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Mathematics
WAEC / WASSCE 2016
Geometry and Trigonometry
Solution
What sum of money will amount to D10,400 in 5 years at 6% simple interest?
A
D8,000.00
B
D10,000.00
C
D12,000.00
D
D16,000.00
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
A = P + 1
I = A - P
= 10,400 - P
Now using I = \(\frac{P \times T \times R}{100}\)
i.e. 10,400 - P = \(\frac{P \times 5 \times 6}{100}\)
= 100(10,400 - P) = 30P
10(10,400 - P) = 3P
104,000 - 10P = 3P
104,000 - 10P = 3P
104,000 = 3P + 10P
= 104,000 = 13P
P = \(\frac{104,000}{100}\)
P = D8,000
Source: Myschool Past Questions Archive (Record #46097)
Mathematics
WAEC / WASSCE 2016
Algebra
Solution
The roots of a quadratic equation are \(\frac{4}{3}\) and -\(\frac{3}{7}\). Find the equation
A
21x2 - 19x - 12 = 0
B
21x2 + 37x - 12 = 0
C
21x2 - x + 12 = 0
D
21x2 + 7x - 4 = 0
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Let x = \(\frac{4}{3}\), x = -\(\frac{3}{7}\)
Then 3x = 4, 7x = -3
3x - 4 = 0, 7x + 3 = 0
(3x - 4)(7x + 3) = 0
21x2 + 9x - 28x - 12 = 0
21x2 - 19x - 12 = 0
Source: Myschool Past Questions Archive (Record #46098)
Mathematics
WAEC / WASSCE 2016
Number and Numeration
Solution
Find the values of y for which the expression \(\frac{y^2 - 9y + 18}{y^2 + 4y - 21}\) is undefined
A
6, -7
B
3, -6
C
3, -7
D
-3, -7
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{y^2 - 9y + 18}{y^2 + 4y - 21}\)
Factorize the denominator;
Y2 + 7y - 3y - 21
= y(y + 7) -3 (y + 7)
= (y - 3)(y + 7)
Hence the expression \(\frac{y^2 - 9y + 18}{y^2 + 4y - 21}\) is undefined
when y2 + 4y - 21 = 0
ie. y = 3 or -7
Source: Myschool Past Questions Archive (Record #46100)
Mathematics
WAEC / WASSCE 2016
Number and Numeration
Solution
Given that 2x + y = 7 and 3x - 2y = 3, by how much is 7x greater than 10?
A
1
B
3
C
7
D
17
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
2x + y = 7...(1)
3x - 2y = 3...(2)
From (1), y = 7 - 2x for y in (2)
3x - 2(7 - 2x) = 3
3x - 14 + 4x = 3
7x + 3 + 14 = 17
x = \(\frac{17}{7}\)
Hence, 7 x \(\frac{17}{7}\)
= 17 - 10
= 7
Source: Myschool Past Questions Archive (Record #46103)
Mathematics
WAEC / WASSCE 2016
Number and Numeration
Solution
Simplify; \(\frac{2}{1 - x} - \frac{1}{x}\)
A
\(\frac{x + 1}{x(1 - x)}\)
B
\(\frac{3x - 1}{ x(1 - x)}\)
C
\(\frac{3x + 1}{ x(1 - x)}\)
D
\(\frac{x - 1}{ x(1 - x)}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\frac{2}{1 - x} - \frac{1}{x}\) = \(\frac{2x - 1(1 - x)}{x(1 - x)}\)
= \(\frac{2x - 1 + x}{x(1 - x)}\)
= \(\frac{3x - 1}{x(1 - x)}\)
Source: Myschool Past Questions Archive (Record #46106)
Mathematics
WAEC / WASSCE 2016
Number and Numeration
Solution
Make s the subject of the relation: P = S + \(\frac{sm^2}{nr}\)
A
s = \(\frac{mrp}{nr + m^2}\)
B
s = \(\frac{nr + m^2}{mrp}\)
C
s = \(\frac{nrp}{mr + m^2}\)
D
s = \(\frac{nrp}{nr + m^2}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
P = S + \(\frac{sm^2}{nr}\)
P = S(1 + \(\frac{m^2}{nr}\))
P = S(1 + \(\frac{nr + m^2}{nr}\))
nrp = S(nr + m2)
S = \(\frac{nrp}{nr + m^2}\)
Source: Myschool Past Questions Archive (Record #46107)
Mathematics
WAEC / WASSCE 2016
Number and Numeration
Solution
Factorize; (2x + 3y)2 - (x - 4y)2
A
(3x - y)(x + 7y)
B
(3x + y)(2x - 7y)
C
(3x + y)(x - 7y)
D
(3x - y)(2x + 7y)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
(2x + 3y)2 - (x - 4y)2
= (2x + 3y)(2x + 3y) - (x - 4y)(x - 4y)
= 4x2 + 12xy + 9y2 - (x2 - 8xy+ 16y2)
= 4x2 + 12xy + 19y2 - x2 + 8xy - 16y2
= 3x2 + 20xy - 7y2
= 3x2 + 21xy - xy - 7y2
= 3x(x + 7y) - y(x + 7y)
= (3x - y)(x + 7y)
Source: Myschool Past Questions Archive (Record #46109)
Mathematics
WAEC / WASSCE 2016
Number and Numeration
Solution
The curve surface area of a cylinder, 5cm high is 110cm 2. Find the radius of its base. [Take \(\pi = \frac{22}{7}\)]
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 = 2\(\pi\)rh
110 = 2 x \(\frac{22}{7}\) x r x 5
r = \(\frac{110 \times 7}{44 \times 5}\)
= 3.5cm
Source: Myschool Past Questions Archive (Record #46112)
Mathematics
WAEC / WASSCE 2016
Number and Numeration
Solution
The volume of a pyramid with height 15cm is 90cm3. If its base is a rectangle with dimension xcm by 6cm, find the value of x
A
3
B
5
C
6
D
8
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Volume of pyramid = \(\frac{1}{3}\)lbh
90 = \(\frac{1}{3} \times x \times 6 \times 15\)
x = \(\frac{90 \times 33}{6 \times 15}\)
= 3
Source: Myschool Past Questions Archive (Record #46113)
Mathematics
WAEC / WASSCE 2016
Geometry and Trigonometry
Solution
A straight line passes through the points P(1,2) and Q(5,8). Calculate the gradient of the line PQ
A
\(\frac{3}{5}\)
B
\(\frac{2}{3}\)
C
\(\frac{3}{2}\)
D
\(\frac{5}{3}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Let: (x1, y1) = (1, 2)
(x2, y2) = (5, 8)
The gradient m of \(\bar{PQ}\) is given by
m = \(\frac{y_2 y_1}{x_2 - x_1}\)
= \(\frac{8 - 2}{5 - 1}\)
= \(\frac{6}{4}\)
= \(\frac{3}{2}\)
Source: Myschool Past Questions Archive (Record #46117)
Mathematics
WAEC / WASSCE 2016
Number and Numeration
Solution
A straight line passes through the point P(1,2) and Q
(5,8). Calculate the length PQ
A
\(4\sqrt{11}\)
B
\(4\sqrt{10}\)
C
\(2\sqrt{17}\)
D
\(2\sqrt{13}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
|PQ| = \(\sqrt{(x_2 - X- 1) + (y_2 - y_1)^2}\)
= \(\sqrt{(5 - 1)^2 + (8 - 2)^2}\)
= \(\sqrt{4^2 + 6^2}\)
= \(\sqrt{16 + 36}\)
= \(\sqrt{52}\)
= 2\(\sqrt{13}\)
Source: Myschool Past Questions Archive (Record #46119)
Mathematics
WAEC / WASSCE 2016
Geometry and Trigonometry
Solution
If cos \(\theta\) = x and sin 60o = x + 0.5 0o o, find, correct to the nearest degree, the value of \(\theta\)
A
32o
B
40o
C
60o
D
69o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
sin 60o = x + 0.5 0o(given)
0.8660 = x + 0.5
0.8660 - 0.5 = x
x = 0.3660
cos\(\theta\) = x(given)
cos\(\theta\) = 0.3660
Hence, \(\theta\) = cos-1(0.3660)
= 68.53o
= 69o (nearest degree)
Source: Myschool Past Questions Archive (Record #46120)
Mathematics
WAEC / WASSCE 2016
Statistics and Probability
Solution
Age(years)
13
14
15
16
17
Frequency
10
24
8
5
3
The table shows the ages of students in a club. How many students are in the club?
A
50
B
55
C
60
D
65
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Number of students in the club is
10 + 24 + 8 + 5 + 3 = 50
Source: Myschool Past Questions Archive (Record #46123)
Mathematics
WAEC / WASSCE 2016
Statistics and Probability
Solution
\(\begin{array}{c|c}
Age(years) & 13 & 14 & 15 & 16 & 17 \\
\hline
Frequency & 10 & 24 & 8 & 5 & 3
\end{array}\)
Find the median age
A
13
B
14
C
15
D
16
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Median = \(\frac{N}{2}\)th age
= \(\frac{50}{2}\)th age
= 25th age
= 14 years
Source: Myschool Past Questions Archive (Record #46126)
Mathematics
WAEC / WASSCE 2016
Number and Numeration
Diagram
Solution
In the diagram, \(\bar{YW}\) is a tangent to the circle at X, |UV| = |VX| and < VXW = 50º. Find the value of < UXY.
Attached Figure / Diagram
A
70o
B
80o
C
105o
D
110o
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
In the diagram above, \(x_1\) = 50º(angles in alternate segment)
\(x_1\) = \(x_2\)(base angles of isos. \(\Delta\))
< UXY + \(x_2\) + 50º = 180º(sum of angles on a straight line)
< UXY + 50º + 50º = 180º
< UXY + 100º = 180º
< UXY = 180º - 100º
= 80º
Source: Myschool Past Questions Archive (Record #46153)