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Mathematics
UTME / JAMB 2021
Ratios, Proportions and Rates
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
Financial Arithmetic
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
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
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
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)
Mathematics
WAEC / WASSCE 2021
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
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
Linear Inequalities
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)
Mathematics
UTME / JAMB 2021
Functions and Relations
Solution
If g(x) = x\(^2\) + 3x find g(x + 1) - g(x)
A
(x + 2)
B
2(x + 2)
C
(2x + 1)
D
(x2 + 4)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
g(x) = x2 + 3x
When g(x + 1) = (x + 1)^2 + 3(x + 1)
= x\(^2\) + 1 + 2x + 3x + 3
= x\(^2\) + 5x + 4
g(x + 1) - g(x) = x2 + 5x + 8 - (x\(^2\) + 3x)
= x\(^2\) + 5x + 4 - x2 -3x
= 2x + 4 or 2(x + 4)
= 2(x + 2)
Source: WAEC / JAMB / NECO Classroom Archive (Record #60715)
Mathematics
UTME / JAMB 2021
Progressions (AP & GP)
Solution
What is the n-th term of the sequence 2, 6, 12, 20...?
A
4n - 2
B
2(3n - 1)
C
n2 + n
D
n2 + 3n + 2
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Given that 2, 6, 12, 20...? the nth term = n\(^2\) + n
check: n = 1, u1 = 2
n = 2, u2 = 4 + 2 = 6
n = 3, u3 = 9 + 3 = 12
∴ n = 4, u4 = 16 + 4 = 20
Source: WAEC / JAMB / NECO Classroom Archive (Record #60723)
Mathematics
WAEC / WASSCE 2021
Progressions (AP & GP)
Solution
Find the 5th term of the sequence 2,5,10,17....?
A
22
B
24
C
36
D
26
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Simply add odd number starting from '3' to the next number
2
2 + 3 = 5
5 + 5 = 10
10 + 7 = 17
17 + 9 = 26
The fifth term = 26
Source: WAEC / JAMB / NECO Classroom Archive (Record #61141)
Mathematics
UTME / JAMB 2021
Binary Operations
Solution
If the binary operation \(\ast\) is defined by m \(\ast\) n = mn + m + n for any real number m and n, find the identity of the elements under this operation
A
e = 1
B
e = -1
C
e = -2
D
e = 0
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Identity(e) : a \(\ast\) e = a
m \(\ast\) e = m...(i)
m \(\ast\) e = me + m + e
Because m \(\ast\) e = m
: m = me + m + e
m - m = e(m + 1)
e = \(\frac{0}{m + 1}\)
e = 0
Source: WAEC / JAMB / NECO Classroom Archive (Record #60728)