# Mathematics 2021 Past Questions | WAEC

Study the following Mathematics past questions and answers for JAMB, WAEC NECO and Post-JAMB. Get prepared with official past questions and answers for upcoming examinations.

*k*sides is (3k – 10) right angles. Find the size of the exterior

- A. 60\(^o\)
- B. 40\(^o\)
- C. 90\(^o\)
- D. 120\(^o\)

**Correct Option: Answer is A**

In a polygon with n sides, the sum of the angles =

(n – 2)180, where n = the number of sides.

n = k.

So, we have:

(3k – 10)90 = (k – 2)180

270k – 900 = 180k – 360

Simplifying:

90k = 540

k = 6. So, we have a regular hexagon.

Now, each exterior angle = 360/n

We have: 360/6 = 60

**17. **Make U the subject of the relation:

x = \(\frac{2U-3}{3U+2}\)

- A. \(\frac{2x+3}{3x-2}\)
- B. \(\frac{2x-3}{3x-2}\)
- C. \(\frac{2x+3}{2-3x}\)
- D. \(\frac{2x+3}{3x+2}\)

**Correct Option: Answer is A**

x = \(\frac{2U-3}{3U+2}\) =

2U-3= 3Ux + 2x

= 3Ux + 2x =2U-3; 3Ux-2U=-3-2x

= -\(\frac{2x+3}{3x-2}\)

**18. **A trader paid import duty of 38 kobo in the naira on the cost of an engine If a total of N22,800.00 was paid as import duty, calculate the cost of the engine

- A. N60,000.00
- B. N120,000.00
- C. N24,000.00
- D.N18,000.00

**Correct Option: Answer is A**

Let the cost of the engine = X

So, X x N0.38 =22,800

0.38X =22800

X=22800/0.38; X =60,000

**19. **The height of an equilateral triangle is 10\(\sqrt{3}\). Calculate its perimeter.

- A. 20cm
- B. 60cm
- C. 40cm
- D. 30cm

**Correct Option: Answer is B**

equilateral triangle angles are the same as 60

when height is 10√3

10√3 x

so tan60=10√3/(x/2)

√3 = 10√3/(x/2)

x=20

so area is = 1/2 (base) (hight)

= 1/2( 20)(10√3)

= 100√3

perimeter is 20+20+2=60

**20. **In triangle LMN, |LM|=6cm, angle LMN = 90^{o }, angle LNM =x and sinx=3/5. Find the area of triangle LMN.

**A.**60cm^{2}**B.**48cm^{2}**C.**24cm^{2}**D.**30cm^{2}

**Correct Option: Answer is **

**21. **Consider the statements:

P: All students offering Lieutenant (L) also offer History (H);

Q: students offering History (H) do not offer Geography (G). which of the venn diagrams correctly illustrate the two statements?

**Correct Option: Answer is D**

**22. **Find the quadratic equation whose roots are -2q and 5q.

**A.**x^{2 }+3qx -10q^{2 }=0**B.**x^{2 }+3qx +10q^{2 }=0**C.**x^{2 }-3qx +10q^{2 }=0**D.**x^{2 }-3qx -10q^{2 }=0

**Correct Option: Answer is D**

Roots are -2q and 5q

So, (x+2q)(x-5q)=0

x^{2 }-5qx +2qx -10q^{2 }=0

x^{2 }-3qx -10q^{2 }=0

**23. **if tan θ=3/4, 180^{o}<θ<270^{o }, find the value of cos θ.

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

**Correct Option: Answer is C**

**24. **If \(\frac{2}{x-3}\) – \(\frac{3}{x-2}\) = \(\frac{P}{x-3}\)\({x-2}\), find P

**A.**(5-x)**B.**(x+5)**C.**(13-x)**D.**-(5x-13)

**Correct Option: Answer is A**

**25. **The diagonals of a rhombus are 12 cm and 5 cm, calculate its perimeter.

**A.**26cm**B.**24cm**C.**17cm**D.**34cm

**Correct Option: Answer is A**

Perimeter = 2 +

=2 + = 2 x 13 =26

**26.**

In the diagram, triangle XYZ is produced to T. if |XY|=|ZY| and angle XYT = 40^{o }, find angle XZT

**A.**110^{o}**B.**130^{o}**C.**120^{o}**D.**140^{o}

**Correct Option: Answer is A**

**27. **A solid brass cube is melted and recast as a solid cone of height *h* and base radius If the height of the cube is h. find *r* in terms of *h*

- A. r =h
**B. r =**\(\frac{\sqrt{3h}}{π}\)**C.**r = πh**D.****r =**h\(\frac{\sqrt{3}}{π}\)

**28. **Which of the following is not an exterior angle of n regular polygon?

**A.**66^{o}**B.**72^{o}**C.**24^{o}**D.**^{15o}

**Correct Option: Answer is A**

The size of an exterior angle = 360/n

From the options, all options can perfectly divide 360°, except 66°.

**29. **From a point T a man moves 12 *km *due West and then moves 12 *km* due South to another point Q. Calculate the bearing of T from Q.

**A.**225^{o}**B.**315^{o}**C.**045^{o}**D.**135^{o}

**Correct Option: Answer is D**

**30. **In the diagram, O is the centre of the circle PQRS, angle PQR=72^{o }and OR//PS, find angle OPS.

**A.**18\(^o\)**B.**108\(^o\)**C.**54\(^o\)**D.**36\(^o\)

**Correct Option: Answer is A**

### MATHEMATICS PAST QUESTIONS 2020 THEORY

- (a) If A = {multiples of 2}, B = {multiples of 3} and C = {factors of 6} are subsets of μ= {x:1 ≤x 5 ≤ 10} find A ∩ B ∩ C

(b) Tickets for a movie premiere cost $18.00 each while the bulk purchase price for 5 tickets is $80.00. If 4 gentlemen decide to get a fifth person to join them so that they can share the bulk purchase price equally, how much would each person save?

**Solution & Explanation:**

μ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

A = {2, 4, 6, 8, 10}

C = {1, 2, 3, 6}

A` ={1, 3, 5, 7, 9}

B` = {1, 2, 4, 5, 7, 8, 10}

C` = {4, 5, 7, 8, 9, 10}

a` ∩ B` C` = {} or ∅

1(b) bulk cost $80

1 will cost $80/5 = $16

for 5 gentlemen each cost $18.50

total cost = 18.50 x 5

= $92.50

5 cost for $16 each = 5 x $16

= $80 – 12.00

each will save $12.50/5

= $2.50

52