The functions f:x → 2x\(^2\) + 3x -7 and g:x →5x\(^2\) + 7x - 6 are defined on the set of real numbers, R. Find the values of x for which 3f(x) = g(x).
Trả lời
(C)
x = 3 or -5
7
Express \(\frac{4π}{2}\) radians in degrees.
Trả lời
(C)
144º
8
A straight line makes intercepts of -3 and 2 on the x and y axes respectively. Find the equation of the line.
Trả lời
(D)
-2x + 3y - 6 = 0
9
Which of the following is the semi-interquartile range of a distribution?
Trả lời
(D)
1/2 (Upper Quartile - Lower Quartile)
10
Evaluate \(∫^0_{-1}\) (x + 1)(x - 2) dx
Trả lời
(D)
-7/6
11
If 36, p,\(\frac{9}{4}\) and q are consecutive terms of an exponential sequence (G.P), find the sum of p and q.
Trả lời
(D)
9 \(\frac{9}{16}\)
12
Differentiate \(\frac{5x^ 3+x^2}{x}\), x ≠ 0 with respect to x.
Trả lời
(A)
10x + 1
13
Given that \(\frac{8x+m}{x^2-3x-4} ≡ \frac{5}{x+1} + \frac{3}{x-4}\)
Trả lời
(C)
-17
14
If \(x^2+y^2+-2x-6y+5 =0\), evaluate dy/dx when x=3 and y=2.
Trả lời
(A)
2
15
Evaluate\({1_0^∫} x^2(x^3+2)^3\)
Trả lời
(B)
\(\frac{65}{12}\)
16
Given \(\begin{vmatrix} 2 & -3 \\ 1 & 4 \end{vmatrix} \begin{vmatrix} -6 \\ k \end{vmatrix} \begin{vmatrix} 3 \\ -26 \end{vmatrix} = 15\). Solve for k.
Trả lời
(B)
-5
17
A linear transformation T is defined by T: (x,y) → (3x - y, x + 4y). Find the image of (2, -1) under T.
Trả lời
(A)
(7, -2)
18
Evaluate \(4p_2 + 4C_2 - 4p_3\)
Trả lời
(C)
-6
19
Find the coefficient of x\(^2\)in the binomial expansion of \((x + \frac{2}{x^2})^5\)
Trả lời
(A)
10
20
Given that P = {x: x is a multiple of 5}, Q = {x: x is a multiple of 3} and R = {x: x is an odd number} are subsets of μ = {x: 20 ≤ x ≤ 35}, (P⋃Q)∩R.
Trả lời
(B)
{21, 25, 27, 33, 35}
21
A particle moving with a velocity of 5m/s accelerates at 2m/s\(^2\). Find the distance it covers in 4 seconds.
Trả lời
(C)
36m
22
If Un = kn\(^2\) + pn, U\(_1\) = -1, U\(_5\) = 15, find the values of k and p.
Trả lời
(C)
k = 1, p = -2
23
In how many ways can six persons be paired?
Trả lời
(C)
15
24
Solve: \(3^{2x-2} - 28(3^{x-2}) + 3 = 0\)
Trả lời
(D)
x = 0 or x = 3
25
Given that P = (-4, -5) and Q = (2,3), express →PQ in the form (k,θ). where k is the magnitude and θ the bearing.
Trả lời
(A)
(10 units, 053º)
26
If →PQ = -2i + 5j and →RQ = -i - 7j, find →PR
Trả lời
(C)
-i + 12j
27
The table shows the distribution of the distance (in km) covered by 40 hunters while hunting.
Distance(km)
3
4
5
6
7
8
Frequency
5
4
x
9
2x
1
If a hunter is selected at random, find the probability that the hunter covered at least 6km.
Trả lời
(A)
\(\frac{3}{5}\)
28
The table shows the distribution of the distance (in km) covered by 40 hunters while hunting.
What is the mode of the distribution?
Distance(km)
3
4
5
6
7
8
Frequency
5
4
x
9
2x
1
Trả lời
(C)
7
29
If g(x) = √(1-x\(^2\)), find the domain of g(x)
Trả lời
(C)
-1 ≤ x ≤ 1
30
Find the coefficient of x\(^3\)y\(^2\) in the binomial expansion of (x-2y)\(^5\)
Trả lời
(C)
40
31
The first, second and third terms of an exponential sequence (G.P) are (x - 4), (x + 2), and (3x + 1) respectively. Find the values of x.
Trả lời
(A)
\(\frac{-1}{2}, 8\)
32
A body of mass 18kg moving with velocity 4ms-1 collides with another body of mass 6kg moving in the opposite direction with velocity 10ms-1. If they stick together after the collision, find their common velocity.
Trả lời
(A)
\(\frac{1}{2}\) m/s
33
The mean heights of three groups of students consisting of 20, 16 and 14 students each are 1.67m, 1.50m and 1.40m respectively. Find the mean height of all the students.
Trả lời
(B)
1.54m
34
Find correct to the nearest degree, the acute angle formed by the lines y = 2x + 5 and 2y = x - 6
Trả lời
(C)
37\(^∘\)
35
Solve: 4sin\(^2\)θ + 1 = 2, where 0º < θ < 180º
Trả lời
(B)
30º 0r 150º
36
Find the range of values of x for which 2x\(^2\) + 7x - 15 ≥ 0.
Trả lời
(A)
x ≤ -5 or x ≥ \(\frac{3}{2}\)
37
The probability that a student will graduate from college is 0.4. If 3 students are selected from the college, what is the probability that at least one student will graduate?
Trả lời
(C)
0.78
38
The equation of a circle is given as 2x\(^2\) + 2y\(^2\) - x - 3y - 41 = 0. Find the coordinates of its centre.
Trả lời
(B)
(\(\frac{1}{4}\), \(\frac{3}{4}\))
39
The gradient of a function at any point (x,y) 2x - 6. If the function passes through (1,2), find the function.
Trả lời
(D)
x\(^2\) - 6x + 7
40
A particle of mass 3kg moving along a straight line under the action of a F N, covers a line distance, d, at time, t, such that d = t\(^2\) + 3t. Find the magnitude of F at time t.
