**WAEC Mathematics Maths Questions And Answers2021**

1. Which of these numbers is not less than -2?

-1

-3

-4

-5

-6

Solution Solving: -2 is greater than -2, -3, -4, -5, -6 and so on. But -1 is greater than -2.

The Correct Answer is A): Because it is greater than -2.

2. -6 is greater than -2 but less than -7? True or false

True

Both

False

None of the above

Solving for the solution: -6 is greater than any number from -7 to the negative infinity but less than any number from -5 to the positive infinity.

The Correct Answer is C): Because -6 is not greater than -2 and it is not less than -7.

3. Add 26b + 12a + 16a – 4b

22b + 28a

-22b + 28a

22b – 28a

-22b – 28a

Solution Solving for Questions 3: Firstly, you have to Collect like terms. Therefore, we have;

26b – 4b + 12a + 16a.

Next, we have 26b – 4b = 22b

And 12a + 16a = 28a

Therefore, we have 22b + 28a

The Correct Answer is A): 22b + 28a

4. Multiply this equation: (x – 6)(2x + 7)?

2×2 + 5x – 42

2×2 – 5x – 42

2×2 – 5x + 42

2×2 + 5x + 42

-2×2 + 5x – 42

Solving for question 4 solution: Here, we start by removing the bracket

Thus; 2×2 + 7x – 12x – 42

Hence, 2×2 – 5x – 42

The Correct Answer is B): 2×2 – 5x – 42

5. Factorise the following: 5×2 – 15x – 20?

5(x+4)(x+1)

-2(x-4)(x+5)

-5(x+4)(x-1)

5(x-4)(x+1)

Solution Solving to question 5: Firs find the L.C.M of 5, 15 and 20 = 5(x2 – 3x – 4).

= 5(x2 – 4x + x – 4)

= 5{x(x – 4) +1(x – 4)}.

= 5(x-4)(x+1).

The Correct Answer is D): 5(x-4)(x+1)

*Answer any … questions.*

*Write your answers on the answer booklet provided.*

1. A sector of a circle with a radius of 21 cm has an area of 280 cm².

(a) Calculate, correct to 1 decimal place, the perimeter of the sector.

(b) If the sector is bent such that its straight edges coincide to form a cone, calculate, correct to the nearest degree, the vertical angle of the cone. [Take π = 22/7 ]

2. (a) Solve the equation:

(b)

In the diagram, < STQ = *m*, < TUQ = 800, < UPQ = *r*, < PQU = *n* and < RQT = 880. Find the value of (*m* + *n*).

3. A = {2, 4, 6, 8}, B = {2, 3, 7, 9} and C = {x: 3 < x < 9} are subsets of the universal-set

U = {2, 3, 4, 5, 6, 7, 8, 9}.

Find

(a) A n(B’nC’);

(b) (AuB) n(BuC).

4. (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.

5.

6. 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.

7. (a) Using completing the square method, solve, correct to 2 decimal places, the equation 3y2 – 5y + 2 = 0

(b) Given that M=

8. (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 airplane.

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

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

7. Using a 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/.

8. (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) the cost price of the article;

(ii) discount allowed.

9. 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.

10. 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.

11. (a) The total surface area of two spheres is in the ratio of 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.

12.

13. (a) If, find *x* in terms of *y*.

(b) The table shows the distribution of timber production in five Nigerian states in a certain year.

Community | Timber Production (tonnes) |

Cross River Delta Edo Ogun Ondo |
600 900 1800 1500 2400 |

(i) Draw a pie chart to represent the information.

(ii) What percentage of timber produced that year was from Delta?

(iii) If a tonne of timber is sold at N560.00, how much more revenue would Edo state receive than Cross River?

Objective

*Answer *ALL* questions in this section.**Shade your answer in the answer booklet provided.*

1. In a school, 180 students offer mathematics or physics or both. If 125 offer mathematics and 105 offer physics. How many students offer mathematics only?

A.75 B. 80 C. 55 D. 125.

2. Find the value of x for which 3(2^{4x + 3}) = 96

A. 2 B. -2 C. ½ D. -1/2

3. The cost of renovating a 5m square room is N500. What is the cost of renovating a 10m square room?

A. N1,000 B. N2,500 C. 2,000 D. N10,000

4. Find the rate of change of the total surface area S of a sphere with respect to its radius r when r = 2

A. 8 B. 16 C. 10 D. 14

5. Differentiate (cosӨ + sinӨ)^{2} with respect to Ө.

A. 2cos2Ө B. 2sin2Ө C. -2cos2Ө D. -2sin2Ө

6. A binary operation * on the set of rational numbers is defined as x * y = 2x + [x^{3} – y^{3}/x + y]. find -1*2

A. 11 B. -11 C. 8 D. -8

7. A polynomial in x whose zeroes are 2, 1 and -3 is ______

A. x^{3} – 7x + 6

B. x^{3} + 7x – 6

C. x^{3} – 7x – 6

D. x^{3} + 7x + 6

8. Find the range of values of x for which 7x – 3 > 3x + 4

A. x < 7/4

B. x > 7/4

C. 7x < 4

D. -4x < 7

9. 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

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

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

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

A. 1 B. -1 C. 19 D. -19

12. 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

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

A. 2 B. -2 C.13 D. -13

14. 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

15. 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

16. 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)

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

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

18. Simplify: log 6 – 3log 3 + 2/3log 27.

A. 3log 2 B. Log 2 C. Log 3 D. 2log 3

19. Bala sold an article for 6,900.00 nairas and made a profit of 15 percent. Calculate his percentage profit if he had sold for 6600.00.

A. 5 percent B. 10 percent C. 12 percent D. 13 percent

20. If 3P = 4Q and 9P = 8Q-12, find the value of PQ.

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

21. 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.

22. A husband contributes 7% of his income into a fund and his wife contributes 4% of her income. If the husband earns N5,500 per annum (p.a) and his wife earns N4,000 p.a, find the sum of their contribution

to the fund.

A. N1,045 B. N605 C. N545 D. N490.

23. If the children share N10.50K among themselves in the ratio 6:7:8, How much is the largest share?

A. N3.00 B. N3.50 C. N4.00 D. N4.50.

24. A trader makes a loss of 15% when selling an article. Find the ratio, selling price: cost price.

A. 3:20 B. 3:17 C. 17:20 D. 20:23.

25. The ages of three men are in the ratio 3:4:5. If the difference between the ages of the oldest and youngest is 18 years, find the sum of the ages of the three men.

A. 45 years B. 72 years C. 108 years D. 216 years.

26. A bicycle wheel of a radius of 42cm is rolled over a distance of 66m. How many revolutions does it make?

[Take π=22/7]

A. 2.5 B. 5 C. 25 D. 50.

27. If 2x : (x+1) =3:2, what is the value of x?

A. ½ B. 1 C. 1½ D. 3.

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

A. 1/6 B. 1/3 C. ½ C. 2/3.

1. Which of these numbers is not less than -2?

-1,

-3,

-4,

-5.

-6

Solution Solving: -2 is greater than -2, -3, -4, -5, -6 and so on. But -1 is greater than -2.

The Correct Answer is A): Because it is greater than -2.

2. -6 is greater than -2 but less than -7? True or false

True

Both

False

None of the above

Solving for the solution: -6 is greater than any number from -7 to the negative infinity but less than any number from -5 to the positive infinity.

The Correct Answer is C): Because -6 is not greater than -2 and it is not less than -7.

3. Add 26b + 12a + 16a – 4b

22b + 28a

-22b + 28a

22b – 28a

-22b – 28a

Solution Solving for Questions 3: Firstly, you have to Collect like terms. Therefore, we have;

26b – 4b + 12a + 16a.

Next, we have 26b – 4b = 22b

And 12a + 16a = 28a

Therefore, we have 22b + 28a

The Correct Answer is A): 22b + 28a

4. Multiply this equation: (x – 6)(2x + 7)?

2×2 + 5x – 42

2×2 – 5x – 42

2×2 – 5x + 42

2×2 + 5x + 42

-2×2 + 5x – 42

Solving for question 4 solution: Here, we start by removing the bracket

Thus; 2×2 + 7x – 12x – 42

Hence, 2×2 – 5x – 42

The Correct Answer is B): 2×2 – 5x – 42

5. Factorise the following: 5×2 – 15x – 20?

5(x+4)(x+1).

-2(x-4)(x+5)

-5(x+4)(x-1)

5(x-4)(x+1)

Solution Solving to question 5: Firs find the L.C.M of 5, 15 and 20 = 5(x2 – 3x – 4).

= 5(x2 – 4x + x – 4).

= 5{x(x – 4) +1(x – 4)}.

= 5(x-4)(x+1).

The Correct Answer is D): 5(x-4)(x+1)

6. In a school, 180 students offer mathematics or physics or both. If 125 offer mathematics and 105 offer physics. How many students offer mathematics only?

A.75 B. 80 C. 55 D. 125.

7. Find the value of x for which 3(24x + 3) = 96

A. 2 B. -2 C. ½ D. -1/2

8. The cost of renovating a 5m square room is N500. What is the cost of renovating a 10m square room?

A. N1,000 B. N2,500 C. 2,000 D. N10,000

9. Find the rate of change of the total surface area S of a sphere with respect to its radius r when r = 2

A. 8 B. 16 C. 10 D. 14

10. Differentiate (cosӨ + sinӨ)2 with respect to Ө.

A. 2cos2Ө B. 2sin2Ө C. -2cos2Ө D. -2sin2Ө

11. A binary operation * on the set of rational numbers is defined as x * y = 2x + [x3 – y3/x + y]. find -1*2

A. 11 B. -11 C. 8 D. -8

12. A polynomial in x whose zeroes are 2, 1 and -3 is ______

A. x3 – 7x + 6

B. x3 + 7x – 6

C. x3 – 7x – 6

D. x3 + 7x + 6

13. Find the range of values of x for which 7x – 3 > 3x + 4

A. x < 7/4

B. x > 7/4

C. 7x < 4

D. -4x < 7

14. 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

15. Convert 12314 to a number in base 6.

A. 1056

B. 3016

C. 1036

D. 5016

16. Find the slope of the curve y = 3×3 + 5×2 – 3 at (-1, 5).

A. 1 B. -1 C. 19 D. -19

17. Find the area of the region bounded by y = x2 + x – 2 and x-axis

A. 9/2 B. -39/6 C. 8/3 D. 16/3

18. The minimum value of y = x2 – 4x – 5 is ______

A. 2 B. -2 C.13 D. -13

Waec General Mathematics Theory and Answer Paper 2, WASSCE

Copy and complete the table of values for the equation y = 2×2 – 7x – 9 for -3 ≤ x ≤ 6.

X -3 – 2 -1 0 1 2 3 4 5 6

Y 13 -9 -14 -12 6

Using scales of 2 cm to 1 unit on the x-axis and 2 cm to 4 units on the y – axis, draw the graph of y = 2×2 – 7x – 9 for -3 ≤ x ≤ 6.

Use the graph to estimate the:

roots of the equation 2×2 – 7x = 26;

(ii) coordinates of the minimum point of y;

(iii) range of values for which 2×2 – 7x < 9.

Solution to Question 1

The Chief Examiner reported that the majority of the Candidates’ who attempted this question got right the complete table of values for which y = 2×2 – 7x – 9. However, many failed to plot the points on the graph correctly on the graph thereby losing marks. Also, they could not read up values from the graph to answer subsequent questions.

In part (a), the Candidates were expected to complete the table as follows:

X -3 – 2 -1 0 1 2 3 4 5 6

Y 30 13 0 -9 -14 -15 -12 -5 6 21

In part (b), Candidates would then use this table and the scale provided to draw the graph of the relation y = 2×2 – 7x – 9 and use this graph to answer the questions that followed.

In part (c), from the graph, the roots of the equation 2×2 – 7x = 26 were obtained by drawing a line through y = 17 to meet the curve y = 2×2 – 7x – 9. The required roots are – 2.2 ± 0.1 and 5.8 ± 0.1. The coordinates of the minimum point of y is 1.8 ± 0.1, -15 ± 0.4. The ranges -10.1<x<4.5

Question 2

Marks 1 2 3 4 5

Number of students m + 2 m – 1 2m – 3 m + 5 3m – 4

The table shows the distribution of marks scored by some students in a test.

If the mean mark is, find the value of m.

Find the:

(i) inter-quartile range;

(ii) probability of selecting a student who scored at least 4 marks in the test.

The solution to Question 2

x 1 2 3 4 5 Total

f m+2 m-1 2m-3 m+5 3m-4 8m-1

fx m+2 2m-2 6m-9 4m+20 15m-20 28m-9

From the table, and, so that and solving yields m = 3.

In part (b) (i), since m has been gotten to be 3, the table then becomes:

x 1 2 3 4 5

f 5 2 3 8 5

Cf 5 7 10 18 23

Therefore, interquartile range = 4 – 2 = 2.

Finally, in part (b) (ii), the probability of selecting a student who scored at least 4 marks is whereas most Candidates’ made use of at most 4 marks to obtain.

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