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neco model questions vol1 2020 mathematics | Objective

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Question 1 View Details

Simplify \( \frac{\sqrt{72}\times\sqrt{18}}{12} \) and give your answer as an integer.

A. 12

B. 9

Correct C. 3

D. 6

Correct Answer: C

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Question 2 View Details

A closed right circular cylinder of radius \(r\) cm has a hemispherical dome of the same radius attached on its top. The total external surface area (including the curved surface of the cylinder, the base of the cylinder and the dome) is \(600\pi\) cm² and the total volume (cylinder plus dome) is \(400\pi\) cm³. Find the radius \(r\) of the solid, giving your answer correct to two decimal places.

Correct A. 1.34

B. 1.44

C. 1.54

D. 1.24

Correct Answer: A

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Question 3 View Details

Points \(A(2,-1)\) and \(B(5,3)\) are given. Let \(M\) be the midpoint of \(AB\). The line through \(M\) is drawn perpendicular to the line joining \((1,4)\) and \((7,-2)\). Find the coordinates of the point where this perpendicular line meets the \(x\)-axis. Express your answer as an ordered pair.

A. (3, 0)

B. (2.5, 1)

C. (2, 0)

Correct D. (2.5, 0)

Correct Answer: D

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Question 4 View Details

Solve for \(x\) in the equation \(\frac{2}{x-1}+\frac{3}{x+2}=\frac{5}{x^{2}+x-2}\). Give your answer as a fraction in lowest terms.

Correct A. 4/5

B. 4/3

C. 5/4

D. 3/5

Correct Answer: A

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Question 5 View Details

A right circular cone has a total surface area (including its base) of \(154\pi\) cm² and a volume of \(128\pi\) cm³. The height of the cone is greater than its radius. Find the radius of the base, giving your answer correct to two decimal places.

A. 3.14

Correct B. 2.61

C. 2.85

D. 2.45

Correct Answer: B

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Question 6 View Details

Solve the inequality \(|2x - 7| < x^{2} - 4x + 5\) and express the solution set.

Correct A. x<1-\sqrt{3} or x>1+\sqrt{3}

B. x<1+\sqrt{3} or x>1-\sqrt{3}

C. x<1-\sqrt{2} or x>1+\sqrt{2}

D. x<1-\sqrt{3} and x>1+\sqrt{3}

Correct Answer: A

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Question 7 View Details

Find all real values of the parameter \(p\) for which the system of inequalities \(\frac{x-2}{x-p} > 0\) and \(\frac{x-5}{x-p} < 0\) have at least one common solution.

A. p>5

B. p\le5

Correct C. p<5

D. p=5

Correct Answer: C

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Question 8 View Details

The cost \(C\) (in Naira) of producing \(x\) units of a product varies jointly as the square of the number of workers \(w\) and inversely as the speed \(s\) (units per worker per hour). When 5 workers working at a speed of 20 units per hour produce 100 units, the cost is N10,000. Find the cost when 8 workers work at a speed of 25 units per hour to produce 200 units.

Correct A. 40960

B. 43200

C. 38400

D. 40000

Correct Answer: A

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Question 9 View Details

A box is chosen at random from three boxes: Box A contains 2 white and 3 black balls, Box B contains 4 white and 1 black ball, and Box C contains 3 white and 2 black balls. Three balls are drawn sequentially without replacement from the selected box. It is observed that the first two balls drawn are white. (a) What is the probability that the selected box was Box B? (b) Given this information, what is the probability that the third ball drawn is black? Express your final answer as a simplified fraction.

A. 2/3

Correct B. 1/2

C. 1/3

D. 3/4

Correct Answer: B

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Question 10 View Details

A piecewise linear function \(f\) is defined by \(f(x)=2x+1\) for \(0\le x\le 3\) and \(f(x)=-x+10\) for \(3< x\le 6\). Determine the value of \(x\) (to three decimal places) such that the area under the curve from \(x=0\) to that \(x\) equals 20 square units.

A. 4.125

Correct B. 4.256

C. 3.842

D. 4.567

Correct Answer: B

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Question 11 View Details

In the coordinate plane, triangle \(ABC\) has vertices \(A(0,0)\), \(B(8,0)\) and \(C(3,6)\). Find the radius of the circumcircle of triangle \(ABC\).

A. \(\frac{\sqrt{325}}{4}\)

Correct B. \(\frac{\sqrt{305}}{4}\)

C. \(\frac{\sqrt{305}}{5}\)

D. \(\frac{\sqrt{289}}{4}\)

Correct Answer: B

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Question 12 View Details

Two real numbers \(x\) and \(y\) satisfy \(x + y = 6\) and \(x^{2} + y^{2} = 20\). Find the value of \(\dfrac{x^{3} + y^{3}}{x + y}\).

A. 8

B. 14

Correct C. 12

D. 10

Correct Answer: C

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Question 13 View Details

The time \(t\) (in seconds) taken for a particle of mass \(m\) kilograms to travel a distance \(s\) metres under a constant force varies directly as \(\sqrt{s}\) and inversely as \(m\). If a particle of mass \(2\) kg travels \(8\) m in \(4\) s, how many seconds will a particle of mass \(3\) kg take to travel \(18\) m?

A. 5

Correct B. 4

C. 3

D. 6

Correct Answer: B

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Question 14 View Details

The quadratic equation \(x^{2} - (k+4)x + (k+3) = 0\) has two real roots that differ by \(2\). Assuming \(k\) is a non‑negative integer, find the product of the roots.

A. 4

Correct B. 3

C. 2

D. 5

Correct Answer: B

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Question 15 View Details

The sum of the first \(n\) terms of an arithmetic series is given by \(S_{n}=3n^{2}+5n\). Determine the 10th term of the series.

A. 35

B. 118

C. 65

Correct D. 62

Correct Answer: D

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Question 16 View Details

Two classes of students sat for the same mathematics test. Class A has 30 students with a mean score of \(68\) and a variance of \(25\). Class B has 20 students with a mean score of \(73\) and a variance of \(16\). Assuming the combined mean of all 50 students is \(70\), calculate the combined standard deviation of the whole group. Give your answer correct to two decimal places.

A. 5.95

B. 6.03

C. 4.87

Correct D. 5.21

Correct Answer: D

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Question 17 View Details

Find all integer values of \(n\) for which the inequality \(x^{2}-(2n+1)x+n^{2}<0\) is satisfied by exactly two integer values of \(x\). List the possible \(n\).

A. -1

Correct B. 1

C. 0

D. 2

Correct Answer: B

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Question 18 View Details

A shop marks the price of an item at \(\text{₦}M\). It first offers a 10% discount on the marked price and then adds a 5% sales tax on the discounted price. If the final amount paid by a customer is \(\text{₦}540\), determine the original marked price \(M\) (in naira) correct to two decimal places.

A. 585.71

B. 571.00

C. 560.00

Correct D. 571.43

Correct Answer: D

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Question 19 View Details

What is the smallest positive integer that leaves a remainder of 3 when divided by 5 and a remainder of 4 when divided by 7? State the integer.

Correct A. 18

B. 33

C. 28

D. 23

Correct Answer: A

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Question 20 View Details

Solve for the real variable \(x\) in the equation \(\log_{2}(x^{2}-5x+6)=\log_{4}(x+2)\). Give all solutions correct to two decimal places.

A. x≈1.50 and x≈4.80

B. x≈2.10 and x≈5.25

Correct C. x≈1.09 and x≈4.16

D. x≈0.95 and x≈3.87

Correct Answer: C

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Question 21 View Details

The system of linear equations \(3x - 2y = 7\) and \(kx + 4y = 5\) has integer solutions for both \(x\) and \(y\). Find the sum of all integer values of the parameter \(k\) for which this occurs.

A. 4

B. 2

Correct C. 1

D. -1

Correct Answer: C

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Question 22 View Details

For the quadratic equation \(x^{2}-(p+2)x+(p-1)=0\) to have two integer roots, determine the sum of all possible values of the parameter \(p\).

A. 2

B. -1

Correct C. 0

D. 1

Correct Answer: C

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Question 23 View Details

What is the smallest positive integer that is divisible by 8, 9 and 12?

A. 144

B. 96

C. 36

Correct D. 72

Correct Answer: D

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Question 24 View Details

A rectangular garden is to be fenced with 120 m of fencing. Its length \(L\) is twice its width \(W\). Inside the garden a uniform path of width \(w\) is built along all four sides, leaving a central rectangular lawn. If the area of the lawn is exactly half the area of the whole garden, find the width \(w\) of the path (express your answer in simplest exact form).

A. 15 + 5\sqrt{5}

B. 10 - 5\sqrt{5}

C. 5\sqrt{5} - 15

Correct D. 15 - 5\sqrt{5}

Correct Answer: D

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Question 25 View Details

In a universal set \(U\) containing 12 elements, a subset \(A\) has 6 elements. The complement of \(A\cup B\) in \(U\) contains 2 elements, and \(|A\cap B| = 3\). How many elements are in the set \(B\)?

Correct A. 7

B. 5

C. 8

D. 6

Correct Answer: A

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