PROGRESSIONS 1
Find the second term of geometric progression that has a common ratio of
1 2
and sum to
a infinity of 22. 2 Find the number of terms in the geometric progressions 4, −¿ 8, 16, … that must be added up to a give a value of 684. 3 Given 1, x and 25 are three consecutive terms of a sequence. Find the value of x if the sequence. D (a) is an arithmetic progression f (b) is a geometric progression 4
1
́
Given k =1. 01 is a recurring decimal. Find the value of k.
5
The diagram shows several circles where the radii of the circles increase by 1 unit consecutively. Show that the circumferences of the circles form an arithmetic progression but not the areas. Hence, find the total circumferences of the first five circles.
6
Fahmi is allowed to spend an allocation of RM1 million where the maximum withdrawal each day must not exceed twice the amount withdrawn the day before. If Fahmi withdraws RM200 on the first day, determine after how many days the amount the money allocated will be used up.
© Hak Cipta Mooi Hoe Yeap 2014
7
Two food stalls, A and B, sell fried noodles from 8 a.m. to 2 p.m. each day. a)
On one particular day, stall A sells k plates of fried noodles by 9 a.m. and the sale increases constantly by m plates every hour. By 2 p.m., the total sale in 6 hours is 147 plates and the number of plates sold in the last hour is 42. Find the values of k and m.
b)
On that particular day, stall B sells n plates of fried noodles in the first hour and the sale increases constantly by 5 plates every hour. If both food stalls happen to sell exactly the same number of plates by 2 p.m. Find the value of n.
LINEAR LAW
1
The diagram shows part of the graph of y against x. It is known that x and y are related by the equation
¿
bx ab+ x
, where a
and b are constants.
(a) Sketch the graph of straight line of © Hak Cipta Mooi Hoe Yeap 2014
1 y
against
1 x
.
(b) Calculate the values of a and b.
2
Variables x and y are related by the equation
2px +qy=3xy
When a graph of
1 y
. against
1 x
is
drawn, the resulting line has a gradient of
3 1 5
and passes through (
−¿
6,0)
Find the values of p and q.
3
The diagram below shows a straight-line graph of xy against x.
(a) Ex
(b) De
(i) © Hak Cipta Mooi Hoe Yeap 2014
(ii)
4
The variables x and y are related by the equation x2 y = 2 + 3x2. Explain how a straight line graph can be obtained based on this equation.
In a certain experiment, the speed, v ms-1, and the time taken, t of a particle are
5
known to be linearly related. The following table shows the corresponding values of t and v from the experiment. v (m s-1) t (s)
20
30 0.24
40 0.33
0.37
(a) Plot a graph of t against v and draw the line of best fit. (b) Write the equation of the line of best fit obtained (a) (c) From the graph, find the value of v when t = 0.4 s.
6
The variables of x and y are related by the equation 2(y + 1)2 = kx + t, where k
© Hak Cipta Mooi Hoe Yeap 2014
and t are constants. (a) If the graph of (y + 1)2 against x is plotted, a straight line is obtained. Given that line passes through the points (0, 10) and ( k
−¿
5, 0), find the values of
and t. (b) Hence, find the gradient and the intercept on the Y-axis of the straight line obtained by plotting he graph of y2 against (x – y).
INTEGRATION 1
Sketch the graph of y = |x3 + 1| for the domain −¿ 2 ≼ x ≼ 1. Hence, find the area of the
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region bounded by y= |x3 + 1|, the x-axis, the line x = 2 and x = 1.
2
Find the coordinates of points M and N shown in the diagram on the above. Then calculate the area of the shaded region.
3
The volume generated by the shaded region when it is revolved through 360° about the x-axis is 625 π unit3. Find the value of k.
4
Given the point P(2, 5) on the curve with gradient of function 3x2 – 4x + k. The tangent
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at point P is parallel to the straight line y – 2x + 1 = 0. Find the value of k. Hence, find the equation of the curve.
5
The volume generated by the shaded region when it is rotated through 360° about the y-axis 1
is 2 π unit3. Find the value of k.
6
© Hak Cipta Mooi Hoe Yeap 2014
The diagram shows the shaded region bounded by the curve y =
x2 3
+ 1 , the line y = t
and the y-axis. When the shaded region is rotated through 360° about the y-axis, the volume generation is 6 π unit3. Find the value of t.
7
8
Sketch the graph of y = (x + 4)2. Hence, calculate the volume generated when the region bounded by the curve y = (x + 4)2, the x-axis and the line x = 1 is rotated through 360° about the x-axis.
Given that (1, 1) is a stationary point of a curve with gradient (a) the value of k, (b) the equation of the curve, (c) the equation of normal at the point (1, 1)
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dy dx
= –10x + k. Find
