2023 Real WAEC Mathematics Questions and Answers (Essay and Objectives)

Searching for the latest waec mathematics Questions and Answers 2023, WAEC Maths answers, WAEC Mathematics questions and answers, WAEC Mathematics past questions on mathematics? We’ve got you covered.

To some people, Mathematics is the easiest subject, while others find it difficult to understand it. Today, I’ll be sharing with you, WAEC past questions on mathematics that will likely come out in today’s Waec examination.

For candidates who are not aware, note that WAEC questions are primarily set and compiled by the West African Senior School Certificate Examination Board (WASSCE).

To avoid issues like missing scripts/papers, ensure you carefully follow the instructions provided by WAEC.

GENERAL MATHEMATICS/MATHEMATICS (CORE) 1

Symbols that will appear in today’s paper and their meanings:

^ means raise to power.

/ division

SQRT means square root

1. Simplify the expression: 3x² – 4x + 2x² – 5x + 1.

Waec Mathematics Questions and Answers 2023.

I’ll be sharing with you, the best solutions to WAEC Mathematics Questions for 2023, and how you can implement that too in your examination today.

1. Express, correct to three significant figures, 0.003597.

A. 0.359
B. 0.004
C. 0.00360
D. 0.00359

2. Evaluate:  (0.064)^-1/3

A. 5/2
B. 2/5
C. -2/5
D. -5/2

3. Solve:  y+1/2 – 2y-1/3 = 4

A. y = 19
B. y = -19
C. y = -29
D. y = 29

4. Simplify, and correct three significant figures, (27.63)^2 – (12.37)^2

A. 614
B. 612
C. 611
D. 610

5. If  7 + y = 4 (mod 8), find the least value of y, 10<=y<=30

A. 11
B. 13
C. 19
D. 21

6. If  T = (prime numbers) and M = (odd numbers) are subsets of U = (x: 0<x<=10, and x is an integer), find (T’ n M’).

A. (4, 6, 8, 10)
B. (1, 4, 6, 8, 10)
C. (1, 2, 4, 6, 8, 10)
D. (1, 2, 3, 5, 7, 8, 9)

7. Evaluate: log9 base 3 – log8 base 2 /log9 base 3

A. -1/3
B. 1/2
C. 1/3
D. -1/2

8. If 23y = 1111two, find the value of y.

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

9. If 6, P and 14 are consecutive terms in an Arithmetic Progression (A.P), find the value of P.

A. 9
B. 10
C. 6
D. 8

10. Evaluate: 2 (SQRT 28) – 3 (SQRT 50) +  (SQRT 50)

A. 4 (SQRT  7) – 21 (SQRT 2)
B. 4 (SQRT  7) – 11 (SQRT 2)
C. 4 (SQRT  7) – 9 (SQRT 2)
D. 4 (SQRT  7) + (SQRT 2)

11. If m : n = 2 : 1, evaluate 3m^2 – 2n^2 /m^2 + mn

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

12. H varies directly as p and inversely as the square of y. If H = 1, p = 8 and y = 2, find H in terms of p and y

A. H = p /4y^2
B. H = 2p / y^2
C. H = p / 2 y^2
D. H = p / y^2

13. Solve 4x^2 – 16x + 15

A. X = 1 (1/2) or X = -2 (1/2)
B. X = 1 (1/2) or X = 2 (1/2)
C. X = 1 (1/2) or X = -1 (1/2)
D. X = -1 (1/2) or X = -2 (1/2)

14. Evaluate 0.42 divided by 2.5 /0.5 x 2.05, leaving the answer in standard form.

A. 1.639 x 10^2
B. 1.639 x 10^1
C. 1.639 x 10^-1
D. 1.639 x 10^-2

15. Simplify: log6 – 3log3 + 2/3log27.

A. 3log 2
B. Log2
C. Log3
D. 2log3

16. Bala sold an article for 6,900.00 Naira and made a profit of 15 per cent. Calculate his percentage profit if he had sold for 6600.00.

A. 5 per cent.
B. 10 per cent
C. 12 per cent.
D. 13 per cent.

17. If 3p = 4q and 9p = 8q-12, find the value of pq.

A. 12
B. 7
C. -7
D. -12

18. If (0.25)^y = 32, find the value of y.

A. y = -5/2
B. y = -3/2
C. y = 3/2
D. y = 5/2

19. There are 8 boys and 4 girls in a lift. What is the probability that the first person who steps out of the lift will be a boy?

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

20. Simplify: x^2 – 5x – 14 / x^2 – 9x + 14

A. X – 7 /x + 7
B. X + 7 /x – 7
C. X – 2 /x + 4
D. X + 2 /x – 2

21. Which of these values would make 3p – 1 /p^2 – p undefined?

A. 1
B. 1/3
C. -1/3
D. -1

22. The total surface area of a solid cylinder is 165 cm2. If the base diameter is 7 cm, calculate its height. (Take pi = 22/7)

A. 7.5 cm
B. 4.5 cm
C. 4.0 cm
D. 2.0 cm

23. If 2^a = SQRT(64) and b/a = 3, evaluate a^2 + b^2.

A. 250
B. 160
C. 90
D. 48

24. In triangle XYZ, line XZ = 32 cm, angle YXZ = 52 degrees and XZY = 90 degrees. Find, correct to the nearest centimeter, line XZ.

A. 31 cm
B. 25 cm
C. 20 cm
D. 13 cm

25. If log 2 base x = 0.3, evaluate log 8 base x.

A. 2.4
B. 1.2
C. 0.9
D. 0.6

26. An arc subtends an angle of 72 degrees at the centre of a circle. Find the length of the arc if the radius of the circle is 3.5 cm. (Take pi = 22/7)

A. 6.6 cm
B. 8.8 cm
C. 4.4 cm
D. 2.2 cm

27. Make b the subject of the relation lb = 1/2(a+b)h
A. ah /2l – h
B. 2l – h/al
C. al/2l – h
D. al/2 – h

29. Eric sold his house through an agent who charged 8 percent commission on the selling price. If Eric received 117,760.00 dollars after the sale, what was the selling price of the house?

A. 130,000.00 dollars
B. 128,000.00 dollars
C. 125,000.000 dollars
D. 120,000.00 dollars

29. Find the angle which an arc of length 22 cm subtends at the centre of a circle of radius 15 cm. (take pi = 22/7)

A. 70 degrees
B. 84 degrees
C. 96 degrees
D. 156 degrees

30. A rectangular board has a length of 15 cm and width x cm. If its sides are doubled, find its new area.

A. 60x cm squared
B. 45x cm squared
C. 30x cm squared
D. 15x cm squared

31. In the diagram, POS and ROT are straight lines. OPQR is a parallelogram, line OS = line OT and angle OST = 50 degrees. Calculate the value of angle OPQ.

A. 100 degrees
B. 120 degrees
C.140 degrees
D. 160 degrees

32. Factorize completely: (2x + 2y)(x-y) + (2x – 2y)(x + y)

A. 4(x – y)(x + y)
B. 4(x – y)
C. 2(x – y) (x + y)
D. 2(x – y)

33. The interior angles of a polygon are 3x, 2x, 4x, 3x and 6x. Find the size of the smallest angle of the polygon.

A. 80 degrees
B. 60 degrees
C. 40 degrees
D. 30 degrees

34. A box contains 2 white and 3 blue identical balls. If two balls are picked at random from the box, one after the other with replacement, what is the probability that they are of different colours?

A. 2/3
B. 3/5
C. 7/20
D. 12/25

35. Find the equation of a straight line passing through the points (1, -5) and having a gradient of ¾.

A. 3x + 4y – 23 = 0
B. 3x + 4y + 23 = 0
C. 3x – 4y + 23 = 0
D. 3x – 4y – 23 = 0

36. The foot of a ladder is 6 m from the base of an electric pole. The top of the ladder rests against the pole at a point 8 m above the ground. How long is the ladder?

A. 14 m
B. 12 m
C. 10 m
D. 7 m

37. If tan x = 3/4, 0<x<90, evaluate cos x/2sin x

A. 8/3
B. 3/2
C. 4/3
D. 2/3

38. From the top of a vertical cliff 20 m high, a boat at sea can be sighted 75 m away and on the same horizontal position as the foot of the cliff. Calculate, correct to the nearest degree, the angle of depression of the boat from the top of the cliff.

A. 56 degrees
B. 75 degrees
C. 16 degrees
D. 15 degrees

39. In the diagram, O is the centre of the circle of radius 18 cm. If angle ZXY = 70 degrees, calculate the length of arc ZY. (Take pi = 22/7)

A. 11 cm
B. 22 cm
C. 44 cm
D. 80 cm

In the diagram, RT is tangent to the circle at R, angle PQR = 70 degrees, angle QRT = 52 degrees, angle QSR = y and angle PRQ = x. Use the diagram to answer questions 40 and 41

40. Find the value of y.

A. 70 degrees
B. 60 degree
C. 52 degree
D. 18 degree

41. Calculate the value of x

A. 70 degrees
B. 58 degrees
C. 55 degrees
D. 48 degrees

42. Calculate the variance of 2, 4, 7, 8, 9

A. 7.2
B. 6.8
C. 3.5
D. 2.6

43. The fourth term of an Arithmetic Progression (A.P.) is 37 and the first term is -20. Find the common difference.

A. 63
B. 57
C. 19
D. 17

In the diagram, PQ is parallel to RS, angle QFG = 105 degrees and angle FEG = 50 degrees. Use the diagram to answer questions 44 and 45.

44. Find the value of m

A. 130 degrees
B. 105 degrees
C. 75 degrees
D. 55 degrees

45. Find the values of n

A. 40 degrees
B. 55 degrees
C. 75 degrees
D. 130 degrees

46. A box contains 5 red, 6 green and 7 yellow pencils of the same size. What is the probability of picking a green pencil at random?

A. 1/6
B. 1/4
C. 1/3
D. 1/2

47. The pie chart represents fruits on display in a grocery shop. If there are 60 oranges on display, how many apples are there?

A. 90
B. 80
C. 70
D. 40

The following are scores obtained by some students in a test.

8 18 10 14 18 11 13 14 17 15 8 16 13

Use this information to answer questions 48 to 50

48. Find the mode of the distribution

A. 18
B. 14
C. 13
D. 8

49. Find the median score.

A. 14.5
B. 14.0
C. 13.5
D. 13.0

50. How many students scored above the mean score?

A. 10
B. 9
C. 8
D. 7

Are the WAEC objective questions difficult? Let’s quickly move to the Solutions to Last year’s WAEC Mathematics Questions.

Solutions to WAEC Mathematics Questions.

1. A

The two zeros before 3 are not counted since they are not between whole numbers

2. A

0.064^(-1/3) = 5/2

3.  y+1/2 – 2y-1/3 = 4

Multiply through by 6

3y + 3 – 4y + 2 = 24

Collecting like terms

Implies:

y =-19

4. D

5. B

6. U = (1, 2, 3, 4, 5, 6, 7, 8, 9, 10)

T = (2, 3, 5, 7)

M = (1, 3, 5, 7, 5)

(T’ n M’) = the numbers in the union set U but not in T and M

(T’ n M’) = (4, 6, 8, 10)

7. Log9 base 3 – log 8 base 2 / log 9 base 3

Log3^2 base 3 – log2^3 base 2 / log 3^2

2log3 base 3 – 3log2 base 2 / 2log3 base 3

Log3 base 3 = 1

Log 2 base = 1

Reason: Log to its own base is 1

This implies:

2 -3 /2 = -1/2

8. Convert both sides to base ten

2xy^1 + 3Xy^0 = 1×2^3 + 1×2^2 + 1x 2^1 + 1×2^0

2y +3 = 8 + 4 + 2 + 2 + 1

2y + 3 = 15

2y = 15-3

Y = 12/2 = 6

9. 6, p, 14

First term a = 6, third term = 14

Number of terms of A.P = a + (n-1)d

T3 =14 = a + 2d

6 + 2d = 14

Common difference d = 14

P = second term

T2 = a + d = 6 + 4 = 10

10. 4 SQRT(7) – 15 SQRT(2) + 6 SQRT(2)

4 SRT(7) – 9 SRT(2)

11. m/n = 2/1

m = 2n

3(2n)^2 – 2n^2 / 2n^2 +2n^2

12n^2 – 2n^2 / 4n^2 + 2n^2 = 10n^2/6n^2

= 5/3

12. H = kp / y^2 where k = constant, H = 1, p = 8, y = 2

k = Hy^2 /p =  4×1/8 = ½

H = p/2y^2

13. Factorizing:

(4x^2 -6x)(-10x +15)

2x(2x – 3)-5(2x – 3)

2x-5 = 0 or 2x-3 = 0

X = 5/2 or x = 3/2

14. C

15. B

16. 15 percent profit = 115 = 6,900 naira

Let the percent  Bala sold the article at 6600 naira = x

115 = 6,900

X = 6600

Cross multiplying

6900x = 759000

X = 110 percent

The percentage profit if he had sold it at 6600 naira = 110 – 100

= 10 percent

17. 3p = 4q

9p = 8q – 12

p = 4q/3

8q – 12 -(36q/3)

24q – 36 – 36q

-12q = 36

q = -3

3p = -12

p = -4, pq = -3x-4 = 12

18. (0.25)^y = 32

(1/4)^y = 32

2^-2 = 2^5

-2y = 5

y = -5/2

19. C

20. (x-7)(x+2)/ (x+7)(x+2) = (x-7) / (x+7)

21. 3p – 1/p^2 -p

It will be undefined when the denominator p^2 – p = 0

therefore, p = 1 would make it zero

22. Given:

T.S.A = 165 cm^2

D = 7 cm

h = ?

pi = 22/7

T.S.A = 2pirh + 2pir^2

165 -2x(22/7)x3.5^2 = 2x(22/7) x3.5h

165 – 77 = 22h,

h = 88/22

h = 4.0 cm

Are you enjoying the Solutions to WAEC Mathematics Questions? Let’s continue.

23. 2^a = SQRT(64)

2^a = 8

2^a = 2^3

a = 3

but b/a = 3

therefore, b = 3a = 3×3 = 9

a^2 + b^2 = 3^2 + 9^2 = 90

24. Angle XYZ = 180 – (90+52)

180-142 = 38 degrees

From sin rule,

XZ/sin38 = 32/sin52

XZ = 25 cm

26. tita = 72

r = 3.5

pi = 22/7

arc length = 2pir(tita/360)

arc length = 2x( 22/7 )x3.5x(72/360) = 4.4 cm

27. 2lb = (a+b)h

2lb = ah + bh

2lb- bh = ah

b(2l-h) = ah

b = ah/2l-h

28. agent commission = 8 percent

percentage received by eric = 100 – 8 = 92

let the selling price be x

92x/100 = 117760

x = 11776000/92

x = 128000.00 dollars

29. arc length = 2pir(tita/360)

22 = 2×22/7x15xtita/360

tita = 55440/660

tita = 84 degrees

30. l = 15

width = x

if its sides are doubled,

l = 30

width = 2x

area = 30* 2x = 60x cm^2

31. A 32. A 33. B 34. D 35. D 36. C 37.D 38. D 39. C 40. C 41. B42. C 43. C 44. D 45. C46 A 47.A 48. C 49. C 50. A

These questions and solutions are WAEC practice questions to get you prepared for your 2023/2024 WAEC Mathematics Questions.

WAEC Maths Essay and Objective 2023.

Take note that this is not WAEC mathematics expo, rather, it’s the WAEC Mathematics Past questions and answers, and these ones are likely to be repeated questions and answers.

I’ll recommend that you read your books and ensure you study smart. Do not send money to anyone promising to give you the Waec Mathematics expo, questions and answers, they’re fake and their promises usually fail.

What you will see won’t be far from the ones above. I had taken quality time to bring down the solution to a layman’s understanding.

WAEC Mathematics Questions and Answers 2023.

These are the past Waec questions and answers on Mathematics that I’ll recommend that you read through.

a) 5x² – 9x + 1

b) 5x² – 11x + 1

c) 5x² – 9x – 1

d) 5x² – 11x – 1

2. Solve for x: 3(x + 4) – 2(x – 2) = 14.

a) x = 6

b) x = 8

c) x = 10

d) x = 12

3. If 5p + 4 = 34, what is the value of p?

a) p = 6

b) p = 8

c) p = 10

d) p = 12

4. The sum of the interior angles of a triangle is:

a) 90 degrees

b) 180 degrees

c) 270 degrees

d) 360 degrees

5. Simplify: √(16/25).

a) 4/5

b) 2/5

c) 4/25

d) 2/25

6. What is the slope of the line passing through the points (2, 5) and (4, 9)?

a) 1/2

b) 2/3

c) 3/2

d) 2/1

7. Solve for x: 2x – 3(x + 1) = 4 – (x – 1).

a) x = -1

b) x = 1

c) x = 2

d) x = 3

8. What is the value of log₂ 16?

a) 2

b) 3

c) 4

d) 5

9. If a car traveled 240 kilometers in 3 hours, what is its average speed in kilometers per hour?

a) 40 km/h

b) 60 km/h

c) 80 km/h

d) 120 km/h

10. Solve for x: 2(x + 3) – 3(x – 2) = 5x + 4.

a) x = 1/7

b) x = 3/7

c) x = 5/7

d) x = 7/5

11. If 3x + 2 = 14, what is the value of x?

a) x = 4

b) x = 6

c) x = 8

d) x = 10

12. Solve for x: 2(3x + 5) = 4(2x + 3).

a) x = -7

b) x = -5

c) x = -3

d) x = -1

13. What is the value of sin 60°?

a) √2/2

b) 1/2

c) √3/2

d) 1

14. Simplify the expression: 4(2x – 3) + 2(5x + 2).

a) 18x – 2

b) 18x – 6

c) 18x + 2

d) 18x + 6

15. If a square has a perimeter of 36 cm, what is the length of one of its sides?

a) 4 cm

b) 6 cm

c) 8 cm

d) 12 cm

16. Solve for x: 5x – 3 = 2x + 9.

a) x = 4

b) x = 6

c) x = 8

d) x = 12

17. Find the value of 2⁴ × 3³ ÷ 2².

a) 54

b) 72

c) 81

d) 108

18. The equation of a straight line is given as y = 2x + 3. What is the slope of this line?

a) 2

b) 3

c) -2

d) -3

19. A bag contains 5 red balls, 4 blue balls, and 3 green balls. What is the probability of picking a blue ball from the bag?

a) 1/3

b) 4/12

c) 4/11

d) 4/5

20. Solve for x: 2x² + 5x – 3 = 0.

a) x = -3/2 or x = 1/2

b) x = -3/2 or x = 1/3

c) x = -3 or x = 1/2

d) x = -3 or x = 1/3

If 2x + 3 = 7, what is the value of x?

a) x = 2

b) x = 3

c) x = 4

d) x = 5

21. Solve for x: 3(x – 2) + 2 = 4(x + 1).

a) x = -1

b) x = 0

c) x = 1

d) x = 2

22. What is the value of cos 45°?

a) √2/2

b) 1/2

c) √3/2

d) 1

23. Simplify the expression: 2(x – 3) + 3(2x + 5).

a) 7x – 1

b) 7x – 9

c) 7x + 1

d) 7x + 9

24. If the area of a rectangle is 24 square units and its length is 6 units, what is its width?

a) 2 units

b) 3 units

c) 4 units

d) 8 units

25. Solve for x: 4x + 7 = 3x – 5.

a) x = -12

b) x = -7

c) x = -2

d) x = 12

26. Find the value of 5! (5 factorial).

a) 20

b) 60

c) 120

d) 720

27. The equation of a straight line is given as y = -3x + 2. What is the y-intercept of this line?

a) -3

b) -2

c) 2

d) 3

28. In a deck of cards, what is the probability of drawing a spade?

a) 1/13

b) 1/26

c) 1/52

d) 1/4

29. Solve for x: 3x² – 5x + 2 = 0.

a) x = 1/3 or x = 2

b) x = 1/3 or x = 1/2

c) x = 1 or x = 2

d) x = 1 or x = 1/2

Sample Waec Mathematics Theory 2023 Questions and Answers

1. Calculate the area of a rectangle with a length of 6 cm and a width of 4 cm.

2. If a car travels at a speed of 60 km/h for 3 hours, how far does it travel?

3. Solve the equation: 2x + 5 = 17.

4. Calculate the circumference of a circle with a diameter of 10 cm. Use π (pi) as 3.14.

5. A store is offering a 25% discount on an item that costs \$80. How much will the item cost after the discount?

6. Solve the equation: 3(x – 2) + 4 = 10.

7. If the total cost of 5 pens and 3 notebooks is \$18, and each pen costs \$2 and each notebook costs \$4, calculate the cost of one pen.

8. Calculate the volume of a cube with an edge length of 5 cm.

9. A bag contains 12 red marbles and 8 blue marbles. What is the probability of randomly selecting a red marble from the bag?

10. Calculate the simple interest earned on a \$1000 investment with an interest rate of 5% per year over a period of 2 years.

Waec Mathematics Paper 2 – Theory 2023.

1. (a) Solve: 7x + 4 < (4x + 3).
(b) Salem, Sunday, and Shaka all shared the total sum of One thousand, one hundred Naira (N1,100.00). For every N2.00 that Salem gets, Sunday gets fifty kobo and for every N 4.00 Sunday gets, Shaka gets N 2.00. Find Shaka’s share.

2. (a) The angle of depression of a boat from the mid-point of a vertical cliff is 35°. If the boat is 120 m from the foot of the cliff, calculate the height of the cliff.

(b) Towns P and Q are x km apart. Two motorists set out at the same time from P to Q at steady speeds of 60 km/h and 80 km/h. The faster motorist got to Q 30 minutes earlier than the other. Find the value of x.

3. (a) A boy 1.2 m tall, stands 6 m away from the foot of a vertical lamp pole 4.2 m long. If the lamp is at the tip of the pole, represent this information in a diagram.

(b) Calculate the:

(i) length of the shadow of the boy cast by the lamp;
(ii) angle of elevation of the lamp from the boy, correct to the nearest degree.

4. (a) The present ages of a father and his son are in the ratio 10 : 3. If the son is 15 years old now, in how many years will the ratio of their ages be 2 : 1?
b) The arithmetic mean of x, y and z is 6 while that of x, y, z, t, u, v and w is 9. Calculate the arithmetic mean of t, u, v, and w.

5. point H is 20m away from the foot of a tower on the same horizontal ground. From point H, the angle of elevation of point (P) on the tower and the top (T) of the tower are 30o and 50o respectively. Calculate, and correct 3 significant figures:
(a) /PT/;
(b) The distance between H and the top of the tower;
(c) The position of H if the angle of depression of H from the top of the tower is to be 40°.

DISCLAIMER! I’ve said this, and I’ll repeat it here again, these are not the real WAEC Mathematics questions for 2023. However, the above question has been repeated over and over.

We’ve discovered that over the years, candidates who read past questions and answers have better understanding, and can easily grasp the nature of their examinations. I’ll highly recommend that you take note of every question provided on this page.