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neco model questions vol1 2021 mathematics | Objective

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Question 1 View Details

A solid consists of a right circular cylinder of radius \(r\) cm and height \(h\) cm, closed at both ends, with a right circular cone of the same radius \(r\) and height \(\frac{h}{2}\) cm placed on top of the cylinder (the base of the cone coincides with the top base of the cylinder). If the total surface area of the solid (including the base of the cylinder, the curved surface of the cylinder and the curved surface of the cone) is \(600\pi\) cm\(^2\) and the ratio of the height of the cylinder to its radius is \(3:2\), find the total volume of the solid in cubic centimeters. Give your answer in simplest exact form.

Correct A. \(\frac{4000\pi\sqrt{14}}{7}\)

B. \(\frac{2000\pi\sqrt{14}}{7}\)

C. \(\frac{4000\pi\sqrt{7}}{7}\)

D. \(\frac{4000\pi\sqrt{14}}{14}\)

Correct Answer: A

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Question 2 View Details

Two real numbers \(a\) and \(b\) satisfy \(a+b=6\) and \(a^{2}+b^{2}=28\). Find the value of \(a^{3}+b^{3}\).

A. 96

Correct B. 144

C. 108

D. 180

Correct Answer: B

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Question 3 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 five less than the number of red balls. The total number of balls in the bag is 20. Two balls are drawn at random without replacement. What is the probability that the two balls are of different colours? Express your answer as a fraction in lowest terms.

A. 25\/39

B. 27\/38

C. 24\/38

Correct D. 25/38

Correct Answer: D

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Question 4 View Details

If \(x+\dfrac{1}{x}=4\) and \(x\neq0\), find the value of \(x^{3}+\dfrac{1}{x^{3}}\).

Correct A. 52

B. 48

C. 56

D. 50

Correct Answer: A

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Question 5 View Details

The speed \(v\) (in metres per second) of a car varies directly as the square of the gear number \(n\) and inversely as the resistance \(r\) (in kilograms). When the car is in 3rd gear and the resistance is 2 kg, its speed is 48 m s\(^{-1}\). Find the speed of the car when it is in 5th gear and the resistance is 3 kg. Give your answer as an exact fraction.

A. 512/9

B. 400/3

Correct C. 800/9

D. 160/9

Correct Answer: C

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Question 6 View Details

In a universal set \(U = \{1,2,3,4,5,6,7,8,9,10\}\) two subsets \(A\) and \(B\) satisfy \(|A| = 6\), \(|B| = 7\) and the number of elements that belong to exactly one of the sets is 5. Find \(|A \cap B|\).

A. 5

B. 3

Correct C. 4

D. 2

Correct Answer: C

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Question 7 View Details

The time \(t\) (in hours) required to finish a job varies directly as the number of workers \(w\) and inversely as the efficiency \(e\) of the machine (expressed as a decimal). When 8 workers operate a machine of efficiency \(0.5\) the job takes 12 hours. How many workers are needed if the efficiency is increased to \(0.75\) and the job must be completed in 8 hours?

A. 6

B. 10

C. 12

Correct D. 8

Correct Answer: D

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Question 8 View Details

In triangle \(ABC\) the sides \(AB\) and \(AC\) have lengths \(7\text{ cm}\) and \(9\text{ cm}\) respectively. The median drawn from vertex \(A\) to side \(BC\) has length \(6\text{ cm}\).\n\n(a) Find the length of side \(BC\).\n\n(b) Using the result from part (a), determine the area of triangle \(ABC\).

A. BC = 4\\sqrt{7} cm; Area = 14\\sqrt{6} cm^2

B. BC = \\sqrt{120} cm; Area = 15\\sqrt{5} cm^2

C. BC = 2\\sqrt{31} cm; Area = 13\\sqrt{5} cm^2

Correct D. BC = 2\sqrt{29} cm; Area = 14\sqrt{5} cm^2

Correct Answer: D

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Question 9 View Details

Let vectors \(\mathbf{p}\) and \(\mathbf{q}\) lie in a plane. It is given that \(|\mathbf{p}| = 7\), \(|\mathbf{p} + \mathbf{q}| = 10\) and the vectors \(\mathbf{p} - 2\mathbf{q}\) and \(\mathbf{p} + \mathbf{q}\) are perpendicular.\n\n(a) Find the magnitude \(|\mathbf{q}|\).\n\n(b) Determine the angle \(\theta\) between \(\mathbf{p}\) and \(\mathbf{q}\) (give the nearest whole degree).

A. |q| = \\sqrt{125}/3 (≈3.73); θ ≈ 60°

B. |q| = \\sqrt{144}/3 (≈4); θ ≈ 45°

C. |q| = \\sqrt{160}/3 (≈4.21); θ ≈ 40°

Correct D. |q| = sqrt(141)/3 (≈3.95); θ ≈ 50°

Correct Answer: D

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Question 10 View Details

Find the remainder when \(7^{2021}\) is divided by \(100\).

A. 1

Correct B. 7

C. 49

D. 93

Correct Answer: B

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Question 11 View Details

Find the sum of all integer values of \(x\) that satisfy \(|2x - 5| < x + 3\).

A. 30

Correct B. 28

C. 24

D. 26

Correct Answer: B

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Question 12 View Details

The system of equations\n\\[ (k-1)x + 4y = 9 \\ 2x + (k+2) y = k \]\nhas a solution in integers \(x\) and \(y\). Find the sum of all integer values of \(k\) for which this occurs.

A. 0

Correct B. -2

C. -3

D. -1

Correct Answer: B

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Question 13 View Details

A shop sells pens and notebooks. The total revenue from selling 40 pens and the remaining notebooks is \(\text{₦}13,600\). Each pen costs \(\text{₦}200\) more than a notebook, and the total number of items sold is 70. What is the price of a notebook (in \(\text{₦}\))?

Correct A. 80

B. 70

C. 90

D. 120

Correct Answer: A

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Question 14 View Details

A straight line passes through the points \((2,3)\) and \((8,9)\). It also passes through a third point \((5,k)\). Determine the value of \(k\).

A. 9

B. 5

C. 7

Correct D. 6

Correct Answer: D

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Question 15 View Details

A factory produces items with a defect probability of 0.02. Items are inspected in batches of 100. Using the Poisson approximation, estimate how many batches (out of 200) are expected to contain more than 5 defective items. Give your answer rounded to the nearest whole batch.

A. 6

B. 2

C. 4

Correct D. 3

Correct Answer: D

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Question 16 View Details

A solid consists of a right circular cylinder of radius \(r\) cm and height \(h\) cm, with a right circular cone of the same base radius \(r\) cm and height \(h\) cm placed on top of the cylinder. The total surface area of the solid (including the curved surface of the cylinder, the base of the cylinder, and the curved surface of the cone) is \(124\pi\) cm\(^2\), and the total volume is \(200\pi\) cm\(^3\). Find the ratio \(\dfrac{h}{r}\).

A. 6/7

Correct B. 6/5

C. 5/6

D. 7/5

Correct Answer: B

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Question 17 View Details

Find all integer values of \(k\) for which the quadratic equation \(x^{2}-(k+2)x+(k+5)=0\) has two distinct integer roots.

Correct A. k = 5 or k = -5

B. k = 4 or k = -4

C. k = 6 or k = -6

D. k = 5 or k = 6

Correct Answer: A

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Question 18 View Details

The system of linear equations \(3x-2y=p\) and \(5x+4y=7\) has a solution in which \(x\) is twice \(y\). Determine the value of \(p\).

A. 1

B. 3

C. 4

Correct D. 2

Correct Answer: D

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Question 19 View Details

What is the least common multiple of 12, 15 and 20?

A. 120

B. 30

C. 90

Correct D. 60

Correct Answer: D

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Question 20 View Details

Simplify \(\dfrac{2^{5}\cdot5^{2}}{10^{3}}\) and express your answer as a fraction in lowest terms.

A. 4/25

B. 8/5

Correct C. 4/5

D. 2/5

Correct Answer: C

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Question 21 View Details

Solve for \(x\): \(\sqrt{2^{3}\times 8^{x}} = 4^{\,x+1}\).

A. 1

B. -2

C. 0

Correct D. -1

Correct Answer: D

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Question 22 View Details

In right triangle \(ABC\) with \(\angle C = 90^{\circ}\), the hypotenuse \(AB\) measures \(25\) cm. The altitude from \(C\) meets \(AB\) at \(D\) and has length \(7\) cm. Determine the length of segment \(AD\) (the part of the hypotenuse adjacent to vertex \(A\)). Express your answer in simplest surd form.

A. (25+\\sqrt{500})\/2

B. (25+\\sqrt{400})\/2

C. (25-\\sqrt{429})\/2

Correct D. (25+\sqrt{429})/2

Correct Answer: D

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Question 23 View Details

A fabric is priced at ₦1,200 per metre. A customer purchases \(\frac{3}{4}\) of a metre and receives a discount of \(12.5\%\) on the purchase. What amount does the customer pay? Give your answer in naira to the nearest kobo.

A. 900

B. 750

Correct C. 787.5

D. 788

Correct Answer: C

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Question 24 View Details

The graph of a quadratic function \(y = ax^{2} + bx + c\) passes through the points \((0,1)\), \((2,5)\) and \((4,13)\). Determine the \(x\)-coordinate at which the gradient of the curve equals \(6\).

A. 3

B. 4

Correct C. 5

D. 6

Correct Answer: C

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Question 25 View Details

A sequence \(\{g_n\}\) is defined by \(g_1 = 2\), \(g_2 = 5\) and for \(n \ge 3\), \(g_n = g_{n-1} + 2g_{n-2}\). Find the value of \(g_5\).

Correct A. 37

B. 39

C. 35

D. 41

Correct Answer: A

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