if P = {x:x is odd, \(-1 < x \leq 20\)} and Q is {y:y is prime, \(-2 < y \leq 25\), find P \(\cap\) Q
Trả lời
(C)
{3,5,7,11,13,17,19}
9
If S = \(\sqrt{t^2 - 4t + 4}\), find t in terms of S
Trả lời
(B)
S + 2
10
If x - 4 is a factor of x2 - x - k, then k is
Trả lời
(B)
12
11
The remainder when 6p3 - p2 - 47p + 30 is divided by p - 3 is
Trả lời
(B)
42
12
P varies jointly as m and u, and varies inversely as q. Given that p = 4, m = 3 and u = 2 and q = 1, find the value of p when m = 6, u = 4 and q =\(\frac{8}{5}\)
Trả lời
(C)
10
13
If r varies inversely as the square root of s and t, how does s vary with r and t?
Trả lời
(B)
s varies inverely as r2 and t
14
Evaluate 3(x + 2) > 6(x + 3)
Trả lời
(C)
x < -4
15
Solve for x: |x - 2| < 3
Trả lời
(C)
-1 < x < 5
16
The nth term of the progression \(\frac{4}{2}\), \(\frac{7}{3}\), \(\frac{10}{4}\), \(\frac{13}{5}\) is ...
Trả lời
(B)
\(\frac{3n + 1}{n + 1}\)
17
If a binary operation * is defined by x * y = x + 2y, find 2 * (3 * 4)
Trả lời
(A)
24
18
If P = \(\begin{pmatrix} 5 & 3 \\ 2 & 1 \end{pmatrix}\) and Q = \(\begin{pmatrix} 4 & 2 \\ 3 & 5 \end{pmatrix}\), find 2P + Q
If y = x sin x, find \(\frac{\delta y}{\delta x}\)
Trả lời
(D)
sin x + x cos x
21
If y = (2x + 2)\(^3\), find \(\frac{\delta y}{\delta x}\)
Trả lời
(D)
6(2x +2)2
22
The radius of a circle is increasing at the rate of 0.02cms-1. Find the rate at which the area is increasing when the radius of the circle is 7cm.
Trả lời
(D)
0.88cm2S-1
23
Find the mean of t + 2, 2t - 4, 3t + 2 and 2t.
Trả lời
(B)
2t
24
The mean of seven numbers is 10. If six of the numbers are 2, 4, 8, 14, 16 and 18, find the mode.
Trả lời
(B)
8
25
Age
20
25
30
35
40
45
No of people
3
5
1
1
2
3
Calculate the median age of the frequency distribution in the table above
Trả lời
(A)
25
26
If the variance of 3+x, 6, 4, x and 7-x is 4 and the mean is 5, find the standard deviation
Trả lời
(B)
2
27
\(\begin{array}{c|c} Score & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \hline Frequency & 1 & 0 & 7 & 5 & 2 & 3 & 1 & 1 \end{array}\)
The table above shows the scores of 20 students in further mathematics test. What is the range of the distribution?
Trả lời
(A)
7
28
In how many ways can a student select 2 subjects from 5 subjects?
Trả lời
(C)
\(\frac{5!}{2!3!}\)
29
In how many ways can 3 seats be occupied if 5 people are willing to sit?
Trả lời
(A)
60
30
What is the probability that an integer x \((1 \leq x \leq 25)\) chosen at random is divisible by both 2 and 3?
Trả lời
(C)
\(\frac{4}{25}\)
31
A basket contains 9 apples, 8 bananas and 7 oranges. A fruit is picked from the basket, find the probability that it is neither an apple nor an orange.
Trả lời
(B)
\(\frac{1}{3}\)
32
The graph above is correctly represented by
Trả lời
(A)
y = x2 - x - 2
33
In the diagram given, find the value of x.
Trả lời
(B)
40o
34
The value x in the figure given is
Trả lời
(D)
130o
35
The bar chart above shows the allotment of time(in minutes) per week for selected subjects in a certain school. What is the total time allocated to the six subjects per week?
Trả lời
(B)
720mins
36
The pie chart above shows the statistical distribution of 80 students in five subjects in an examination. Calculate how many student offer Mathematics.
Trả lời
(B)
11
37
If the angles of a quadrilateral are (3y + 10)°, (2y + 30)°, (y + 20)° and 4y°. Find the value of y.
Trả lời
(C)
30°
38
A square tile has side 30 cm. How many of these tiles will cover a rectangular floor of length 7.2m and width 4.2m?
Trả lời
(B)
336
39
Find the length of a chord which subtends an angle of 90° at the centre of a circle whose radius is 8 cm.
Trả lời
(D)
\(8\sqrt{2}\) cm
40
A chord of a circle subtends an angle of 120° at the centre of a circle of diameter \(4\sqrt{3} cm\). Calculate the area of the major sector.
Trả lời
(C)
8\(\pi\) cm\(^2\)
41
The locus of the points which is equidistant from the line PQ forms a
Trả lời
(D)
pair of parallel lines to PQ
42
If the midpoint of the line PQ is (2,3) and the point P is (-2, 1), find the coordinate of the point Q.
Trả lời
(D)
(6,5)
43
Find the equation of the perpendicular bisector of the line joining P(2, -3) to Q(-5, 1)
Trả lời
(C)
8y - 14x - 13 = 0
44
In triangle PQR, q = 8 cm, r = 6 cm and cos P = \(\frac{1}{12}\). Calculate the value of p.
Trả lời
(C)
\(\sqrt{92}\) cm
45
If \(\tan \theta = \frac{3}{4}\), find the value of \(\sin \theta + \cos \theta\).
