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neco 2019 mathematics | Objective

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Question 1 View Details

A shop sells two types of pens. The total revenue from selling \(x\) pens of type A and \(y\) pens of type B is ₦12,600. The price per pen of type A is ₦150 more than that of type B. If the number of type A pens sold is twice the number of type B pens minus 30, find the price of each type of pen.

A. Price of type B pen = ₦120; price of type A pen = ₦270

Correct B. Price of type B pen = ₦135; price of type A pen = ₦285

C. Price of type B pen = ₦150; price of type A pen = ₦300

D. Price of type B pen = ₦140; price of type A pen = ₦280

Correct Answer: B

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Question 2 View Details

Points \(A(2,3)\) and \(B(8,k)\) are such that the perpendicular bisector of segment \(AB\) passes through point \(C(5,7)\). Find the value of \(k\) and write the equation of the line through \(C\) that is parallel to \(AB\).

A. k = 5; equation: y = 7

B. k = 3; equation: y = 5

C. k = -1; equation: y = 7

Correct D. k = 3; equation: y = 7

Correct Answer: D

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Question 3 View Details

The graph of a piecewise linear function \(f\) consists of two straight segments. The first segment joins \((0,2)\) to \((4,a)\) and the second joins \((4,a)\) to \((8,6)\). The total area enclosed between the graph and the \(x\)-axis from \(x=0\) to \(x=8\) is \(32\) square units. Determine the value of \(a\).

A. 2

B. 8

C. 6

Correct D. 4

Correct Answer: D

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Question 4 View Details

Given that \(\frac{3}{x}=0.75\), find the value of \(x\) and express \(x\) as a percentage.

A. x = 3; 300%

Correct B. x = 4; 400%

C. x = 12; 1200%

D. x = 0.75; 75%

Correct Answer: B

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Question 5 View Details

Vectors \(\mathbf{a}\) and \(\mathbf{b}\) satisfy \(|\mathbf{a}|=5\), \(|\mathbf{b}|=7\). The vector \(\mathbf{c}=2\mathbf{a}-\mathbf{b}\) is perpendicular to \(\mathbf{d}=\mathbf{a}+3\mathbf{b}\). Find the angle between \(\mathbf{a}\) and \(\mathbf{b}\) in degrees, correct to the nearest integer.

A. 45

B. 70

C. 90

Correct D. 56

Correct Answer: D

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Question 6 View Details

A solid consists of a right circular cylinder of radius \( r \) cm and height \( h \) cm, surmounted by a right circular cone having the same base radius \( r \) and height \( \frac{h}{2} \). The total surface area of the solid, excluding the base of the cylinder, is \( 500 \) cm\(^2\) and its total volume is \( 1000 \) cm\(^3\). Find the radius \( r \) of the solid (to one decimal place).

Correct A. 10.2

B. 12.0

C. 9.8

D. 11.5

Correct Answer: A

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Question 7 View Details

In a class of 30 students, the scores on Test A have mean \( 68 \) and standard deviation \( 8 \). The scores on Test B have mean \( 75 \) and standard deviation \( 10 \). The correlation coefficient between the two tests is \( 0.6 \). (i) Find the mean and standard deviation of the total score (Test A + Test B) for a randomly selected student. (ii) Assuming the total score is approximately normally distributed, calculate the probability that a student's total score exceeds \( 160 \). Express the probability as a decimal rounded to two places.

A. 0.05

B. 0.25

Correct C. 0.15

D. 0.10

Correct Answer: C

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Question 8 View Details

The time \( t \) (in minutes) required to fill a tank is directly proportional to the volume \( V \) of water and inversely proportional to the square of the pressure \( P \) applied. If it takes 12 minutes to fill a 1800‑litre tank when the pressure is 3 atm, how many minutes will it take to fill a 2400‑litre tank under a pressure of 4 atm?

A. 12

Correct B. 9

C. 8

D. 10

Correct Answer: B

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Question 9 View Details

A frustum of a right circular cone has a lower base radius of \( 10 \) cm, a slant height of \( 13 \) cm and a total surface area (including both bases) of \( 800 \) cm\(^2\). Find the radius of the upper base (to one decimal place).

Correct A. 1.7

B. 2.5

C. 0.9

D. 3.1

Correct Answer: A

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Question 10 View Details

In a cyclic quadrilateral \(ABCD\), the side lengths are \(AB=8\) cm, \(BC=5\) cm, \(CD=7\) cm and \(DA=6\) cm. The angle \(\angle ABC\) is \(60^{\circ}\). Find the length of diagonal \(BD\) (to two decimal places).

A. 10.95

B. 11.84

Correct C. 12.29

D. 13.07

Correct Answer: C

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Question 11 View Details

If \\( a + b = 4 \\) and \\( a^{2} + b^{2} = 10 \\), evaluate \\( \\frac{a^{3} + b^{3}}{a + b} \\).

A. 8

B. 10

Correct C. 7

D. 6

Correct Answer: C

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Question 12 View Details

The quadratic equation \\( x^{2} - (k+1)x + k = 0 \\) has two distinct real roots whose ratio is \\( 2:1 \\). Determine the integer value of \\( k \\) and then find the sum of the roots.

A. k = 3, sum = 4

B. k = 0, sum = 1

Correct C. k = 2, sum = 3

D. k = 1, sum = 2

Correct Answer: C

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Question 13 View Details

In a school of 100 students, the numbers studying Mathematics (M), Physics (P) and Chemistry (C) are \\(|M| = 60\\), \\(|P| = 50\\) and \\(|C| = 40\\). Exactly 10 students study all three subjects. The number of students who study exactly two of the subjects is twice the number who study only Mathematics. Find the number of students who study only Mathematics.

A. 18

B. 12

Correct C. 15

D. 20

Correct Answer: C

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Question 14 View Details

Points \\(A(2,-1)\\) and \\(B(5,3)\\) are given. Let \\(P\\) be the point on line \\AB\\ that is equidistant from the origin \\O(0,0)\\ and the point \\C(1,4)\\. (i) Find the coordinates of \\P\\. (ii) Determine the distance \\OP\\ (expressed in simplest radical form).

A. P\\left(\\frac{139}{38},\\frac{23}{19}\\right), OP = \\frac{\\sqrt{21436}}{38}

Correct B. P\left(\frac{139}{38},\frac{23}{19}\right), OP = \frac{\sqrt{21437}}{38}

C. P\\left(\\frac{139}{38},\\frac{24}{19}\\right), OP = \\frac{\\sqrt{21437}}{38}

D. P\\left(\\frac{138}{38},\\frac{23}{19}\\right), OP = \\frac{\\sqrt{21437}}{38}

Correct Answer: B

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Question 15 View Details

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

Correct A. 9.47 cm

B. 8.23 cm

C. 10.12 cm

D. 7.95 cm

Correct Answer: A

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Question 16 View Details

If the numbers are \(a\) and \(b\) with \(a>b\), then \(a+b=20\) and \(a-b = 3b-2\). Find \(a\).

Correct A. \frac{78}{5}

B. \frac{70}{5}

C. \frac{38}{3}

D. \frac{82}{5}

Correct Answer: A

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Question 17 View Details

A quantity is increased by 20% and then the resulting amount is decreased by 10% of the new amount, giving 108. What was the original quantity?

A. 90

B. 108

Correct C. 100

D. 120

Correct Answer: C

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Question 18 View Details

Solve for \(x\): \(\frac{2x-5}{x+3} > 1\).

A. (-\infty,3) \cup (8,\infty)

Correct B. (-\infty,-3) \cup (8,\infty)

C. (-\infty,-3) \cup (5,\infty)

D. (-3,\infty)

Correct Answer: B

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Question 19 View Details

A cylindrical tank has radius \(r\) cm and height \(h\) cm. Initially the tank is half full of water. A solid right circular cone with the same radius \(r\) and height \(\frac{h}{3}\) is placed inside the tank, standing on its base at the bottom, and is completely submerged. By what percentage does the water level rise? Express your answer to the nearest whole percent.

Correct A. 22

B. 25

C. 20

D. 30

Correct Answer: A

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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, and the number of green balls is 5 less than the number of red balls. Two balls are drawn at random without replacement and it is observed that the two balls are of different colours. What is the probability that one of the drawn balls is red? Give your answer as a fraction in lowest terms.

A. \frac{8}{10}

B. \frac{7}{9}

Correct C. \frac{8}{9}

D. \frac{2}{3}

Correct Answer: C

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Question 21 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). If it takes 12 minutes to fill a 300‑litre tank when the pressure is 9 kPa, how long will it take to fill a 450‑litre tank when the pressure is increased to 16 kPa?

A. 10.8

B. 12.0

Correct C. 13.5

D. 15.0

Correct Answer: C

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Question 22 View Details

In a universe \(U = \{1,2,3,4,5,6,7,8\}\) two sets \(A\) and \(B\) satisfy \(|A| = |B|\), \(A\cup B = \{1,2,3,4,5,6\}\) and \(A\cap B = \{2,4\}\). Let \(C = U \setminus (A\cup B)\). Find \(|C|\).

A. 3

B. 1

Correct C. 2

D. 0

Correct Answer: C

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Question 23 View Details

A retailer sells type X pens at \(\text{\u20A6}120\) each and type Y pens at \(\text{\u20A6}180\) each. In one day the total revenue was \(\text{\u20A6}3600\) and the number of type Y pens sold was twice the number of type X pens sold plus 4. How many pens of each type were sold that day?

A. 7 type X pens and 14 type Y pens

B. 8 type X pens and 20 type Y pens

Correct C. 6 type X pens and 16 type Y pens

D. 5 type X pens and 15 type Y pens

Correct Answer: C

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Question 24 View Details

Simplify \(\sqrt{50} - \sqrt{2}\) and express the result in the form \(a\sqrt{2}\) where \(a\) is an integer.

A. 5\sqrt{2}

B. 6\sqrt{2}

Correct C. 4\sqrt{2}

D. 3\sqrt{2}

Correct Answer: C

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Question 25 View Details

A quadratic equation \(x^{2} - kx + 21 = 0\) has two distinct integer roots that differ by 4. Find the value of \(k\) and the roots.

A. k = 22, roots 1 and 21

Correct B. k = 10, roots 3 and 7

C. k = 8, roots 2 and 6

D. k = 12, roots 4 and 8

Correct Answer: B

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