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Mathematics
NECO SSCE 2002
Indices, Logarithms & Surds
If sin θ = \(\frac{\sqrt{3}}{2}\) and 0 < θ < 180°, what is cos θ ?
A
\(\frac{1}{\sqrt{3}}\)
B
\(\frac{2}{\sqrt{3}}\)
C
\(\frac{1}{2}\)
D
\(\frac{\sqrt{3}}{2}\)
E
\(\sqrt{3}\)
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 #42179)
Mathematics
NECO SSCE 2002
Fractions, Decimals, Percentages & Approximations
Three sets of rice x, y and z are sold for N15.00, N35.00 and N60.00 respectively per kg. It they are mixed in the ratio of 1: 3 : 2, what is the cast per kg of the mixture?
A
N45.00
B
N42.50
C
N40.00
D
N35.50
E
N25.80
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 #42182)
Mathematics
NECO SSCE 2002
Fractions, Decimals, Percentages & Approximations
Solution
When a shirt is sold for N12000.00, a loss of 20% is recorded. How much should it be sold for to gain 20%?
A
N4800.00
B
N400
C
N1800.00
D
N1500.00
E
N960.00
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
When a shirt is sold for ₦12,000 at a 20% loss, it means ₦12,000 is 80% of the cost price.
Find the Cost Price (CP)
CP = \(\frac{12,000}{80\%} = \frac{12,000}{0.8}\) = ₦15,000
Find the selling price for 20% gain
To gain 20%, the new selling price should be 120% of the cost price.
SP = 120\(\% \text{ of } ₦15,000 = 1.2 \times\) 15,000 = ₦18,000.
Source: Myschool Past Questions Archive (Record #42187)
Mathematics
NECO SSCE 2002
Linear, Simultaneous & Quadratic Equations
What must be added to 3x2 - 5x to make it a perfect square?
A
\(\frac{36}{25}\)
B
\(\frac{25}{36}\)
C
-\(\frac{25}{36}\)
D
-\(\frac{5}{6}\)
E
-\(\frac{6}{5}\)
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 #42195)
Mathematics
NECO SSCE 2002
Inequalities & Linear Programming
Twice a number, x, is added to 5, the result is at least 11. What is the range of values of x?
A
x > 3
B
x ≥ 3
C
x ≤ 3
D
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 #42197)
Mathematics
NECO SSCE 2002
Plane Geometry, Polygons & Circle Theorems
Simplify [1 ÷ (x + 1)] - [2 ÷ (x - 1)] + [3 ÷ (x2 - 1)]
A
- 3x ÷ (x2 - 1)
B
- x ÷ (x2 -1)
C
x ÷ (x2 - 1)
D
(x + 1) ÷ (x2 - 1)
E
(x + 4) ÷ (x2 - 1)
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 #42199)
Mathematics
NECO SSCE 2002
Plane Geometry, Polygons & Circle Theorems
The mean heights of 3 groups of students consisting of 20, 16 and 14 students are 1.67m, 1.50m and 1.40m Respectively. What is the mean height of all the students?
A
1.52m
B
1.53m
C
1.54
D
1.55m
E
1.56m
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 #42201)
Mathematics
NECO SSCE 2002
Trigonometry, Elevation & Bearings
Solution
A girl on top of a storey building 36m high dropped a N10.00 note on the ground below. If the angle of depression of the N10.00 note is 35^\circ, how far is the money from the girl?
A
20.64m
B
29.48m
C
44.49m
D
49.55m
E
62.76m
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
make a sketch
using trig.ratios
Sin\(\theta\) = \(\frac{opp}{hyp}\)
Sin35 = \(\frac{36}{hyp}\)
hyp = \(\frac{36}{sin35}\) = 62.76m
∴ the distance between the girl and the #10.00 note = 62.76m.
Source: Myschool Past Questions Archive (Record #42205)
Mathematics
NECO SSCE 2002
Fractions, Decimals, Percentages & Approximations
After what length of time will N2400.00 yield an interest of N60.00 at 1\(\frac{1}{2}\)% per annum?
A
2\(\frac{4}{5}\) years
B
1\(\frac{2}{3}\) years
C
1\(\frac{1}{2}\) years
D
1 years
E
\(\frac{3}{5}\) year
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 #42209)
Mathematics
NECO SSCE 2002
Linear, Simultaneous & Quadratic Equations
Solution
Solve the equation: \(\frac{1}{3}x\) + \(\frac{2}{5}\) = \(\frac{3}{4}x\) - \(\frac{1}{6}\)
A
\(\frac{17}{30}\)
B
\(\frac{65}{102}\)
C
\(\frac{25}{34}\)
D
\(\frac{102}{75}\)
E
\(\frac{34}{25}\)
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
\(\frac{1}{3}x\) + \(\frac{2}{5}\) = \(\frac{3}{4}x\) - \(\frac{1}{6}\)
collect like terms
\(\frac{2}{5}\) + \(\frac{1}{6}\) = \(\frac{3}{4}x\) - \(\frac{1}{3}x\)
\(\frac{17}{30}\) = \(\frac{5x}{12}\)
cross multiply
150x = 204
x = \(\frac{204}{150}\) = \(\frac{34}{25}\)
Source: Myschool Past Questions Archive (Record #42213)
Mathematics
NECO SSCE 2002
Plane Geometry, Polygons & Circle Theorems
Solution
An amount of money is shared among P,Q and R such that for every 3P gets, Q gets 2 and for every 1Q gets, R gets 4. Find P: Q : R
A
3 : 1 : 4
B
3 : 2 : 1
C
3 : 2 : 4
D
3 : 3 : 4
E
3 : 2 : 8
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
P gets 3 Q gets 2, Q gets 1 and R gets R
When Q gets 1 then P will get \(\frac{3}{2}\)
P : Q: R = \(\frac{3}{2}\) : 1 : 4
multiplying through by 2, we have
3 : 2: 8.
Source: Myschool Past Questions Archive (Record #42215)
Mathematics
NECO SSCE 2002
Plane Geometry, Polygons & Circle Theorems
Simplify 2a2 -4ab - 6a2 - 10ab + 5ab - 5a2
A
-9(a + b)
B
9(a + b)
C
-9a (a + b)
D
9a(a - b)
E
9b(a + b)
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 #42218)
Mathematics
NECO SSCE 2002
Trigonometry, Elevation & Bearings
A boy leaves station X on a bearing of 035° to station y which is 21km away. He then travels to another station Z on a bearing of 125°. If Z is directly East of X, what is the distance from X to his present position?
A
3.0km
B
12.04km
C
17.2km
D
34.18km
E
36.61km
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 #42220)
Mathematics
NECO SSCE 2002
Mensuration (Areas, Perimeters & Volumes)
Solution
The length, breadth and height of a cuboid are 8cm, 7\(\frac{1}{2}\)cm and 6\(\frac{1}{2}\) cm respectively. What Is its volume in m3 (leave your answer in standard form)?
A
3.9 × 10-1m3
B
3.9 × 10-2m3
C
3.9 × 10-3m3
D
3.9 × 10-4m3
E
3.9 × 10-5m3
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Given: L = 8cm, B = 7\(\frac{1}{2}\)cm = 7.5cm, H = 6\(\frac{1}{2}\)cm = 6.5cm
Volume of cuboid = LBH = 8 x 7.5 x 6.5 = 390cm\(^3\) but in m\(^3\) = \(\frac{390}{1000000}\) = 0.00039m\(^3\)
0.00039m\(^3\) = 3.9 x 10\(^{-4}\)m\(^3\)
Source: Myschool Past Questions Archive (Record #42224)
Mathematics
WAEC / WASSCE 2002
Indices, Logarithms & Surds
Solution
(a) Simplify : \((2a + b)^{2} - (b - 2a)^{2}\)
(b) Given that \(S = K\sqrt{m^{2} + n^{2}}\); (i) make m the subject of the relations ; (ii) if S = 12.2, K = 0.02 and n = 1.1, find, correct to the nearest whole number, the positive value of m.
medium Difficulty
Verified Correct Answer: Option
Step-by-Step Mathematical Solution
(a) \((2a + b)^{2} - (b - 2a)^{2}\)
Using the method of difference of two squares,
\((2a + b)^{2} - (b - 2a)^{2} = ((2a + b) + (b - 2a))((2a + b) - (b - 2a))\)
= \((2b)(4a)\)
= \(8ab\).
(b)(i) \(S = K\sqrt{m^{2} + n^{2}}\)
\(S^{2} = K^{2}[m^{2} + n^{2}]\)
\(\frac{S^{2}}{K^{2}} = m^{2} + n^{2}\)
\(m^{2} = \frac{S^{2}}{K^{2}} - n^{2}\)
\(m = \sqrt{\frac{S^{2}}{K^{2}} - n^{2}}\)
(ii) When S = 12.2, K = 0.02, n = 1.1
\(m = \sqrt{\frac{12.2^{2}}{0.02^{2}} - (1.1^{2})}\)
\(m = \sqrt{\frac{148.84}{0.0004} - 1.21}\)
\(m = \sqrt{372,098.79}\)
= \(609.999 \approxeq 610\)
Source: Myschool Past Questions Archive (Record #53314)