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Mathematics
WAEC / WASSCE 2024
Geometry and Trigonometry
Diagram
Solution
In the diagram above, O is the centre of the circle. If | \(\overline{OA}\) = 25 cm and |\(\overline{AB}\) = 40 cm, find |\(\overline{OH}\)|
Attached Figure / Diagram
A
15 cm
B
20 cm
C
25 cm
D
30 cm
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Line OH divides Line AB into two halves, therefore, Line AH = Line HB = 20cm
Considering \(\triangle\) AOH
(\(\overline{OH})^2\) = 25\(^2\) - 20\(^2\) = 625 - 400 = 225
Taking the square root of both sides
(\(\overline{OH}\) = \(\sqrt{225}\) = 15 cm
Source: Myschool Past Questions Archive (Record #71802)
Mathematics
WAEC / WASSCE 2024
Geometry and Trigonometry
Solution
A car valued at $ 600,000.00 depreciates by 10% each year. What will be the value of the car at the end of two years?
A
$ 120,000.00
B
$ 480,000.00
C
$ 486,000.00
D
$ 540,000.00
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Using P\(_n\) = P\(_o\)(1 - \(\frac{r}{100})^n\)
= 600,000(1 - \(\frac{10}{100})^2\)
= 600,000(0.90)\(^2\) = $486,000.00
Source: Myschool Past Questions Archive (Record #71803)
Mathematics
WAEC / WASSCE 2024
Geometry and Trigonometry
Solution
Given that P is 25 m on a bearing of 330º from Q, how far south of P is Q?
A
25.2 m
B
21.7 m
C
19.8 m
D
18.5 m
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Sin 60º = \(\frac{d}{25}\)
d = Sin 60º x 25 = 21.6506m ≈ 21.7m
Source: Myschool Past Questions Archive (Record #71804)
Mathematics
WAEC / WASSCE 2024
Number and Numeration
Solution
The length and breadth of a cuboid are 15 cm and 8 cm respectively. If the volume of the cuboid is 1560 cm\(^3\), calculate the total surface area.
A
976cm\(^2\)
B
838cm\(^2\)
C
792cm\(^2\)
D
746cm\(^2\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Volume of a cuboid = LBH = 1560cm\(^2\)
V = 15 x 8 x H = 1560
H = \(\frac{1560}{15 \times 8}\) = 13cm
Total surface area of a cuboid = 2(LB + LH + BH)
= 2((15 x 8) + ( 15 x 13) + ( 8 x 13))
= 2(120 + 195 + 104) = 2(419) = 838 cm\(^2\)
Source: Myschool Past Questions Archive (Record #71805)
Mathematics
WAEC / WASSCE 2024
Number and Numeration
Solution
The number 1621 was subtracted from 6244 in base x. If the result was 4323, find x.
A
Seven
B
Eight
C
Nine
D
Ten
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Given that \( 6244_x - 1621_x = 4323_x \), find the value of \( x \).
{Step 1: Convert to decimal:}
\[6244_x = 6x^3 + 2x^2 + 4x + 4\]
\[1621_x = 1x^3 + 6x^2 + 2x + 1\]
\[4323_x = 4x^3 + 3x^2 + 2x + 3\]
f{Step 2: Set up the equation:}
\[(6x^3 + 2x^2 + 4x + 4) - (1x^3 + 6x^2 + 2x + 1) = 4x^3 + 3x^2 + 2x + 3\]
{Step 3: Simplify the left side:}
\[(6x^3 - 1x^3) + (2x^2 - 6x^2) + (4x - 2x) + (4 - 1) = 5x^3 - 4x^2 + 2x + 3\]
{Step 4: Set the equation:}
\[5x^3 - 4x^2 + 2x + 3 = 4x^3 + 3x^2 + 2x + 3\]
{Step 5: Combine like terms:}
\[5x^3 - 4x^3 - 4x^2 - 3x^2 + 2x - 2x + 3 - 3 = 0\]
\[x^3 - 7x^2 = 0\]
{Step 6: Factor the equation:}
\[x^2(x - 7) = 0\]
{Step 7: Solutions:}
\[x = 7 \quad (\text{valid}), \quad x = 0 \quad (\text{not valid})\]
\Thus, the base \( x \) is 7
Source: Myschool Past Questions Archive (Record #71806)
Mathematics
WAEC / WASSCE 2024
Number and Numeration
Solution
Factorize completely: 27x\(^2\) - 48y\(^2\)
A
3(3x + 4y)(3x - 4y)
B
3(3x + 4y)(3x + 4y)
C
3(9x - 16y)(9x + 16y)
D
3(9x - 16y)(9x - 16y)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
27x\(^2\) - 48y\(^2\) = 3(9x\(^2\) - 16y\(^2\))
difference of two squares
3((3x)\(^2\) - (4y)\(^2\)) = 3((3x - 4y)(3x + 4y))
Source: Myschool Past Questions Archive (Record #71822)
Mathematics
WAEC / WASSCE 2024
Number and Numeration
Solution
For what values of x is \(\frac{x - 3}{4}\) + \(\frac{x + 1}{8}\) \(\geq\) 2 ?
A
x \(\geq\) 5
B
x \(\geq\) 6
C
x \(\geq\) 7
D
x \(\geq\) 8
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{x - 3}{4}\) + \(\frac{x + 1}{8}\) \(\geq\) 2
multiply through by the LCM of 4, 8, and 1 = 8
8(\(\frac{x - 3}{4}\)) + 8(\(\frac{x + 1}{8}\)) \(\geq\) 8 x 2
2(x - 3) + (x + 1) \(\geq\) 16
2x - 6 + x + 1 \(\geq\) 16
3x - 5 \(\geq\) 16
3x \(\geq\) 16 + 5 = 21
x \(\geq\) \(\frac{21}{3}\)
x \(\geq\) 7
Source: Myschool Past Questions Archive (Record #71823)
Mathematics
WAEC / WASSCE 2024
Geometry and Trigonometry
Diagram
Solution
In the diagram above, < SQR = 52º and < PRT = 16º. Find the value of the angle marked y
Attached Figure / Diagram
A
64\(^0\)
B
68\(^0\)
C
112\(^0\)
D
128\(^0\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Source: Myschool Past Questions Archive (Record #71824)
Mathematics
WAEC / WASSCE 2024
Geometry and Trigonometry
Diagram
Solution
In the diagram above, JKL is a tangent to the circle GHIK at K. Find the value of the angle marked x
Attached Figure / Diagram
A
93º
B
55º
C
42º
D
23º
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\angle\)KGL = 87º (exterior angle of a cyclic quadrilateral)
\(\angle\)KGL + \(\angle\)GLK + \(\angle\)LKG = 180º
87º + x + 38º = 180º
x = 180 - 87 - 38 = 55º
Source: Myschool Past Questions Archive (Record #71826)
Mathematics
WAEC / WASSCE 2024
Number and Numeration
Solution
A cone and a cylinder are of equal volume. The base radius of the cone is twice the radius of the cylinder. What is the ratio of the height of the cylinder to that of the cone?
A
5: 4
B
4: 3
C
3: 2
D
3: 4
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Vol of cylinder = \(\pi\)r\(^2\)H = vol of cone = \(\frac{1}{3}\)\(\pi\)r\(^2\)h
H = height of cylinder and h = height of cone
Let y = radius of cylinder = y, then radius of cone = 2y
\(\pi\)y\(^2\)H = \(\frac{1}{3}\)\(\pi\)(2y)\(^2\)h
y\(^2\)H = \(\frac{1}{3}\)4y\(^2\)h ( \(\pi\) cancels out and cross multiplying)
The ratio of the height of the cylinder to that of the cone = \(\frac{\text{H}}{\text{h}}\) = \(\frac{4y^2}{3y^2}\)
= \(\frac{4}{3}\) = 4: 3 (y\(^2\) cancels out )
Source: Myschool Past Questions Archive (Record #71827)
Mathematics
WAEC / WASSCE 2024
Number and Numeration
Diagram
Solution
Find, correct to the nearest whole number, the value of h in the diagram above.
Attached Figure / Diagram
A
15 m
B
22 m
C
23 m
D
18 m
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
From the diagram on the right-hand side above,
x\(^2\) = 20\(^2\) - 19\(^2\) = 39 ( from Pythagoras theorem)
x = \(\sqrt{39}\) = 6.245m
As can be seen from the diagram on the right-hand side above,
h = x + 17 = 6.245 + 17 = 23.245 m ≈ 23 m(to the nearest whole number)
Source: Myschool Past Questions Archive (Record #71828)
Mathematics
WAEC / WASSCE 2024
Geometry and Trigonometry
Solution
The gradient of the line joining the points P(2, -8) and Q(1, y) is -4. Find the value of y
A
2
B
4
C
-4
D
-3
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
P(2, -8) and Q(1, y)
Gradient of slope(m) = \(\frac{y_2 - y_1}{x_2 - x_1}\)
- 4 = \(\frac{y - (-8))}{1 - 2}\)
-4 = \(\frac{y + 8}{- 1}\)
cross multiplying
4 = y + 8
y = 4 - 8 = -4
Source: Myschool Past Questions Archive (Record #71829)
Mathematics
WAEC / WASSCE 2024
Geometry and Trigonometry
Diagram
Solution
In the diagram above, \(\overline{PQ}\) || \(\overline{RS}\), \(\angle\)WYZ = 44º and \(\angle\)WXY = 50º. Find \(\angle\)WTX
Attached Figure / Diagram
A
65º
B
68º
C
86º
D
90º
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\angle\)XWY = \(\angle\)ZYW = 44º (alternate \(\angle\)s)
Considering \(\triangle\)WTX
\(\angle\)W + \(\angle\)T + \(\angle\)X = 180º
44 + \(\angle\)T + 50 = 180
\(\angle\)T = 180 - 44 - 50 = 86º
Source: Myschool Past Questions Archive (Record #71830)
Mathematics
WAEC / WASSCE 2024
Geometry and Trigonometry
Solution
The perimeter of a rectangular garden is 90 m. If the width is 7 m less than the length, find the length of the garden.
A
19 m
B
23 m
C
24 m
D
26 m
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Let the length of the garden be x, then, the width = x - 7
perimeter of rectangle = 2(L + B) = 90 m
= 2(x + x - 7) = 90
= 2x - 7 = 45 ( after dividing through by 2)
= 2x = 45 + 7 = 52
x = \(\frac{52}{2}\) = 26 m
Thus, the length of the rectangular garden = 26 m.
Source: Myschool Past Questions Archive (Record #71831)
Mathematics
WAEC / WASSCE 2024
Geometry and Trigonometry
Solution
Four of the angles of a hexagon sum up to 420º. If the remaining angles are equal, find the value of each of the angles.
A
60\(^O\)
B
100\(^O\)
C
120\(^O\)
D
150\(^O\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Hexagon = 6 sides
Sum of interior angles of a regular hexagon = (n - 2)180 = (6 - 2)180 = 4 x 180 = 720º
But 4 of these angles sum up to 420º and the remaining ones are equal.
Let the remaining two that are equal = 2x
SuM of the angles = 420 + 2x = 720º
2x = 720 - 420 = 300
x = \(\frac{300}{2}\) = 150º
Thus, the value of each of the remaining angles = 150º
Source: Myschool Past Questions Archive (Record #71832)