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Linear Questions
1. Determine the inequalities that represent and satisfies the unshaded region (3 mks)
2. Write down the inequalities that satisfy the u shaded region in the figure below. (4mks)
3. Find all integral values that satisfy the inequality 2x + 3 5x – 3 > -8. (3mks)
4. a) Find the range of values x which satisfied the following inequalities simultaneously. (2 mks)
4x – 9 < 6 + x
8 – 3x < x + 4
b) Represent the range of values of x on a number line. (1 mark)
5. Solve the inequality
<
<
(2mks)
6. (a) Show by shading the unwanted region the area represented by 
and
on the grid provided (8 mks)
(b) Calculate the area of the enclosed region (2 mks)
7. Solve the inequality below and write down the integral values that satisfy the equality -3x + 2 < x + 6 ≤ 17 – 2x (3 mks)
8. State all the integral values of a which satisfy the inequality
(3mks)
9. Solve the inequality ½ x -2 3x – 2 <2 + ½ x and state the integral values which satisfy this inequalities. (3 marks)
10. Write down the inequalities that satisfy the given region simultaneously. (3mks)
11. Write down the inequalities that define the unshaded region marked R in the figure below. (3mks)
12. Write down all the inequalities represented by the regions R. (3mks)
13. a) On the grid provided draw the graph of y = 4 + 3x – x2 for the integral values
of x in the interval -2 X 5. Use a scale of 2cm to represent 1 unit on the x – axis and 1
cm to represent 1 unit on the y – axis. (6mks)
b) State the turning point of the graph. (1mk)
c) Use your graph to solve.
(i) -x2 + 3x + 4 = 0
(ii) 4x = x2 (3mks)
14. Solve the following inequality (3 marks)
15. The diagram below shows the graphs of y = 3/10 x – 3/2, 5x + 6y = 3 and x = 2
By shading the unwanted region, determine and label the region R that satisfies the three
inequalities; y ≥ 3/10 x – 3/2,
5x + 6y ≥ 30 and x ≥ 2
16. The cost of 7 shirts and 3 pairs of trousers is shs. 2950 while that of 5 pairs of trousers and 3 shirts
is less by 200. How much will Dan pay for 2 shirts and 2 pairs of trousers?
17. Mr. Wafula went to the supermarket and bought two biros and five pencils at sh.120.
Whereas three biros and two pencils cost him sh.114. Find the cost of each biros and pencils
18. A father is twice as old as his son now. Ten years ago, the ratio of their ages was 5:2.
Find their present ages
19. List the integral values of x which satisfy the inequalities below:-
2x + 21 15 – 2x x + 6
20. Find the equation of a line which passes through (-1, -4) and is perpendicular to the line:-
y + 2x – 4 = 0
21. John bought two shirts and three pairs of trousers at Kshs. 1750. If he had bought three shirts
and two pairs of trousers, he would have saved Kshs. 250. Find the cost of a shirt and a trouser.
22. Express the recurring decimal 3.81 as an improper fraction and hence as a mixed number
23. Karani bought 4 pencils and 6 biro pens for shs.66 and Mary bought 2 pencils and 5 biro
pens for shs.51
(a) Find the price of each item
(b) Ondieki spent shs.228 to buy the same type of pencils and biro pens. If the number
of biro pens he bought were 4 more than the number of pencils, find the number of
pencils he bought
24. Two consecutive odd numbers are such that the difference of twice the larger number
and twice the smaller number is 21.Find the product of the numbers
25. The size of an interior angle of a regular polygon is 3xo while its exterior angle is (x-20)o.
Find the number of sides of the polygon
26. Five shirts and four pairs of trousers cost a total of shs.6160. Three similar shirts and
a pair of trouser cost shs.2800. Find the cost of four shirts and two pairs of trousers
27. Two pairs of trousers and three shirts costs a total of Shs.390. Five such pairs of trousers and two shirts cost a total of Shs.810. Find the price of a pair of trouser and a shirt
Linear Answers
1 | (0,3), (3,0) |
B1 B1 B1
| ||||||
2. | (a) x -4 (b) y = -x y + x 0 (c) Grad = = ¾ y = mx + c 0 = ¾ (8) + c c = -6 y = ¾ x – 6 y – ¾ x > -6 | B1
B1
M1 M1 | ||||||
04 | ||||||||
3. | 2x + 3 5x – 3 -3x -6 x 2 5x – 3 > -8 5x > -5 x > -1 -1 < x 2 Integral values 0,. 1, 2 |
B1
B1
B1 | ||||||
03 | ||||||||
4. |
x < 5 8 – 3x < x + 4 1 < x b) 1 < x < 5 |
M1
M1 A1 | ||||||
5. |
|
M1
A1 2 | ||||||
7 | -3x + 2 < x + 6 x > 1 x + 6 ≤ 17 − 2x x ≤ 3⅔ 2, 3 |
B1 B1
B1 3 | ||||||
8. |
15a + 10 8a + 12 7a 2 a 0.2857
6(2a + 3) 5(4a + 15) -8a/-8 57/-8 a -7.125; -7.125 a 0.28 Integral values -7, -6, -5, -4, -3, -2, -1 |
1
M1
B1 B1 | ||||||
03 | ||||||||
9. ½ x – 2 3 – 2 ; 3x -2 < + ½ x
O
7/2x 5/2x < 4
O x – B1 x < 8/5 B1
x = 0, 1 A1
3
10. | y 2, x > -3 (3,-3) & (-3,1) M = 1 + 3 = 4 = -2 -3 – 3 -6 3 y = – 2 x + c 3 -3 = -2 x 3 + c 3 -3 = -2+c c = -1 y = 1/3x – 2, inequality y < 1/3x – 2 Equn y = –2x – 1 (3,-3) & (4,2) 3 M = 2- -3 = 5 = 5 Equn y > –2x – 1 4-3 1 3 Y = 5x + c -3 = 5(3) + c -3 – 15= c C = -18 Y = 5x – 18 inequality y 5x – 18 |
B1
B1
B1 |
Both B0 if any one is wrong
For Ineq | ||||||||||||||||||||||||||
03 | |||||||||||||||||||||||||||||
11. | -4x + 2y 4 y 0 x + y 4 | B1 B1 B1 | |||||||||||||||||||||||||||
03 | |||||||||||||||||||||||||||||
12. |
| B1 B1 B1 | |||||||||||||||||||||||||||
03 | |||||||||||||||||||||||||||||
13. |
b) turning point 1.5, 6.25 c) i) Line y = 0 x = –1 or x = 4 x = -1 or x = 4 ii) – 4x – x2 = 0 4 – x = y
x = 0 or x = 4 |
B2
S1 P1 C1 L1
B1
B1
B1
B1 | For all values | ||||||||||||||||||||||||||
10 | |||||||||||||||||||||||||||||
14 |
|
M1
M1
A1
|
| ||||||||||||||||||||||||||
3marks | |||||||||||||||||||||||||||||
4 + 3x -x2 = y
15. The diagram below shows the graphs of
Y = 3 x – 3 , 5x + 6y = 30 and x = 2
10 2
By shading the unwanted region, determine and label the region R that satisfies the three inequalities;
Y ≥ 3x – 3, 5x + 6y ≥ 30 and x ≥ 2 (2 mks)
10 2
L1 y = 3x – 3 at (0, 0)
10 2 0 ≥ 2 *
Picking P(0,0)
0≥ – 3
2
L2 5x + 6y = 30
At (0, 0) 5x + 6y ≥ 30
0≥ 30 *
16. 7s + 3t = 2950 ………………….(i) x 5
3s + 5t = 2750 …………………..(ii) x 3
35s + 15t = 14750
9s + 15t = 8250
26s = 6500
s = 250
t = 2750 – 3(250) = 400
5
2t + 2s = 2(400) + 2(250)
= shs. 1,300
17. Let the cost of a biro be b
Pencil be p
2b + 5p = 120 x 3
3b + 2p = 114 x 2
6b + 15p = 360
6b + 4p = 228
11p = 132
P = 121
2b + 60 = 120
2b = 60
b = 30
The cost of 1 biro is 30/=
The cost of 1 pencil is 12/=
18. Let son’s present age be n yrs
Father’s age is 2n yrs
Ten years ago: son’s age n -10
Father’s age 2n -10
Son’s present age = 30yrs
Father’s present age = 2x 30 = 60yrs
19. 2x + 21 15 – 2x 15 – 2x x + 6
4x 0.6 -3 x -9
x – 1 ½ x ≤3
⇒ – 1 ½ x ≤ 3
Values are -1, 0, 1, 2, 3.
20. y = -2x + 4
gradient of h line is ½
Equation y + 4 = ½
x + 1
2y + 8 = x + 1
2y – x + 7 = 0
21. 2s + 3t = 1750
3s + 2t = 1500
4s + 6t = 3500 2t = 1500 – 600
9s + 6t = 4500 t = 450
5s = 1000
s = 200
Shirt = sh 200
Trouser = sh 450
22. Let r = 3.818181…
100r = 381.818181
99r = 378 = 42
99 11
= 39/11
23. (a) Let cost of pencils be x and biro pens to be y
4x + 6y = 66
2x + 5y = 51
4x + 6y = 66
4x + 10y = 102
4y = 96
y = 24
Correct substitution
x = 3
Pencils = shs.9
Biro pens = 3
(b) 9p + 3b = 228…(i)
b –y = 4
b = 4 + r ………..(ii)
substituting for b in ……….(i)
p2 + 5p – 288 = 0
p = -5 25 – 4 x 1 x -228
2 x 1
P = 13 (to the nearest whole no.)
b= 4+ 13 = 17
24. 3x – 2 (x + 2) = 21
X = 25
Large No = 25 + 2 = 27
product = 25 x 27 = 695
25. x -20 + 3x = 180oC
4x = 200
x = 50o
26. 5x + 4y = 6160
4(3x + y = 2800
-7x = – 5040
x = 720
y = 640
4(720) + 2(640) = 4160
27. 2x + 3y = 390
5x + 2y = 810
15x + 6y = 2430
4x + 6y = 780
11x = 1650
x = 150
A pair of trouser =sh150
A shirt = sh30
