2022

Age 3 4 5 6 7 8 9 10
No. of children 2 6 5 4 6 9 8 5
The table shows the distribution of ages of a number of children in a school. If the mean of the distribution is 7, find the;
(a) value of x, (b) standard deviation of their ages.
Solution & Explanation
Mean = (3×2 +4×6 + 5×5 + 6x + 7×6 + 8×9 + 9×8 + 10×5) ÷ (2 + 6 + 5 + x + 6 + 9 + 8 + 5)
7 = (291 + 6x) ÷ (41+x)
7(41+x) = 291 + 6x
287 + 7x = 291 + 6x
x = 4
(b)
Age(x in yrs) No.of child Fx2
3 2 18
4 6 96
5 5 125
6 4 144
7 6 294
8 9 576
9 8 648
10 5 500

Σf = 45 Σfx2 = 2401

Standard deviation = √196/45 = √4.3555
= 2.087

(a) Copy and complete the table of values for y = 3Sinx + 7Cosx for 0°
xº 0 20 40 60 80 100 120 140 160 180
y 7.0 4.2 -0.9

(b) Using a scale of 2cm to 20° on the x-axis and 2cm to 2 units on the y-axis, draw the graph of y = 3Sinx + 7Cosx for 0°
(c) Using the graph, find the;
(i) value of y when x= 150°,
(i) range of values of x for which y > 0.

Solution& Explanation
a
xº 0 20 40 60 80 100 120 140 160 180
y 7.0 7.6 7.3 6.1 4.2 1.7 -0.9 -3.4 -5.6 7.0

B
(C)(i) From the graph, When x is 150° y = -4.6 ± 0.2
(ii) Range of value of x for which y > is x: 0º ≤ x ≤ 113

Item food & drinks fuel Rent Building project Education Saving
Percentage% 35 7.5 1.0 15 17.5 x

The table shows the monthly expenditure (in percentages) of Mr. Okafor’s salary.
(a) Calculate the percentage of Mr. Okafor’s salary that was. put into salary.
(b) Illustrate the information on a pie chart.
(c) If Mr. Okafor’s annual gross salary is $28,800.00 and he pays tax of 12%.
Calculate: (i) his monthly tax; (ii) amount saved each month.

Solution& Explanation
(a) 35 + 7.5 + 10 + 15 + 17.5 + x = 100
85 + x = 100.
x = 100 – 85
x = 15
(b)
(c) income tax = 12/100∗28,800
= $3,456.00
Monthly tax = 3456/12
= $288.00

(ii) Monthly net salary = 1/12(288−3456)
= $2,112.00
Amount saved each month = 15/100∗2112
= $316.80

(a) A man purchased 180 copies of a book at N250.00 each. He sold y copies at N300.00 each and the rest at a discount of 5 kobo in the Naira of the cost price.
If he made a profit of N7,125.00, find the value of y.
(b) A trader bought x bags of rice at a cost C = 24x + 103 and sold them at a price, S = x220−33x 220−33 .
Find the expression for the profit (i) If 20 bags of rice were sold,
(ii) calculate the percentage profit.

Solution& Explanation
(a) Total cost 180 x 250
=N45,000.00
Total selling price = 300y + (180-y) x 250 x 95100
300y + 42750 -237.5y

= 62.5y + 42750

Profit = 62.5y + 42750 -4500
7125 = 62.5y – 2250
9375 = 62.5y
y = 150

(b) Profit = x2 /20−33x
(24x+ 103)
9x – x2 /20 – 103

(ii) Cost = 24(20) +103 = 583.00
Selling Price =33(20) – 202 /20
= 640
Percentage profit = 640−583/583 x 100%
= 9.78%

MATHEMATICS 2022 WAEC THEORY

(a) Given that (7 -2x), 9, (5x + 17) are consecutive terms of a Geometric Progression (G. P) with common ratio, r>0, find the values of x.
(b) Two positive numbers are in the ratio 3:4. The sum of thrice the first number and twice the second is 68. Find the smaller number.

Solution & Explanation

a. Here’s how to find the values of x:

Set up the equation using the common ratio:
– In a geometric progression, the ratio of consecutive terms is constant.
– Therefore, we have:
(9 / (7 – 2x)) = ((5x + 17) / 9)

Cross-multiply and simplify:
– Multiply both sides by 9 * (7 – 2x) to eliminate fractions:
9 * 9 = (5x + 17) * (7 – 2x)
– Expand both sides:
81 = 35x – 10x^2 + 119 – 34x
0 = -10x^2 + x + 38

Factor the quadratic equation:
– The equation factors as:
-10x^2 + x + 38 = -(5x – 2)(2x – 19) = 0

Solve for x:
– Set each factor equal to 0 and solve for x:
5x – 2 = 0 → x = 2/5
2x – 19 = 0 → x = 19/2

Therefore, the possible values of x are x = 2/5 or x = 19/2.

b. Let’s solve this step-by-step:

1Represent the numbers:

Since the ratio is 3:4, let the first number be 3x and the second number be 4x.
Set up the equation based on the information:

We know that the sum of thrice the first number and twice the second is 68. So, the equation is:
3(3x) + 2(4x) = 68
9x + 8x = 68

3Combine like terms and solve for x:
17x = 68
x = 4

4Find the smaller number:
Remember, the first number was represented by 3x. So, the smaller number is:
Smaller number = 3 * 4 = 12

Therefore, the smaller number in this ratio is 12