Exam Body

Year

Subject

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neco 2023 mathematics | Objective

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Question 1 View Details

If \( \log_{2}x = \log_{4}y \) and \( \sqrt{x}=3 \), find the value of \(y\).

A. 9

B. 64

Correct C. 81

D. 27

Correct Answer: C

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Question 2 View Details

Let \(A = 2x^{2} - 5x + 3\) and \(B = x^{2} - 3x + 2\). If \( \dfrac{A}{B}=k\) where \(k\) is an integer, find the sum of all integer values of \(x\) that satisfy this condition.

A. 4

B. 1

C. 6

Correct D. 3

Correct Answer: D

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Question 3 View Details

A shop makes a profit of \(N5\) on each pen sold and \(N12\) on each notebook sold. In one day the total profit was \(N103\) and the number of pens sold was three more than twice the number of notebooks sold. How many pens were sold that day?

A. 10

B. 9

Correct C. 11

D. 12

Correct Answer: C

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Question 4 View Details

The parabola \( y = x^{2} - 4x + 3 \) and the circle \( (x-2)^{2} + (y+1)^{2} = 9 \) intersect at two points \(P\) and \(Q\). Find the length of segment \(PQ\).

A. \\sqrt{2\\sqrt{37} - 4}

B. \\sqrt{2\\sqrt{37} + 2}

Correct C. \sqrt{2\sqrt{37} - 2}

D. \\sqrt{2\\sqrt{31} - 2}

Correct Answer: C

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Question 5 View Details

Solve for \(0^{\circ} \le \theta < 360^{\circ}\) the equation \( 2\sin\theta + \sqrt{3} = \tan\theta \). Give the sum of all solutions (in degrees) correct to the nearest integer.

A. 276

B. 300

C. 264

Correct D. 288

Correct Answer: D

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Question 6 View Details

In a beverage, the ratio of sugar (in cups) to milk (in liters) is \(\frac{2}{3}\) : 1.5. If a vendor wants to make a batch using 9 liters of milk, how many cups of sugar are required? Express your answer as a whole number of cups.

Correct A. 4

B. 6

C. 3

D. 5

Correct Answer: A

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Question 7 View Details

Simplify the expression \(\frac{2^{3}\times\sqrt{8}}{4^{1.5}}\) and give your answer in simplest radical form.

Correct A. 2\\sqrt{2}

B. 8\sqrt{2}

C. 2\sqrt{3}

D. 4\sqrt{2}

Correct Answer: A

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Question 8 View Details

A straight line passes through the points \((2,3)\) and \((8,k)\) and meets the x‑axis at \((10,0)\). Find the value of \(k\) and then determine the y‑coordinate of the point on the line where \(x=5\). Express your final answer as an improper fraction.

Correct A. \frac{15}{8}

B. \frac{5}{8}

C. \frac{3}{8}

D. \frac{15}{4}

Correct Answer: A

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Question 9 View Details

The parabola \(y=ax^{2}+bx+c\) has its vertex at \((-2,-5)\) and passes through the point \((1,4)\). Determine the value of \(a\) and then find the y‑coordinate of the point on the parabola where \(x=2\).

A. 9

B. 15

C. 13

Correct D. 11

Correct Answer: D

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Question 10 View Details

In right‑angled triangle \(ABC\) with \(\angle C=90^{\circ}\), the altitude from \(C\) to the hypotenuse \(AB\) meets \(AB\) at \(D\). Given \(CD=6\) cm and \(AD=8\) cm, find the length of side \(BC\) and the radius of the circumcircle of \(\triangle ABC\). Give your answers in centimeters to two decimal places where necessary.

A. BC=8.00 cm, R=6.00 cm

Correct B. BC=7.50 cm, R=6.25 cm

C. BC=7.50 cm, R=5.50 cm

D. BC=7.20 cm, R=6.80 cm

Correct Answer: B

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Question 11 View Details

A solid consists of a right circular cylinder of radius \( r \) cm and height \( h \) cm. A hemisphere of the same radius is attached to the top of the cylinder. On one lateral side of the cylinder a right square pyramid whose base side length is \( 2r \) cm and whose height is \( \dfrac{h}{2} \) cm is attached, sharing its square base with a rectangular portion of the cylinder's lateral surface. The total surface area of the solid, excluding the base of the cylinder that rests on the floor, is \( 1500 \) cm\(^2\). If the height of the cylinder is three times its radius (\( h = 3r \)) and \( \pi = \dfrac{22}{7} \), find the radius \( r \) correct to two decimal places.

A. 8.12

B. 7.05

Correct C. 7.55

D. 6.84

Correct Answer: C

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Question 12 View Details

In a class of 120 students, 10 students failed all three mathematics tests (Algebra, Geometry and Trigonometry). The numbers who passed the three tests are: Algebra - 70 students, Geometry - 60 students, Trigonometry - 50 students. The numbers who passed both Algebra and Geometry, both Algebra and Trigonometry, and both Geometry and Trigonometry are 30, 20 and 15 respectively. How many students passed exactly one of the three tests?

A. 55

Correct B. 45

C. 35

D. 40

Correct Answer: B

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Question 13 View Details

Find all integer values of \( n \) that satisfy both \( \dfrac{2n-5}{n+3} > 1 \) and \( n^{2}-4n-12 \le 20 \). Then give the sum of all such integers.

A. -2

B. -6

Correct C. -4

D. 0

Correct Answer: C

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Question 14 View Details

When the integer \( 7^{2023} \) is divided by 1000, what is the remainder?

A. 7

B. 401

Correct C. 343

D. 49

Correct Answer: C

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Question 15 View Details

The system of linear equations\n\\[\n\begin{cases}\n2x + ky = 7\\\n3x - 4y = 5\n\end{cases}\n\\]\nhas a unique solution \((x, y)\) in which both \(x\) and \(y\) are integers. Find all integer values of \(k\) for which this occurs.

A. 0, 2

B. 5, -1

Correct C. -3, 1

D. -2, 4

Correct Answer: C

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Question 16 View Details

Given that \(a + b = 6\) and \(ab = 5\), find the value of \(\frac{a^{3} + b^{3}}{a + b}\).

Correct A. 21

B. 36

C. 31

D. 30

Correct Answer: A

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Question 17 View Details

Express the repeating decimal \(0.\overline{27}\) as a fraction in lowest terms.

Correct A. 3/11

B. 3/10

C. 7/24

D. 27/100

Correct Answer: A

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Question 18 View Details

In the diagram, the universal set contains 100 elements. The numbers of elements in the sets are: \(|A| = 40\), \(|B| = 35\), \(|C| = 30\); the intersections are \(|A \cap B| = 15\), \(|A \cap C| = 12\), \(|B \cap C| = 10\), and \(|A \cap B \cap C| = 5\). How many elements belong to none of the three sets?

Correct A. 27

B. 30

C. 25

D. 22

Correct Answer: A

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Question 19 View Details

The quadratic equation \(2x^{2} - kx + 8 = 0\) has equal roots. Determine the value of \(k\) and then find the sum of the squares of the roots.

A. 16

B. -8

Correct C. 8

D. 4

Correct Answer: C

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Question 20 View Details

An arithmetic sequence has first term \(a_{1}\) and common difference \(d\). The sum of the first 5 terms is 70 and the sum of the first 9 terms is 210. Find the value of the 10th term.

Correct A. 140/3

B. 130/3

C. 140/4

D. 150/3

Correct Answer: A

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Question 21 View Details

The quadratic equation \(x^{2} - kx + 12 = 0\) has two distinct positive integer roots whose product is 12. The sum of the squares of the roots is 85 and the difference between the roots is 7. Find the value of \(k\) and then compute \(\frac{1}{k} + \frac{1}{12}\).

Correct A. k = 11, \frac{23}{132}

B. k = 12, \frac{25}{132}

C. k = 11, \frac{24}{132}

D. k = 10, \frac{23}{120}

Correct Answer: A

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Question 22 View Details

In a school, 150 students study Mathematics (M), Physics (P) and Chemistry (C). The numbers are \(|M| = 80\), \(|P| = 70\), \(|C| = 60\). Exactly 20 students study all three subjects. The number of students who study both Mathematics and Physics is twice the number who study both Physics and Chemistry. Find the number of students who study exactly one of the three subjects.

A. 100

Correct B. 110

C. 130

D. 115

Correct Answer: B

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Question 23 View Details

The time \(t\) (in hours) required to finish a job varies directly as the square of the number of workers \(w\) and inversely as the square of an efficiency factor \(e\). If 6 workers with efficiency \(e = 0.8\) complete the job in 5 hours, how many workers are needed to complete the same job in 4 hours if the efficiency is reduced to \(e = 0.5\)? Express your answer in simplest radical form.

A. \frac{5\sqrt{5}}{2}

Correct B. \frac{3\sqrt{5}}{2}

C. \frac{3\sqrt{5}}{4}

D. \frac{3\sqrt{2}}{2}

Correct Answer: B

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Question 24 View Details

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

A. 8.73

Correct B. 9.46

C. 10.12

D. 7.95

Correct Answer: B

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Question 25 View Details

An electronic gadget is sold after a successive discount of 10% followed by an additional 5% on the reduced price. The final selling price is \(\text{₦}15{,}120\). What was the original price before any discounts? Furthermore, if a sales tax of 8% is applied to the original price, what is the amount of tax payable? Give your answers rounded to two decimal places.

A. Original price = ₦16,800.00; Tax = ₦1,344.00

B. Original price = ₦17,684.21; Tax = ₦1,209.60

Correct C. Original price = ₦17,684.21; Tax = ₦1,414.74

D. Original price = ₦17,788.24; Tax = ₦1,423.06

Correct Answer: C

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