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Mathematics
WAEC / WASSCE 2018
Geometry and Trigonometry
(a) Using a scale of 2cm to 2units on both axes, draw on a sheet of graph paper two perpendicular axes 0x and 0y for - 10 \(\leq\) x \(\leq\) 10 and -10 \(\leq\) y \(\leq\)10
(b) Given the points P(3, 2). Q(-1. 5). R(0. 8) and S(3, 7). draw on the same graph, indicating clearly the vertices and their coordinates, the:
(i) quadrilateral PQRS;
(ii) image P\(_1\)Q\(_1\)R\(_1\)S\(_1\) of PQRS under an anticlockwise rotation of 90\(^o\) about the origin where P \(\to\) P\(_1\), Q \(\to\) \(Q_1\), R \(\to\) \(R_1\) and S \(\to\) \(S_1\)
(iii) image P\(_2\)Q\(_2\)R\(_2\)S\(_2\) of P\(_1\)Q\(_1\)R\(_1\)S\(_1\) under a reflection in the line y - x = 0 where P\(_1\) \(\to\) P\(_2\), Q\(_1\) \(\to\) \(Q_2\), R\(_1\) \(\to\) \(R_2\) and S\(_1\) \(\to\) \(S_2\)
(c) Describe precisely the single transformation T for which T : PQRS \(\to\) P\(_2\)Q\(_2\)R\(_2\)S\(_2\)
(d) The side P\(_1\)Q\(_1\) of the quadrilateral P\(_1\)Q\(_1\)R\(_1\)S\(_1\) cuts the x-axis at the point W. What type of quadrilateral is P\(_1\)S\(_1\)R\(_1\)W?
medium Difficulty
Verified Correct Answer: Option
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option .
Source: Myschool Past Questions Archive (Record #56419)
Mathematics
WAEC / WASSCE 2017
Geometry and Trigonometry
Diagram
Solution
The diagram shows a circle centre O. if
Attached Figure / Diagram
A
12\(^o\)
B
15\(^o\)
C
29\(^o\)
D
34\(^o\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
SOT = 2 x 46 (< at the centre is twice < at circumference) = 92
2x + 92 = 180( sum of
x = \(\frac{180- 92}{2}\) = 44º
< STO = 44º - 29º
= 15\(^o\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #50152)
Mathematics
WAEC / WASSCE 2017
Number and Numeration
Diagram
Solution
Find the value of m in the diagram
Attached Figure / Diagram
A
72\(^o\)
B
68\(^o\)
C
44\(^o\)
D
34\(^o\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
2x + m = 180
x + m = 112
x = 122 - m
2(112 - m) + m = 180
224 - 2m + m = 180
224 - m = 180
224 - 180 = m
m = 44\(^o\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #50188)
Mathematics
WAEC / WASSCE 2017
Number and Numeration
Solution
The average age of a group of 25 girls is 10year. If one girl, aged 12 years and 4 months joins the group, find the new average age of the group
A
10.1 years
B
9.3 years
C
8.7 years
D
8 . 3 years
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
x = 10 ; 10 = \(\frac{x}{25}\)
x = 250
x = \(\frac{250 + 12.4}{26}\)
x = 10.09
x = 10.1 years
Source: WAEC / JAMB / NECO Classroom Archive (Record #50023)
Mathematics
WAEC / WASSCE 2017
Number and Numeration
Solution
Make x the subject of the relation d = \(\sqrt{\frac{6}{x} - \frac{y}{2}}\)
A
x = \(\frac{6 + 12}{d^2 + y}\)
B
x = \(\frac{12}{d^2 - y}\)
C
x = \(\frac{12}{y} - 2d^2\)
D
x = \(\frac{12}{2d^2 + y}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
d = \(\sqrt{\frac{6}{x} - \frac{y}{2}}\)
\(d^2 = \frac{6}{x} - \frac{y}{2}\)
\(2xd^2 = 12 - xy\)
\(2xd^2 + xy = 12\)
x = \(\frac{12}{2d^2 + y}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #50125)
Mathematics
UTME / JAMB 2017
Geometry and Trigonometry
Solution
Find the number of ways that the letters of the word EXCELLENCE be arranged
A
\(\frac{10!}{2!2!2!}\)
B
\(\frac{10!}{4!2!}\)
C
\(\frac{10!}{4!2!2!}\)
D
\(\frac{10!}{2!2!}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
EXCELLENCE
It is a ten-letter word = 10!
Since we have repeating letters, we have to divide to remove the duplicates accordingly. There are 4 Es, 2 Cs, 2 Ls
∴ there are: \(\frac{10!}{4!2!2!}\) ways to arrange
Source: WAEC / JAMB / NECO Classroom Archive (Record #46346)
Mathematics
UTME / JAMB 2017
Number and Numeration
Solution
Given T = { even numbers from 1 to 12 }
N = {common factors of 6, 8 and 12}
Find T ∩ N
A
{2, 3}
B
{2, 3, 4}
C
{3, 4, 6}
D
{2}
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
T = {evenn numbers from 1 to 12}
N = {common factors of 6,8 and 12}
Find T ∩ N
T = {2, 4, 6, 8, 10, 12}
N = {2}
T ∩ N = {2} i.e value common to T & N
Source: Myschool Past Questions Archive (Record #46321)
Mathematics
UTME / JAMB 2017
Algebra
Solution
What is the next number in the series 2, 1, \(\frac{1}{2}\), \(\frac{1}{4}\)...
A
\(\frac{1}{3}\)
B
\(\frac{2}{8}\)
C
\(\frac{3}{7}\)
D
\(\frac{1}{8}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
2, 1, \(\frac{1}{2}\), \(\frac{1}{4}\).....
There are 4 terms in the series
Therefore the next number will be the 5th term
Tn = ar\(^{n − 1}\) (formular for geometric series)
a = first term = 2
r = common rate = \(\frac{\text{next term}}{\text{previous term}}\) = \(\frac{1}{2}\)
n = number of terms
T5 = 5th term = ?
T5 = ar\(^{5 - 1}\)
= ar\(^4\)
= 2 × (ar\(^{n − 1}\))4
= 2 × \(\frac{1}{16}\)
= \(\frac{1}{8}\)
Source: Myschool Past Questions Archive (Record #46322)
Mathematics
UTME / JAMB 2017
Statistics and Probability
Solution
If U = {x : x is an integer and 1 \le x \le 20 }
E1 = {x: x is a multiple of 3}
E2 = {x: x is a multiple of 4} and an integer is picked at random from U, find the probability that it is not in E2
A
\(\frac{3}{4}\)
B
\(\frac{3}{10}\)
C
\(\frac{1}{4}\)
D
\(\frac{1}{20}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}
E1 = {3, 6, 9, 12, 15, 18}
E2 = {4, 8, 12, 16, 20}
Probability of E2 = \(\frac{5}{20}\) i.e \(\frac{\text{Total number in}E_2}{\text{Entire number in set}}\)
Probability of set E2 = 1 − \(\frac{5}{20}\)
= \(\frac{15}{20}\)
= \(\frac{3}{4}\)
Source: Myschool Past Questions Archive (Record #46323)
Mathematics
UTME / JAMB 2017
Number and Numeration
Solution
The curved surface area of a cylinder 5cm high is 110cm2. Find the radius of its base
π = \(\frac{22}{7}\)
A
2.6cm
B
3.5cm
C
3.6cm
D
7.0cm
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Curved surface area of cylinder = 2πrh
110 = 2 × \(\frac{22}{7}\) × r × 5
r = \(\frac{110 \times 7}{44 \times 5}\)
= 3.5cm
Source: Myschool Past Questions Archive (Record #46324)
Mathematics
UTME / JAMB 2017
Number and Numeration
Solution
If two graphs Y = px2 + q and y = 2x2 − 1 intersect at x =2, find the value of p in terms of q
A
q − \(\frac{8}{7}\)
B
7 − \(\frac{q}{4}\)
C
8 − \(\frac{q}{2}\)
D
7 + \(\frac{q}{8}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Y = Px2 + q
Y = 2x2 - 1
Px2 + q = 2x2 - 1
Px2 = 2x2 - 1 - q
p = \(\frac{2x^2 - 1 - q}{x^2}\)
at x = 2
P = \(\frac{2(2)^2 - 1 - q}{2^2}\)
= \(\frac{2(4) - 1 -q}{4}\)
= \(\frac{8 - 1 - q}{4}\)
P = \(\frac{7 - q}{4}\)
Source: Myschool Past Questions Archive (Record #46325)
Mathematics
UTME / JAMB 2017
Number and Numeration
Solution
Evaluate (\(\sin\)45º + \(\sin\)30º ) in surd form
A
\(\frac{\sqrt{3}}{2\sqrt{2}}\)
B
√3 − \(\frac{1}{2}\)
C
\(\frac{1}{2}\)√2
D
\(\frac{1 +\sqrt{2}}{2}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
hypotenuse
sin = \(\frac{1}{2}\)
\(\sin45 = \frac{1}{\sqrt{2}}\)
= \(\frac{2}{2}\)
∴ (sin45 + sin30)
= \(\frac{1}{\sqrt{2}} + \frac{1}{2}\)
= \(\frac{\sqrt{2}}{2}\) + \(\frac{1}{2}\)
= \(\frac{\sqrt{2} + 1}{2}\)
= \(\frac{1 + \sqrt{2}}{2}\)
Source: Myschool Past Questions Archive (Record #46326)
Mathematics
UTME / JAMB 2017
Geometry and Trigonometry
Solution
If y = x Sin x, find \(\frac{dy}{dx}\) when x = \(\frac{\pi}{2}\)
A
\(\frac{- \pi}{2}\)
B
-1
C
1
D
\(\frac{ \pi}{2}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
y = xsinx
\(\frac{dy}{dx}\) = \(1 \sin x + x \cos x\)
= \(\sin x + x \cos x\)
At x = \(\frac{\pi}{2}\)
= sin\(\frac{\pi}{2}\) + \(\frac{\pi}{2} \cos {\frac{\pi}{2}}\)
= 1 + \(\frac{\pi}{2}\) \times 0
= 1
Source: Myschool Past Questions Archive (Record #46327)
Mathematics
UTME / JAMB 2017
Geometry and Trigonometry
Solution
If temperature t is directly proportional to heat h, and when t = 20oC, h = 50 J, find t when h = 60J
A
24oC
B
20oC
C
34oC
D
30oC
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
t ∝ h, t = 20, h
t = ? h = 60
t = kh where k is constant
20 = 50k
k = \(\frac{20}{50}\)
k = \(\frac{2}{5}\)
when h = 60, t = ?
t = \(\frac{2}{5}\) × 60
t = 24oC
Source: Myschool Past Questions Archive (Record #46328)
Mathematics
UTME / JAMB 2017
Number and Numeration
Evaluate 1 - (\(\frac{1}{5}\) x \(\frac{2}{3}\)) + ( 5 + \(\frac{2}{3}\))
A
4
B
3
C
2\(\frac{2}{3}\)
D
\(\frac{98}{15}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option D.
Source: Myschool Past Questions Archive (Record #46329)