1.
Find the co-ordinates of a point on x-axis, which is at a distance of 5 units from the point (6, -3).
2.
A wooden block of weight 16N is placed on a rough surface. If the co-efficient of friction between both surfaces is 0.25, the least horizontal force required to move the block is
3.
Factorize the polynomial x 3 - x 2 - 25x + 25
4.
Simplify without calculator: ((3-1 - 9-1) / 6)1/3
6.
Differentiate the function w.r.t x: y = 4(x² - 3)
8.
A force of 20N, applied parallel to the surface of a horizontal table is just sufficient to make a block of mass 4kg move on the table. What is the coefficient of friction between the surfaces of the block and the table? (g = 10m/s²)
9.
A box contains 5 blue balls, 3 black balls and 2 red balls of the same size.
A ball is selected at random from the box and then replaced.
A second ball is then selected.
Find the probability of obtaining two blue balls or two black balls
10.
A curve has equation y = x³ -4x² - 3x + 18, find dy/dx
11.
Evaluate:
log(0.75)³
if log 7.5 = log 32
12.
Solve for x in the logarithmic equation:
logx 8 = 3
13.
The points of intersection between a straight line and the curve y = -x² + x + 2
give the roots of the equation x² - 2x - 1 = 0.
The equation of the line is
14.
Decompose into partial fractions : (5x2 + 12x + 3) / x(x + 1)2
15.
The table below shows the velocity V m/s of a particle in a relation to time t s within a period of t seconds
t 0 1 2 3 4 5 6
V 10 12 15 16 11 5 3
Use trapezoid rule:
1/2 h(y1 +2y2 + 2y3 + ... + yn)
Find the approximate distance traveled
16.
Given that sin(A+B) = sinA cosB + cosA sinB, without using mathematical tables or calculator, evaluate sin 105°.
18.
Differentiate w.r.t x: x-4x³
19.
Divide 2x³ + 11x² + 17x + 6 by 2x + 1
20.
An object dropped from rest has position s = 7t² metres below its starting point. At what time does the object have velocity of 35 m/s.
22.
Find the variance and the standard deviation, respectively of the data below
-3, -5, -7, 2, 5, 0, 4, 6
23.
Three guests X, Y and Z arrive in that order for a dinner party.
If guests are served randomly, the probability that the three guests will be served in the sequence of their arrival is
24.
Expand (1-x)³, using binomial theorem.
Hence find the value of (0.999)³ correct to five decimal places.
25.
P is a probability function of an exhaustive set S = {w, x, y, z}.
If P(x) = 1/4, P(y) = 1/3, P(z) = 1/6,
then P(w) is
26.
Find a positive value of p if the expression 2x² - px - + p leaves a remainder 6 when divided by x-p
27.
When the expression pm² + qm + 1 is divided by m- 1, it has a remainder of 2 and when divided by m + 1 it has a remainder of 4. Find pq
29.
The velocity of a particle is given by v =3t² + 8t. Find the acceleration when t = 3s
31.
A ball is thrown vertically upwards and its height s metres after t seconds is given by s = 16t - 4t². Find the time when the velocity is 8 m/s.
34.
The length of each of a metal cube increases at the rate of 0.025cm²s-¹ when heated.
Find the rate of increase in cm²s-¹ of the total surface area of the cube,
when the length of each side is 6cm
40.
If sinθ = -5/13, where θ is an angle between 270° and 360°,
calculate , without using mathematical tables,
the values of sin2θ
42.
If y = sin²x,
find the rate at which y changes with respect to x
43.
The velocity v m/s of a body moving at any time t, is given by v = 2t² - 1/3t³ + 10, determine the values of t at which the acceleration of the particle is zero.
44.
A curve y has gradient
dy/dx = 3x² - 6x + 2.
If the curve passes through the origin,
find its equation.
45.
Tireni throws a coin twice.
The coin is biased so the probability of landing a head is 2/5.
Find the probability that she throws two tails
46.
Find a positive angle between 0° and 360° that is equivalent to -315°
47.
Find the coefficient of x³ in the binomial expansion of (2-5x)7
49.
Given that tan²θ + sec²θ = 3,
the value of θ
(for 0°<θ<90°) is
50.
In a Year 12 class of 45 students, every student has to offer either Chemistry or Economics or both.
If 25 students offer Chemistry while 34 offer Economics,
how many students offer both subjects?
51.
Find the minimum value of cos2 θ + sec2 θ
52.
GATE Academy registers 300 candidates for an examination.
180 of the candidates offer Economics and 70 offer Geography.
80 candidates offer neither Economics nor Geography.
The number of candidates offering both Economics and Geography is
53.
If x + 1 is a factor of x3 + 3x2 + kx + 4, find the value of k
54.
If x is positive, and the standard deviation of x-1, x+1, 3, 2x-1 and x+3 is 2√2, find the value of x and hence calculate the mean deviation
57.
A train has an initial velocity of 44m/s and an acceleration of -4m/s². Its velocity after 10 seconds is
58.
Tireni stands on a spring scale placed in a lift. The lift descends at constant velocity. As a result, the scale reads a weight
59.
The values of θ for which
sin θ = cos θ are, within the range 0° < θ < 360°,
60.
The letters of the word MISSISSIPPI are cut and placed in a bag.
If one letter is drawn randomly from the bag,
the probability that it is neither an I nor a S is
