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Mathematics
WAEC / WASSCE 2021
Logarithms
Solution
If log\(_{10}\) 2 = m and log\(_{10}\) 3 = n, find log\(_{10}\) 24 in terms of m and n.
A
3m + n
B
m + 3n
C
4mn
D
3mn
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
log\(_{10}\) 24 = log\(_{10}\) 8 \(\times\) log\(_{10}\) 3
where log\(_{10}\) 8 = 3 log\(_{10}\) 2 = 3 \(\times\) m
and log\(_{10}\) 3 = n
: log\(_{10}\) 24 = 3m + n
Source: WAEC / JAMB / NECO Classroom Archive (Record #61140)
Mathematics
WAEC / WASSCE 2021
Surds
Solution
Simplify 2√7- \(\frac{14}{√7} + \frac{7}{√21}\)
A
\(\frac{√21}{21}\)
B
7\(\frac{√21}{21}\)
C
\(\frac{√21}{3}\)
D
3√21
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
2\sqrt7- \(\frac{14}{\sqrt7} + \frac{7}{\sqrt21}\)
L.C.M is \sqrt21
\(\frac{\sqrt21 * 2\sqrt7 - \sqrt3 *14 + 7}{\sqrt21}\)
=\(\frac{2 * 7\sqrt3 - 14\sqrt3 + 7}{\sqrt21}\)
= \(\frac{14\sqrt3 - 14\sqrt3 + 7}{\sqrt21}\)
=\(\frac{7}{\sqrt21}\)
or
\(\frac{7 \times \sqrt21}{\sqrt21 \times \sqrt21}\)
= \(\frac{7 \times \sqrt21}{21}\) or \(\frac{\sqrt21}{3}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #61165)
Mathematics
WAEC / WASSCE 2021
Fractions, Decimals, Percentages & Approximation
Solution
correct 0.007985 to three significant figures.
A
0.0109
B
0.0800
C
0.00799
D
0.008
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
To round to three significant figures, look at the fourth significant figure. It's a 5 , so round up or round down if below 5.
To round to two significant figures, look at the third significant figure. It's an 8 , so round up.
Source: WAEC / JAMB / NECO Classroom Archive (Record #61137)
Mathematics
WAEC / WASSCE 2021
Fractions, Decimals, Percentages & Approximation
Solution
What number should be subtracted from the sum of 2 \(\frac{1}{6}\) and 2\(\frac{7}{12}\) to give 3\(\frac{1}{4}\)?
A
\(\frac{1}{3}\)
B
1\(\frac{1}{2}\)
C
1\(\frac{1}{6}\)
D
\(\frac{1}{2}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
The sum of 2 \(\frac{1}{6}\) and 2\(\frac{7}{12}\)
= \(\frac{13}{6}\) + \(\frac{31}{12}\)
= \(\frac{13 \times 2 + 31}{12}\)
= \(\frac{26 + 31}{12}\)
= \(\frac{57}{12}\)
What should be subtracted from \(\frac{57}{12}\) to give 3\(\frac{1}{4}\)
\(\frac{57}{12}\) - y = 3\(\frac{1}{4}\)
: y = \(\frac{57}{12}\) - 3\(\frac{1}{4}\) = \(\frac{57}{12}\) - \(\frac{13}{4}\)
y = \(\frac{57 - 3 \times 13}{12}\) = \(\frac{57 - 39}{12}\)
y = \(\frac{18}{12}\)
y = \(\frac{3}{2}\) or 1\(\frac{1}{2}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #61144)
Mathematics
WAEC / WASSCE 2021
Fractions, Decimals, Percentages & Approximation
Solution
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)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\frac{2}{x-3}\) - \(\frac{3}{x-2}\)
= \(\frac{2(x -2) -3(x - 3)}{(x-3)(x -2)}\)
= \(\frac{2x -4 -3x + 9}{(x-3)(x -2)}\)
= \(\frac{5 - x}{(x-3)(x -2)}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #61247)
Mathematics
WAEC / WASSCE 2021
Fractions, Decimals, Percentages & Approximation
Solution
Find, correct to two decimal, the mean of 1\(\frac{1}{2}\), 2\(\frac{2}{3}\), 3\(\frac{3}{4}\), 4\(\frac{4}{5}\), and 5\(\frac{5}{6}\).
A
3.71
B
3.70
C
3.69
D
3.72
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
The mean = sum of 1\(\frac{1}{2}\), 2\(\frac{2}{3}\), 3\(\frac{3}{4}\), 4\(\frac{4}{5}\), and 5\(\frac{5}{6}\) divided by their quantity.
Mean = ( 1\(\frac{1}{2}\) + 2\(\frac{2}{3}\) + 3\(\frac{3}{4}\) + 4\(\frac{4}{5}\) + and 5\(\frac{5}{6}\) ) / 5
= 3.708 or 3.71( 2 d.p )
Source: WAEC / JAMB / NECO Classroom Archive (Record #61365)
Mathematics
WAEC / WASSCE 2021
Fractions, Decimals, Percentages & Approximation
Solution
A box contains 40 identical balls of which 10 are red and 12 are blue. if a ball is selected at random from the box what is the probability that it is neither red nor blue?
A
\(\frac{9}{20}\)
B
\(\frac{3}{10}\)
C
\(\frac{1}{4}\)
D
\(\frac{11}{20}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Total number = 40
number of red = 10
Pr (R) = \(\frac{10}{40}\)
Pr(blue) = \(\frac{12}{40}\)
probability (neither red nor blue)
= 1 - \(\frac{10}{40}\) - \(\frac{12}{40}\)
= \(\frac{40 -12 -10}{40}\)
= \(\frac{18}{40}\) or \(\frac{9}{20}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #61462)
Mathematics
WAEC / WASSCE 2021
Fractions, Decimals, Percentages & Approximation
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 & Set Operations
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 & Set Operations
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
WAEC / WASSCE 2021
Financial Arithmetic
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
WAEC / WASSCE 2021
Operations on Algebraic Expressions
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
Operations on Algebraic Expressions
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
Change of Subject of Formula
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
Change of Subject of Formula
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)