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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)
Mathematics
NECO SSCE 2002
Indices, Logarithms & Surds
Solution
If \(\frac{t}{L}\) = \(\sqrt{(\frac{4\pi^2}{g}})\), what is the value of g when L = 4.5; t = 5 secs
A
3.20 ms2
B
11.31 ms2
C
32.00 ms2
D
56.57 ms2
E
160.00 ms2
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{t}{L}\) = \(\sqrt{(\frac{4\pi^2}{g}})\)
Take square of both sides
\(\frac{t^2}{L^2}\) = \(\frac{4\pi^2}{g}\)
Cross multiply
t\(^2\)g = L\(^2\)4\(\pi\)\(^2\)
g = \(\frac{4\pi^2L^2}{t^2}\)
g = \(\frac{4 \times 4.5 \times 4.5 \pi^2}{5^2}\)
g = \(\frac{799.44}{25}\) = 31.9776 ≈ 32m/s\(^2\)
Source: Myschool Past Questions Archive (Record #42078)
Mathematics
NECO SSCE 2002
Permutations, Combinations & Probability
The probability that a student will pass a mathematics test is ⅗. If 3 students are chosen at random, what is the probability that at least 2 of them will pass the test?
A
\(\frac{27}{125}\)
B
\(\frac{9}{25}\)
C
\(\frac{72}{125}\)
D
\(\frac{76}{125}\)
E
\(\frac{81}{125}\)
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 #42107)
Mathematics
NECO SSCE 2002
Mensuration (Areas, Perimeters & Volumes)
Solution
What is the total surface area of a cylinder with radius 2cm and height 1.5cm, correct to 2 significant figures?
A
440cm\(^2\)
B
220cm\(^2\)
C
88cm\(^2\)
D
44cm\(^2\)
E
22cm\(^2\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
T.S.A of a cylinder = \(2\pi r (r + h)\)
= \(2 \times \frac{22}{7} \times 2 (2 + 1.5)\)
= 44 cm\(^2\)
Source: Myschool Past Questions Archive (Record #42130)
Mathematics
NECO SSCE 2002
Permutations, Combinations & Probability
One bag contains 4 white balls and 2 black balls. Another bag contains 3 white balls and 5 black balls, if one ball is drawn from each bag, what is the probability that both are white?
A
\(\frac{2}{3}\)
B
\(\frac{3}{8}\)
C
\(\frac{7}{24}\)
D
\(\frac{1}{4}\)
E
\(\frac{1}{24}\)
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 #42154)
Mathematics
NECO SSCE 2002
Linear, Simultaneous & Quadratic Equations
A quadratic equation with roots -1\(\frac{1}{2}\) and \(\frac{1}{4}\) is
A
x2 + 3x + 4 = 0
B
8x2 + 10x + 3 = 0
C
8x2 +12x – 3 = 0
D
8x2 + 10x-3.= 0
E
8x2 + 12x + 3 = 0
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 #42161)
Mathematics
NECO SSCE 2002
Linear, Simultaneous & Quadratic Equations
Solution
What are the factors of 2x\(^2\) - xy - 3y\(^2\) ?
A
(2x + 3y)(x + y)2
B
(2x + 3y)(x + y)
C
(2x + 3y)(x - y)
D
(2x - 3y)(x + y)
E
(2x - 3y)(x - y)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
2x\(^2\) - xy - 3y\(^2\)
= 2x\(^2\) + 2xy - 3xy - 3y\(^2\)
= 2x(x + y) - 3y(x + y)
= (2x - 3y)(x + y)
Source: Myschool Past Questions Archive (Record #42170)