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Mathematics
WAEC / WASSCE 2002
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram O is the center of the circle, ∠SOR = 64^\circ and ∠PSO = 36^\circ. Calculate ∠PQR
Attached Figure / Diagram
A
100o
B
96o
C
94o
D
86o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
< OSR = < ORS = \(\frac{180^\circ - 64^\circ}{2}\) = 58^\circ
< PSR = 36^\circ + 58^\circ = 94^\circ
< PSR + < PQR = 180^\circ
94^\circ + < PQR = 180^\circ \(\implies\) < PQR = 180^\circ - 94^\circ = 86^\circ
Source: Myschool Past Questions Archive (Record #26565)
Mathematics
WAEC / WASSCE 2002
Plane Geometry, Polygons & Circle Theorems
Solution
Given that \(p = x-\frac{1}{x} and\hspace{1mm}q = x^2 + \frac{1}{x^2}\) express q in terms of p.
A
(p2 + 2)
B
(p - 2) 2
C
(p + 2) 2
D
(p2 - 2)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Given \(p = x - \frac{1}{x}\); \(q = x^2 + \frac{1}{x^2}\).
\(p^2 = (x - \frac{1}{x})(x - \frac{1}{x})\)
\(p^2 = x^2 + \frac{1}{x^2} - 2\)
\(p^2 = q - 2 \implies q = p^2 + 2\)
Source: Myschool Past Questions Archive (Record #26566)
Mathematics
WAEC / WASSCE 2002
Permutations, Combinations & Probability
Solution
The number of goals scored by a school team in 10 netball matches are as follows: 3, 5, 7, 7, 8, 8, 8, 11, 11, 12. Find the probability that in a match, the school team will score at most 8 goals.
A
\(\frac{7}{10}\)
B
\(\frac{2}{5}\)
C
\(\frac{3}{5}\)
D
\(\frac{1}{5}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Number of at most 8 goals = 7
P(at most 8 goals) = \(\frac{7}{10}\)
Source: Myschool Past Questions Archive (Record #26567)
Mathematics
WAEC / WASSCE 2002
Indices, Logarithms & Surds
Which of the following is not a rational number?
A
-5
B
\(\sqrt{4}\)
C
\(3\frac{3}{4}\)
D
\(\sqrt{90}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option D.
Source: Myschool Past Questions Archive (Record #26568)
Mathematics
WAEC / WASSCE 2002
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram, LMT is a straight line. lf O is the centre of circle LMN, OMN = 20^\circ, LTN = 32^\circ and |NM| = |MT|, find LNM.
Attached Figure / Diagram
A
44o
B
46o
C
52o
D
70o
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
< MNT = < MTN = 32^\circ
< NMT = 180^\circ - 2(32^\circ) = 116^\circ
< OMN + < NMT + < LMO = 180^\circ
20^\circ + 116^\circ + < LMO = 180^\circ \(\implies\) < LMO = 180^\circ - 136^\circ = 44^\circ
< LMN = < LMO + < OMN
= 44^\circ + 20^\circ = 64^\circ
< NOM = 180^\circ - 2(20^\circ) = 140^\circ
< NLM = \(\frac{1}{2} \times < NOM = 70^\circ\)
< LNM + < LMN + < NLM = 180^\circ
< LNM + 64^\circ + 70^\circ = 180^\circ
< LNM = 180^\circ - 134^\circ = 46^\circ
Source: Myschool Past Questions Archive (Record #26569)
Mathematics
NECO SSCE 2002
Sets, Logic & Venn Diagrams
Solution
Given that the universal set U={14,15,16,17,18,19,20}, J ={16,19,20} and K= {14,15,18}, find (J' ∩ K')1.
A
{17}
B
{16, 17, 19, 20}
C
{1, 4, 15, 17, 18}
D
{14, 15, 16, 18, 19, 20}
E
{14, 15, 16, 17, 18, 19, 20}
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
U = {14,15,16,17,18,19,20}
J' = {14,15,17,18}
K' = {16,17,19,20}
(J' \(\cap\) K') = {17}
(J' \(\cap\) K')' = {14,15,16,18.19,20}
Source: Myschool Past Questions Archive (Record #41976)
Mathematics
NECO SSCE 2002
Indices, Logarithms & Surds
Solution
Evaluate 1.25 \times 10\(^2\) \times 0.125 \times 10\(^3\) \times 12.5 \times 10\(^{-4}\) leaving your answer in standard form
A
1.995 × 103
B
1.95 × 102
C
1.95 × 101
D
1.95 × 10-2
E
1.95 × 10-3
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Where 1.25 \times 10\(^2\) = 125
0.125 \times 10\(^3\) = 125
12.5 \times 10\(^{-4}\) = 0.00125
: 125 x 125 x 0.00125
= 19.53125 or 1.95 x 10\(^1\)
Source: Myschool Past Questions Archive (Record #42011)
Mathematics
NECO SSCE 2002
Mensuration (Areas, Perimeters & Volumes)
What is the volume of a cube if the diagonal of one of the sides is \(\sqrt{50}\)cm?
A
7.07cm\(^3\)
B
50.0cm\(^3\)
C
125.0cm\(^3\)
D
353.4cm\(^3\)
E
625.0cm\(^3\)
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 #42018)
Mathematics
NECO SSCE 2002
Mensuration (Areas, Perimeters & Volumes)
A cone was developed from a sector of a circle with radius10cm and an angle at the centre of 108°. What is the radius of the cone?
A
9.0cm
B
8.5cm
C
7.2cm
D
4.3cm
E
3.0cm
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option E.
Source: Myschool Past Questions Archive (Record #42021)
Mathematics
NECO SSCE 2002
Plane Geometry, Polygons & Circle Theorems
If , sT = \(\sqrt{\frac{[(a + T)T]}{a}}\) what does T equal?
A
T = (a2s2 – 1)
B
T = (a2s2– 1) ÷ a
C
T = a ÷ (a2 - s2)
D
T = a ÷ (a2s2 – 1)
E
T = (as – 1)2
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option D.
Source: Myschool Past Questions Archive (Record #42034)
Mathematics
NECO SSCE 2002
Mensuration (Areas, Perimeters & Volumes)
What is the total surface area of a cuboid whose dimensions are 12cm × 8cm × 3cm?
A
312cm\(^2\)
B
96cm\(^2\)
C
36cm\(^2\)
D
24cm\(^2\)
E
12cm\(^2\)
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 #42040)
Mathematics
NECO SSCE 2002
Trigonometry, Elevation & Bearings
Solution
If sin 30^\circ = 0.5, what is the cosine of its complement?
A
-0.866
B
-0.5
C
0.5
D
0.866
E
1
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
To find the cosine of the complement of \(30^\circ\), we first calculate the complement:
\(90^\circ - 30^\circ = 60^\circ\)
Next, we need to find \( \cos 60^\circ \). The known trigonometric value is:
\(\cos 60^\circ = 0.5\)
Therefore, the cosine of the complement of \(30^\circ\) is: 0.5
Source: Myschool Past Questions Archive (Record #42044)
Mathematics
NECO SSCE 2002
Permutations, Combinations & Probability
Solution
A petrol attendant recorded the number of vehicles that bought petrol from him for -3 hours and recorded 12 cars and 27 buses. What is the probability that the next vehicle will be a bus?
A
\(\frac{4}{39}\)
B
\(\frac{4}{13}\)
C
\(\frac{5}{13}\)
D
\(\frac{6}{13}\)
E
\(\frac{9}{13}\)
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
Prob = \(\frac{ no of expected outcome}{ no of total outcome}\)
no of cars = 12, no of buses = 27
no of total outcome = 12 + 27 = 39
no of expected outcome = 27
Prob( next vehicle will be bus) = \(\frac{27}{39} = \frac{9}{13}\)
Source: Myschool Past Questions Archive (Record #42062)
Mathematics
NECO SSCE 2002
Plane Geometry, Polygons & Circle Theorems
Solution
Two parallel chords of a circle are respectively 46cm and 40cm long. If the radius of the circle is 25cm and the centre of the circle lies between the two chords, what is the distance between the chords?
A
7cm
B
15cm
C
22cm
D
26cm
E
30cm
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Let the two parallel chords be AB = 46 cm and CD = 40 cm.
Radius of the circle, r = 25 cm.
The centre O lies between the two chords.
Draw perpendiculars from O to the chords (these perpendiculars bisect the chords).
- Half of AB = 23 cm
- Half of CD = 20 cm
Distance from centre to each chord:
For chord AB (46 cm):
d\(_1 = \sqrt{r^2 - 23^2} = \sqrt{625 - 529} = \sqrt{96} = 4\sqrt{6} \approx 9.80 \text{ cm}\)
For chord CD (40 cm):
d\(_2 = \sqrt{r^2 - 20^2} = \sqrt{625 - 400} = \sqrt{225} = 15 \text{ cm}\)
Since the centre lies between the two chords, the distance between the chords is: d\(_1 + d_2 = 4\sqrt{6} + 15 \text{ cm}\)
Approximate value: ≈ 24.80 cm
Source: Myschool Past Questions Archive (Record #42064)
Mathematics
NECO SSCE 2002
Indices, Logarithms & Surds
The angle of elevation of the top (T) of a palm tree from a point (R) on the ground is 30°. The distance from R to the base (B) of the palm tree is 120m. What is the distance between T and R?
A
60m
B
60\(\sqrt{3}\)m
C
80\(\sqrt{3}\)m
D
120\(\sqrt{3}\)m
E
240m
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 #42070)