The sum to infinity of a GP is 100, find its first term if the common ratio is -\(\frac{1}{2}\)
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(A)
150
15
PQR is a triangle such that |PQ| = |QR| = 8cm and QPR = 60º. Find the area of \(\angle\) PQR
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(A)
16\(\sqrt{3}cm^2\)
16
The Venn diagram above shows the number of students offering physics and chemistry in a class of 65. What is the probability that a student selected from the class offers physics and chemistry if every students offers at least one subject?
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(A)
\(\frac{2}{13}\)
17
From the top of a building 10m high, the angle of elevation of a fruit on top of a tree 25m is 30º. Calculate the horizontal distance between the building and the tree.
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(A)
15\(\sqrt{3}\)m
18
A boy bought Oranges at the rate of #24.00 for 5 and sold it at the rate of # 30.00 for 4 Oranges. Find the profit made of the ones sold
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(C)
# 10.80
19
Differentiate y = (5x + 1)\(^4\)
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(A)
20 (5x + 1)\(^3\)
20
Simplify \(\frac{ 5 + \sqrt{7}}{3 + \sqrt{7}}\)
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(B)
4 - \(\sqrt{7}\)
21
Find the perimeter of a triangle whose vertices pass through ( 3, 2), (4, 5) and (6, 2) in surd form.
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(C)
3 + \(\sqrt{10} + \sqrt{13}\)
22
Find the 7\(^{th}\) term of the sequence -10, 50, -250 ...........
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(C)
-156250
23
The scores of students in a test are recorded as follows: 4, 3, 3, 2, 1, 2, 5, 7, 8, 3, and 5. Find the mode of the mark.
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(B)
3
24
P(x, 4) and Q( 10, 8) are two points joined by a straight line in a plane. If the midpoint of the line is (9, 6), find the value of x.
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(C)
8
25
Find x if \(\frac{16^{2 + x}}{4} = 64^x\)
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(A)
3
26
Given that P is the set of all prime numbers between 0 and 10, and Q is the set of all odd numbers between 0 and 10. Find the union of elements in P that are not in Q and the elements in Q that are not in P.
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(D)
{1, 2, 9}
27
In the diagram above, T represents the construction of angle .....
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(B)
30\(^0\)
28
Convert the number 10111.11\(_{two}\) to a mixed number.
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(B)
23\(\frac{3}{4}\)
29
Subtract 14256\(_{seven}\) from 20045\(_{seven}\)
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(B)
2456\(_{seven}\)
30
The average age of the four female teachers in a school is 40 and the average age of eight male teachers in the school is 25. Calculate the average age of the teachers in the school.
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(D)
30
31
How many proper and improper subsets are there in the set K = { a, b, c, d, e}?
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(C)
32
32
Differentiate Cos25º - Sin 25º
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(A)
- ( Sin25º + Cos25º)
33
The mean of the numbers 13, 16, x, 18, 21, 2x, 35, is 22. Find the value of x
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(B)
17
34
Find the variance of a group of data whose standard deviation is 12.34 to the nearest whole number.
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(C)
152
35
Calculate the standard deviation of the following scores 5, 4, 6, 7, and 8
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(A)
\(\sqrt{2}\)
36
From a class of 5 girls and 7 boys, a committee consisting of 2 girls and 3 boys is to be formed. How many ways can this be done?
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(A)
350 ways
37
In how many ways can a committee of 5 be selected from a group of 7 males and 3 females, if the committee must have one female?
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(A)
105ways
38
A bag contains 7 red and 4 black identical balls. Two balls were picked at random from the bag and replaced each time. Find the probability the two balls were of same colour.
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(B)
\(\frac{65}{121}\)
39
U varies directly as the square root of V when U = 24, V = 9, find the value of V when U = 16.
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(B)
4
40
If B varies inversely as c\(^{\frac{1}{3}}\) and C = 27 when B = 2, find the value of the constant of proportionality K.
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(B)
6
41
Find the roots of x\(^3\) - 19x - 30=0
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(C)
5, -3 and -2
42
If x is inversely proportional to y and x = 9 when y = 4, find the law containing x and y
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(B)
x = \(\frac{36}{y}\)
43
Given P = \(\begin{bmatrix}1 & 2\\2 & 3\end{bmatrix}\), find P\(^2\) - 4P - I where I is the identity matrix
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(B)
\(\begin{bmatrix}0 & 0\\0 & 0\end{bmatrix}\)
44
If A = \(\begin{pmatrix}3 & 2 & 1\\4 & 2 & -1\end{pmatrix}\) and B = \(\begin{pmatrix}1 & 4\\0 & 1\\3 & 2\end{pmatrix}\). Find A\(^T\) + B, ( where T means transpose)
