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Mathematics
WAEC / WASSCE 1997
Plane Geometry, Polygons & Circle Theorems
Solution
Simplify log39 + log315 - log35
A
log319
B
log3
C
3
D
1
E
o
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
log3 (9 x 15)/5 = log327 = 3
Source: Myschool Past Questions Archive (Record #23858)
Mathematics
WAEC / WASSCE 1997
Plane Geometry, Polygons & Circle Theorems
Solution
Solve me equation: 2/3 (x + 5) = 1/4(5x - 3)
A
11/7
B
18/23
C
3
D
43/7
E
7
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
2/3 (x + 5) = 1/4(5x - 3)
8x + 40 = 15x - 9
-7x = -49
x = 7
Source: Myschool Past Questions Archive (Record #23859)
Mathematics
WAEC / WASSCE 1997
Linear, Simultaneous & Quadratic Equations
Solution
Which of the following equations has its roots as 4 and -5?
A
x2 + 4x - 20 = 0
B
x2 + x + 20 = 0
C
x2 - x + 20 = 0
D
x2 + x - 20 = 0
E
x2 - x - 20 = 0
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
(x - 4)(x + 5) = 0
x\(^2\) + 5x - 4x - 20 = 0
x\(^2\) + x - 20 = 0
Source: Myschool Past Questions Archive (Record #23860)
Mathematics
WAEC / WASSCE 1997
Linear, Simultaneous & Quadratic Equations
Solution
Solve the equations: 4x -y = 11; 5x + 2y = 4.
A
x = 6, y = 13
B
x = -2, y = -3
C
x = -2, y = 3
D
x = 2, y = -3
E
x = 2, y = 3.
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
4x - y = 11....(1) x 2 8x - 2y = 22....(3)
5x + 12y = 4....(2) x 1 5x + 2y = 4....(4)
add eqn (3) and (4)
13x = 26
x = 2
4(2) - y = 11 \(\implies\) y = 8 - 11
y = -3.
Source: Myschool Past Questions Archive (Record #23861)
Mathematics
WAEC / WASSCE 1997
Variations
Solution
P varies inversely as the square of W. When W = 4, P = 9. Find the value of P when W = 9
A
729/16
B
6
C
4
D
16/9
E
4/3
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
P α 1/w2; P = K/W2
9 = K/42; 9 = K/16
K = 9 x 16 = 144
P = K/W2; when w = 9
P = 144/92 = 144/81 = 16/9
Source: Myschool Past Questions Archive (Record #23863)
Mathematics
WAEC / WASSCE 1997
Inequalities & Linear Programming
Diagram
If x varies over the set of real numbers, which of the following is illustrated in the diagram above?
Attached Figure / Diagram
A
-2 ≤ x < 3
B
-2 < x ≤ 3
C
-2 < x < 3
D
-2 ≤ x ≤ 3
E
x ≥ 3
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option B.
Source: Myschool Past Questions Archive (Record #23864)
Mathematics
WAEC / WASSCE 1997
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the triangle XYZ , XM is the altitude from X to YZ.XY = 13cm, XZ = 15cm and YM = 5cm. Find the length of YZ
Attached Figure / Diagram
A
9cm
B
12cm
C
14cm
D
19.85cm
E
23cm
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
XM = \sqrt132 - 52 = 12cm
MZ = 152 - 122 = 9cm
YZ = 9 + 5 = 14cm
Source: Myschool Past Questions Archive (Record #23865)
Mathematics
WAEC / WASSCE 1997
Mensuration (Areas, Perimeters & Volumes)
Solution
Two points P and Q are on longitude 67^\circW. Their latitudes differ by 90^\circ. Calculate their distance apart in terms of \pi. (Take radius of the earth = 6400km).
A
6400πkm
B
6400km/π
C
3200πkm
D
3200km
E
3200km/π
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
P(67^\circW, 0^\circN)
Q(67^\circW 90^\circN), R = 6400km
Distance PQ =
90/360 x 2 x 6400 \pi
= 3200\pikm
Source: Myschool Past Questions Archive (Record #23866)
Mathematics
WAEC / WASSCE 1997
Plane Geometry, Polygons & Circle Theorems
Solution
The length of the two parallel sides of trapezium are 6cm and 10cm and the perpendicular distance between them is 5cm. Find the area of the trapezium
A
21cm2
B
4Ocm2
C
8Ocm2
D
150cm2
E
300cm2
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Area = 1/2(6 + 10) x 5
40cm2
Source: Myschool Past Questions Archive (Record #23867)
Mathematics
WAEC / WASSCE 1997
Mensuration (Areas, Perimeters & Volumes)
Solution
Calculate the total surface area of a solid cone of slant height 15cm and base radius 8cm in terms of π
A
64πcm2
B
12Oπcm2
C
184πcm2
D
200πcm2
E
32Oπcm2
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Total surface are of a cone
= πr(r + l)
= π x 8 (8 + 150)
= 184πcm2
Source: Myschool Past Questions Archive (Record #23868)
Mathematics
WAEC / WASSCE 1997
Mensuration (Areas, Perimeters & Volumes)
Solution
The cross-section of a prism is a right-angled triangle 3cm by 4cm by 5cm. The height of the prism is 8cm. Calculate its volume
A
48cm3
B
6Ocm3
C
96cm3
D
120cm3
E
24Ocm3
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Volume = base area x height
= 1/2 x 4 x 3 x 8
= 48cm3
Source: Myschool Past Questions Archive (Record #23869)
Mathematics
WAEC / WASSCE 1997
Plane Geometry, Polygons & Circle Theorems
Solution
Find the radius of a circle in which an arc of length 44cm subtends angle 200^\circ at the centre of the circle. [Take \pi = 22/7]
A
3.9cm
B
12.6cm
C
25.2cm
D
38.4cm
E
124.5cm
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
44 = 200/360 x 2 x 22/7 x r
r = 360 x 7 x 44/200 x 2 x 22
= 12.6cm
Source: Myschool Past Questions Archive (Record #23870)
Mathematics
WAEC / WASSCE 1997
Trigonometry, Elevation & Bearings
Diagram
Solution
The diagram above is a triangle XYZ whose area is 23.5cm2. XY =1Ocm and YZ = 8cm, calculate θ correct to the nearest degree.
Attached Figure / Diagram
A
34o
B
35o
C
36o
D
37o
E
40o
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Area = 1/2 x y x yz sinθ
23.5 = 1/2 x 10 x 8 sinθ
sinθ = 23.5 x 2/10 x 8 = 0.5875
θ = sin-1 0.5875 = 36o
Source: Myschool Past Questions Archive (Record #23871)
Mathematics
WAEC / WASSCE 1997
Plane Geometry, Polygons & Circle Theorems
Which of the following is not necessarily sufficient for the construction of a triangle?
A
Three sides
B
Two sides and an included angle
C
Two sides and a right angle
D
Two sides and an angle
E
Two angles and a side.
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 #23872)
Mathematics
WAEC / WASSCE 1997
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram, EF//QR, PE = 2cm, EQ = 4cm and FR = 6cm. Find x
Attached Figure / Diagram
A
2cm
B
3cm
C
4cm
D
5cm
E
6cm
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
2/2 + 4 = x/x + 6
2x + 12 = 6x
4x = 12
x = 3cm
Source: Myschool Past Questions Archive (Record #23873)