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Mathematics
WAEC / WASSCE 2006
Plane Geometry, Polygons & Circle Theorems
Solution
If x + y = 12 and 3x - y = 20, find the value of 2x - y
A
8
B
10
C
12
D
15
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
x + y = 12
+ 3x - y = 20
---------------
4x = 32
x = 8
x + y = 12; 8 + y = 12; y = 12 - 8
= 4
2x - y = 2(8) - 4; 16 - 4 = 12
Source: Myschool Past Questions Archive (Record #36179)
Mathematics
WAEC / WASSCE 2006
Linear, Simultaneous & Quadratic Equations
Diagram
Solution
Which of these equations best describes the points of intersection of the curve and the line?
Attached Figure / Diagram
A
\(x^2 + 5x - 6 = 0\)
B
x2 - 5x - 6 = 0
C
x2 + x - 6 = 0
D
x2 - x - 6 = 0
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
The roots are -3 and 1
x = -3 and x = 1
y = (x + 3)(x - 1)
= x2 - x + 3x - 3
y = x2 + x - 6 = 0
Source: Myschool Past Questions Archive (Record #36181)
Mathematics
WAEC / WASSCE 2006
Indices, Logarithms & Surds
Solution
If loga270 - loga10 + loga \(\frac{1}{3}\) = 2, what is the value of a?
A
3
B
4
C
5
D
6
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
loga270 - loga10 + loga\(\frac{1}{3}\) = 2
loga270 + loga\(\frac{1}{3}\) - loga10 = 2
loga(270\(\frac{\frac{1}{3}}{10}\)) = 2
loga9 = 2
aa = 9
a = \(\sqrt{9}\) = 3
Source: Myschool Past Questions Archive (Record #36185)
Mathematics
WAEC / WASSCE 2006
Plane Geometry, Polygons & Circle Theorems
Solution
a conical water-jug is 7cm in diameter and 6cm deep. find the volume of water it can hold. [Take \(\pi = \frac{22}{7}\)]
A
22cm2
B
44cm3
C
77cm3
D
3082
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Volume = \(\frac{1}{3} \pi r^2h = \frac{1}{3} \times \frac{22}{7} \times \frac{7}{2} \times \frac{7}{2} \times \frac{6}{1}\)
V = \(\frac{6468}{84}\)
= 77cm3
Source: Myschool Past Questions Archive (Record #36187)
Mathematics
WAEC / WASSCE 2006
Algebraic Expressions, Polynomials & Factorisation
Solution
If p = [\(\frac{Q(R - T)}{15}\)]\(^ \frac{1}{3}\), make T the subject of the relation
A
T = R + \(\frac{P^3}{15Q}\)
B
T = R - \(\frac{15P^3}{Q}\)
C
T = R + \(\frac{P^3}{15Q}\)
D
T = 15R - \(\frac{Q}{P^3}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Cubic both sides; P3 = \(\frac{Q(R - T)}{15}\)
(cross multiplication) Q(R - T) = 15P3
(divide both sides by Q); R - T = 15\(\frac{1}{Q}\)
(subtract r from both sides) - T = \(\frac{15P^3}{Q - R}\)
T = R - \(\frac{15P^3}{Q}\)
Source: Myschool Past Questions Archive (Record #36189)
Mathematics
WAEC / WASSCE 2006
Fractions, Decimals, Percentages & Approximations
Solution
A seller allows 20% discount for cash payment on the marked price of his goods. What is the ratio of the cash payment to the marked price
A
1:4
B
1:5
C
3:4
D
4:5
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
(1 - \(\frac{20}{100}\)) = cash payment fraction= \(\frac{4}{5}\)
The ratio of the cash payment to the marked price = 4:5
Source: Myschool Past Questions Archive (Record #36190)
Mathematics
WAEC / WASSCE 2006
Mensuration (Areas, Perimeters & Volumes)
Solution
The wheel of a tractor has a diameter 1.4m. What distance does it cover in 100 complete revolutions? [Take \(\pi = \frac{22}{7}\)]
A
140m
B
220m
C
280m
D
440m
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
radius = \(\frac{diameter}{2}\) = \(\frac{1.4}{2}\)
= 0.7m
circumference = 2\(\pi r = 2 \times \frac{22}{7} \times 0.7m = 4.4m\)
distance covered = 4.4m x 100 = 440m
Source: Myschool Past Questions Archive (Record #36191)
Mathematics
WAEC / WASSCE 2006
Sets, Logic & Venn Diagrams
Solution
If p = {1, 3, 5, 7, 9} and Q = {2, 4, 6, 8, 10} are subsets of a universal set. U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. What are the elements of P1 \(\cap\) Q1?
A
{1, 3, 5, 7, 9}
B
[2, 4, 6, 8, 10}
C
\(\varnothing\)
D
{1, 2, 6, 8, 10}
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
P1 = {2, 4, 6, 8, 10}; {1, 3, 5, 7, 9}
P1 \(\cap\) q1 = {} or \(\varnothing\)
Source: Myschool Past Questions Archive (Record #36192)
Mathematics
WAEC / WASSCE 2006
Plane Geometry, Polygons & Circle Theorems
Solution
The values of three angles at a point are 3y - 45o, y + 25o and yo . Find the value of y.
A
40o
B
58o
C
68o
D
76o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
(3y - 450 + (y + 25) + t = 360o(angles at a point)
3y - 45 + y + 25 + y = 360
5y = 360 + 20
5y = 380
y = \(\frac{380}{5}\)
= 76o
Source: Myschool Past Questions Archive (Record #36193)
Mathematics
WAEC / WASSCE 2006
Fractions, Decimals, Percentages & Approximations
Solution
A rectangular carpet 2.5m long and 2.4m wide covers 5% of a rectangular floor. Calculate the area of the floor
A
30m2
B
57m2
C
120m2
D
225m2
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Area of carpet = 2.5 x 2.4 = 6
Let F represent the floor
6 = 5% of F
6 = \(\frac{5}{100}\) x F
5F = 6 x 100
F = 6 x \(\frac{100}{5}\)
= 120m2
Source: Myschool Past Questions Archive (Record #36194)
Mathematics
WAEC / WASSCE 2006
Statistics (Data Representation, Central Tendency & Dispersion)
Which of the following is not a measure of centre tendency?
A
mean
B
mode
C
range
D
median
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 #36197)
Mathematics
WAEC / WASSCE 2006
Plane Geometry, Polygons & Circle Theorems
Solution
The temperature in a chemical plant was -5oC at 2.00 am. The temperature fell by 6oC and then rose again by 7oC. What was the final temperature?
A
-6oC
B
-4oC
C
4oC
D
8oC
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Temperature = -5oC
It fell by 6oC = -5oC - 6oC
= -11oC
Then rose by 7oC = -11 + 7
= -4oC (final temperature)
Source: Myschool Past Questions Archive (Record #36199)
Mathematics
WAEC / WASSCE 2006
Indices, Logarithms & Surds
Solution
Simplify \(\frac{20}{5\sqrt{28} - 2 \sqrt{63}}\)
A
\(\frac{5\sqrt{7}}{7}\)
B
\(\frac{5\sqrt{5}}{7}\)
C
\(\frac{7\sqrt{5}}{7}\)
D
\(\frac{7\sqrt{7}}{5}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\frac{20}{5 \sqrt{4 \times 7} - 2\sqrt{9 \times 7}}\)
\(\frac{20}{10 \sqrt{7} - 6\sqrt{7}}\)
= \(\frac{20 \sqrt{7}}{4 \sqrt{7}}\)
= \(\frac{5\sqrt{7}}{7}\)
Source: Myschool Past Questions Archive (Record #36200)
Mathematics
WAEC / WASSCE 2006
Trigonometry, Elevation & Bearings
Solution
A ladder 16m long leans against an electric pole. If the ladder makes an angle of 65o with the ground, how far up the electric pole does its top reach
A
6.8m
B
14.5m
C
17.7m
D
34.3m
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Sin 65o = \(\frac{x}{16}\)
x = 16x sin 65
= 16 x 0.9063
x = 14.5m
Source: Myschool Past Questions Archive (Record #36201)
Mathematics
WAEC / WASSCE 2006
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram, PQUV, PQTU, QRTU and QRST are parallelograms. |UV| = 4.8cm and the perpendicular distance between PR and VS is 5cm. Calculate the area of quadrilateral PRSV
Attached Figure / Diagram
A
96cm2
B
72cm2
C
60cm2
D
24cm2
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
|VU| = |UT| = |TS|
|VS| = (4.8) x 3 = 14.4cm
|PQ| = |QR| = 4.8
|PR| = (4.8) x 2 = 9.6cm
Since quad. PRSV is a trapezium of height 5cm
Area of quad. PRSV = \(\frac{1}{2}(a + b)h\)
= \(\frac{1}{2}(14.4 + 9.6) \times 5\)
= \(\frac{1}{2}(24) \times 5\)
12 x 5 = 60cm2
Source: Myschool Past Questions Archive (Record #36202)