}{3\sqrt{\pi}}\ \text{cm}^{3}\ \text{(approximately }1505\text{ cm}^{3}) \)

C. \( \frac{8000}{\sqrt{\pi}}\ \text{cm}^{3}\ \text{(approximately }4515\text{ cm}^{3}) \)

D. \( \frac{8500}{3\sqrt{\pi}}\ \text{cm}^{3}\ \text{(approximately }1605\text{ cm}^{3}) \)

Correct Answer: B

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Question 19 View Details

The total production cost \(C\) (in Naira) for \(x\) units of a product varies with the square of the number of units plus a fixed overhead, i.e., \(C = a x^{2} + k\). When 100 units are produced the cost is ₦5 000, and when 200 units are produced the cost is ₦18 000. Determine the overhead cost \(k\) and then compute the total cost for producing 150 units.

Correct A. \( k = \frac{2000}{3}\ \text{Naira}, \; C_{150}=\frac{31250}{3}\ \text{Naira} \;(\approx 10416.67\text{ N}) \)

B. \( k = \frac{1800}{3}\ \text{Naira}, \; C_{150}=\frac{30000}{3}\ \text{Naira} \;(\approx 10000\text{ N}) \)

C. \( k = \frac{2500}{3} \ \text{Naira}, \; C_{150}= \frac{33750}{3} \text{Naira} \;(\approx 11250\text{ N}) \)

D. \( k = \frac{2200}{3} \text{Naira}, \; C_{150}= \frac{33000}{3} \text{Naira} \;(\approx 11000\text{ N}) \)

Correct Answer: A

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Question 20 View Details

Express the fraction \(\frac{7}{12}\) as a decimal. Write the decimal in repeating notation and state the length of the repetend.

A. 0.58\overline{3}, length = 2

Correct B. 0.58\overline{3}, length = 1

C. 0.5\overline{83}, length = 2

D. 0.583\overline{3}, length = 1

Correct Answer: B

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Question 21 View Details

The sum of the first \(n\) terms of a sequence is given by \(S_n = a n^{2} + b n + c\), where \(a, b, c\) are constants. It is known that the 4th term of the sequence is \(20\) and the 7th term is \(41\). Determine the values of \(a\) and \(b\) (assume \(c = 0\) because the sum of zero terms is zero) and then find the sum of the first ten terms.

A. 295

Correct B. 305

C. 315

D. 325

Correct Answer: B

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Question 22 View Details

In a geometric progression the sum of the first three terms is \(26\) and the sum of the first six terms is \(728\). Find the common ratio and the value of the fifth term.

A. r = 4, 5th term = 256

B. r = 3, 5th term = 108

Correct C. r = 3, 5th term = 162

D. r = 2, 5th term = 96

Correct Answer: C

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Question 23 View Details

A number is written as the repeating decimal \(0.\overline{36}\). Express the number as a fraction in lowest terms and give its value as a percentage.

A. \( 5/13 and 38.\overline{46}\% \)

Correct B. \( 4/11 and 36.\overline{36}\% \)

C. \( 7/20 and 35.\overline{0}\% \)

D. \( 3/8 and 37.\overline{5}\% \)

Correct Answer: B

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Question 24 View Details

In a school of 120 students, 78 study Mathematics, 65 study Physics and 50 study Chemistry. The numbers studying both Mathematics and Physics and both Mathematics and Chemistry are 30 and 20 respectively, while the number studying both Physics and Chemistry is 27. It is also known that the number of students who study all three subjects equals the number who study none of the three subjects. How many students study none of the three subjects?

A. 0

B. 5

Correct C. 2

D. 8

Correct Answer: C

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Question 25 View Details

Find the smallest positive integer that is divisible by \(6\) and leaves a remainder of \(3\) when divided by \(9\).

Correct A. 12

B. 6

C. 21

D. 15

Correct Answer: A

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