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Mathematics
WAEC / WASSCE 2004
Trigonometry, Elevation & Bearings
Solution
A point on the ground is 5m away from the foot of a vertical wall 7 m high, Calculate, correct to the nearest degree, the angle of depression of the point from the top of the wall
A
36o
B
44o
C
46o
D
54o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
θ= angle of depression of the point from the top of the wall
\(tan\theta = \frac{7}{5}=1.4; \theta = tan^{-1}(1.400)\
\theta = 54.4^{\circ}; \theta = 54^{\circ}\) to the nearest degree
Source: Myschool Past Questions Archive (Record #26669)
Mathematics
UTME / JAMB 2004
Statistics (Data Representation, Central Tendency & Dispersion)
Diagram
Solution
The graph above shows the cumulative frequency curve of the distribution of marks in a class test. What percentage of the students scored more than 20 marks?
Attached Figure / Diagram
A
68%
B
40%
C
17%
D
8%
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
class mark x
Cumulative. frequency
frequency
9
1
1
14
6
5
19
15
9
24
17
2 ↓
29
24
7 ↓
34
25
1 ↓
Total frequency = 25.
% students scoring over 20 marks = \(\frac{10}{25}\) x 100% = 40%
y-axis (Scale of the graph: 1cm to 0.5 units)
NOTE: (frequency of scores greater than 20 starts from 2 and ends at 1)
(To get frequency, subtract the cumulative frequency from down to upward)
Source: Myschool Past Questions Archive (Record #33117)
Mathematics
NECO SSCE 2004
Mensuration (Areas, Perimeters & Volumes)
Solution
Find the surface area of a sphere whose radius is 3.5cm, correct your answer to one decimal place (\pi = \(\frac{22}{7}\))
A
12.8cm2
B
25.7cm2
C
77.0cm2
D
154.0cm2
E
179.7cm2
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Surface area of a sphere
\(A = 4\pi r^2 \)
\(r = 3.5 = \frac{7}{2},\quad \pi = \frac{22}{7}\)
\(A = 4 \times \frac{22}{7} \times \left(\frac{7}{2}\right)^2 = 4 \times \frac{22}{7} \times \frac{49}{4}\) = 154
Source: Myschool Past Questions Archive (Record #42247)
Mathematics
NECO SSCE 2004
Indices, Logarithms & Surds
Solution
Two angles of a triangle are 45º each and its longest side is 12cm. Find the length of one of the other sides
A
12cm
B
9\(\sqrt{2}\)cm
C
6\(\sqrt{2}\)cm
D
6cm
E
3\(\sqrt{2}\)cm
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Two angles of a triangle are 45º each and its longest side is 12cm, this simply describes an isosceles triangle
two equal angles and two equal sides
using Pythagoras theorem,
\(x^2 + x^2 = 12^2\)
\(2x^2\) = 144
\(x^2\) = 72( after dividing b/sides by 2)
x = \(\sqrt{72} = 6\sqrt{2}\)cm.
Source: Myschool Past Questions Archive (Record #42248)
Mathematics
NECO SSCE 2004
Sequences & Series (AP & GP)
Solution
The nth term of a sequence is given as \(4 \times 3^{(3 - n)}\). Calculate the third term.
A
12
B
32
C
4
D
3
E
1
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(4 \times 3^{(3 - n)}\)
for the third term, n = 3
then
\(4 \times 3^{(3 - 3)}\) = \(4 \times 3^{0}\) = 4 x 1 = 4.
Source: Myschool Past Questions Archive (Record #42249)
Mathematics
NECO SSCE 2004
Variations
If y varies inversely as x2, how does x vary with y?
A
x varies inversely as y2
B
x varies inversely as \(\sqrt{y}\)
C
x varies directly as y2
D
x varies directly as \(\sqrt{y}\)
E
x varies directly as y
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 #42250)
Mathematics
NECO SSCE 2004
Indices, Logarithms & Surds
Find the area of a triangle ABC such that a = 16cm, b = 14cm, c = 12cm, leave your answer in surd form
A
5\(\sqrt{15}\)cm2
B
7\(\sqrt{15}\)cm2
C
21\(\sqrt{3}\)cm2
D
21\(\sqrt{5}\)cm2
E
21\(\sqrt{15}\)cm2
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 #42287)
Mathematics
NECO SSCE 2004
Sequences & Series (AP & GP)
Solution
If the first term of an AP is 1.2 and the common difference is also 2, what is the mean of the first five terms?
A
2
B
4
C
5
D
8
E
10
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Given the first term \( a = 1.2 \) and common difference \( d = 2 \), the first five terms of the AP are:
\(a_1 = 1.2\)
\(a_2 = 1.2 + 2 = 3.2\)
\(a_3 = 1.2 + 4 = 5.2 \)
\(a_4 = 1.2 + 6 = 7.2 \)
\(a_5 = 1.2 + 8 = 9.2\)
The sum of the first five terms is:
\(\text{Sum} = 1.2 + 3.2 + 5.2 + 7.2 + 9.2 = 26\)
The mean is calculated as:
\(\text{Mean} = \frac{26}{5} = 5.2\)
Thus, the mean of the first five terms is \(5.2\).
Source: Myschool Past Questions Archive (Record #42289)
Mathematics
NECO SSCE 2004
Mensuration (Areas, Perimeters & Volumes)
The angle subtended by a diameter of a circle at the circumference is a/an
A
acute angle
B
obtuse angle
C
reflex angle
D
right angle
E
supplementary angle
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 #42291)
Mathematics
NECO SSCE 2004
Fractions, Decimals, Percentages & Approximations
Calculate (0.05 × 0.025) ÷ (4.25 × 3.35) and express your answer in standard form
A
8.7796 × 105
B
8.7796 × 104
C
8.7796 × 103
D
8.7796 × 10-3
E
8.7796 × 10-5
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 #42293)
Mathematics
NECO SSCE 2004
Plane Geometry, Polygons & Circle Theorems
The expression 4x2 - 4 has the following as its factors EXCEPT
A
x - 1
B
x + 1
C
x2 -1
D
4x + 1
E
4x - 4
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 #42295)
Mathematics
NECO SSCE 2004
Linear, Simultaneous & Quadratic Equations
Solve the equation: \(\frac{3}{[2(x - 2)]} - \frac{2}{[3(2 - x)]} = 0\)
A
3
B
2
C
\(\frac{3}{2}\)
D
\(\frac{2}{3}\)
E
-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 #42308)
Mathematics
NECO SSCE 2004
Linear, Simultaneous & Quadratic Equations
A car travels at an average speed of 75km/h. Find its speed in metres per second.
A
270m/s
B
208m/s
C
27.0m/s
D
20.8m/s
E
2.08m/s
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 #42309)
Mathematics
NECO SSCE 2004
Linear, Simultaneous & Quadratic Equations
What must be added to b2-3ab to make it a perfect square?
A
-3a
B
-\(\frac{3}{2}\)
C
\(\frac{9}{4}\)
D
\(\frac{9a}{4}\)
E
\(\frac{9^2}{4}\)
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 #42310)
Mathematics
NECO SSCE 2004
Fractions, Decimals, Percentages & Approximations
A sales boy gave a change of N75.00 to a buyer instead of N80.00, calculate his percentage error, correct to one decimal place?
A
6.00%
B
6.20%
C
6.30%
D
6.60%
E
6.70%
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 #42311)