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Mathematics
WAEC / WASSCE 1994
Indices, Logarithms & Surds
Solution
Simplify: 16\(^{\frac{5}{4}}\) x 2\(^{-3}\) x 3\(^0\)
A
0
B
2
C
4
D
10
E
20
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
16\(^{\frac{5}{4}}\) x 2\(^{-3}\) x 3\(^0\)
= \((2^4)^{\frac{5}{4}} \times 2^{-3} \times 1\)
= \(2^5 \times 2^{-3} \times 1\)
= \(2^2\)
= 4.
Source: Myschool Past Questions Archive (Record #23466)
Mathematics
WAEC / WASSCE 1994
Indices, Logarithms & Surds
Solution
simplify; 2lo\(g_3\) 6 + lo\(g_3\) 12 - lo\(g_3\) 16
A
2
B
3
C
2 - 2log32
D
3 - log32
E
4 - log32
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
2lo\(g_3\) 6 + lo\(g_3\) 12 - lo\(g_3\) 16
= \(\log_3 6^2 + \log_3 12 - \log_3 16\)
= \(\log_{3} (\frac{36 \times 12}{16})\)
= \(\log_{3} (27)\)
= \(\log_{3} 3^3\)
= \(3 \log_{3} 3\)
= 3
Source: Myschool Past Questions Archive (Record #23468)
Mathematics
WAEC / WASSCE 1994
Number Bases & Modular Arithmetic
What is the number whose logarithm to base 10 is \(\bar{3}.4771\)?
A
3.0
B
0.3
C
0.03
D
0.003
E
0.0003
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 #23471)
Mathematics
WAEC / WASSCE 1994
Fractions, Decimals, Percentages & Approximations
Solution
A house bought for N100,000 was later auctioned for N80,000. Find the loss percent.
A
20%
B
30%
C
40%
D
50%
E
60%
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Loss = N(100,000 - 80,000)
= N20,000.
Loss percentage = \(\frac{20,000}{100,000} \times 100%\)
= 20%
Source: Myschool Past Questions Archive (Record #23475)
Mathematics
WAEC / WASSCE 1994
Fractions, Decimals, Percentages & Approximations
Solution
A string is 4.8m. A boy measured it to be 4.95m. Find the percentage error.
A
\( \frac{5}{16} \)%
B
\(1\frac{5}{16} \)%
C
\( 3\frac{1}{33} \)%
D
\( 3\frac{1}{8} \)%
E
25%
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
4.95m - 4.8m = 0.15m
\(\frac{0.15}{4.8} \times 100%\)
= \(\frac{25}{8}\)
= \(3\frac{1}{8} %)
Source: Myschool Past Questions Archive (Record #23480)
Mathematics
WAEC / WASSCE 1994
Sequences & Series (AP & GP)
Solution
The sum of the 1st and 2nd terms of an A.P. is 4 and the 10th term is 19. Find the sum of the 5th and 6th terms.
A
11
B
20
C
21
D
22
E
24
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(T_{n} = a + (n - 1) d\) (terms of an A.P)
\(T_{1} = a\)
\(T_{2} = a + d\)
\(T_{10} = a + 9d\)
\(a + a + d = 2a + d = 4 ... (i)\)
\(a + 9d = 19 ... (ii)\)
(ii) x 2: \(2a + 18d = 38 ... (iii)\)
(iii) - (i) : \(17d = 34 \implies d = 2\)
\(2a + 2 = 4 \implies 2a = 2\)
\(a = 1\)
\(T_{5} + T_{6}\)
= \((a + 4d) + (a + 5d)\)
= \(2a + 9d\)
= \(2(1) + 9(2)\)
= 20
Source: Myschool Past Questions Archive (Record #23481)
Mathematics
WAEC / WASSCE 1994
Sets, Logic & Venn Diagrams
Solution
E = (integers \(\leq\) 20), P = (multiples of 3), Q = (multiples of 4), what are the elements of P'∩Q?
A
(12)
B
(4, 8, 16, 20)
C
(3, 6, 9, 15, 18)
D
(1,2,5,7,10,11,13,17,19)
E
(3, 4, 6, 8, 9, 12, 15, 16, 18, 20)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
E = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}
P = {3, 6, 9, 12, 15, 18}
Q = {4, 8, 12, 16, 20}
P' = {1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20}
P' \(\cap\) Q = {4, 8, 16, 20}
Source: Myschool Past Questions Archive (Record #23482)
Mathematics
WAEC / WASSCE 1994
Plane Geometry, Polygons & Circle Theorems
Solution
Given that 2p - m = 6 and 2p + 4m = 1, find the value of (4p + 3m).
A
1
B
3
C
5
D
7
E
9
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
2p - m = 6 ... (i)
2p + 4m = 1 ... (ii)
From (i), m = 2p - 6.
2p + 4(2p - 6) = 1
2p + 8p - 24 = 1
10p = 1 + 24 = 25
p = 2.5
m = 2(2.5) - 6
= 5 - 6
= -1
\(\therefore\) 4p + 3m = 4(2.5) + 3(-1)
= 10 - 3
= 7
Source: Myschool Past Questions Archive (Record #23485)
Mathematics
WAEC / WASSCE 1994
Linear, Simultaneous & Quadratic Equations
Which of the following is a point on the curve y = x\(^2\) - 4x + 7?
A
(0,6)
B
(1,4)
C
(2,0)
D
(7,0)
E
(3,2)
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 #23488)
Mathematics
WAEC / WASSCE 1994
Plane Geometry, Polygons & Circle Theorems
Solution
If 8x- 4 = 6x- 10, find the value of 5x,
A
-35
B
-15
C
-3
D
3
E
7
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
8x - 4 = 6x - 10
8x - 6x = -10 + 4
2x = -6
x = -3
\(\therefore\) 5x = 5(-3)
= -15
Source: Myschool Past Questions Archive (Record #23490)
Mathematics
WAEC / WASSCE 1994
Linear, Simultaneous & Quadratic Equations
Solution
For what value of x is the expression \(\frac{x^2 + 15x + 50}{x - 5}\) not defined ?
A
-10
B
-5
C
o
D
5
E
10
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{x^2 + 15x + 50}{x - 5}\)
It is undefined when x - 5 = 0.
That is at x = 5.
Source: Myschool Past Questions Archive (Record #23491)
Mathematics
WAEC / WASSCE 1994
Inequalities & Linear Programming
Solution
If x is positive, for what range of values of x is 4 + 3x < 10?
A
0 < x < 2
B
x < 2
C
1 < x < 2
D
0 3 4
E
0 > x > 2
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
4 + 3x < 10
3x < 10 - 4
3x < 6
x < 2
Therefore, the solution is 0 < x < 2
Source: Myschool Past Questions Archive (Record #23492)
Mathematics
WAEC / WASSCE 1994
Differentiation & Applications
Diagram
Solution
In the graph above, the gradient of the curve at the point P is
Attached Figure / Diagram
A
-11 3
B
-3 4
C
3/7
D
3/4
E
11 3
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
-1-(-3)/-2-(-0.5) = 2/-1.5 = 20/-15 = -113
Source: Myschool Past Questions Archive (Record #23494)
Mathematics
WAEC / WASSCE 1994
Coordinate Geometry
Diagram
Solution
What is the equation of the line PQ?
Attached Figure / Diagram
A
y = x - 5
B
y = x + 3
C
y = x + 5
D
y = 2x + 3
E
y = 2x - 3
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
The points P(-2, 3) and Q(2, 7) are on the line.
Gradient of the line = \(\frac{7 - 3}{2 - (-2)}\)
= \(\frac{4}{4}\)
= 1
y = x + b
To find the intercept, we have
7 = 2 + b or 3 = -2 + b.
Solving for b, we get b = 5.
\(\therefore\) The line is y = x + 5.
Source: Myschool Past Questions Archive (Record #23495)
Mathematics
WAEC / WASSCE 1994
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
Which of the following equations can be solved by the points of intersection P and Q of the curve and the line PQ?
Attached Figure / Diagram
A
x2 - 2 = 0
B
x2 - 4 = 0
C
x2 + 6 = 0
D
X2 - X – 2 = 0
E
x2 - x + 4 = 0
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
The points of intersection of the curve and the line are at x = -2 and x = 2.
\(\therefore\) (x + 2) = 0; (x - 2) = 0.
(x + 2)(x - 2) = 0
\(x^2 - 4 = 0\)
Source: Myschool Past Questions Archive (Record #23496)