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Mathematics
WAEC / WASSCE 2015
Number and Numeration
Solution
The sum 11011\(_2\), 11111\(_2\) and 10000\(_2\) is 10m10n0\(_2\). Find the value of m and n.
A
m = 0, n = 0
B
m = 1, n = 0
C
m = 0, n = 1
D
m = 1, n = 1
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
.
Source: Myschool Past Questions Archive (Record #45695)
Mathematics
WAEC / WASSCE 2015
Geometry and Trigonometry
Solution
A trader bought an engine for $15,000.00 outside Nigeria. If the exchange rate is $0.075 to N1.00, how much did the engine cost in Naira?
A
N250,000.00
B
N200,000.00
C
N150,000.00
D
N100,000.00
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
N1.00 = $0.075
N X = $15,000
X = \(\frac{1.00 \times 15000}{0.075}\)
= N200,000.00
Source: Myschool Past Questions Archive (Record #45696)
Mathematics
WAEC / WASSCE 2015
Number and Numeration
Solution
If \(\frac{27^x \times 3^{1 - x}}{9^{2x}} = 1\), find the value of x.
A
1
B
\(\frac{1}{2}\)
C
-\(\frac{1}{2}\)
D
-1
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\frac{27^x \times 3^{1 - x}}{9^{2x}} = 1\)
\(\frac{3^{3x} \times 3^{1 - x}}{3^{2(2 - x)}} = 3^0\)
\(3^{3x} \times 3^{1 - x} \div 3^{4x} = 3^0\)
\(3^{(3x + 1 - x - 4x)} = 3^0\)
\(3^{(1 - 2x)} = 3^0\)
since the bases are equal,
1 - 2x = 0
- 2x = -1
x = \(\frac{1}{2}\)
Source: Myschool Past Questions Archive (Record #45697)
Mathematics
WAEC / WASSCE 2015
Algebra
Solution
Find the 7th term of the sequence: 2, 5, 10, 17, 26,...
A
37
B
48
C
50
D
63
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
GIVEN: 2, 5, 10, 17, 26,.
The numbers are increasing by odd value.
1st term = 2
2nd term = 5
3rd term = 10
4th term = 17
5th term = 26
6th term = 37
7th term = 50
Always add 2 to the difference between the two preceding numbers and add this to the later number to get the next term.
Source: Myschool Past Questions Archive (Record #45699)
Mathematics
WAEC / WASSCE 2015
Number and Numeration
Solution
If 2n = y, Find 2\(^{(2 + \frac{n}{3})}\)
A
4y\(^\frac{1}{3}\)
B
4y\(^-3\)
C
2y\(^\frac{1}{3}\)
D
2y\(^-3\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
If 2n = y,
then, 2\(^{(2 + \frac{n}{3})}\) = 22 x 2\(^\frac{n}{3}\)
= 4 x (2n)\(^{\frac{1}{3}}\)
But y = 2n, hence
2\(^{(2 + \frac{n}{3})}\) = 4 x y\(^{\frac{1}{3}}\)
= 4y\(^\frac{1}{3}\)
Source: Myschool Past Questions Archive (Record #45705)
Mathematics
WAEC / WASSCE 2015
Number and Numeration
Solution
Factorize completely: 6ax - 12by - 9ay + 8bx
A
(2a - 3b)(4x + 3y)
B
(3a + 4b)(2x - 3y)
C
(3a - 4b)(2x + 3y)
D
(2a + 3b)(4x -3y)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
6ax - 12by - 9ay + 8bx
= 6ax - 9ay + 8bx - 12by
= 3a(2x - 3y) + 4b(2x - 3y)
= (3a + 4b)(2x - 3y)
Source: Myschool Past Questions Archive (Record #45706)
Mathematics
WAEC / WASSCE 2015
Algebra
Solution
Find the equation whose roots are \(\frac{3}{4}\) and -4
A
4x2 - 13x + 12 = 0
B
4x2 - 13x - 12 = 0
C
4x2 + 13x - 12 = 0
D
4x2 + 13x + 12 = 0
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Let x = \(\frac{3}{4}\) or x = -4
i.e. 4x = 3 or x = -4
(4x - 3)(x + 4) = 0
therefore, 4x2 + 13x - 12 = 0
Source: Myschool Past Questions Archive (Record #45707)
Mathematics
WAEC / WASSCE 2015
Number and Numeration
Solution
Adding 42 to a given positive number gives the same result as squaring the number. Find the number
A
14
B
13
C
7
D
6
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Let the given positive number be x
Then x + 42 = \(x^2\)
0 = \(x^2\) - x - 42
or \(x^2\) - x - 42 = 0
\(x^2\) - 7x + 6x - 42 = 0
x(x - 7) + 6(x - 7) = 0
= (x + 6)(x - 7) = 0
x = -6 or x = 7
Hence, x = 7
Source: Myschool Past Questions Archive (Record #45711)
Mathematics
WAEC / WASSCE 2015
Algebra
Solution
Ada draws the graph of y = x2 - x - 2 and y = 2x - 1 on the same axes. Which of these equations is she solving?
A
x2 - x - 3 = 0
B
x2 - 3x - 1 = 0
C
x2 - 3x - 3 = 0
D
x2 + 3x - 1 = 0
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Given; y = x2 - x - 2, y = 2x - 1
Using y = y, gives
x2 - x - 2 = 2x - 1
x2 - 3x - 2 + 1 = 0
therefore, x2 - 3x - 1 = 0
Source: Myschool Past Questions Archive (Record #45712)
Mathematics
WAEC / WASSCE 2015
Number and Numeration
Solution
The volume of a cone of height 3cm is 38\(\frac{1}{2}\)cm3. Find the radius of its base. [Take \(\pi = \frac{22}{7}\)]
A
3.0cm
B
3.5cm
C
4.0cm
D
4.5cm
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Using V = \(\frac{3}{1} \pi r^2h\),
so, 38\(\frac{1}{2} = \frac{1}{3} \times \frac{22}{7} \times r^2 \times 3\)
\(\frac{77}{2} = \frac{22}{7} \times r^2\)
r2 = \(\frac{77 \times 7}{2 \times 22}\)
r2 = \(\frac{49}{4}\)
Hence, r = \(\sqrt{\frac{49}{4}}\)
= 3\(\frac{1}{2}\)
Source: Myschool Past Questions Archive (Record #45724)
Mathematics
WAEC / WASSCE 2015
Number and Numeration
Solution
The dimension of a rectangular tank are 2m by 7m by 11m. If its volume is equal to that of a cylindrical tank of height 4cm, calculate the base radius of the cylindrical tank. [Take \(\pi = \frac{22}{7}\)]
A
14cm
B
7m
C
3\(\frac{1}{2}\)m
D
1\(\frac{3}{4}\)m
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Volume of rectangular tank = L x B x H
= 2 x 7 x 11
= 154cm3
volume of cylindrical tank = \(\pi r^2h\)
154 = \(\frac{22}{7} \times r^2 \times 4\)
r2 = \(\frac{154 \times 7}{22 \times 4}\)
= \(\frac{49}{4}\)
r = \(\sqrt{\frac{49}{4}} = \frac{7}{2}\)
= 3\(\frac{1}{2}\)m
Source: Myschool Past Questions Archive (Record #45741)
Mathematics
WAEC / WASSCE 2015
Geometry and Trigonometry
Diagram
Solution
In the diagram, O is the centre. If PQ//RS and ∠ONS = 140^\circ, find the size of ∠POM.
Attached Figure / Diagram
A
40o
B
50o
C
60o
D
80o
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
In the diagram above,
∠MNO = 140^\circ and angles on a straight line is 180^\circ
: ∠NMO = (180 - 140)^\circ = 40^\circ
Hence; ∠POM = 40^\circ ( alternate angle ∠S)
Source: Myschool Past Questions Archive (Record #45754)
Mathematics
WAEC / WASSCE 2015
Geometry and Trigonometry
Diagram
Solution
In the diagram, PTR is a tangent to the centre O. If angles TON = 108^\circ, Calculate the size of angle PTN
Attached Figure / Diagram
A
132o
B
126o
C
108o
D
102o
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
In the diagram; 108^\circ + x + x = 180^\circ (sum of angle in a triangle)
108^\circ + 2x = 180^\circ
x = 180^\circ - 108^\circ
= 72^\circ
x = \(\frac{72^o}{2}\)
= 36^\circ
(Angle between tangent and a chord through the point of contact)
Hence, angle PTN = 90 + 36
= 126^\circ
Source: Myschool Past Questions Archive (Record #45757)
Mathematics
WAEC / WASSCE 2015
Geometry and Trigonometry
Diagram
Solution
In the diagram, PQ//RT, QR//SU,
Attached Figure / Diagram
A
134o
B
132o
C
96o
D
48o
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
In the diagram; a = b = 48º (alternate < S)
x = 180 ^\circ - b (angles on a str. line)
x = 180º - 48º
= 132º
Source: Myschool Past Questions Archive (Record #45767)
Mathematics
WAEC / WASSCE 2015
Geometry and Trigonometry
Diagram
Solution
In the diagram, O is the centre, \(\bar{RT}\) is a diameter, < PQT = 33\(^o\) and
Attached Figure / Diagram
A
73o
B
67o
C
57o
D
37o
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
In the diagram given, < PRT = 3\(^o\) (Change in same segment)
< TPR = 90\(^o\) (angle in a semicircle)
Hence, < PTR = 180\(^o\) - (90 + 33)\(^o\)
= 180\(^o\) - 123\(^o\)
= 57\(^o\)
Source: Myschool Past Questions Archive (Record #45775)