ADDITIONAL MATHEMATICS FORM 4, 2022
TOPICS: PROGRESSIONS, LINEAR LAW & COORDINATE
GEOMETRY
1.
2.
3.
4.
5.
6.
7.
Given that the first three terms of an arithmetic progression are 𝑘 + 4, 3𝑘 + 2, 10. Find
(a) the value of k
[2]
(b) the sum of the first 20 terms of the progression.
[500]
n
It is given that the sum of the first n terms of an arithmetic progression is S n = [19 − 5n] . Find
2
th
the n term.
[12 − 5n ]
The sum to infinity of a geometric progression is 4 and the second term is 1. Find the common
ratio of the progression.
[ ½]
n
3 
The sum of the first n terms of arithmetic progression, is given by S n =  5 + n  . Find
4
2 
(a) the value of the first term and the common difference.
[7]
(b) the sum of all the terms from the fifth term to the eighteenth term.
[- 2]
It is given that 𝑟 = 0.260606 … . = 0.2 + 𝑠, where s is the recurring decimal. Express s as in the
form of sum to infinity in the simplest form of fraction.
[2/33]
Aqil wants to compile books in his school’s resource center. He arranged the books in height with
the thickness of the first book which was at the bottom being 3 cm. Each subsequent book has the
same thickness, 2 cm. Find
(a) the total thickness of the book when compiles eleven books.
[23]
(b) the number of books that have been stacked when the height of the book stack is 31 cm. [15]
Find the number of integers between 70 and 250 that are multiple of 11. Then, calculate the sum of
all the integers which are not multiples of 11.
[16, 26088]
8.
9.
[5/4]
Given a geometric progression in which all the terms are positive and decreasing the difference
25
between the first term and the second term is 1.75 and the sum to infinity is
. Find the first term
7
and the common ratio of the progression.
[ a = 2.5, r = 0.3 ]
10.
[25380]
11.
12.
Calculate
(a) the value of n
[ n = 13 ]
(b) the value of x
[x = 48]
(c) the difference in distance travelled by particle P and particle Q before they stopped.
[858]
Given an arithmetic progression 8,12,16,……, find
(a) the sum of the first 18th terms
[756]
th
(b) the sum of the first n terms.
[ S n = 6n + 2n 2 ]
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13.
[a = 25 , d = - 3]
14.
Car A travels 47 cm in the 1st second , 45 cm in 2nd second , 43 cm in 3rdsecond and so on.
Car B travels 25 cm in the 1st second , 24 cm in 2nd second , 23 cm in 3rdsecond and so on.
Find
(a) the distance when particle A travels in 11th second
[ 29]
(b) The time , in second, when both cars meet.
[n = 24 ]
15.
(a) Find the value of n if k = 4 and the sum of areas of the first n circles is 31 cm2
(b) Find the sum to infinity of the series of circles if k = 2.
[n = 5]
[40/3]
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16.
(a) Find the non-linear equation which relates
(b) Given that x = 3 find the value of y.
y
1
against .
2
x
x
[ y = −3x + 15 x 2 ]
[ y = 126]
17.
Graph
(a) Find the value of p and of q.
[p = 2, q = 3]
(b) Hence , determine whether the point (4 ,10) lies on the straight line.
[ No]
18.
[a = ½ , b = -2/5]
19.
(a) Express the equation y = 1000a x in linear form used to obtain the straight line
(b) Find the value of a and of b.
[(a)
(b) a = 0.01 , b = 3 ]
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20.
(a) Find the coordinate of K
[K(0,2)]
3
(b) Express y in term of x.
(c ) Find y when x = 16
(d) Find x when y = 2700
[ y = 100 x 4 ]
[ y = 800 ]
[x = 81 ]
21.
(b) Use the graph in 21(a) to find the value of
(i) r
(ii) s
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22.
(a) based on the table given , construct a table for the values of
y
1
and 2
x
x
(b)
( c) use the graph in 22(b) to find the value of
(i) a
(ii) b
(iii) y when x = 1.32
23.
(a)
(b)
(c ) use your graph to find
(i) the value of p
(ii) the value of q
(iii) the value of y when x = 3.6
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24.
1
1
[ y = − x − 3 or y = − x + 10 ]
2
2
25.
Find the coordinate of point B.
[B ( -2 , 2)]
26.
(a) Find the value of w and of z.
(b) Find the gradient of the straight line.
[w = 3, z =-2]
[ m = 1]
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27.
[ y = -2x + 45 , need to be moved]
28.
(a) Find the value of s.
[ s = 6]
(b) Show that the straight lines PQ and QR are perpendicular to each other.
(c ) Hence , find the values of h and of k.
[h = 2 , k = 5]
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29.
(a) Find the equation of the perpendicular bisector of line AC.
[ y = −5 x + 13 ]
(b) Calculate the area of the triangle ABC
[ 25 ]
(c ) A point P moves such that its distance from point A is always half of its distance from point B.
Find the equation of the locus of P.
[ 3x 2 + 3 y 2 − 52 x − 16 y + 192 = 0 ]
30.
(a) Given the area of triangle OKL is 20 unit2, find the value of p.
[p = -2]
 4 28 
(b) Point T  , −  lies on the straight-line KL. Find KT : TL .
5 
5
[ 8 : 32 ]
(c) Point S moves such that 2SK = SL. Find the equation of the locus S. [ 3x 2 + 3 y 2 + 24 x + 8 y − 80 = 0 ]
31.
[m=2, n=3]
32.
Given A (2 ,1) and B (-4,9). Find the equation of the perpendicular bisector of the straight line
3
23
AB.
[ y = x+ ]
4
4
~END OF QUESTIONS ~
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