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neco 2020 mathematics | Objective

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Question 1 View Details

In the coordinate plane the points A(2,3), B(-1,5) and C(4,-2) are plotted. A line through C is perpendicular to line AB. Find the coordinates of the point where this perpendicular line meets the x‑axis.

A. (\frac{14}{3}, 0)

B. (\frac{16}{5}, 0)

C. (\frac{8}{3}, 0)

Correct D. (\frac{16}{3}, 0)

Correct Answer: D

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Question 2 View Details

An arithmetic sequence has first term \(a\) and common difference \(d\). The sum of the first five terms is 40 and the sum of the sixth to tenth terms is 65. Find the tenth term of the sequence.

A. 8

B. 13

C. 22

Correct D. 15

Correct Answer: D

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Question 3 View Details

A shop sells two items. Item X costs \(\mathrm{₦}80\) each and item Y costs \(\mathrm{₦}65\) each. The total revenue from selling a number of items is \(\mathrm{₦}5,550\). Moreover, the number of X items sold exceeds the number of Y items sold by 20% of the total number of items sold. How many of each item were sold?

A. X = 40, Y = 35

Correct B. X = 45, Y = 30

C. X = 50, Y = 25

D. X = 42, Y = 33

Correct Answer: B

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Question 4 View Details

In a plane two vectors \(\mathbf{a}\) and \(\mathbf{b}\) satisfy \(|\mathbf{a}| = 5\), \(|\mathbf{b}| = 7\) and the vector \(\mathbf{a}+\mathbf{b}\) is perpendicular to \(2\mathbf{a}-\mathbf{b}\). Find the angle between \(\mathbf{a}\) and \(\mathbf{b}\) in degrees (give your answer to one decimal place).

A. 97.5°

Correct B. 91.6°

C. 84.2°

D. 108.3°

Correct Answer: B

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Question 5 View Details

A bar graph shows the sales (in thousands of naira) of five products A, B, C, D and E. The heights of the bars are: A = 12, C = 20, D = 16. The total sales of all five products is 73. It is also known that the sales of product B are four more than twice the sales of product E. Determine the sales of products B and E.

A. B = 7, E = 18

B. B = 16, E = 9

C. B = 20, E = 5

Correct D. B = 18, E = 7

Correct Answer: D

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Question 6 View Details

In triangle \(ABC\) the sides have lengths \(AB=7\) cm, \(BC=8\) cm and \(AC=9\) cm. The internal bisector of angle \(B\) meets side \(AC\) at \(D\). Find the length of \(BD\) (in cm).

A. \dfrac{8}{7}\sqrt{14}

Correct B. \dfrac{8}{5}\sqrt{14}

C. \dfrac{8}{5}\sqrt{13}

D. \dfrac{7}{5}\sqrt{14}

Correct Answer: B

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Question 7 View Details

The Venn diagram shows three sets \(A\), \(B\) and \(C\). The numbers in the regions are: \(A\) only: 10, \(B\) only: 8, \(C\) only: 6, \(A\cap B\) only: 5, \(A\cap C\) only: 4, \(B\cap C\) only: 3, and \(A\cap B\cap C\): 2. How many elements belong to at least two of the sets?

Correct A. 14

B. 12

C. 13

D. 15

Correct Answer: A

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Question 8 View Details

An equilateral triangular garden has side length \(20\) m. A uniform path of width \(x\) metres is built around the garden, so that the outer boundary is a larger similar equilateral triangle. If the area of the path alone is \(300\) m\(^2\), find \(x\) (in metres).

A. 10\\big(\\sqrt{1+\\sqrt{3}}+1\\big)

B. 10\\big(\\sqrt{2+\\sqrt{3}}-1\\big)

Correct C. 10\big(\sqrt{1+\sqrt{3}}-1\big)

D. 10\\big(\\sqrt{1-\\sqrt{3}}-1\\big)

Correct Answer: C

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Question 9 View Details

A bag contains 5 red, 4 blue and 3 green balls. Two balls are drawn sequentially without replacement. What is the probability that the second ball is green given that at least one of the two drawn balls is red?

Correct A. 1/6

B. 1\/3

C. 1\/4

D. 2\/5

Correct Answer: A

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Question 10 View Details

The quadratic equation \(x^{2}-(k+2)x+(2k-3)=0\) has two distinct integer roots. Find the sum of all possible values of \(k\).

A. 8

Correct B. 4

C. 6

D. 2

Correct Answer: B

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Question 11 View Details

A set of seven numbers consists of 10, 14, 18, 22, 26, a, b. The mean of the seven numbers is \(18\). The range of the set is \(16\). The product \(ab = 288\). Find the ordered pair \((a,b)\) with \(a<b\).

A. (16, 18)

B. (9, 32)

C. (8, 36)

Correct D. (12, 24)

Correct Answer: D

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Question 12 View Details

When the integer \(7845312\) is divided by \(9\), what is the remainder?

Correct A. 3

B. 6

C. 8

D. 0

Correct Answer: A

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Question 13 View Details

Solve for \(x\) in degrees, where \(0^{\circ}<x<180^{\circ}\), satisfying \(\sin 2x = \sqrt{3}\cos x\).

A. 30°, 45°, 150°

B. 15°, 105°, 165°

C. 30°, 75°, 150°

Correct D. 60°, 90°, 120°

Correct Answer: D

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Question 14 View Details

If \(x + \frac{1}{x} = 3\), find the value of \(x^{5} + \frac{1}{x^{5}}\).

A. 130

Correct B. 123

C. 124

D. 119

Correct Answer: B

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Question 15 View Details

Given that \(a+b=5\) and \(a^{2}+b^{2}=13\), find the value of \(a^{3}+b^{3}\).

A. 50

Correct B. 35

C. 125

D. 95

Correct Answer: B

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Question 16 View Details

Solve the inequality \( |3x - 7| \le 2x + 5 \) and find the sum of all integer solutions.

A. 92

B. 68

C. 84

Correct D. 78

Correct Answer: D

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Question 17 View Details

A right circular cone is placed inside a right circular cylinder so that the cone's base coincides with the cylinder's base and the vertex lies on the top face of the cylinder. If the total surface area of the cone (including its base) equals the lateral surface area of the cylinder, find the ratio of the cylinder's height to its radius.

Correct A. 4/3

B. 3/4

C. 2/3

D. 5/4

Correct Answer: A

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Question 18 View Details

Find the integer value of \(p\) for which the inequality \(x^{2}-(p+2)x+(2p-3)<0\) is satisfied by every real number \(x\) in the interval \((1,4)\). Give the sum of all such integer values of \(p\).

A. 5

B. 2

C. 4

Correct D. 3

Correct Answer: D

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Question 19 View Details

Simplify \(\displaystyle \frac{3^{4}\cdot9}{27^{2}}\times\sqrt{\frac{16}{81}}\) and express the answer as a fraction in lowest terms.

A. 8/9

B. 2/9

Correct C. 4/9

D. 4/27

Correct Answer: C

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Question 20 View Details

Two numbers have a sum of 30. When the first number is increased by 5 and the second number is decreased by 2, their product becomes 200. Determine the two numbers.

A. 5 and 25

Correct B. 3 and 27

C. 8 and 22

D. 12 and 18

Correct Answer: B

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Question 21 View Details

In the diagram, triangle ABC has \(\angle A = 40^\circ\), \(\angle B = 70^\circ\) and side \(AB = 12\) cm. Point D lies on side \(BC\) such that \(BD:DC = 1:2\). Find the length of \(AD\) correct to two decimal places.

A. 12.58

Correct B. 11.36

C. 9.87

D. 10.24

Correct Answer: B

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Question 22 View Details

Find the smallest positive integer that leaves a remainder of 2 when divided by 5 and a remainder of 3 when divided by 7.

A. 52

B. 12

Correct C. 17

D. 22

Correct Answer: C

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Question 23 View Details

The line \(3x + 4y = 12\) has slope \(-\frac{3}{4}\). Points \(A(2,3)\) and \(B(8,k)\) are such that line \(AB\) is perpendicular to the given line. Determine the integer value of \(k\) and then give the coordinates of the midpoint \(M\) of \(AB\).

A. (4,7)

B. (5,6)

Correct C. (5,7)

D. (6,8)

Correct Answer: C

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Question 24 View Details

A solid consists of a right circular cylinder of radius \(r\) cm and height \(h\) cm, surmounted by a right circular cone of the same radius \(r\) and height \(\frac{h}{2}\) cm. The total surface area (including the base of the cylinder but not the top of the cone) is \(600\pi\) cm\(^2\), and the dimensions satisfy \(h = 3r\). Find the volume of the solid, correct to the nearest cubic centimetre.

A. 6200

B. 6050

Correct C. 6187

D. 6300

Correct Answer: C

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Question 25 View Details

An arithmetic sequence has first term \(a_{1}\) and common difference \(d\). The sum of the first 5 terms is 40 and the sum of the first 9 terms is 100. Find the 12th term of the sequence.

Correct A. 22

B. 20

C. 26

D. 24

Correct Answer: A

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