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neco model questions vol1 2023 mathematics | Objective

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Question 1 View Details

A three‑digit number is formed by writing the digit 7 twice followed by the digit 5, i.e. 775. What is the remainder when this number is divided by \(9\)?

Correct A. 1

B. 0

C. 2

D. 3

Correct Answer: A

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Question 2 View Details

Two boxes are identical in appearance. Box A contains 2 red and 3 green balls; Box B contains 4 red and 1 green ball. A box is selected at random, then two balls are drawn without replacement from the selected box. Given that both drawn balls are red, what is the probability that Box B was selected?

A. 5/7

B. 1/7

C. 2/3

Correct D. 6/7

Correct Answer: D

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Question 3 View Details

Find the smallest integer greater than \(1000\) that is divisible by \(7\) and leaves a remainder of \(3\) when divided by \(9\).

A. 1015

B. 1092

Correct C. 1029

D. 1035

Correct Answer: C

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Question 4 View Details

In right‑angled triangle \(ABC\) with \(\angle B = 90^{\circ}\), the legs are \(AB = 6\) cm and \(BC = 8\) cm. Point \(D\) lies on the hypotenuse \(AC\) such that \(AD:DC = 1:2\). Find \(\sin \angle ABD\).

Correct A. 2*sqrt(13)/13

B. 4*sqrt(13)\/13

C. sqrt(13)\/13

D. 2*sqrt(13)\/7

Correct Answer: A

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Question 5 View Details

A Venn diagram shows three overlapping sets \(A\), \(B\) and \(C\). The numbers in the regions are: \(A\) only = ?, \(B\) only = 12, \(C\) only = ?, \(A\cap B\) only = 8, \(B\cap C\) only = 7, \(A\cap C\) only = 5, \(A\cap B\cap C\) = 4, and 6 elements belong to none of the sets. The universal set contains 60 elements. It is also known that set \(C\) contains exactly 25 elements. Find the number of elements that belong to set \(A\).

A. 28

B. 30

C. 24

Correct D. 26

Correct Answer: D

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Question 6 View Details

In triangle ABC, side a = 12 cm opposite angle A and side b = 15 cm opposite angle B. Angle B exceeds angle A by 20°. Find the measure of angle C (in degrees) correct to one decimal place.

Correct A. 64.6

B. 70.2

C. 84.6

D. 55.4

Correct Answer: A

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Question 7 View Details

The quadratic function \(y = ax^{2} + bx + c\) passes through the points \((0,1)\) and \((2,5)\). Its vertex lies on the straight line \(y = x - 2\). Determine the y‑coordinate of the vertex.

A. -1.50

Correct B. -1.25

C. -2.00

D. -0.75

Correct Answer: B

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Question 8 View Details

The terms in odd positions of a sequence form an arithmetic progression with first term 5 and common difference \(d\). The terms in even positions form a geometric progression with first term 2 and common ratio \(r\). If the sum of the first six terms of the whole sequence is 100 and the sum of the three odd‑positioned terms is 45, find the sixth term of the sequence, giving your answer to two decimal places.

A. 45.12

Correct B. 43.64

C. 41.58

D. 39.87

Correct Answer: B

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Question 9 View Details

In right triangle \(ABC\) with \(\angle B = 90^{\circ}\), the legs have lengths \(AB = 6\) cm and \(BC = 8\) cm. The circle with diameter \(AC\) passes through \(B\). A second point \(D\) on this circle (different from \(B\)) satisfies \(BD = 5\) cm and is nearer to \(C\) than to \(A\). Compute the length of \(CD\) (in cm) correct to two decimal places.

A. 3.45

B. 5.00

C. 4.12

Correct D. 3.93

Correct Answer: D

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Question 10 View Details

Let \(x\) satisfy the quadratic equation \(2x^{2} - 5x + 3 = 0\). Evaluate \(\displaystyle \frac{x^{3} + 6x^{2} - 7x + 2}{x^{2} - 3x + 2}\).

Correct A. -33.5

B. -35.0

C. -30.0

D. -31.5

Correct Answer: A

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Question 11 View Details

Solve the inequality \(\frac{x^{2}-5x+6}{x-2}\ge 2\) and express the solution set in interval notation.

A. (-∞,5]

B. (5,∞)

Correct C. [5,∞)

D. [4,∞)

Correct Answer: C

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Question 12 View Details

In the coordinate plane the points A(1,2) and B(4,6) are shown. The line AB is extended to meet the y‑axis at point C, and a horizontal line through B meets the y‑axis at point D. Find the area of quadrilateral ABCD.

A. 16/3

B. 10/3

Correct C. 32/3

D. 32/5

Correct Answer: C

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Question 13 View Details

Evaluate \(\frac{3}{4}\div\left(\frac{2}{5}-\frac{1}{10}\right)+0.2\). Give your answer as a decimal.

A. 1.9

B. 3.2

Correct C. 2.7

D. 2.5

Correct Answer: C

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Question 14 View Details

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

A. 12

B. 24

C. 6

Correct D. 18

Correct Answer: D

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Question 15 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 next five terms (terms 6 to 10) is 70. Find the eighth term of the sequence.

A. 18

B. 15

C. 12

Correct D. 14

Correct Answer: D

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Question 16 View Details

A positive integer leaves a remainder of 3 when divided by 7 and a remainder of 5 when divided by 9. What is the smallest such integer?

A. 65

Correct B. 59

C. 53

D. 71

Correct Answer: B

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Question 17 View Details

The graph shows the speed \(v\) (in metres per second) of a car as a function of time \(t\) (in seconds). The speed varies linearly between the points \((0,0)\), \((2,4)\), \((5,4)\) and \((7,10)\). Calculate the total distance travelled by the car from \(t=1\) s to \(t=6\) s.

Correct A. 20.5

B. 22.0

C. 24.5

D. 18.5

Correct Answer: A

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Question 18 View Details

In a school of 150 pupils, 78 study Mathematics, 65 study Physics and 50 study Chemistry. The numbers of pupils studying both Mathematics and Physics, both Mathematics and Chemistry, and both Physics and Chemistry are 30, 25 and 20 respectively. Ten pupils study all three subjects. How many pupils study none of these subjects?

A. 44

B. 32

Correct C. 22

D. 12

Correct Answer: C

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Question 19 View Details

Evaluate \( \log_{3} 27 + \log_{27} 9 \).

Correct A. 11/3

B. 13/3

C. 4/3

D. 5/3

Correct Answer: A

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Question 20 View Details

A shop offers a 15 % discount on an item and then a further 10 % discount on the reduced price. If the final price after both discounts is ₦1,200, what was the original price of the item? Express your answer as an exact fraction in naira.

A. 1600\/1

B. 24000\/17

C. 4800\/7

Correct D. 80000/51

Correct Answer: D

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Question 21 View Details

The vectors \(\mathbf{a}\) and \(\mathbf{b}\) lie in a plane with \(|\mathbf{a}| = 5\) cm, \(|\mathbf{b}| = 12\) cm and the angle between them \(45^{\circ}\). Determine the scalar \(k\) for which the vector \(\mathbf{c}= \mathbf{a}+k\mathbf{b}\) is perpendicular to \(\mathbf{b}\). Then find the magnitude of \(\mathbf{c}\).

A. k = \\frac{5\\sqrt{2}}{24}, \\; |\\mathbf{c}| = \\frac{5\\sqrt{2}}{2}

B. k = -\\frac{5\\sqrt{2}}{12}, \\; |\\mathbf{c}| = \\frac{5\\sqrt{2}}{4}

C. k = -\\frac{5}{24}, \\; |\\mathbf{c}| = \\frac{5\\sqrt{2}}{2}

Correct D. k = -\frac{5\sqrt{2}}{24}, \; |\mathbf{c}| = \frac{5\sqrt{2}}{2}

Correct Answer: D

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Question 22 View Details

Vector \(\mathbf{p}=3\mathbf{i}-4\mathbf{j}\) and vector \(\mathbf{q}=a\mathbf{i}+b\mathbf{j}\) are in the same plane. Their resultant \(\mathbf{r}=\mathbf{p}+\mathbf{q}\) has magnitude \(10\) and makes an angle of \(30^{\circ}\) with the positive \(x\)-axis. Find the ordered pair \((a,b)\).

Correct A. a = 5\sqrt{3} - 3, \; b = 9

B. a = 5\\sqrt{3} - 6, \\; b = 9

C. a = 5\\sqrt{3} - 3, \\; b = -9

D. a = 5\\sqrt{3} + 3, \\; b = 9

Correct Answer: A

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Question 23 View Details

An initial data set of 15 observations has a mean of 48 and a standard deviation of 6. Five additional observations are then added, and the combined data set of 20 observations has a mean of 50 and a standard deviation of 8. Find (i) the sum of the five new observations, and (ii) the standard deviation of those five observations.

A. Sum = 260, standard deviation = 9

B. Sum = 300, standard deviation = 12

C. Sum = 280, standard deviation = 8

Correct D. Sum = 280, standard deviation = 10

Correct Answer: D

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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 hemisphere of the same radius. The total surface area, including the base of the cylinder, is \(800\ \text{cm}^2\) and the total volume is \(1000\ \text{cm}^3\). Determine the radius \(r\) correct to two decimal places.

Correct A. r \approx 2.62\text{ cm}

B. r \\approx 2.78\\text{ cm}

C. r \\approx 3.10\\text{ cm}

D. r \\approx 2.45\\text{ cm}

Correct Answer: A

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Question 25 View Details

Find the value of \(x\) if \(x = 3^{\log_{3} 4} + \sqrt{16} - \log_{10} 100\).

A. 2

Correct B. 6

C. 4

D. 8

Correct Answer: B

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