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Question 1 Report
Four boys and ten girls can cut a field in 5 hours if the boys work at \( \frac{5}{4} \) the rate at which the girls work. How many boys will be needed to cut the field in 3 hours?
Question 2 Report
Question 3 Report
Convert 241 in base 5 to base 8,
2415 = 2 x 52 + 4 x 5 + 1 x 5 + 1 x 5o
50 + 20 + 1 = 7110
Convert 7110 to base 8
87188R781R080R1
= 1078
Question 4 Report
If \( \tan \theta = \frac{m^2-n^2}{2mn} \) find \( \sec \theta \)
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Question 6 Report
If \( P = \frac{2}{3}\left(\frac{1-r^2}{n^2}\right) \), find n when r = \( \frac{1}{3} \) and p = 1
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Question 9 Report
= 3x < -9
∴ x < -3
Question 10 Report
In the figure, PQRS is a rectangle. If the shaded area is 72 sq. cm, find h.
Question 11 Report
Simplify without using tables \( \frac{\log_2 6}{\log_2 8} - \frac{\log_2 3}{\log_2 \frac{1}{2}} \)
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Question 21 Report
Simplify \( \frac{x^2-y^2}{2x^2+xy-y^2} \)
x2−y22x2+xy−y2
2x2+xy−y2=2x2−xy+2xy−y2
= x(2x−y)+y(2x−y)
= (x+y)(2x−y)
x2−y22x2+xy−y2=(x+y)(x−y)(x+y)(2x−y)
= x−y2x−y
Question 22 Report
Question 23 Report
An \( (n-2)^2 \) sided figure has n diagonals, find the number n of diagonals for a 25 sided figure
Answer Details
Question 24 Report
Make \(y\) the subject of the formula \(Z = x^2 + \frac{1}{y^3}\)
Question 25 Report
Reduce each number to two significant figures and then evaluate \( \frac{0.021741 \times 1.2047}{0.023789} \)
Question 26 Report
In the figure, find the value of x
Question 27 Report
Simplify without using tables \( \frac{2\sqrt{14}\times3\sqrt{21}}{7\sqrt{24}\times2\sqrt{98}} \)
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Question 30 Report
In the diagram, PQRS is a circle center O. PQR is a diameter and ∠PRQ = 40o. Calculate ∠QSR.
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Question 38 Report
The figure is an example of the construction of a
Question 39 Report
Evaluate without using tables \( (0.008)^{\frac{1}{3}} \times (0.16)^{-\frac{3}{2}} \)
Question 40 Report
In the diagram above, QR // TS, QR : TS = 2.3, Find the ratio of the area of triangle PQR to the area of the trapezium QRST.
A△PQRATP(QRST)=12×2×h112×h2(2+3)
25×h1h2=25×2
= 45
Question 41 Report
Question 42 Report
The goals scored by 40 football teams from three league divisions are recorded below:
| Number of goals | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| frequency | 4 | 3 | 15 | 16 | 1 | 0 | 1 |
What is the total number of goals scored by all the terms?
Question 43 Report
Question 44 Report
Below are the scores of group of students in a music test:
| Scores | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| No of students | 3 | 6 | 10 | 8 | 6 | 5 | 2 | 4 | 12 |
If CF(x) is the number of students with scores less than or equal to x, find CF(6)
CF (6) = 5 + 6 + 8 + 10 + 6 + 3
= 38
Question 45 Report
Question 46 Report
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