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Mathematics
WAEC / WASSCE 2017
Geometry and Trigonometry
Solution
An arc of a circle of radius 7.5cm is 7.5cm long. Find, correct to the nearest degree, the angle which the arc subtends at the centre of the circle. [Take \(\pi = \frac{22}{7}\)]
A
29\(^o\)
B
57\(^o\)
C
65\(^o\)
D
115\(^o\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
lac = \(\frac{\theta}{360}\) x 2\(\pi\)r
7.5 = \(\frac{\theta}{360}\) x 2 x \(\frac{22}{7}\) x 7.5
7.5 = \(\frac{330\theta}{2520}\)
\(\theta\) = \(\frac{7.5}{0.1309}\)
\(\theta\) = 57.29
\(\theta\) = 57 \(^o\)
Source: Myschool Past Questions Archive (Record #49990)
Mathematics
WAEC / WASSCE 2017
Geometry and Trigonometry
Solution
The dimensions of water tank are 13cm, 10cm and 70cm. If it is half-filled with water, calculate the volume of water in litres
A
4.55 litres
B
7.50 litres
C
8.10 litres
D
9.55 litres
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Vol of a cubiod = L x b x h
v = 13cm x 10cm x 70cm
= 9100cm
Since it is half-filled = \(\frac{9100}{2}\)cm
= 4550cm
4550cm \(\to\) 4.55 litres
Source: Myschool Past Questions Archive (Record #49995)
Mathematics
WAEC / WASSCE 2017
Geometry and Trigonometry
Which of the following is true about parallelogram?
A
opposite angles are supplementary
B
opposite angles are complementary
C
opposite angles are equal
D
opposite angles are reflex angles
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 #50000)
Mathematics
WAEC / WASSCE 2017
Geometry and Trigonometry
Solution
Calculate the gradient (slope) of the joining points (-1, 1) and (2, -2)
A
-1
B
\(\frac{-1}{2}\)
C
\(\frac{1}{2}\)
D
1
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Gradient = m = \(\frac{y_2 - y_1}{x_2 - x_1}\)
= \(\frac{-2 -1}{2 + 1}\)
= \(\frac{-3}{3}\)
= -1
Source: Myschool Past Questions Archive (Record #50001)
Mathematics
WAEC / WASSCE 2017
Geometry and Trigonometry
A bearing of 320\(^o\) expressed as a compass bearing is
A
N 50\(^o\) W
B
N 40\(^o\) W
C
N 50\(^o\) E
D
N 40\(^o\) E
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 #50005)
Mathematics
WAEC / WASSCE 2017
Geometry and Trigonometry
Solution
Given that cos 30\(^o\) = sin 60\(^o\) = \(\frac{3}{2}\) and sin 30\(^o\) = cos 60\(^o\) = \(\frac{1}{2}\), evaluate \(\frac{tan 60^o - 1}{1 - tan 30^o}\)
A
\(\sqrt{3 - 2}\)
B
2 - \(\sqrt{3}\)
C
\(\sqrt{3}\)
D
-2
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
From the figure above, tan30º = \(\frac{1}{\sqrt3}\) and tan60º = \(\sqrt{3}\)
so \(\frac{tan60 - 1}{1 - tan30}\)
= \(\frac{\sqrt{3}}{1}\div(1 - (\frac{1}{\sqrt{3}}\)))
= \(\frac{\sqrt{3} - 1}{1}\div\frac{\sqrt{3} - 1}{\sqrt3}\)
= \(\frac{\sqrt{3} - 1}{1}\times \frac{\sqrt3}{\sqrt{3} - 1}\) = \(\sqrt{3}\)
Source: Myschool Past Questions Archive (Record #50014)
Mathematics
WAEC / WASSCE 2017
Geometry and Trigonometry
Solution
Three exterior angles of a polygon are 30\(^o\), 40\(^o\) and 60\(^o\). If the remaining exterior angles are 46\(^o\) each, name the polygon.
A
decagon
B
nonagon
C
octagon
D
hexagon
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Sum of all exterior angles is 360\(^o\)
360\(^o\) (30\(^o\) - 40\(^o\))
360 - (130\(^o\))
230\(^o\)
remaining is 46\(^o\) = \(\frac{230}{46}\) = 5
5 + 3 = 8 sides; Octagon
Source: Myschool Past Questions Archive (Record #50029)
Mathematics
WAEC / WASSCE 2017
Geometry and Trigonometry
Diagram
Solution
The diagram shows a circle O. If < ZYW = 33\(^o\) , find < ZWX
Attached Figure / Diagram
A
33\(^o\)
B
57\(^o\)
C
90\(^o\)
D
100\(^o\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
In
Source: Myschool Past Questions Archive (Record #50157)
Mathematics
WAEC / WASSCE 2017
Geometry and Trigonometry
Diagram
Solution
In the diagram, PQ and PS are tangents to the circle O. If PSQ = m,
Attached Figure / Diagram
A
103\(^o\)
B
123\(^o\)
C
133\(^o\)
D
143\(^o\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
< SQP = 180 - (90 + 33) < on a ----
= 180 - (123)
= 57\(^o\)
Therefore, (m + n) = 123\(^o\)
Source: Myschool Past Questions Archive (Record #50161)
Mathematics
WAEC / WASSCE 2017
Geometry and Trigonometry
Solution
Marks
0
1
2
3
4
5
Frequency
7
4
18
12
8
11
The table gives the distribution of marks obtained by a number of pupils in a class test. Using this information, Find the median of the distribution
A
4
B
3
C
1
D
2
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Median is \(\frac{n}{2} = \frac{6}{2}\)
= 3
Median = 3
Source: Myschool Past Questions Archive (Record #50171)
Mathematics
WAEC / WASSCE 2017
Geometry and Trigonometry
Solution
Marks
0
1
2
3
4
5
Frequency
7
4
18
12
8
11
The table gives the distribution of marks obtained by a number of pupils in a class test. Using this information, find the first quartile
A
1.0
B
1.5
C
2.0
D
2.5
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
First quartile = \(\frac{n}{4} = \frac{60}{4}\) = 15
The 15th value is 2
Source: Myschool Past Questions Archive (Record #50174)
Mathematics
WAEC / WASSCE 2017
Geometry and Trigonometry
Solution
A stationary boat is observed from a height of 100m. If the horizontal distance between the observer and the boat is 80m, calculate, correct to two decimal places, the angles of depression of the boat from point of observation
A
36.87\(^o\)
B
39.70\(^o\)
C
51.34\(^o\)
D
53.13\(^o\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Tan \(x^o = \frac{100m}{80}\)
Tan \(x^o = Tan^{-1} 1.25\)
x = 51.34\(^o\)
Source: Myschool Past Questions Archive (Record #50186)
Mathematics
WAEC / WASSCE 2017
Geometry and Trigonometry
Diagram
Solution
In the diagram, RPS is a diameter of the circle RSP, RP is produced to T and TS is a tangent to the circle at S. If < PRS = 24\(^o\), calculate the value of < STR
Attached Figure / Diagram
A
24\(^o\)
B
42\(^o\)
C
48\(^o\)
D
66\(^o\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
RSP = 90 < substance in semi a circle
RPS = 180 - (90 + 24)
= 180 - (114)
= 66
TPS = 180 - 66
= 114
RST = 24
< STR = 180 - (114 + 24)
= 180 - 138
= 42\(^o\)
Source: Myschool Past Questions Archive (Record #50190)
Mathematics
WAEC / WASSCE 2017
Geometry and Trigonometry
Solution
(a) If \((y - 1)\log_{10}4 = y\log_{10}16\), without using Mathematics tables or calculator, find the value of y.
(b) When I walk from my house at 4km/h, I will get to my office 30mins later than when I walk at 5km/h. Calculate the distance between my house and office.
medium Difficulty
Verified Correct Answer: Option
Step-by-Step Mathematical Solution
(a) \((y - 1)\log_{10} 4 = y\log_{10} 16\)
\((y - 1)\log_{10} 4 = y \log_{10} 4^{2}\)
\((y - 1)\log_{10} 4 = 2y\log_{10} 4\)
Equating both sides, we have
\(y - 1 = 2y \implies -1 = 2y - y\)
\(\therefore y = -1\)
(b) Let the distance from my house to the office = c.
At 4km/h, the time taken to get to the office from the house = \(\frac{c}{4} hr\)
At 5km/h, the time taken to get to the office from the house = \(\frac{c}{5} hr\)
\(\frac{c}{4} = \frac{c}{5} + \frac{30}{60}\)
\(\frac{c}{4} - \frac{c}{5} = \frac{1}{2}\)
\(\frac{c}{20} = \frac{1}{2} \implies c = 10km\)
Source: Myschool Past Questions Archive (Record #52324)
Mathematics
WAEC / WASSCE 2017
Geometry and Trigonometry
Solution
(a) The angle of depression of a point P on the ground from the top T of a building is 23.6^\circ. If the distance from P to the foot of the building is 50m, calculate, correct to the nearest metre, the height if the building.
(b)
In the diagram, \(PT // SU, QS // TR, /SR/ = 6cm\) and \(/RU/ = 10 cm\). If the area of \(\Delta TRU = 45 cm^{2}\), calculate the area of the trapezium QTUS.
medium Difficulty
Verified Correct Answer: Option
Step-by-Step Mathematical Solution
(a)
\(< P = 23.6^\circ\) (Alternate angle)
\(\tan 23.6 = \frac{x}{50}\)
\(x = 50\tan 23.6\)
= \(50 \times 0.4369\)
= \(21.845 m \approxeq 22 m\) (to the nearest metre)
(b) Given that \(\Delta TRU = 45cm^{2}\)
\(\implies \frac{1}{2}(bh) = 45\)
\(10h = 45 \times 2 = 90\)
\(h = 9cm\)
Area of trapezium = \(\frac{1}{2}(a + b)h\), where \(a = 6cm; b = 10 + 6 = 16cm; h = 9cm\)
= \(\frac{1}{2}(6 + 16) \times 9\)
= \(11 \times 9\)
= \(99 cm^{2}\)
Source: Myschool Past Questions Archive (Record #52329)