Question Library
Browse, filter, and study verified past examination questions with step-by-step mathematical reasoning.
Searching 18,000+ Questions...
Sifting topics, KaTeX formulas & verified solutions
Showing 19726–19740 of 29821 verified questions
Sort by:
Mathematics
WAEC / WASSCE 1999
Mensuration (Areas, Perimeters & Volumes)
Solution
The height of a pyramid on square base is 15cm. If the volume is 80cm\(^3\), find the length of the side of the base
A
3.3cm
B
5.3cm
C
4.0cm
D
8.0cm
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Volume = \(\frac{1}{3} b^2 h\)
\(\therefore b = \sqrt{\frac{3v}{h}}\)
\(b = \sqrt{\frac{3(80)}{15}} \)
\(b = \sqrt{16} = 4.0 cm\)
Source: Myschool Past Questions Archive (Record #26405)
Mathematics
WAEC / WASSCE 1999
Indices, Logarithms & Surds
Solution
Simplify 3.72 x 0.025 and express your answer in the standard form
A
\(9.3\times 10^3\)
B
\(9.3\times 10^2\)
C
\(9.3\times 10^{-2}\)
D
\(9.3\times 10^{-3}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(3.72 \times 0.025 = 0.093 = 9.3\times 10^{-2}\)
Source: Myschool Past Questions Archive (Record #26406)
Mathematics
WAEC / WASSCE 1999
Number Bases & Modular Arithmetic
Solution
Two numbers 2\(4_x\) and 31\(_y\) are equal in value when converted to base ten. Find the equation connecting x and y
A
2x = 3(y - 1)
B
4x - y = 1
C
3y + 2x = 3
D
3y = 2 (x + 3)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
24\(_x\) = 31\(_y\)
\(2 \times x^1 + 4 \times x^0 = 3 \times y^1 + 1 \times y^0\)
\(2x + 4 = 3y + 1 \implies 2x = 3y + 1 - 4\)
\(2x = 3y - 3 = 3(y - 1)\)
Source: Myschool Past Questions Archive (Record #26407)
Mathematics
WAEC / WASSCE 1999
Linear, Simultaneous & Quadratic Equations
Solution
A car travel at x km per hour for 1 hour and at y km per hour for 2 hours. Find its average speed
A
\(\frac{2x + 2y}{3}kmh^{-1}\)
B
\(\frac{x + y}{3}kmh^{-1}\)
C
\(\frac{x + 2y}{3}kmh^{-1}\)
D
\(\frac{2x + y}{3}kmh^{-1}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Travelled x km/h for 1 hour \(\therefore\) traveled x km in the first hour.
Traveled y km/h for 2 hours \(\therefore\) traveled 2y km in the next 2 hours.
Average speed = \(\frac{x + 2y}{1 + 2}\)
= \(\frac{x + 2y}{3} kmh^{-1}\)
Source: Myschool Past Questions Archive (Record #26408)
Mathematics
WAEC / WASSCE 1999
Fractions, Decimals, Percentages & Approximations
Solution
The height and base of a triangle are in ratio 1:3 respectively. If the area of the triangle is 216 cm\(^2\), find the length of the base.
A
24cm
B
36cm
C
72cm
D
144cm
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Area = \(\frac{1}{2} \times base \times height\)
\(height : base = 1 : 3\)
\(\implies base = 3 \times height\)
Let height = h;
Area = \(\frac{1}{2} \times 3h \times h = 216\)
\(3h^2 = 216 \times 2 = 432\)
\(h^2 = \frac{432}{3} = 144\)
\(h = \sqrt{144} = 12.0 cm\)
\(\therefore base = 3 \times 12 = 36 cm\)
Source: Myschool Past Questions Archive (Record #26409)
Mathematics
WAEC / WASSCE 1999
Mensuration (Areas, Perimeters & Volumes)
Solution
Water flows from a tap into cylindrical container at the rate 5\picm\(^3\) per second. If the radius of the container is 3cm, calculate the level of water in the container at the end of 9 seconds.
A
2cm
B
5cm
C
8cm
D
15cm
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Volume of water after 9 seconds = \(5\pi \times 9 = 45\pi cm^3\)
Volume of cylinder = \(\pi r^2 h\)
\(\therefore \pi r^2 h = 45\pi\)
\(\pi \times 3^2 \times h = 45\pi\)
\(\implies 9h = 45 \)
\(h = 5 cm\)
(where h = height of the water after 9 secs)
Source: Myschool Past Questions Archive (Record #26410)
Mathematics
WAEC / WASSCE 1999
Inequalities & Linear Programming
Solution
Amina had m mangoes. She ate 3 and shared the remainder equally with her brother Uche. Each had at least 10. Which of the following inequalities represents the statements above.
A
\(\frac{m}{2}-3\le 10\)
B
\(\frac{m}{2}-3\ge 10\)
C
\(\frac{m-3}{2}\ge10\)
D
\(\frac{m-3}{2}\le10\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Total number of mangoes = m
Amina ate 3 mangoes \(\implies\) Remainder = m - 3
Shared equally with Uche \(\implies \frac{m - 3}{2}\)
\(\frac{m - 3}{2} \geq 10\)
Source: Myschool Past Questions Archive (Record #26411)
Mathematics
WAEC / WASSCE 1999
Inequalities & Linear Programming
Diagram
Solution
Which of the following pairs of inequalities is represented on the number line?
Attached Figure / Diagram
A
\(x<-2 and x\ge1\)
B
\(x\ge -2 and x>1\)
C
\(x\le -2 and x\ge1\)
D
\(x1\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
the line graph shows that \(x\le -2\) and \(x\ge1\)
Source: Myschool Past Questions Archive (Record #26412)
Mathematics
WAEC / WASSCE 1999
Linear, Simultaneous & Quadratic Equations
Solution
If \(x^2 +15x + 50 = ax^2 + bx + c = 0\). Which of the following statement is not true?
A
x = -5
B
x = 10
C
x + 10 = 0
D
bc = 750
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(x^2 + 15x + 50 = 0\)
\(x^2 + 5x + 10x + 50 = 0\)
\(x(x + 5) + 10(x + 5) = 0\)
\((x + 5)(x + 10) = 0\)
x + 5 = 0 or x + 10 = 0.
Comparing \(x^2 + 15x + 50\) with \(ax^2 + bx + c\), b = 15 and c = 50.
\(\therefore\) bc = 750.
Source: Myschool Past Questions Archive (Record #26413)
Mathematics
WAEC / WASSCE 1999
Linear, Simultaneous & Quadratic Equations
Solution
The root of a quadratic equation in x, are -m and 2n. Find the equation
A
\(x^2 + x(m - 2n)-2mn=0\)
B
\(x^2 - x(m - 2n)-2mn=0\)
C
\(x^2 - x(m - 2n)+2mn=0\)
D
\(x^2 + x(m - 2n)+2mn=0\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
x = -m \(\implies\) x + m = 0;
x = 2n \(\implies\) x - 2n = 0.
\(\implies (x + m)(x - 2n) = 0\)
\(x^2 + mx - 2nx - 2mn = 0\)
\(x^2 + x(m - 2n) - 2mn = 0\)
Source: Myschool Past Questions Archive (Record #26414)
Mathematics
WAEC / WASSCE 1999
Permutations, Combinations & Probability
Solution
A survey shows that 28% of all the men in a village wear size 9 shoes. What is the probability that a man selected at random in the village wears size 9 shoes?
A
\(\frac{7}{25}\)
B
\(\frac{41}{50}\)
C
\(\frac{1}{2}\)
D
1
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
P(man picked at random wears size 9 shoes) = \(\frac{28}{100}\)
= \(\frac{7}{25}\)
Source: Myschool Past Questions Archive (Record #26415)
Mathematics
WAEC / WASSCE 1999
Inequalities & Linear Programming
Solution
Solve the inequality 2x + 3 < 5x
A
\(x>1\)
B
\(x<\frac{3}{7}\)
C
\(x>\frac{3}{7}\)
D
\(x>-1\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
2x + 3 < 5x
3 < 3x
\(\frac{3}{3}\) < x
1 < x
x > 1
Source: Myschool Past Questions Archive (Record #26416)
Mathematics
WAEC / WASSCE 1999
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram, DE||BC, |AD| = x cm and |DB| = |AE| = ycm. Find |CE| in terms of x and y
Attached Figure / Diagram
A
x
B
\(\frac{x^2}{y}\)
C
\(\frac{y}{x^2}\)
D
\(\frac{y^2}{x}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{x}{x+y}=\frac{y}{x+CE}\\
xy + xCE = xy + y^2\\
∴xCE = y^2\\
CE=\frac{y^2}{x}\)
Source: Myschool Past Questions Archive (Record #26417)
Mathematics
WAEC / WASSCE 1999
Plane Geometry, Polygons & Circle Theorems
Diagram
Describe the locus L shown in the diagram below
Attached Figure / Diagram
A
Locus of points equidistant from X and Y
B
Locus of points equidistant from X and Z
C
Locus of points equidistant from \(\bar{ZX}\) and \(\bar{ZY}\)
D
Locus of points equidistant from \(\bar{XY}\) and \(\bar{ZY}\)
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 #26418)
Mathematics
WAEC / WASSCE 1999
Plane Geometry, Polygons & Circle Theorems
Diagram
Which of the following statements is true from the diagram above?
Attached Figure / Diagram
A
m + n = 90o
B
m = n
C
n > 45o
D
m o
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 #26419)