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Mathematics
WAEC / WASSCE 2021
Fractions, Decimals, Percentages & Approximations
Solution
(a) Mr Sarfo borrowed $25,000 from Afiak financial services at 21% simple interest per annum for 3 years if he was able to pay back the loan in two years at equal yearly installments how much did he pay each year?
(b) Two consecutive numbers are such that the sum of thrice the smaller and twice the larger is 17.
find correct through three significant figures the smaller number as a percentage of the sum of the two numbers
medium Difficulty
Verified Correct Answer: Option
Step-by-Step Mathematical Solution
(a) interests = \(\frac{25000 *3 * 21}{100}\)
= $ 15750.00
amount paid = 25000 + 15750
= $40,750.00
amounts paid by year = 40750.00 / 2
= $ 20375.00
(b) let's be consecutive numbers be X and X + 1
3X + 2(X + 1) = 17
3X + 2X + 2 = 17
5x = 15
x = 3
some of the numbers = 3 + 4 = 7
Percentage = \(\frac{3}{7}\) * 100
= 42.857 or 42.9%
Source: WAEC / JAMB / NECO Classroom Archive (Record #61467)
Mathematics
WAEC / WASSCE 2021
Sets, Logic & Venn Diagrams
Solution
if p = {-3
A
0
B
-3, -2, -1, 0 and 1
C
-2, -1 and 0
D
-1, 0 and 1
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
p = {-3
Source: WAEC / JAMB / NECO Classroom Archive (Record #61142)
Mathematics
WAEC / WASSCE 2021
Sets, Logic & Venn Diagrams
Diagram
consider the statements:
P = All students offering Literature(L) also offer History(H);
Q = Students offering History(H) do not offer Geography(G).
Which of the Venn diagram correctly illustrate the two statements?
Attached Figure / Diagram
A
A
B
B
C
C
D
D
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option C.
Source: WAEC / JAMB / NECO Classroom Archive (Record #61226)
Mathematics
UTME / JAMB 2021
Fractions, Decimals, Percentages & Approximations
Solution
Three children shared a basket of mangoes in such a way that the first child took \(\frac{1}{4}\) of the mangoes and the second \(\frac{3}{4}\) of the remainder. What fraction of the mangoes did the third child take?
A
\(\frac{3}{16}\)
B
\(\frac{7}{16}\)
C
\(\frac{9}{16}\)
D
\(\frac{13}{16}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
You can use any whole numbers (eg. 1. 2. 3) to represent all the mangoes in the basket.
If the first child takes \(\frac{1}{4}\) it will remain 1 - \(\frac{1}{4}\) = \(\frac{3}{4}\)
Next, the second child takes \(\frac{3}{4}\) of the remainder
which is \(\frac{3}{4}\) i.e. find \(\frac{3}{4}\) of \(\frac{3}{4}\)
= \(\frac{3}{4}\) x \(\frac{3}{4}\)
= \(\frac{9}{16}\)
the fraction remaining now = \(\frac{3}{4}\) - \(\frac{9}{16}\)
= \(\frac{12 - 9}{16}\)
= \(\frac{3}{16}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #60674)
Mathematics
UTME / JAMB 2021
Fractions, Decimals, Percentages & Approximations
Solution
Musa borrows N10.00 at 2% per month simple interest and repays N8.00 after 4 months. How much does he still owe?
A
N10.80
B
N10.67
C
N2.80
D
N2.67
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
I = \(\frac{PRT}{100}\)
= \(\frac{10 \times 2 \times 4}{100}\)
= \(\frac{4}{5}\)
= 0.8
Total amount = N10.80
He pays N8.00
Remainder = 10.80 - 8.00
= N2.80
Source: WAEC / JAMB / NECO Classroom Archive (Record #60707)
Mathematics
UTME / JAMB 2021
Fractions, Decimals, Percentages & Approximations
Solution
At what rate would a sum of N100.00 deposited for 5 years raise an interest of N7.50?
A
\(\frac{1}{2}\)%
B
2\(\frac{1}{2}\)%
C
1.5%
D
25%
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Interest I = \(\frac{PRT}{100}\)
∴ R = \(\frac{100 \times 1}{100 \times 5}\)
= \(\frac{100 \times 7.50}{500 \times 5}\)
= \(\frac{750}{500}\)
= \(\frac{3}{2}\)
= 1.5%
Source: WAEC / JAMB / NECO Classroom Archive (Record #60672)
Mathematics
WAEC / WASSCE 2021
Fractions, Decimals, Percentages & Approximations
A trader paid import duty of 38 kobo in the naira on the cost of an engine. If a total of #22,800.00 was paid as import duty, calculate the cost of the engine.
A
#60,000.00
B
#120,000.00
C
#24,000.00
D
#18,000.00
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option A.
Source: WAEC / JAMB / NECO Classroom Archive (Record #61202)
Mathematics
UTME / JAMB 2021
Variations
Solution
If w varies inversely as \(\frac{uv}{u + v}\) and w = 8 when
u = 2 and v = 6, find a relationship between u, v, w.
A
uvw = 16(u + v)
B
16uv = 3w(u + v)
C
uvw = 12(u + v)
D
12uvw = u + v
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
W \(\alpha\) \(\frac{\frac{1}{uv}}{u + v}\)
∴ w = \(\frac{\frac{k}{uv}}{u + v}\)
= \(\frac{k(u + v)}{uv}\)
w = \(\frac{k(u + v)}{uv}\)
w = 8, u = 2 and v = 6
8 = \(\frac{k(2 + 6)}{2(6)}\)
= \(\frac{k(8)}{12}\)
k = 12
i.e 12 ( u + v) = uwv
Source: WAEC / JAMB / NECO Classroom Archive (Record #60713)
Mathematics
WAEC / WASSCE 2021
Algebraic Expressions, Polynomials & Factorisation
Solution
Mensah is 5 years old and joyce is thrice as old as mensah. In how many years will joyce be twice as old as Mensah?
A
3 years
B
10 years
C
5 years
D
15 years
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Mensah’s age is 5. Thus,
Joyce’s age is 15 (5*3=15)
The difference between their ages is 10 (15–5=10)
As we ought to find how many years Joyce’s age will be twice of Mensah’s age, we should write down the following :
15+X=2*(5+X)
15+X=10+2X lets add (-10-X) to both sides of the equation and
15+X-10-X = 10+2X-10-X
5=X —-> X=5
After 5 years Joyce’s age will be 20 (15+5=20)
After 5 years Mensah’s age will be 10 (5+5=10)
After 5 years Joyce will be twice as old as Mensah (10*2=20)
Source: WAEC / JAMB / NECO Classroom Archive (Record #61146)
Mathematics
WAEC / WASSCE 2021
Algebraic Expressions, Polynomials & Factorisation
Solution
.(a) In APQR, ∠PQR= 90°. If its area is 216cm\(^2\) and |PQ|:|QR| is 3:4, find |PR|.
(b) The present ages of a man and his son are 47 years and 17 years respectively. In how many years would the man's age be twice that of his son?
medium Difficulty
Verified Correct Answer: Option
Step-by-Step Mathematical Solution
(a) \(\frac{1}{2}\)IPQ||gr|= 216
\(\frac{|PQ|}{|QR|}\) = \(\frac{3}{4}\)
PQ= \(\frac{3}{4}\)
\(\frac{1}{2}\) * \(\frac{3}{4}\)|QR|||QR| = 216
|QR|\(^2\) = \(\frac{216 * 4 * 2}{3}\)
|QR|= \sqrt576 = 24cm
|PQ| =\(\frac{3}{4}\) x 24 =18cm
|PR| = \sqrt(24\(^2\) + 18\(^2\)) = 30cm
(b) Let m be the number of years:
47 + m =2(17+m)
47 + m = 34 + 2m
2m - m = 47 - 34
m = 13 years
Source: WAEC / JAMB / NECO Classroom Archive (Record #61505)
Mathematics
WAEC / WASSCE 2021
Algebraic Expressions, Polynomials & Factorisation
Solution
make u the subject in x =\(\frac{2u-3}{3u + 2}\)
A
u = \(\frac{2x + 3}{3x - 2}\)
B
u = \(\frac{2x - 3}{3x - 2}\)
C
u = \(\frac{2x + 3}{2 - 3x}\)
D
u = \(\frac{2x + 3}{3x + 2}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
x =\(\frac{2u-3}{3u + 2}\)
cross multiply
x(3u + 2) = 2u - 3
3ux + 2x = 2u - 3
collect like terms of u
2x + 3 = 2u - 3ux
\(\frac{2x + 3}{2 - 3x}\) = u
Source: WAEC / JAMB / NECO Classroom Archive (Record #61200)
Mathematics
WAEC / WASSCE 2021
Algebraic Expressions, Polynomials & Factorisation
Solution
A solid brass cube is melted and recast as a solid cone of height h and base radius r. If the height of the cube is h, find r in terms of h.
A
r = h
B
r = √\(\frac{3h^2}{π}\)
C
r = πh
D
r = h √\(\frac{3}{h}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Volume of cube = H. H. H. = H\(^3\)
the volume of a cone is, V=\(\frac{1}{3}\)\pir\(^2\)h.
Volume of cube = the volume of a cone
H\(^3\) = \(\frac{1}{3}\)\pir\(^2\)h.
\(\frac{3{H}^3}{\pih}\) = r\(^2\)
\sqrt\(\frac{3{H}^3}{\pih}\) = r
h \sqrt\(\frac{3H^2}{\pi}\) = r
Source: WAEC / JAMB / NECO Classroom Archive (Record #61299)
Mathematics
WAEC / WASSCE 2021
Linear, Simultaneous & Quadratic Equations
Solution
Find The quadratic Equation Whose Roots Are -2q And 5q.
A
3x\(^2\) + 3qx - 10q\(^2\)
B
x\(^2\) + 3qx + 10q\(^2\)
C
x\(^2\) - 3qx + 10q\(^2\)
D
x\(^2\) - 3qx - 10q\(^2\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
x\(^2\) - (sum of roots)x + (products of roots) = 0
x\(^2\) - (-2q + 5q) + (-2q * 5q) = 0
x\(^2\) -(3q) + (-10q\(^2\)) = 0
x\(^2\) -3q - 10q\(^2\) = 0
Source: WAEC / JAMB / NECO Classroom Archive (Record #61232)
Mathematics
WAEC / WASSCE 2021
Linear, Simultaneous & Quadratic Equations
Solution
(a) Copy and complete the table of values for the relation y=2x\(^2\) - x - 2 for 4 ≤ x ≤ 4.
x
-4
-3
-2
-1
0
1
2
3
4
y
19
-2
26
(b) Using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y-axis, draw the graph of y = 2x\(^2\) - x - 2 for 4 ≤ x ≤ 4.
(c) On the same axes, draw the graph of y = 2x + 3.
(d) Use the graph to find the: (i) roots of the equation 2x-3r-5 0; (i) range of values of x for which 2x\(^2\) -x - 2<0.
medium Difficulty
Verified Correct Answer: Option
Step-by-Step Mathematical Solution
x
-4
-3
-2
-1
0
1
2
3
4
y
34
19
8
1
-2
-1
4
13
26
SEE THE GRAPH ABOVE
(c) Straight line graph of y = 2x + 3
(d) The roots of 2x\(^2\) -3x - 5 = 0 are x = -1 \pm 0.1 or 2.5 \pm 0.1
(ii) The range of values of x for which - x - 2 < 0 is (-0.7\pm 0.1) < x < (1.3 \pm 0.1)
Source: WAEC / JAMB / NECO Classroom Archive (Record #61504)
Mathematics
UTME / JAMB 2021
Inequalities & Linear Programming
Solution
List all integers satisfying the inequality in -2 < 2x-6 < 4
A
2,3,4 and 5
B
2,3
C
2,5
D
3,4
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
-2 < 2x - 6 AND 2x - 6 < 4
-2 + 6 <2x AND 2x < 4 + 6
4 <2x AND 2x < 10
: 2
Source: WAEC / JAMB / NECO Classroom Archive (Record #60732)