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Linear Questions

 

1.  Determine the inequalities that represent and satisfies the unshaded region (3 mks)

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2.  Write down the inequalities that satisfy the u shaded region in the figure below. (4mks)

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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 inequalityImage From EcoleBooks.com<Image From EcoleBooks.com<Image From EcoleBooks.com (2mks)

6.  (a) Show by shading the unwanted region the area represented by Image From EcoleBooks.comImage From EcoleBooks.com  Image From EcoleBooks.comandImage From EcoleBooks.com on the grid provided (8 mks)

(b) Calculate the area of the enclosed region (2 mks)

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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

 Image From EcoleBooks.com   (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)

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11.  Write down the inequalities that define the unshaded region marked R in the figure below. (3mks)

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12.  Write down all the inequalities represented by the regions R.  (3mks)  

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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)

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15.  The diagram below shows the graphs of y = 3/10 x – 3/2, 5x + 6y = 3 and x = 2

 

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 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)

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B1

B1

B1

 

 

2.

(a) x  -4

(b) y = -x

y + x  0

(c) Grad = Image From EcoleBooks.com

 = 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.

  1. 4x – 9 < 6 + x

x < 5

8 – 3x < x + 4

1 < x

b) 1 < x < 5

 

M1

 

M1

A1

 

5.

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M1

 

 

 

 

A1

2

7

-3x + 2 < x + 6

x > 1

x + 6 ≤ 17 − 2x

x ≤ 3⅔

2, 3

 

B1

B1

 

B1

3

 

8.

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15a + 10  8a + 12

7a  2

a  0.2857

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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.

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B1

B1

B1

 
  

03

 

13.

 

X

-2

-1

0

1

2

3

4

5

1.5

Y

-6

0

4

6

6

4

0

-6

6.255

 

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b) turning point 1.5, 6.25

c) i) Line y = 0 x =

1 or x = 4

x = -1 or x = 4

ii) Image From EcoleBooks.com4 + 3x -x2 = y

4x – x2 = 0

4 – x = y

x

0

4

y

4

0

 

x = 0 or x = 4

 

B2

 

 

 

 

 

 

S1

P1

C1

L1

 

 

 

 

 

 

 

 

 

 

 

 

 

B1

 

 

B1

 

B1

 

 

 

 

 

B1

For all values

  

10

 

14

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Image From EcoleBooks.com

Image From EcoleBooks.com

 

 

 

 

 

 

M1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

M1

 

 

 

A1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  

3marks

 

 

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

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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


 




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