Mathematic 2023 Practice Questions

Mathematics JAMB Practice Questions & Answers 2023
Set 1

1. .In a class of 40 students, 32 offer Mathematics, 24 offer Physics and 4 offer neither Mathematics nor Physics. How many offer both Mathematics and Physics?

A. 4
B. 8
C. 16
D. 20

Correct Answer: Option D

2.Find the values of x for which

x+24 – 2x−33 < 4

A. x < 8
B. x > -6
C. x < 4
D. x > -3

Correct Answer: Option B

Find N

A. 65
B. 23
C. 17
D. 91

Correct Answer: Option C

4. If X, Y can take values from the set (1, 2, 3 ,4), find the probability that the product of X and Y is not greater than 6

B. 516

C. 12
D. 38

Correct Answer: Option C

Explanation

Each multiplication of elements gives 16 results out of which the ones that are not greater than 6 are asterisked (*) and they are 8 in numbers

Pr(product of x and y NOT > 6 ) = 816

= 12

The pie chart shows the monthly expenditure of a public servant. The monthly expenditure on housing is twice that of school fees. How much does the worker spend on housing if his monthly income is N7200?

A. 1000
B. 2000
C. 3000
D. 4000

6. Evaluate 5−3log2 x 2 2log3

A. 8
A. 18

B. 118
C. 25

Correct Answer: Option B

7. A trader realises 10x – x2

Naira profit from the sale of x bags of corn. How many bags will give him the maximum profit?

A. 7
B. 6
C. 5
D. 4

Correct Answer: Option C

Explanation

Profit (P) = 10x − x2

Maximum profit can be achieved when the differential of profit with respect to number of bags(x) is 0

i.e. dpdx

= 0

dpdx

= 10 – 2x = 0

10 = 2x

Then x = 102

= 5

Answer is C

8. If y = 23five

101

three

, find y, leaving your answer in base two

A. 1110
B. 10111
C. 11101
D. 111100

Correct Answer: Option B

Find the value of x in the diagram

A. 10°
B. 28°
C. 36°
D. 40°

Correct Answer: Option D

Explanation

The diagram shows angles at a point, the total angle at a point is 360

x – 10 + 4x – 50 + 2x + 3x + 20 = 360

10x – 40 = 360

10x = 360 + 40

10x = 400

x = 40010

x = 40

10. Solve for t in the equation 34t + 13(21 – t) = 11

A. 913

B. 713
C. 5
D. 935

Correct Answer: Option D

Explanation

34t + 13(21 – t) = 11

Multiply through by the LCM of 4 and 3 which is 12

12 x(34t) + 12 x (13

(21 – t)) = (11 x 12)

9t + 4(21 – t) = 132

9t + 84 – 4t = 132

5t + 84 = 132

5t = 132 – 84 = 48

t = 485

t = 9 35

Answer is D

11. A school girl spends 14of her pocket money on books and 13

on dress. What fraction remains?

A. 56

B. 712
C. 512
D. 16

Correct Answer: Option C

12. If xa+1 + yb= 1. Make y the subject of the relation.

A. b(a+1−x)a+1

B. a+1b(a−x+1)

C. a(b−x+1)b+1
D. ba(b−x+1)

Correct Answer: Option A

13. Calculate the total surface area of a cupboard which measures 12cm by 10cm by 8cm

A. 1920cm2

B. 592cm2
C. 296cm2
D. 148cm2

Correct Answer: Option B

Explanation

Total surface area of a cupboard is given by the equation A = 2(lb + bh + lh) L = 12, b = 10, h = 8

A = 2((12 x 10) + (10 x 8) + (12 x 8))

A = 2(120 + 80 + 96)

A = 2 x 296

A = 592cm2

Answer is B

14. Convert 0.04945 to two significant figures

A. 0.040
B. 0.049
C. 0.050
D. 0.49

Correct Answer: Option C

15. The probabilities that John and James pass an examination are 34

and

respectively. Find the probability of both boys failing the examination.

A. 110

B. 210
C. 920
D. 1120

Correct Answer: Option D

Explanation

Pr(both John and James passed)

= 34

x 35 = 920

Pr(john and james failed)= 1- Pr(john and james passed)

= 1 – 920

= 1120

Answer is D

16. An arc of a circle of radius 14cm subtends angle 300° at the centre. Find the perimeter of the sector formed by the arc (take π = 227)

A. 14.67cm
B. 42.67cm
C. 101.33cm
D. 513.33cm

Correct Answer: Option C

17. Simplify

2523+2516(15)76×(15)16

A. 25
A. 15

B. 1
C. 125

Correct Answer: Option B

Make T the subject of the relation.

A. T = R+P315Q

B. T = R−15P3Q
C. T =R – 15P3Q
D. T = 15R+QP3

Correct Answer: Option C

19.What is the place value of 9 in the number 3.0492?

A. 910000

B. 91000
C. 9100
D. 910

Correct Answer: Option B

20. If the simple interest on a sum of money invested at 3% per annum for 212

years is N123, find the principal.

A. N676.50
B. N820
C. N1,640
D. N4,920

Correct Answer: Option C

21. A machine valued at N20,000 depreciates by 10% every year. What will be the value of the machine at the end of two years?

A. N16,200
B. N14,200
C. N12,000
D. N8,000

Correct Answer: Option A

Explanation

Since it depreciates by 10% At the end of first year, its value = 90% of 20000

= 90100 x 20000 =18000

At the end of second year, its value = 90% of 18000

= 90100 x 18000 = ₦16,200

Answer is A

22. The table shown gives the marks scored by a group of student in a test. Use the table to answer the question given.

Mark	0	1	2	3	4	5
Frequency	1	2	7	5	4	3

What is the median mark?

A. 1
B. 2
C. 3
D. 4

Correct Answer: Option C

Explanation

Total frequency = 1 + 2 + 7 + 5 + 4 + 3 = 22

Median is the middle number

= Nth2

term = 22th2 = 11th term

Going in ascending order, 11th term is 3, going in descending order 11th term is 3

Median = 3 + 32 = 62 = 3

Answer is C

23. The table shown gives the marks scored by a group of student in a test. Use the table to answer the question given.

Mark	0	1	2	3	4	5
Frequency	1	2	7	5	4	3

What is the probability of selecting a student from the group that scored 2 or 3

A. 111

B. 522
C. 722
D. 611

Correct Answer: Option D

24 A boy walks 800m in 20 minutes. Calculate his average speed in Km/H

A. 2.4
B. 4
C. 24

Correct Answer: Option A

25.A car uses one litre of petrol for every 14km. If one litre of petrol cost N63.00, how far can the car go with N900.00 worth of petrol?

A. 420Km
B. 405Km
C. 210Km
D. 200Km

Correct Answer: Option D

Explanation

since 1litre cost ₦63

So ₦900 is the cost of 90063

litres

= 14.2857litres of petrol

nbsp; The car uses 1 litre for 14km

So 14.2857 litres will be used for (14.2857 x 14)

= 200km

Answer is D

In the diagram, GI is a tangent to the circle at H. If EF||GI, calculate the size of ∠EHF

A. 126°
B. 72°
C. 54°
D. 28°

Correct Answer: Option B

27. How many times, correct to the nearest whole number, will a man run round a circular track of diameter 100m to cover a distance of 1000m?

A. 3
B. 4
C. 5
D. 6

Correct Answer: Option B

Explanation

In terms of distance, a circle has a total distance or perimeter of 2π or π

Where r is radius and D is the diameter

So perimeter = 227

x 100

= 314.2857m

To cover a distance of 1000m, he is going to round the circular track for 1000314.2857

= 3.18

It means it is on the number 4 round after the third round he is going to cover up to 1000m

Use the cummulative frequency curve to answer the question. Estimate the median of the date represented on the graph

A. 35.5
B. 36.5
C. 37.5
D. 38.5

Correct Answer: Option A

Use the cummulative frequency curve to answer the question. What is the 80th percentile?

A. 45.5
B. 46.5
C. 47.5
D. 48.5

Correct Answer: Option C

30. 0.00256×0.00640.025×0.08

A. 8.8 x 10−1

B. 8.8 x 10−2
C. 8.8 x 10−3
D. 8.8 x 103

31. Two sisters, Taiwo and Kehinde, own a store. The ratio of Taiwo’s share to Kehinde’s is 11:9. Later Kehinde sells 23

of her share to Taiwo for N720.00. Find the value of the store

A. N1,080.00
B. N2,400.00
C. N3,000.00
D. N3,600.00

Correct Answer: Option B

32. A room is 12m long, 9m wide and 8m high. Find the cosine of the angle which a diagonal of the room makes with the floor of the room

A. 1517

B. 917
C. 815
D. 1217

Correct Answer: Option A

33. Divide the L.C.M of 48, 64 and 80 by their H.C.F

A. 20
B. 30
C. 48
D. 60

Correct Answer: Option D

34. Find the equation of the line through (5,7) parallel to the line 7x + 5y = 12

A. 5x + 7y = 20
B. 7x + 5y = 70
C. xy = 7
D. 15x + 17y = 90

Correct Answer: Option B

35. A man’s initial salary is N540.00 a month and increases after each period of six months by N36.00 a month. Find his salary in the eight month of the third year.

A. N828.00
B. N756.00
C. N720.00
D. N684.00

Correct Answer: Option C

Explanation

Since the salary increases by 36 after every 6 months

Every 6 months that can be counted on the eight month of the third year is 5

(i.e. 2 times in the first year, 2 times in the second year and once in the third year)

His salary then = initial salary + increment

= 540 + 5(36)

= 540 + 180

= ₦720.00

It can also be solves using a sequence in form of an AP

Answer is C

36. A man stands on a tree 150cm high and sees a boat at an angle of depression of 74°. Find the distance of the boat from the base of the tree.

A. 52cm
B. 43cm
C. 40cm
D. 15cm

Correct Answer: Option B

Explanation

Tan 74 = 150/x

x = 150/tan 74

= 43.01cm

37. Integrate the expression 6x2– 2x + 1

A. 3x3 – 2x2 + x + c
B. 2x3– x2+ x + c
C. 2x3– 3x2+ c
D. x3+ x2– x + c

Correct Answer: Option B

38. In how many ways can the letters LEADER be arranged?

A. 72
B. 144
C. 360
D. 720

Correct Answer: Option C

Explanation

The word LEADER has 1L 2E 1A 1D and 1R making total of 6! 61!2!1!1!1! = 6!2!

= 6×5×4×3×2×12×1

= 360

39.

In the figure below, /MX/ = 8cm, /XN/ = 12cm, /NZ/ = 4cm and ∠ XMN = ∠ XZY. Calculate /YM/

A. 32cm
B. 24 cm
C. 16 cm
D. 12 cm

Correct Answer: Option C

Explanation

From the figure,

∠ XMN = ∠ XZY

Angle X is common

So, ∠ XNM = ∠ XYZ

Then from the angle relationship

XMXZ

= XNXY = MNZY XM = 8, XZ = 12 + 4 = 16,

XN = 12, XY = 8 + YM

816

= 12(8+YM) Cross multiply

8(8 + YM) = 192

64 + 8YM = 192

8YM = 128

YM = 1288

= 16cm

40. Express 495g as a percentage of 16.5kg

A. 3%
B. 3 13%
C. 15%
D. 30%

Correct Answer: Option A

Explanation

The two numbers must be expressed in the same unit. To convert 495g to kg, it will be divided by 1000

495g = 4951000

= 0.495kg

To express in percentage, 0.495 will be divided by 16.5 and then multiplied by 100

% will be added to the answer 0.495016.5

x 100

= 3%

41. Evaluate (2√3 – 4) (2√3 + 4)

A. -4
B. -2
C. 2
D. 4

Correct Answer: Option A

Explanation

2√3 – 4) ( 2√3 + 4)

= 12 + 8√3 – 8√3 – 16

= 12 – 16

= -4

The two expressions in the bracket are conjugate of each other

42. Find the equation of the tangent at the point (2, 0) to the curve y = x2– 2x

A. y = 2x – 4
B. y = 2x + 4
C. y = 2x – 2
D. y = 2x + 2

Correct Answer: Option A

Explanation

The gradient to the curve is found by differentiating the curve equation with respect to x

So dydx 2x – 2

The gradient of the curve is the same with that of the tangent.

At point (2, 0) dydx = 2(2) – 2

= 4 – 2 = 2

The equation of the tangent is given by (y – y1) dydx (x – x1)

At point (x1, y1) = (2, 0)

y – 0 = 2(x – 2)

y = 2x – 4

Use the quadratic equation curve to answer this questions

What is the 80th percentile?

A. -5.3
B. 0.5
C. 3
D. 8

Correct Answer: Option A

44. Evaluate log2 8 – log3 1919

A. -1 112

B. -1
C. 1
D. 5

Correct Answer: Option D

Explanation

log2 8 – log3 19

= log 2 23 – log3 9−1

= log2 23 – log3 3−2

Based on law of logarithm

= 3 log2 2 – (-2 log3 3)

But log2 2 = 1,

log3 3 = 1

So, = 3 + 2

= 5

45. Tanθ is positive and Sinθ is negative. In which quadrant does θ lies

A. Second only
B. Third only
C. Fourth only
D. First and third only

Correct Answer: Option B

Explanation

First quadrant: Sin, Cos and Tan are all positive

Second quadrant: Sin is positive, Cos is negative and Tan is negative

Third quadrant: Tan is positive, Sin is negative and Cos is negative

Fourth quadrant: Cos is positive, Sin is negative and Tan is negative

The correct option is the third quadrant only where Tanθ is positive and Sinθ is negative

Correct Answer: Option B

Explanation

The total number of students is ∑ f = 3 + 4 + 5 + 6 + 7 + 6 + 5 + 4

= 40

The figure below is a Venn diagram showing the elements arranged within sets A,B,C,ε.

Use the figure to answer this question

What is n(A U B)1 ?

A. 2
B. 3
C. 4
D. 7

Correct Answer: Option C

Explanation

A = (p, q, r, t, u, v)

B = (r, s, t, u)

A U B = Elements in both A and B = (p, q, r, s, t, u, v)

(A U B)1 = elements in the universal set E but not in (A U B)= (w, x, y, z)

n(A U B) 1 = number of the elements in (A U B)1 = 4

48. What is the loci of a distance 4cm from a given point P?

A. A straight line of length 4cm
B. a circle of radius 4cm
C. perpendicular to point P at 4cm
D. a circle of diameter 4cm

Correct Answer: Option B

49. Given that Sin (5x− 28)o = Cos(3x − 50)o, Ox < 90o

Find the value of x

A. 14o

B. 21o
C. 32o
D. 39o

Correct Answer: Option B

Explanation

Sin(5x – 28) = Cos(3x – 50)………..i

But Sinα = Cos(90 – α)

So Sin(5x – 28) = Cos(90 – [5x – 28])

Sin(5x – 28) = Cos(90 – 5x + 28)

Sin(5x – 28) = Cos(118 – 5x)………ii

Combining i and ii

Cos(3x – 50) = Cos(118 – 5x)

3x – 50 = 118 – 5x

Collecting the like terms

3x + 5x = 118 + 50

8x = 168

x = 1688

x = 21o

Answer is B

50. Find the average of the first four prime numbers greater than 10

A. 20
B. 19
C. 17
D. 15

Correct Answer: Option D

Explanation

Prime numbers are numbers that has only two factors (i.e 1 and itself). They are numbers that are only divisible by 1 and their selves. First four Prime numbers greater than 10 are 11, 13, 17 and 19

Average = sum of numbers / number

= frac(11+13+17+19)4

= 604

= 15

What is the modal age?

A. 4
B. 5
C. 6
D. 7

Correct Answer: Option B

Explanation

The modal age is the age with the highest frequency, and that is age 5 years with f of 7

52. Convert 0.04945 to two significant figures

A. 0.040
B. 0.049
C. 0.050
D. 0.49

Correct Answer: Option B

Explanation

0.04945 to 2s.f is 0.049

53. Calculate 243six– 243five

expressing your answer in base 10

A. 0
B. 1
C. 26
D. 46

Correct Answer: Option C

Explanation

Since they are of different base, convert to base 10

243six

= (2 x 62) + (4 x 61) + (3 x 60)

= 72 + 24 + 3 = 99 base 10

243six

= 2 x 52 + 4 x 51 +3 x 50

50 + 20 + 3 = 73 base 10

Subtracting them, 99 – 73

= 26

54. Evaluate ∫215xdx

A. 1.47
B. 2.67
C. 3.23
D. 3.47

Correct Answer: Option D

Explanation

∫5x

dx = 5 ∫1x = 5Inx

Since the integral of 1x

is Inx

∫2

1∫ 5x dx = 5

dx = 5 (In<2 – InIn1)

= 3.4657

= 3.47

55. Tossing a coin and rolling a die are two separate events. What is the probability of obtaining a tail on the coin and an even number on the die?

A. 116

B. 16
C. 14
D. 38
Correct Answer: Option C

Explanation

P( tail on a coin) = 12

Even numbers on a care 2, 4 and 6

P( even number on a die) = 36

= 12 P( tail on a coin and even number on a die) = 12

x 12 = 14

56. Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
- A. 210
- B. 1050
- C. 21400
- D. 25200
Correct Answer: Option A

Explanation

To form words having 3 consonants and 2 vowels out of 7 consonants and 4 vowels, the number of such words is 7/3C x 4/2C = 35 x 6

= 210
57. From a point P, R is 5km due West and 12km due South. Find the distance between P and R’.
- A. 5km
- B. 12km
- C. 13km
- D. 17km
Correct Answer: Option C

Explanation

Using Pythagoras theorem

PR2

= 52 + 122

25 + 144 = 169

PR = √(169)= 13km

Answer is C

58. if y = 23five+ 101three

find y leaving your answer in base two
A. 1110
B. 10111
C. 11101
D. 111100

Correct Answer: Option B

Explanation

First we convert the numbers to base ten

23five

= 2 x 51 + 3 x 50

= 10 + 3 = 13

101five

= (1 x 32) + (0 x 31) + (1 x 30)

= 9 + 0 + 1 = 10

So, y = 13 + 10 = 23

To convert 23 to base 2 (as in the diagram above)

Y = 23

= 10111five

Answer is B

59. A box contains two red balls and four blue balls. A ball is drawn at random from the box and then replaced before a second ball is drawn. Find the probability of drawing two red balls.

A. 23

B. 13
C. 14
D. 19

Correct Answer: Option D

Explanation

Total number of balls = 2 + 4 = 6

P(of picking a red ball) = 26

= 13 P(of picking a blue ball) = 46

= 23 With replacement,

P( picking two red balls) = 13

× 13 = 19

Which one of the following gives the members of the set A1 n B n C?

A. Φ
B. {s}
C. {t, u}
D. {y, z}

Correct Answer: Option A

Explanation

A1 = Elements in the universal set but not in A = {s, w, x, y, z}

B = {r, s. t, u}

C = {t, u, v, w, x}

A1 n B n C = elements common to the three sets = none = empty set = Φ

61. If P = [Q(R−T)15] 13

make T the subject of the relation

A. T = R+P315Q

B. T = R−15P3Q
C. T = R−15P3Q
D. T = 15R−QP3

Correct Answer: Option C

Explanation

Taking the cube of both sides of the equation give

= Q(R−T)15 Cross multiplying

15P3

= Q(R – T)

Divide both sides by Q

15P3Q

= R – T

Rearranging gives

T = R – 15P3Q

= RQ−15P3Q

Answer is C

62. Calculate the area of an equilateral triangle of side 8cm

A. 8√3
B. 16
C. 4√3
D. 16√3

Correct Answer: Option D

Explanation

An equilateral triangle has all sides equal and all angles equal as 600

Area = 12

absinθ

Area = 12

x 8 x 8 x sin60

= 12

x 64 x 32−−√ = 16√3 cm2

63. The pie chart shows the monthly expenditure of a public servant. The monthly expenditure on housing is twice that of school fees. How much does the worker spend on housing if his monthly income is ₦7200?

A. ₦1000
B. ₦2000
C. ₦3000
D. ₦4000

Correct Answer: Option B

Explanation

Let the monthly expenditure angle for school fees is x, then that of housing will be 2x. Since the total angle in the circle is 360.

Using 90 as the angle for transport

So, x + 2x + 120 + 90 = 360

3x + 210 = 3605

3x = 360 – 210

= 150

x = 1503

= 50

So the angle for housing is 2x = 2 × 50

= 100

Amount spent on housing = 100360

× 7200

= ₦2000

64.Approximate 0.9875 to 1 decimal place.

A. 1.1
B. 1.0
C. 0.9
D. 0.10

Correct Answer: Option B

Explanation

9 is on one decimal place, the next number to it is 8 which will be rounded up to 1 because it is greater than 5 and then added to 9 to give 10, 10 cannot be written, it will then be rounded up to 1 and added to 0.

So the answer is 1.0

65.Simplify 2512× 8−23

A. 114

B. 214
C. 6
D. 10

Correct Answer: Option A

Explanation

Using law of indices

2512

× 8−23 = √25 x (8–√3

) -2

= 5 x 2-2

= 5 x 122

= 114 Answer is A

66. From a point R, 300m north of P, a man walks eastwards to a place; Q which is 600m from P. Find the bearing of P from Q correct to the nearest degree

A. 026o

B. 045o
C. 210o
D. 240o

Correct Answer: Option D

Explanation

Cos θ = adjhyp

= 300600

= 0.5

θ = Cos – 10.5

= 60

∠ RPQ = ∠ PQs

So the bearing of P from Q is 180 + 60 = 240o

Answer is D

67. Add 54 eightand 67eight

giving your answers in base eight

A. 111
B. 121
C. 123
D. 143

Correct Answer: Option D

Explanation

54 eight

and 67eight = 1438

Starting with normal addition, 4 + 7 gives 11

(it is more than the base, 8) 8 goes in 11 just 1 time, remaining 3, the remainder will be written, and the 1 will be added to the sum of 5 and 6 which gives 12 altogether, 8 goes in 12 one time remaining 4, the remainder 4 was written and then the 1 that was the quotient was then written since nothing to add the 1 to.

So answer is 143 in base eight

Mathematics JAMB Practice Questions & Answers 2023Set 1

Correct Answer: Option C

Explanation

Explanation

Profit (P) = 10x − x2

Explanation

Explanation

Correct Answer: Option A

Explanation

Correct Answer: Option C

Explanation

Correct Answer: Option B

Explanation

Explanation

Correct Answer: Option A

Explanation

Correct Answer: Option B

27. How many times, correct to the nearest whole number, will a man run round a circular track of diameter 100m to cover a distance of 1000m?

Correct Answer: Option B

Explanation

Explanation

Explanation

Explanation

Correct Answer: Option C

Explanation

Correct Answer: Option A

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Correct Answer: Option C

Explanation

Explanation

Sin(5x – 28) = Cos(3x – 50)………..i

Correct Answer: Option D

Explanation

Correct Answer: Option B

Explanation

Correct Answer: Option B

Explanation

Correct Answer: Option C

Explanation

Correct Answer: Option D

Explanation

Correct Answer: Option C

Explanation

Correct Answer: Option A

Explanation

Correct Answer: Option C

Explanation

Correct Answer: Option B

Explanation

Correct Answer: Option D

Explanation

Correct Answer: Option A

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Correct Answer: Option C

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Correct Answer: Option D

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Correct Answer: Option B

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Correct Answer: Option B

Explanation

Correct Answer: Option A

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Correct Answer: Option D

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Correct Answer: Option D

Explanation

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Mathematics JAMB Practice Questions & Answers 2023
Set 1