2023 Waec Gce Mathematics Questions and answer: The West African Examinations Council GCE is an examination body in Nigeria that conducts the Senior Secondary Certificate Examination and the General Certificate in Education in June/July and December/January respectively.

### 2023 WAEC GCE MATHEMATICS SOLUTIONS

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**Gce Mathematics Past QuestionsGce Mathematics**

** Past Questions And Answer Pdf**

**Gce Maths Past Questions Pdf**

**2023 Waec Gce Mathematics Questions and answer**

**Gce Maths Past Paper**

**Gce Maths Past Questions 2018**

**Waec Gce Mathematics Past Questions**

**Neco Gce Mathematics Past Questions**

**Gce Further Mathematics Past Questions**

**Neco Gce Mathematics Past Questions**

**2020 Waec Gce Mathematics Questions and answers.**

**Neco Gce Mathematics Past Questions and Answers**

The Neco maths exam takes **2hours 45minute for all paper I (objectives) and paper II (essay)**. In this post, we will be posting out the 2023 Waec Gce mathematics questions for all candidates that will participate in the 2023 Waec examination.

**Section I [Objective]
****Answer all questions in Part I.**

**Write your answers on the answer booklet provided.**

The following Waec Gce Maths questions 2023 are questions to expect in the 2023 Waec Gce examination. Note that sometimes the objective might come first before theory vise-versa

1. Given that y varies inversely as the square of x. if x=3 when y=100, find the equation connecting x and y

(a) yx2=300

(b). yx2=900

(c) yx2=100x9100x9

(d) y = 900×2

2. Find the value of x for which 32four = 22 base x

(a). three

(b) five

(c) Six

(d) seven

3. Simplify: 2 whole number1/4 x 3 whole number1/2 ÷4 whole number3/8

(a). 5/9

(b) 1 whole number1/5

(c) 1 whole number 1/4

(d) 1 whole number 4/5

4. There are 250 boys and 150 girls in a school. If 60% of the boys and 40% of the girls play football. What percentage of the school play football?

(a). 40.0%

(b) 42.2%

(c) 50.0%

(d) 52.5%

5. If log10 (6 x−4) x-4) – log10 2=1, solve for xx

(a). 2

(b) 3

(c) 4

(d) 5

6. If F = 9C/5+ 32, find C when F = 98.6

(a) 30

(b) 37

(c) 39

(d) 41

7. If y ÷ 2 x = 4 and y−3x=−1, find the value of (x+y)

(a) 3

(b) 2

(c) 1

(d) -1

8. If x:y:z=2:3:4, Evaluate 9x+3y/6z−2y

(a)1 whole number1/2

(b) 2

(c) 2 whole number1/2

(d) 3

9. Simplify: 2−18m^2/1+3m

(a) 2(1+3m)

(b) 2(2+3m2)

(c) 2(1-3m)

(d) 2(1-3m2)

10. A curve is such that when y = 0, x = -2 or x=3. Find the equation for the curve.

(a). y= x^2-5 x -6

(b). y= x^2+5x−6

(c) y= x2+x−6

(d) y=x^2- x-6

11. The volume of a cylindrical tank, 10m high is 385m3. Find the diameter of the tank. Take π=22/7

(a). 14 m

(b). 10 m

(c). 7 m

(d). 5 m

12. The surface of a sphere is 7927cm27927cm2. Find correct to the nearest whole number, its volume. Take [π=22/7]

(a)113 cm^3

(b) 131cm^3

(c) 311cm^3

(d) 414cm^3

13. A piece of thread of length 21.4cm is used to form a sector of a circle of radius 4.2cm on a piece of cloth. Calculate, correct to the nearest degree, the angle of the sector. Take π=22/7

(a) 1700

(b) 1770

(c) 1820

(d) 1920

14. In the diagram which of the following ratios is equal to ∣PN∣ / ∣PQ∣

(a) ∣PN∣/ ∣PR∣

(b). ∣PM∣/∣PQ∣

(c)∣PM∣/∣PR∣

(d) ∣PR/ ∣PQ∣

15. Simplify 361/2 x 64-1/3 x 50

A. o

B. 1\24

C. 2/3

D. 11/3

E. 71/2

16. Find the quadratic equation whose roots are x = -2 or x = 7

A. x2 + 2x – 7 = 0

B. x2 – 2x + 7 = 0

C. x2 + 5 +14 = 0

D. x2 – 5x – 14 = 0

E. x2 + 5x – 14 = 0

17. A sales girl gave a change of N1.15 to a customer instead of N1.25. Calculate her percentage error

A. 10%

B. 7%

C. 8.0%

D. 2.4%

E. 10%

18. What is the probability of having an odd number in a single toss of a fair die?

A. 1/6

B. 1/3

C. 1/2

D. 2/3

E. 5/6

19. If the total surface area of a solid hemisphere is equal to its volume, find the radius

A. 3.0cm

B. 4.5cm

C. 5.0cm

D. 9.0cm

20. If 23x + 101x = 130x, find the value of x

A. 7

B. 6

C. 5

D. 4

21. Simplify: (34−2334−23) x 11515

A. 160160

B. 572572

C. 110110

D. 1710710

22. Simplify:(103√5√−15‾‾‾√1035−15)2

A. 75.00

B. 15.00

C. 8.66

D. 3.87

23. The distance, d, through which a stone falls from rest varies directly as the square of the time, t, taken. If the stone falls 45cm in 3 seconds, how far will it fall in 6 seconds?

A. 90cm

B. 135cm

C. 180cm

D. 225cm

24. Which of following is a valid conclusion from the premise. “Nigeria footballers are good footballers”?

A. Joseph plays football in Nigeria therefore he is a good footballer

B. Joseph is a good footballer therefore he is a Nigerian footballer

C. Joseph is a Nigerian footballer therefore he is a good footballer

D. Joseph plays good football therefore he is a Nigerian footballer

25. On a map, 1cm represent 5km. Find the area on the map that represents 100km2.

A. 2cm2

B. 4cm2

C. 8cm2

D. 8cm2

26. Simplify; 3n−1×27n+181n3n−1×27n+181n

A. 32n

B. 9

C. 3n

D. 3n + 1

27. What sum of money will amount to D10,400 in 5 years at 6% simple interest?

A. D8,000.00

B. D10,000.00

C. D12,000.00

D. D16,000.00

28. Make s the subject of the relation: P = S + sm2nrsm2nr

A. s = mrpnr+m2mrpnr+m2

B. s = nr+m2mrpnr+m2mrp

C. s = nrpmr+m2nrpmr+m2

D. s = nrpnr+m2nrpnr+m2

29. Factorize; (2x + 3y)2 – (x – 4y)2

A. (3x – y)(x + 7y)

B. (3x + y)(2x – 7y)

C. (3x + y)(x – 7y)

D. (3x – y)(2x + 7y)

30. The curve surface area of a cylinder, 5cm high is 110cm 2. Find the radius of its base. [Take π=227π=227]
A. 2.6cm

B. 3.5cm

C. 3.6cm

D. 7.0cm

31. The volume of a pyramid with height 15cm is 90cm3. If its base is a rectangle with dimension xcm by 6cm, find the value of x

A. 3

B. 5

C. 6

D. 8

32. Calculate the gradient of the line PQ

A. 3535

B. 2323

C. 3232

D. 5353

33. A straight line passes through the point P(1,2) and Q

(5,8). Calculate the length PQ

A. 411‾‾‾√411

B. 410‾‾‾√410

C. 217‾‾‾√217

D. 213‾‾‾√213

34. If cos θθ = x and sin 60o = x + 0.5 0o < θθ < 90o, find, correct to the nearest degree, the value of θθ

A. 32o

B. 40o

C. 60o

D. 69o

35. Evaluate: (64^1/2+ 125^1/3)64^1/2+ 125^1/3

(a). 121

(b). 144

(c) 169

(d). 196

36. The common ratio of a Geometric Progression is 2. If the 5th term is greater than the 1st term by 45, find

A. 3

B. 8

C. 45

D. 48

E. 90

37. In a class of 80 students, every student has to offer Economics or Geography or both. If 65 students offered Economics and 50 offered Geography, how many students offered both subjects.

A. 15

B. 30

C. 35

D. 45

E. 50

38. Some red balls were put in a basket containing 12 white balls and 16 blue balls. If the probability of picking a red ball from the basket is 3/7, how many red balls were introduced?

A. 13

B.20

C. 12

D. 21

39. Convert 1231_{4} to a number in base 6.

A. 105_{6
}B. 301_{6
}C. 103_{6
}D. 501_{6}

40. Find the slope of the curve y = 3x^{3} + 5x^{2} – 3 at (-1, 5).

A. 1

B. -1

C. 19

D. -19

41. Find the area of the region bounded by y = x^{2} + x – 2 and x – axis.

A. 9/2

B. -39/6

C. 8/3

D. 16/3

42. The minimum value of y = x^{2} – 4x – 5 is ______

A. 2

B. -2

C.13

D. -13

43. 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

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**Section II [Essay]
****Answer any FIVE questions in Part II.**

**Write your answers on the answer booklet provided.**

Question 1.

In the diagram, L.PTQ = L.PSR = 900, /PQ/ = 10 ern, /PS/ = 14.4 cm and /TQ/ = 6 cm.

Calculate the area of quadrilateral QRST.

(b) Two opposite sides of a square are each decreased by 10% while the other two are each increased by 15% to form a rectangle. Find the ratio of the area of the rectangle to that of the square.

Math GCE Observation.

We advise that students should always remember to apply the concept of similar triangles correctly.

Furthermore, students should try and recognize the quadrilateral as a trapezium, this will help in finding its area.

Part (b) Candidates were expected to show that:

/PT/ = …./102 – 62 = 8 cm. m: =!J2L i.e ~ = 14.4.Hence, /SR/ = 10.8 cm.

/TO/ /SR/ 6 /SR/

Area of quadrilateral QRST = Yz (6 + 10.8) x 6.4 = 53.76 cm2. Don’t subtract the area of triangle PQT from triangle PRS.

This was also in order. In part (b) if the side of the square was y, then new breadth = 90 x y = 0.9y.

100

New length = 115 x Y = 1.15y. New area = 1.15y x 0.9y = 1.035/.

100

Hence, ratio = 1.035y² : y² = 1.035 : 1 or 207:200 .

In a class of 40 students, 18 passed Mathematics, 19 passed Accounts, 16 passed Economics, 5 passed Mathematics and Accounts only, 6 passed Mathematics only, 9 passed Accounts only, 2 Accounts and Economics only. If each student offered at least one of the subjects,

(a) How many students failed in all the subjects?

(b) Find the percentage number who failed in at least one of Economics and Mathematics.

(c) Calculate the probability that a student selected at random failed in Accounts.

Question 2.

(a) Copy and complete the table of values for the relation V = -X² + X + 2 for -3 ≤ x ≥ 3.

(b) Using scales of 2 cm to 1 unit on the x-axis and 2 cm to 2 units on the v-axis, draw a graph of the relation

y = -X² + X + 2.

(c) From the graph, find the:

(i)Minimum value of y;

(ii)Roots of the equation X² – x -2 = 0;

(iii)Gradient of the curve at x = -0.5.

3. (a) P varies directly as Q and inversely as the square of R. If P = 1 when Q = 8 and R = 2, find the value of Q when P = 3 and R = 5.

(b) An aeroplane flies from town A(20oN, 60oE) to town B(20oN, 20oE).

(i) If the journey takes 6 hours, calculate, correct to 3 significant figures, the average speed of the aeroplane.

(ii) If it then flies due north from town B to town C, 420 km away, calculate, correct to the nearest degree, the latitude of town C.

[Take radius of the earth = 6400 km and π = 3.142]

4. Using ruler and a pair of compasses only,

(a) construct a rhombus PQRS of side 7 cm and ÐPQR = 60o;

(b) locate point X such that X lies on the locus of points equidistant from PQ and QR and also equidistant from Q and R;

(c) measure /XR/.

5. (a) In a class of 50 students, 30 offered History, 15 offered History and Geography while 3 did not offer any of the two subjects.

(i) Represent the information on a Venn diagram.

(ii) Find the number of candidates that offered: History only; Geography only.

(b) A trader sold an article at a discount of 8% for N 828.00. If the article was initially marked to gain 25%, find the

(i) cost price of the article;

(ii) discount allowed.

6. The area of a rectangular football field is 7200m2 while its perimeter is 360m. calculate the:

(a) dimensions of the field;

(b) cost of clearing the field at N6.50 per square meter, leaving a margin of 2m wide along the longer sides;

(c) percentage of the part not cleared.

7. Two fair dice are thrown.

M is the event described by “the sum of the scores is 10” and

N is the event described by “the difference between the scores is 3”.

(a) Write out the elements of M and N.

(b) Find the probability of M or N.

(c) Are M and N mutually exclusive? Give reasons.

8. (a) The total surface area of two spheres are in the ratio 9 : 49. If the radius of the smaller sphere is 12 cm, find, correct to the nearest cm3, the volume of the bigger sphere.

(b) A cyclist starts from a point X and rides 3 km due West to a point Y. At Y, he changes direction and rides 5 km North-West to a point Z.

(i) How far is he from the starting point, correct to the nearest km?

(ii) Find the bearing of Z from X, to the nearest degree.

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