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Mathematics
WAEC / WASSCE 2011
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
The graph represents the relation y = xo2 - 3x - 3. Find the value of x for which x2 - 3x = 7
Attached Figure / Diagram
A
-1.55, 4.44
B
1.55, -4.55
C
-1.55, -4.55
D
1.55, 4.55
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
x2 - 3x = 7
x2 - 3x - 7 = 0
What can you add to both sides of the equation to give the same value of y = x2 - 3x - 3
The number is 4
x2 - 3x - 7 + 4 = 4
x2 - 3x - 3 = 4
but y = x2 - 3x - 3
y = 4; So are y = 4 draw a line parallel to x axis, to cut or intersect the graph. At these points look down to see the corresponding values on x axis
This give -1.55 and 4.55
Source: Myschool Past Questions Archive (Record #36674)
Mathematics
WAEC / WASSCE 2011
Plane Geometry, Polygons & Circle Theorems
Solution
Simplify \(\frac{m}{n} + \frac{(m - 1)}{5n} = \frac{(m - 2)}{10n}\) where n \(\neq\) 0
A
\(\frac{m - 3}{10n}\)
B
\(\frac{11m}{10n}\)
C
\(\frac{m + 1}{10n}\)
D
\(\frac{11m + 4}{10n}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\frac{m}{n} + \frac{(m - 1)}{5n} - \frac{(m - 2)}{10n}\); \(\frac{10m + 2(m - 1) - 1(m - 2)}{10m}\)
= \(\frac{10m + 2m - 2 - m + 2}{10n}\)
= \(\frac{10m + 2m - m - 2 + 2}{10n}\)
= \(\frac{11m}{10n}\)
Source: Myschool Past Questions Archive (Record #36676)
Mathematics
WAEC / WASSCE 2011
Indices, Logarithms & Surds
Solution
If \(\sqrt{72} + \sqrt{32} - 3 \sqrt{18} = x \sqrt{8}\), Find the value of x
A
1
B
\(\frac{3}{4}\)
C
\(\frac{1}{2}\)
D
\(\frac{1}{4}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\sqrt{72} + \sqrt{32} - 3\sqrt{18} = x\sqrt{8}\)
= \(\sqrt{36 \times 2} + \sqrt{16 \times 2} - 3\sqrt{2 \times 9}\)
= x\(\sqrt{2 \times 4}\)
= 6\(\sqrt{2} + 4\sqrt{2} - 9\sqrt{2} = 2 \times \sqrt{2}\)
\(\sqrt{2} (6 + 4 - 9) = 2x\sqrt{2}\)
\(\sqrt{2} = 2x \sqrt{2}\) divide both sides by \(\sqrt{2}\)
\(\frac{\sqrt{2}}{\sqrt{2}} = \frac{ 2x\sqrt{2}}{\sqrt{2}}\)
1 = 2x
2x = 1
x = \(\frac{1}{2}\)
Source: Myschool Past Questions Archive (Record #36677)
Mathematics
WAEC / WASSCE 2011
Variations
Solution
G varies directly as the square of H, If G is 4 when H is 3, find H when G = 100
A
15
B
25
C
75
D
225
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
G \(\alpha\) H2
G = KH2
4 = K(3)2
4 = 9k; K = \(\frac{4}{9}\)
100 = \(\frac{4}{9}H^2\)
4H2 = 900
H2 = \(\frac{900}{4}\)
H2 = 225
H = \(\sqrt{225}\)
H = 15
Source: Myschool Past Questions Archive (Record #36678)
Mathematics
WAEC / WASSCE 2011
Sets, Logic & Venn Diagrams
Solution
Given that n(p) = 19, m(P \(\cup\) Q) = 38 and n(P \(\cap\) Q) = 7, Find n(C)
A
26
B
31
C
36
D
50
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
n(P \(\cup\) Q) = m(P \(\cap\) C)
38 = 19 = n(C) - 7
n(C) = 38 - 12
= 26
Source: Myschool Past Questions Archive (Record #36679)
Mathematics
WAEC / WASSCE 2011
Plane Geometry, Polygons & Circle Theorems
Solution
What must be added to (2x - 3y) to get (x - 2y)?
A
5y - x
B
y - x
C
x - 5x
D
x - y
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
What must be added to 2x - 3y = Difference between x - 2y and 2x - 3y
x - 2y - 2y - (2x - 3y); x - 2y - 2x + 3y
= x - 2x + 3y - 2y
= y - x
Source: Myschool Past Questions Archive (Record #36681)
Mathematics
WAEC / WASSCE 2011
Plane Geometry, Polygons & Circle Theorems
Solution
Simplify 1\(\frac{3}{4} - (2 \frac{1}{3} + 4)\)
A
3\(\frac{5}{12}\)
B
2\(\frac{7}{12}\)
C
-4 \(\frac{7}{12}\)
D
-5 \(\frac{7}{12}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
1\(\frac{3}{4} - (2 \frac{1}{3} + 4)\) = \(\frac{7}{4} - (\frac{7}{3} + \frac{4}{1})\); \(\frac{7 + 12}{3}\)
\(\frac{7}{4} - \frac{19}{3} = \frac{21 + 76}{12}\)
= \(\frac{-55}{12} = -4 \frac{7}{12}\)
Source: Myschool Past Questions Archive (Record #36682)
Mathematics
WAEC / WASSCE 2011
Linear, Simultaneous & Quadratic Equations
Solution
Find the smaller value of x that satisfies the equation x\(^2\) + 7x + 10 = 0
A
-5
B
-2
C
2
D
5
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
x\(^2\) + 7x + 10 = 0
x2 + 5x + 2x + 10 = 0
x(x + 5) + 2(x + 5) = 0
(x + 2)(x + 5) = 0
x + 2 = 0 or x + 5 = 0
x = -2 or x = -5
the smaller value x = -5
Source: Myschool Past Questions Archive (Record #36685)
Mathematics
WAEC / WASSCE 2011
Coordinate Geometry
The perpendicular bisectors of the sides of an acute-angled triangle are drawn. Which of these statements is correct? They intersect
A
on one of the vertices
B
at a midpoint of a side
C
inside the triangle
D
outside the triangle
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 #36686)
Mathematics
WAEC / WASSCE 2011
Fractions, Decimals, Percentages & Approximations
Solution
A rectangular garden measures 18.6m by 12.5m. Calculate, correct to three significant figures, the area of the garden
A
230m2
B
231m2
C
232m2
D
233m2
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
A = L x B
= (18.6 x 12.5)m2
= 232.5m2
= 233m2
Source: Myschool Past Questions Archive (Record #36687)
Mathematics
WAEC / WASSCE 2011
Indices, Logarithms & Surds
Solution
in a quiz competition, a student answers n questions correctly and was given D(n + 50) for each question correctly answered. If he gets D600.00 altogether, how many questions did he answer correctly?
A
18
B
15
C
12
D
10
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
let the number of question = n
n(n + 50) = 600
n2 + 50n - 600 - 0 by quadratic formular
x = \(\frac{b \pm \sqrt{b^2 - 4ac}}{2}\)
n = \(\frac{-50 \pm \sqrt{50^2 - 4(1) (-600)}}{2(1)}\)
= \(\frac{-50 \pm \sqrt{4900}}{2}\)
= \(\frac{-50 + 70}{2}\)
= \(\frac{20}{2}\)
= 10
Source: Myschool Past Questions Archive (Record #36690)
Mathematics
WAEC / WASSCE 2011
Plane Geometry, Polygons & Circle Theorems
Solution
If 27x = 9y. Find the value of \(\frac{x}{y}\)
A
\(\frac{1}{3}\)
B
\(\frac{2}{3}\)
C
1\(\frac{1}{2}\)
D
3
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
27x = 9y
33x = 32y
3x = 2y
Source: Myschool Past Questions Archive (Record #36691)
Mathematics
WAEC / WASSCE 2011
Trigonometry, Elevation & Bearings
Solution
a boy looks through a window of a building and sees a mango fruit on the ground 50m away from the foot of the building. If the window is 9m from the ground, calculate, correct to the nearest degree, the angle of depression of the mango from the window
A
9o
B
10o
C
11o
D
12o
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
tan \(\theta\) = \(\frac{9}{50}\) = 0.18
\(\theta = tan^{-1} 0.18\)
\(\theta\) = 10.20
Source: Myschool Past Questions Archive (Record #36692)
Mathematics
WAEC / WASSCE 2011
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
The diagram shows a cyclic quadrilateral PQRS with its diagonals intersecting at K. Which of the following triangles is similar to triangle QKR?
Attached Figure / Diagram
A
\(\bigtriangleup\) PQK
B
\(\bigtriangleup\) PKS
C
\(\bigtriangleup\) SKR
D
\(\bigtriangleup\) PSR
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
It is angle PKS, angles in the same segment. Therefore, PKS is congruent with QKR
Source: Myschool Past Questions Archive (Record #36698)
Mathematics
WAEC / WASSCE 2011
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram, PO and OR are radii, |PQ| = |QR| and reflex o. Calculate the value x
Attached Figure / Diagram
A
60o
B
55o
C
50o
D
45o
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
o
Also o
( o
x + R = 360 - 240 = 120; Since x = R
x + x = 120
2x = 120
Since x = R
x + x = 120
2x = 120
x = \(\frac{120}{2}\)
= 60o
Source: Myschool Past Questions Archive (Record #36699)