The sum to infinity of a GP is 100, find its first term if the common ratio is -\(\frac{1}{2}\)
Răspuns
(A)
150
15
PQR is a triangle such that |PQ| = |QR| = 8cm and QPR = 60º. Find the area of \(\angle\) PQR
Răspuns
(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?
Răspuns
(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.
Răspuns
(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
Răspuns
(C)
# 10.80
19
Differentiate y = (5x + 1)\(^4\)
Răspuns
(A)
20 (5x + 1)\(^3\)
20
Simplify \(\frac{ 5 + \sqrt{7}}{3 + \sqrt{7}}\)
Răspuns
(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.
Răspuns
(C)
3 + \(\sqrt{10} + \sqrt{13}\)
22
Find the 7\(^{th}\) term of the sequence -10, 50, -250 ...........
Răspuns
(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.
Răspuns
(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.
Răspuns
(C)
8
25
Find x if \(\frac{16^{2 + x}}{4} = 64^x\)
Răspuns
(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.
Răspuns
(D)
{1, 2, 9}
27
In the diagram above, T represents the construction of angle .....
Răspuns
(B)
30\(^0\)
28
Convert the number 10111.11\(_{two}\) to a mixed number.
Răspuns
(B)
23\(\frac{3}{4}\)
29
Subtract 14256\(_{seven}\) from 20045\(_{seven}\)
Răspuns
(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.
Răspuns
(D)
30
31
How many proper and improper subsets are there in the set K = { a, b, c, d, e}?
Răspuns
(C)
32
32
Differentiate Cos25º - Sin 25º
Răspuns
(A)
- ( Sin25º + Cos25º)
33
The mean of the numbers 13, 16, x, 18, 21, 2x, 35, is 22. Find the value of x
Răspuns
(B)
17
34
Find the variance of a group of data whose standard deviation is 12.34 to the nearest whole number.
Răspuns
(C)
152
35
Calculate the standard deviation of the following scores 5, 4, 6, 7, and 8
Răspuns
(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?
Răspuns
(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?
Răspuns
(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.
Răspuns
(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.
Răspuns
(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.
Răspuns
(B)
6
41
Find the roots of x\(^3\) - 19x - 30=0
Răspuns
(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
Răspuns
(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
Răspuns
(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)
