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Mathematics
WAEC / WASSCE 2012
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram, O is a circle centre of the circle PQRS and o. If o, find x
Attached Figure / Diagram
A
108o
B
172o
C
130o
D
50o
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
xo = 86 x 2(angle at centre = 2 x angle at circumference)
= 172o
Source: Myschool Past Questions Archive (Record #36806)
Mathematics
WAEC / WASSCE 2012
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
The diagram is a circle centre O. If < SPR = 2m and < SQR = n, express m in terms of n
Attached Figure / Diagram
A
m = \(\frac{n}{2}\)
B
m = 2n
C
m = n - 2
D
m = n + 2
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
If < SPR = 2m then < SQR = 2m but < AQR was n
n = 2m
m = \(\frac{n}{2}\)
Source: Myschool Past Questions Archive (Record #36807)
Mathematics
WAEC / WASSCE 2012
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram, MQ//RS, o and o. Find the value of x
Attached Figure / Diagram
A
150o
B
110o
C
100o
D
95o
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
L + 30o - 180o(Sum of o - 30o = 150o
L = q = 150o(opposite o(alt. o(sum of o + c 180
c = 180 - 30
c = 150o
b = a = 30o (opp o (opp o = 180o (sum of o + k + 70o = 180
k + 100o = 180
k = 180 - 100
k = 80o
x + 80o = 180(sum of o - 80o
x = 100o
Source: Myschool Past Questions Archive (Record #36809)
Mathematics
WAEC / WASSCE 2012
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
Is the diagram, MN, PQ and RS are three intersecting straight lines. Which of the following statements is/are true? i. t = y ii. x + y + z + m = 180o iii. x + m + n = 180o iv. x + n = m + z
Attached Figure / Diagram
A
i and iv
B
ii
C
iii
D
iv
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
m + y + x = 180o(sum of < s on straight line)
y = n(vertically opp. angle)
m + n + x = 180o
Source: Myschool Past Questions Archive (Record #36810)
Mathematics
WAEC / WASSCE 2012
Trigonometry, Elevation & Bearings
Diagram
Solution
The position of three ships P,Q and R at sea are illustrated in the diagram. The arrows indicated the North direction. The bearing of Q from P is 050o and < PQR = 72o. Calculate the bearing of R and Q
Attached Figure / Diagram
A
155o
B
80o
C
158o
D
91o
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
< NPQ = < PQB = 50º(alt. < s)
< PQB = 50º
< PQR = < PQR < PQB + < QBR = 72º
< QBR = < PQR - < PQB = 72º - 50º
= 22º
< NQR = 180 - < QBR = 180º - 22 = 158º, the bearing of R from Q = 158º
Source: Myschool Past Questions Archive (Record #36811)
Mathematics
WAEC / WASSCE 2012
Statistics (Data Representation, Central Tendency & Dispersion)
Diagram
Solution
The bar chart shows the frequency distribution of marks scored by students in a class test. How many students are in the class?
Attached Figure / Diagram
A
10
B
24
C
25
D
30
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
6 + 8 + 6 + 5 = 25
Source: Myschool Past Questions Archive (Record #36813)
Mathematics
WAEC / WASSCE 2012
Statistics (Data Representation, Central Tendency & Dispersion)
Diagram
Solution
The bar chart shows the frequency distribution of marks scored by students in a class test. Calculate the mean of the distribution.
Attached Figure / Diagram
A
6.0
B
3.0
C
2.4
D
1.8
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\begin{array}{c|c} x & f & fx\\ \hline 1 & 6 & 6 \\
2 & 8 & 16\\ 3 & 8 & 18\\ 4 & 5 & 20\end{array}\)
mean x = \(\frac{\sum fx}{\sum f}\)
= \(\frac{60}{25}\)
x = 2.4
Source: Myschool Past Questions Archive (Record #36814)
Mathematics
WAEC / WASSCE 2012
Statistics (Data Representation, Central Tendency & Dispersion)
Diagram
Solution
The bar chart shows the frequency distribution of marks scored by students in a class test. What is the median of the distribution?
Attached Figure / Diagram
A
2
B
4
C
6
D
8
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
median = (\(\frac{N + 1}{2}\))th = (\(\frac{25 + 1}{2}\))th
= \(\frac{26th}{2}\)
= 13th
the 13th is 2
Source: Myschool Past Questions Archive (Record #36815)
Mathematics
WAEC / WASSCE 2012
Linear, Simultaneous & Quadratic Equations
Diagram
The graph is that of y = 2x2 - 5x - 3. For what value of x will y be negative? What is the gradient of y = 2x2 - 5x - 3 at the point x = 4?
Attached Figure / Diagram
A
11.1
B
10.5
C
10.3
D
9.9
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: Myschool Past Questions Archive (Record #36818)
Mathematics
WAEC / WASSCE 2012
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram, MN//PO, < PMN = 112º, < PNO = 129º, < NOP = 37º and < MPN = yo. Find the value of y
Attached Figure / Diagram
A
51o
B
54o
C
56o
D
68o
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
in the diagram;
x = 180º - ( 129 + 37)º = 14º ( sum of angles in a △)
z = x = 14º ( alternate angles are equal )
y = 180º - ( 112 + z )º = 14º ( sum of angles in a △)
y = 180º - ( 112 + 14)º = 54º
Source: Myschool Past Questions Archive (Record #36821)
Mathematics
WAEC / WASSCE 2012
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
The diagram is a circle with centre P. PRST are points on the circle. Find the value of < PRS
Attached Figure / Diagram
A
144o
B
72o
C
40o
D
36o
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Reflex o(angles at a point)
i.e. 2x + 8x = 360o
10x = 360o
x = \(\frac{360}{10}\)
= 36o
o
< PRS = 144
Source: Myschool Past Questions Archive (Record #36823)
Mathematics
WAEC / WASSCE 2012
Plane Geometry, Polygons & Circle Theorems
Diagram
The diagram is a circle of radius |QR| = 4cm. \(\bar{R}\) is a tangent to the circle at R. If TPO = 120o, find |PQ|.
Attached Figure / Diagram
A
2.32cm
B
1.84cm
C
0.62cm
D
0.26cm
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: Myschool Past Questions Archive (Record #36824)
Mathematics
WAEC / WASSCE 2012
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram, |SR| = |QR|. o and o, find < PRQ
Attached Figure / Diagram
A
65o
B
45o
C
25o
D
19o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
o (angle in the same segment)
o(sum of interior angles of a \(\bigtriangleup\))
i.e. o + 48o = 180
o
but o
Source: Myschool Past Questions Archive (Record #36825)
Mathematics
WAEC / WASSCE 2012
Linear, Simultaneous & Quadratic Equations
Diagram
Solution
The graph is that of y = 2x2 - 5x - 3. For what value of x will y be negative? For what value of x will y be negative?
Attached Figure / Diagram
A
-\(\frac{1}{2} \leq x\) < 3
B
-\(\frac{1}{2} < x \leq 3\)
C
-\(\frac{1}{2} < x < 3\)
D
-\(\frac{1}{2} \leq x \leq 3\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
2x2 - 5x - 3 = 0
2x2 - 6x + x - 3 = 0
2x(x - 3) + 1(x - 3) = 0
(2x + 1)(x - 3) = 0
2x + 1 = 0
2x = -1
x = -\(\frac{1}{2}\)
x - 3 = 0
-\(\frac{1}{2}\) < x < 3
Source: Myschool Past Questions Archive (Record #36826)
Mathematics
WAEC / WASSCE 2012
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
The diagram is a polygon. Find the largest of its interior angles
Attached Figure / Diagram
A
300o
B
100o
C
120o
D
150o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Sum of interior angles = 3602
i.e 3x + 2x + 2x + x + 4x = 360o
12x = 360
x = \(\frac{360}{12}\)
x = 30o
x + c = 180
30o + c = 180
c = 180 - 30
c = 150o
Source: Myschool Past Questions Archive (Record #36827)