Find the domain of \(g(x) = \frac{4x^{2} - 1}{\sqrt{9x^{2} + 1}}\)
คำตอบ
(D)
\(x: x \in R\)
3
Given that \(f(x) = 3x^{2} - 12x + 12\) and \(f(x) = 3\), find the values of x.
คำตอบ
(A)
1, 3
4
A binary operation * is defined on the set of real numbers, by \(a * b = \frac{a}{b} + \frac{b}{a}\). If \((\sqrt{x} + 1) * (\sqrt{x} - 1) = 4\), find the value of x.
คำตอบ
(D)
3
5
If \(4x^{2} + 5kx + 10\) is a perfect square, find the value of k.
คำตอบ
(D)
\(\frac{4\sqrt{10}}{5}\)
6
If the polynomial \(f(x) = 3x^{3} - 2x^{2} + 7x + 5\) is divided by (x - 1), find the remainder.
คำตอบ
(D)
13
7
\(P = {1, 3, 5, 7, 9}, Q = {2, 4, 6, 8, 10, 12}, R = {2, 3, 5, 7, 11}\) are subsets of \(U = {1, 2, 3, ... , 12}\). Which of the following statements is true?
คำตอบ
(C)
\((R \cap P) \subset (R \cap U)\)
8
If \(\log_{3}a - 2 = 3\log_{3}b\), express a in terms of b.
คำตอบ
(C)
\(a = 9b^{3}\)
9
If \(\alpha\) and \(\beta\) are the roots of \(2x^{2} - 5x + 6 = 0\), find the equation whose roots are \((\alpha + 1)\) and \((\beta + 1)\).
คำตอบ
(B)
\(2x^{2} - 9x + 13 = 0\)
10
Resolve \(\frac{3x - 1}{(x - 2)^{2}}, x \neq 2\) into partial fractions.
คำตอบ
(C)
\(\frac{1}{2(x - 2)} + \frac{5x}{2(x- 2)^{2}}\)
11
If \(\alpha\) and \(\beta\) are the roots of the equation \(2x^{2} + 5x + n = 0\), such that \(\alpha\beta = 2\), find the value of n.
Find the coefficient of \(x^{3}\) in the binomial expansion of \((x - \frac{3}{x^{2}})^{9}\).
คำตอบ
(A)
324
14
The general term of an infinite sequence 9, 4, -1, -6,... is \(u_{r} = ar + b\). Find the values of a and b.
คำตอบ
(B)
a = -5, b = 14
15
If \(\begin{vmatrix} k & k \\ 4 & k \end{vmatrix} + \begin{vmatrix} 2 & 3 \\ -1 & k \end{vmatrix} = 6\), find the value of the constant k, where k > 0.
คำตอบ
(C)
3
16
How many numbers greater than 150 can be formed from the digits 1, 2, 3, 4, 5 without repetition?
คำตอบ
(C)
291
17
The first term of a Geometric Progression (GP) is \(\frac{3}{4}\), If the product of the second and third terms of the sequence is 972, find its common ratio.
Out of 70 schools, 42 of them can be attended by boys and 35 can be attended by girls. If a pupil is selected at random from these schools, find the probability that he/ she is from a mixed school.
คำตอบ
(B)
\(\frac{1}{10}\)
31
The marks scored by 4 students in Mathematics and Physics are ranked as shown in the table below
Mathematics
3
4
2
1
Physics
4
3
1
2
Calculate the Spearmann's rank correlation coefficient.
คำตอบ
(C)
0.6
32
Given that \(a = i - 3j\) and \(b = -2i + 5j\) and \(c = 3i - j\), calculate \(|a - b + c|\).
คำตอบ
(B)
\(3\sqrt{13}\)
33
What is the probability of obtaining a head and a six when a fair coin and and a die are tossed together?
คำตอบ
(D)
\(\frac{2}{3}\)
34
If \(\overrightarrow{OX} = \begin{pmatrix} -7 \\ 6 \end{pmatrix}\) and \(\overrightarrow{OY} = \begin{pmatrix} 16 \\ -11 \end{pmatrix}\), find \(\overrightarrow{YX}\).
คำตอบ
(D)
\(\begin{pmatrix} -23 \\ 17 \end{pmatrix}\)
35
A body of mass 28g, initially at rest is acted upon by a force, F Newtons. If it attains a velocity of \(5.4ms^{-1}\) in 18 seconds, find the value of F.
