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Mathematics
WAEC / WASSCE 2001
Plane Geometry, Polygons & Circle Theorems
Solution
Evaluate \(\frac{1}{2}+\frac{3}{4}of\frac{2}{5}\div 1\frac{3}{5}\)
A
\(\frac{15}{16}\)
B
\(\frac{11}{16}\)
C
\(\frac{49}{50}\)
D
\(3\frac{1}{5}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\frac{1}{2} + (\frac{3}{4} \text{ of } \frac{2}{5}) \div 1\frac{3}{5}\)
= \(\frac{1}{2} + (\frac{3}{4} \times \frac{2}{5}) \div \frac{8}{5}\)
= \(\frac{1}{2} + \frac{3}{10} \div \frac{8}{5}\)
= \(\frac{1}{2} + (\frac{3}{10} \times \frac{5}{8})\)
= \(\frac{1}{2} + \frac{3}{16}\)
= \(\frac{11}{16}\)
Source: Myschool Past Questions Archive (Record #26482)
Mathematics
WAEC / WASSCE 2001
Plane Geometry, Polygons & Circle Theorems
Solution
A man is four times as old as his son. The difference between their ages is 36 years Find the sum of their ages
A
45 years
B
48 years
C
60 years
D
74 years
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Let the sons age be x. The father is 4x
∴ 4x - x = 36; 3x = 36; x = 12
The son is 12 years and the father is 12 x 4 = 48.
The sum of their ages (12 + 48) years = 60years
Source: Myschool Past Questions Archive (Record #26483)
Mathematics
WAEC / WASSCE 2001
Plane Geometry, Polygons & Circle Theorems
Solution
Given that y = px + q and y = 5 when x = 3, while y = 4 when x = 2, find the value of p and q.
A
p = 1, q = 3
B
p = 1, q = 2
C
p = -2, q = 3
D
p = 3, q = -2
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
y = px + q
5 = 3p + q ... (i)
4 = 2p + q ... (ii)
(i) - (ii) : p = 1
\(\therefore\) 5 = 3(1) + q
\(\implies\) q = 5 - 3 = 2
(p, q) = (1, 2)
Source: Myschool Past Questions Archive (Record #26484)
Mathematics
WAEC / WASSCE 2001
Linear, Simultaneous & Quadratic Equations
Solution
Evaluate \(\frac{x^2 + x - 2}{2x^2 + x -3}\) when x = -1
A
-2
B
-1
C
\(-\frac{1}{2}\)
D
1
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{x^2 + x - 2}{2x^2 + x - 3}\)
= \(\frac{x^2 + 2x - x - 2}{2x^2 + 3x - 2x - 3}\)
= \(\frac{x(x + 2) - 1(x + 2)}{x(2x + 3) - 1(2x + 3)}\)
= \(\frac{(x - 1)(x + 2)}{(x - 1)(2x + 3)}\)
= \(\frac{x + 2}{2x + 3}\)
At x = -1,
= \(\frac{-1 + 2}{2(-1) + 3}\)
= \(\frac{1}{1}\)
= 1
Source: Myschool Past Questions Archive (Record #26485)
Mathematics
WAEC / WASSCE 2001
Linear, Simultaneous & Quadratic Equations
Solution
Factorize \(6x^2 + 7x - 20\)
A
(6x - 5)(x + 4)
B
2(3x-5)(x+2)
C
(3x+4)(2x-5)
D
(3x-4)(2x+5)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(6x^2 + 7x - 20\)
= \(6x^2 + 15x - 8x - 20\)
= \(3x(2x + 5) - 4(2x + 5)\)
= \((3x - 4)(2x + 5)\)
Source: Myschool Past Questions Archive (Record #26486)
Mathematics
WAEC / WASSCE 2001
Plane Geometry, Polygons & Circle Theorems
Solution
Simplify \(\frac{2x-1}{3}-\frac{x+3}{2}\)
A
\(\frac{x+3}{6}\)
B
\(\frac{x+8}{6}\)
C
\(\frac{x-11}{6}\)
D
\(\frac{x-4}{6}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{2x - 1}{3} - \frac{x + 3}{2}\)
= \(\frac{2(2x - 1) - 3(x + 3)}{6}\)
= \(\frac{4x - 2 - 3x - 9}{6}\)
= \(\frac{x - 11}{6}\)
Source: Myschool Past Questions Archive (Record #26487)
Mathematics
WAEC / WASSCE 2001
Plane Geometry, Polygons & Circle Theorems
Solution
If \(\frac{y-3}{2}<\frac{2y-1}{3}\), which of the following is true?
A
y > 7
B
y < -7
C
y > -7
D
y < 7
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{y - 3}{2} < \frac{2y - 1}{3}\)
\(3(y - 3) < 2(2y - 1)\)
\(3y - 9 < 4y - 2\)
\(3y - 4y < -2 + 9\)
\(-y < 7\)
\(y > -7\)
Source: Myschool Past Questions Archive (Record #26488)
Mathematics
WAEC / WASSCE 2001
Fractions, Decimals, Percentages & Approximations
Solution
if \(\frac{4m+3n}{4m-3n}=\frac{5}{2}\), find the ratio m:n
A
7:4
B
4:3
C
3:4
D
4:7
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\frac{4m + 3n}{4m - 3n} = \frac{5}{2}\)
\(5(4m - 3n) = 2(4m + 3n)\)
\(20m - 15n = 8m + 6n\)
\(20m - 8m = 6n + 15n\)
\(12m = 21n\)
\(\frac{21}{12} = \frac{m}{n}\)
\(m : n = 7 : 4\)
Source: Myschool Past Questions Archive (Record #26489)
Mathematics
WAEC / WASSCE 2001
Linear, Simultaneous & Quadratic Equations
Solution
If \(2x^2 + kx - 14 = (x+2)(2x-7)\), find the value of K
A
-3
B
5
C
9
D
11
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(2x^2 + kx - 14 = (x+2)(2x-7)\)
∴2\(x^2 + kx - 14 = 2x^2 - 3x - 14\)
equating coefficient K = -3
Source: Myschool Past Questions Archive (Record #26491)
Mathematics
WAEC / WASSCE 2001
Linear, Simultaneous & Quadratic Equations
Solution
which of the following is not quadratic expression?
A
\(y = 2x^2 - 5x\)
B
\(y=x(x-5)\)
C
\(y = x^2 - 5\)
D
y = 5(x-1)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
A quadratic equation is an equation of the second order. The highest power in the equation is 2.
Source: Myschool Past Questions Archive (Record #26492)
Mathematics
WAEC / WASSCE 2001
Linear, Simultaneous & Quadratic Equations
Solution
The graph of the curve \(y = 2x^2 - 5x - 1\) and a straight line PQ were drawn to solve the equation \(2x^2 - 5x + 2 = 0\)
What is the equation of the straight line PQ?
A
y = -1
B
y = 1
C
y = 3
D
y = -3
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Let the straight line PQ = y
2x\(^2\) - 5x - 1 - y = 2x\(^2\) - 5x + 2
y = 2x\(^2\) - 5x - 1 - 2x\(^2\) + 5x - 2
y = -3
Source: Myschool Past Questions Archive (Record #26493)
Mathematics
WAEC / WASSCE 2001
Plane Geometry, Polygons & Circle Theorems
Solution
Subtract (-y + 3x + 5z) from (4y - x - 2z)
A
5y - 4x - 7z
B
3y + 2x + 3z
C
-5y + 4x + 7z
D
2x - 5y + 3z
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
(4y - x - 2z) - (-y + 3x + 5z)
= 4y + y - x - 3x - 2z - 5z
= 5y - 4x - 7z
Source: Myschool Past Questions Archive (Record #26494)
Mathematics
WAEC / WASSCE 2001
Indices, Logarithms & Surds
Solution
If \(y \propto \frac{1}{\sqrt{x}}\) and x = 16 when y = 2, find x when y = 24
A
\(\frac{1}{9}\)
B
\(\frac{1}{6}\)
C
\(\frac{1}{3}\)
D
\(\frac{2}{3}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(y \propto \frac{1}{\sqrt{x}}\)
\(y = \frac{k}{\sqrt{x}}\)
When x = 16, y = 2.
\(2 = \frac{k}{\sqrt{16}} \implies 2 = \frac{k}{4}\)
\(k = 8\)
\(y = \frac{8}{\sqrt{x}}\)
When y = 24,
\(24 = \frac{8}{\sqrt{x}}\)
\(\sqrt{x} = \frac{8}{24} = \frac{1}{3}\)
\(\therefore x = (\frac{1}{3})^2\)
\(x = \frac{1}{9}\)
Source: Myschool Past Questions Archive (Record #26495)
Mathematics
WAEC / WASSCE 2001
Plane Geometry, Polygons & Circle Theorems
Solution
If 2x : (x +1) = 3:2, what is the value of x?
A
\(\frac{1}{2}\)
B
1
C
\(1\frac{1}{2}\)
D
3
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
2x : (x + 1) = 3:2
\(\frac{2x}{x+1} = \frac{3}{2}\)
4x = 3x + 3
4x - 3x = 3
x = 3
Source: Myschool Past Questions Archive (Record #26496)
Mathematics
WAEC / WASSCE 2001
Plane Geometry, Polygons & Circle Theorems
Solution
The bearing S40^\circE is the same as
A
040o
B
050o
C
130o
D
140o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
= 180^\circ - 40^\circ
= 140^\circ
Source: Myschool Past Questions Archive (Record #26497)