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).
отговор
(C)
x = 3 or -5
7
Express \(\frac{4π}{2}\) radians in degrees.
отговор
(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.
отговор
(D)
-2x + 3y - 6 = 0
9
Which of the following is the semi-interquartile range of a distribution?
отговор
(D)
1/2 (Upper Quartile - Lower Quartile)
10
Evaluate \(∫^0_{-1}\) (x + 1)(x - 2) dx
отговор
(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.
отговор
(D)
9 \(\frac{9}{16}\)
12
Differentiate \(\frac{5x^ 3+x^2}{x}\), x ≠ 0 with respect to x.
отговор
(A)
10x + 1
13
Given that \(\frac{8x+m}{x^2-3x-4} ≡ \frac{5}{x+1} + \frac{3}{x-4}\)
отговор
(C)
-17
14
If \(x^2+y^2+-2x-6y+5 =0\), evaluate dy/dx when x=3 and y=2.
отговор
(A)
2
15
Evaluate\({1_0^∫} x^2(x^3+2)^3\)
отговор
(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.
отговор
(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.
отговор
(A)
(7, -2)
18
Evaluate \(4p_2 + 4C_2 - 4p_3\)
отговор
(C)
-6
19
Find the coefficient of x\(^2\)in the binomial expansion of \((x + \frac{2}{x^2})^5\)
отговор
(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.
отговор
(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.
отговор
(C)
36m
22
If Un = kn\(^2\) + pn, U\(_1\) = -1, U\(_5\) = 15, find the values of k and p.
отговор
(C)
k = 1, p = -2
23
In how many ways can six persons be paired?
отговор
(C)
15
24
Solve: \(3^{2x-2} - 28(3^{x-2}) + 3 = 0\)
отговор
(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.
отговор
(A)
(10 units, 053º)
26
If →PQ = -2i + 5j and →RQ = -i - 7j, find →PR
отговор
(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.
отговор
(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
отговор
(C)
7
29
If g(x) = √(1-x\(^2\)), find the domain of g(x)
отговор
(C)
-1 ≤ x ≤ 1
30
Find the coefficient of x\(^3\)y\(^2\) in the binomial expansion of (x-2y)\(^5\)
отговор
(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.
отговор
(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.
отговор
(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.
отговор
(B)
1.54m
34
Find correct to the nearest degree, the acute angle formed by the lines y = 2x + 5 and 2y = x - 6
отговор
(C)
37\(^∘\)
35
Solve: 4sin\(^2\)θ + 1 = 2, where 0º < θ < 180º
отговор
(B)
30º 0r 150º
36
Find the range of values of x for which 2x\(^2\) + 7x - 15 ≥ 0.
отговор
(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?
отговор
(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.
отговор
(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.
отговор
(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.
