Non-Calculator Algebra - Wikispaces Algebra... · · 2016-11-14Non-Calculator Algebra Exercise...

Non-Calculator

Algebra Exercise Book

CfE Level 4 Expressions and Equations (4.14, 4.15)

National 5 Expressions and Formulae

Name ________________

Non-Calculator Algebra Sheet 1 Due Date _______________________________

A. Simplify:-

1. 5(2x + 6) 2. 5(3 – 4y) 3. 2x(6 + x) 4. 5 – 2(x – 4)

5. 25 2a b b 6.

24 6x y x 7. 5 10y y 8. 24

2

x

x

9. 3

5 5

y 10.

4 6

y y 11.

3 2

6 7

x x 12.

7

7

x

x

B. Solve :-

13. 3(x + 2) = 15 14. 4(5 – x) = x 15. 4

5( 4)2

xx

16. 4x + 5 > 17 17. 3( 1) 2( 4)x x 18. 12 - x > 5x

19. 2 36x 20. 22 18x 21. 15

5 3y

Non-Calculator Algebra Sheet 2 Due date _______________________________

A. Simplify:-

1. 2x(2x + 5) 2. 7(3x – 4y) 3. 2y(9 – 3x) 4. 12 – 2(x – 7)

5. 37 3a b b 6.

25 6x y xy 7. 25 100y y 8.

59

6

x

x

9. 3

7 7

y 10.

6 9

y y 11.

3 2

5 8

x x 12.

6

7

y

p

B. Solve :-

13. 3(x - 2) = -12 14. 7(9 – x) = 2x 15. 6

5( 3)2

xx

16. 4x + 5 ≤ 17 17. 3( 1) 2( 4)x x 18. 21 - 2x > 5x

19. 2 144x 20. 22 450x 21. 8

4 8y


A. Expand and simplify:-

1. 2(x - 4) -7(2x + 5) 2. (x + 4)(x + 6) 3. (2y+3)(y – 3) 4. (3x – 6)(2x – 5)

5. 5 29 3a b b 6.

2 72 5x y xy 7. 2(5 )y 8.

9

4

12

8

x

x

9. 3

6 9

y 10.

2

4 6

x x 11.

3 2

3 7

x x 12.

6

7

p

p

B. Solve :-

13. 3(x - 2) = -1(x+ 3) 14. 7(9 – x) = -2x 15. 5

5( 1)3

xx

16. 2(x + 5) ≤ 17 17. 3(1 ) 2( 4)x x 18. (x + 1)(x + 5) = x(x + 5)

19. 2 81x 20. 22 8x 21. 7

3 16y



1. 2(x - 3) -7(2x + 3) 2. (x + 3)(x - 3) 3. (3y + 3)(y – 3) 4. (3x – 3)(2x – 3)

5. 6 89 7a b b 6.

7 6 27 4x y x y 7. 2(7 )y 8.

9

2

16

6

x

x

9. 3

10 15

y 10.

2

6 8

x x 11.

3 2

5 7

x x 12.

4

9

p

p

B. Solve :-

13. 3(x - 8) = -1(x + 3) 14. 7(6 – x) = -2x 15. 5

4( 1)3

xx

16. 2(x + 9) ≤ 17 17. 3(2 ) 2( 5)x x 18. 2(x + 1)(x + 5) = x(2x + 5)

19. 2 49x 20. 22 18x 21. 7

5 16y



1. 2(5x - 3) -8(2x + 3) 2. (x + 0.5)(x – 0.5) 3. (4y + 4)(y – 4) 4. (3x – 1)(5x – 1)

5. 8 2 810 7a b b 6.

3 3 4 56 3x y x y 7. 3(2 )y 8.

8

5

14

7

x

x

9. 2

12 5

y x 10.

7

9 6

x x 11.

3 2

7 21

x x 12.

m n

p q

B. Solve :-

13. 2(x + 9) ≤ - 7 14. 3(2 ) 2(5 )x x 15. 3(x + 1)(x + 5) = x(3x + 5)

16. 2 49x 17. 22 18x 18. 7

5 16y

C. Change the subject of each formula to y :-

19. 4 5x y 20. 3 4 9x y 21. 3ty

xm



1. 4(3x - 3) -5(4x + 4) 2. (x + 0.1)(x – 0.1) 3. (5y + 3)(y – 3) 4. (6x – 1)(5 – x)

5. 5 8 25 7a b b 6.

6 3 4 24 8x y x y 7. 3(3 )y 8.

9

4

18

9

x

x

9. 2

7 5

y x 10.

7

12 8

x x 11.

3 2

6 15

x x 12.

a b

c d

B. Solve :-

13. 2(x - 9) ≤ - 7 14. 5(2 3 ) 2(7 )x x 15. 4(x + 1)(x + 2) = x(4x + 5)

16. 2 16x 17. 22 72x 18. 4

5 6x


19. 2 4 5x y 20. 3 4 9x y 21. 7yp

xw

Non-Calculator Algebra Sheet 7 Name _______________________________


1. 2(5x - 3) -3(4x - 1) 2. (x + 10)(x – 10) 3. (7y + 2)(y – 2) 4. (2x + 1)(5 – x)

5. 2 3 44 6a b b 6.

3 4 5 62 9x y x y 7. 4(2 )y 8.

7

2

18

6

x

x

9. 2

9 5

y x 10.

3

12 8

x x 11.

3 2

4 6

x x 12.

e f

g h

B. Solve :-

13. 2(y - 4) ≤ - 3 14. 2(3 ) 3(7 )x x 15. 2(x + 2)(x + 1) = x(2x + 5)

16. 2 169x 17. 25 45x 18. 5

6 4x


19. 4 5x y 20. 3 4 9 0x y 21. 2

3yt

xw



1. 6( 12 x - 3) -3(4 - x) 2. (x + 2 )(x – 2 ) 3. (7y - 3)

2 4. (x + 1)(x + 2)(x +3)

5. 12 7 213

6a b b 6. 2 3 4 515

2x y x y 7. 32(2 )y 8.

6

5

21

6

x

x

9. 2

6 5

p x 10.

3 3

12 8

x x 11.

3 2

4 6 2

x x x 12.

1 1

4 6x y

B. Solve :-

13. 2(y - 4) ≤ - 3(y - 2) 14. ( 3)( 4) 0x x 15. (2x + 5)(x - 1) = 0

16. 2 100 0x 17. 2 6 0x x 18. 3 1

94x


19. 5y + 3 – 2x = 0 20. 3 4 9 0y x 21. 2t

psty



1. 8( 14 x - 3) -3(4 - x) 2. (x + 3 )(x – 3 ) 3. (5 - 3y)

2 4. (x + 2)(x + 3)(x -4)

5. 8 9 217

14a b b 6. 6 7 225

10x y x y 7. 43(2 )y 8.

9

4

24

9

x

x

9. 2

4

p x

y 10.

7 3

10 8

x x 11.

3 2

( 2) ( 1)x x

12.

1 2

4 3

y

B. Solve :-

13. 4(y - 6) ≤ - 7(y - 1) 14. ( 9)( 1) 0x x 15. (2x - 7)(3x + 1) = 0

16. 24 36 0x 17. 2 9 18 0x x 18. 2 −3

𝑥= −

1

5


19. 5 + 3y – 2x = 0 20. 3 4 9 6y x 21. 2

5t

xyy


A. Expand and/or Simplify:-

1. (4x – 5y)2 2. (x + 1)(x + 2)(x + 3) 3. 4 9 7 21

414a b a b 4.

1 3

2 26 7a a

5. 5 3

2

y y

y

6. 6 7 22

510x y x y 7.

3 43(2 )y 8.

1

2

1

4

14

6

x

x

9. 6 8

x x 10.

7 3

y y 11.

3 2

5 6

x x 12.

3 5

4x x

B. Rationalise the denominator :-

13. 5

3 14.

2 5

2 15.

3

7 2

C. Solve :

16. 29 25 0x 17. 2 6 9 0x x 18. 26 1 0x x

D. Change the subject of each formula to y :-

19. 6 - 2y + x = 0 20. 2

22

yx

r 21.

2 360

y

r



1. (4x – √7)2 2. 5√2 + √18 + √50 3. 1 3 23

420a b ab 4.

3 3

5 5100 0.7a a

5. 2 3

7

y y

y

6. 6 7 42

515x y x 7.

7 3(3 )y 8.

2

3

1

5

x

x

9. 5

6 6

m m 10.

4 9

y y 11.

8 2

5 6

x

x 12.

3

4 6

x

x

B. Evaluate :-

13. 24 14.

1

327

15.

3

225

C. Solve :

16. 24 6 0x x 17. 2 6 9x x 18. 26 0x x


19. x = 15 - 3y 20. 2

25

yx

r 21.

2 10x r y



1. (3x – √7)(2x + √7) 2. (4 – 3x)(2x – 1) 3. ( 2x – 1 )3 4. 5x

3 × 4x

-5

5. 5

2

6

9

y

y 6.

2 15 53 4x x

7.

15 3(5 )y 8. 2 3 7 81

43a b a b

9. 3 5m

y y 10.

5 7

7 3

x y 11.

3 5

2 7x x 12.

2

5 15

8 4x x

B. Evaluate :-

13. 52 14.

1

3125

15.

3

216

C. Solve :

16. 28 20 0x x 17. 2 2 15x x 18. 210 2 0x x


19. 5x = 15 - 10y 20. 2

27

yr

r 21.

21 10x r y



1. (7y – √3)(7y + √3) 2. 8(3 – 2x)2 3. (3x

5)2 4. 9x

11 × 4x

-3

5. 5

8

12

9

y

y 6.

327 76 4x x

7.

12 4(3 )y 8. 2 3 7 71

93a b a b

9. 3 5

2m m 10.

2( 1) 3

4 3

x x 11.

7 5

10 7

y

x x 12.

3

6 9

7 14x x

B. Evaluate :-

13. 52 14.

2

3125

15. 3

24

C. Solve :

16. 25 20 0x x 17. 2 5 24x x 18. 26 7 3 0x x


19. 6x = 6 - 6y 20. 2

27r

yr 21.

22 1 10x r y



1. (y – √7)(y + √7) 2. 3(4 – 2x)2 3. (2y

5)4 4. 8x

11 × 8x

-3

5. 7

2

15

9

y

y 6.

527 76 8x x

7.

13 5(2 )y 8. 2 3 1 71

510a b a b

9. 2 5

3 7y y 10.

2(3 ) 3

5 3

x x 11.

7 5

10 7

x x

y 12.

2

3

6 15

7 14

x

x

B. Evaluate :-

13. 410 14.

3

225

15.

11

29

C. Solve :

16. 212 28 0x x 17. 2 7 12x x 18. 22 5 12 0x x


19. 24x = 12 - 6y2 20.

2

6 2

5

r

yr 21. 2

360

ya r



1. (y – √6)(y - √6) 2. 3(4 – x)2 3. (2y

5)-3

4. 5x-4

× 8x-3

5. 3

2

15

21

y

y

6.

347 790 2x x

7.

15 3(2 )y 8. 2 3 3 71

721a b a b

9. 7 5

3y y 10.

3(9 ) 5

5 3

x x 11.

7 5

15 21

x x

y 12.

2

7

9 15

21 14

x

x

B. Evaluate :-

13.

1

2100

14.

2

327

15.

11

216

C. Solve :

16. 22 18 0x 17. 2 11 18x x 18. 22 6 0x x


19. 4x = 7 - 2y2 20.

6 21

5

r

y 21. 2

360

ya r



1. (y – 3)(y – 3x + 1) 2. -2(9 – x)2 3. (2x

2y

5)-3

4. 4x-9

× 7x8

5. 3

4

18

21

y

y

6.

4 27 719 2x x

7.

14 4(2 )y 8. 2 6 5 81

621a b a b

9. 4 5

1 2y y

10.

2 6

( 3)y y y

11.

7 3

5

9 7

14 27

x x

x

12. 2 2 4

7

9 15

21 7

x y y

x

B. Evaluate :-

13.

1

281

14.

1

327

15. 19

C. Solve :

16. 23 75 0x 17. 2 2 1x x 18. 22 3 35 0x x

D. Change the subject of each formula to x :-

19. y - b = m(x – a) 20. 5 150

sin y x 21. 34

3V x



1. (y – 3)(1 – 3y + y2) 2. 12 - (3 – x)

2 3. (2x

4 )-3

4. 8x-20

× 7x8

5. 3

2

7

21

y

y

6.

5 16 67x x

7.

14

13(8 )y 8. 6 6 5 81

129a b a b

9. 1 1

2y y

10.

2 6

( 3) ( 3)y y y

11.

8 3

5

9 7

7 6

x x

x

12. 2 4

3 7

x y

y x

B. Evaluate :-

13. 1

2121

14.

1

3125 15. 2

3

C. Solve :

16. 29 64 0x 17. 2 20 9x x 18. 23 4 0x x

D. Change the subject of each formula to x :-

19. y - b = ½ (x – a) 20. 5 70

y x 21. 21

3V x h



1. (2y – 3)(1 – 6y – y2) 2. -14 - (3y – 2x)

2 3. (0.5x

-4 )-3

4. 7x-20

÷ 70x-12

5. 12𝑥𝑦4

18𝑥2𝑦−3 6.

2𝑦+5

10+

𝑦−2

15 7.

2𝑎−7

8−

𝑎+4

6 8.

3𝑞+4

9−

4𝑞+3

12

B. Make the variable in [ ] the subject

9. [ a ] 10. [ 𝜔 ] 11. [ a ] 12. [ m ]

𝑣2 = 𝑢2 − 2𝑎𝑠 𝐸 =𝑘𝜔2

2𝑎 𝑠 = 𝑢𝑡 +

1

2𝑎𝑡2 𝐴 =

𝑚𝑎

𝑀 + 𝑚

C. Evaluate :-

13. 625−3

4 14. (√2435

)−2

15. 32−2

5

D. Solve :-

16. 121𝑥2 − 400 = 0 17. 169 − 81𝑥2 = 0 18. 𝑥2 +𝑥

6=

5

2

E. Express in the form (𝑥 + 𝑝)2 + q

19. 𝑥2 + 6𝑥 − 4 20. 𝑥2 − 8𝑥 + 3 21. 𝑥2 − 12𝑥 − 15



1. (4y2 – 3)(2y – 5y

2– 6y

3) 2. (4y + 2)

2 – (2y – 3x)

2 3. (4 x

-5 )-4

(2 x5

)-2

4. 225x16

÷ 15x-9

5. √72√48 6. 𝑦−3

𝑦−2+

𝑦−2

𝑦−3 7.

𝑎−4

24−

𝑎+4

16 8.

𝑥

𝑥+3−

𝑥−4

2𝑥+6


9. [ u ] 10. [ 𝑘 ] 11. [ u ] 12. [ a ]

𝑣2 = 𝑢2 − 2𝑎𝑠 𝐸 =𝑘𝜔2

2𝑎 𝑠 = 𝑢𝑡 +

1

2𝑎𝑡2 𝐴 =

𝑚𝑎

𝑀 + 𝑚

C. Evaluate :-

13. 64−4

3 14. (√325

)−2

15. 64−2

3

D. Solve :-

16. 64𝑥2 − 49 = 0 17. 30𝑥2 + 7𝑥 − 15 = 0 18. 𝑥2 +𝑥

4= 1.875

E. Express in the form (𝑥 + 𝑝)2 + q

19. 𝑥2 + 12𝑥 − 21 20. 𝑥2 − 𝑥 + 2 21. 𝑥2 − 9𝑥 − 5



1. (a – b – c)(d – e – f) 2. (2y – 5x) 2

– (3y – 4x)2 3. (4x

-2 )3(

1

2x

5 )-2

4. 1024x-4

÷ 256x-5

5. √108√48 6. 𝑦−3

𝑦−2+

𝑦−2

𝑦−3 7.

𝑎−4

4𝑎−

𝑎+4

6𝑎 8.

𝑥

𝑥+4−

𝑥−4

2𝑥+8


9. [ s ] 10. [ 𝑎 ] 11. [ t ] 12. [ M ]

𝑣2 = 𝑢2 − 2𝑎𝑠 𝐸 =𝑘𝜔2

2𝑎 𝑠 =

1

2𝑎𝑡2 𝐴 =

𝑚𝑎

𝑀 + 𝑚

C. Evaluate :-

13. 275

3 14. (√2568

)−4

15. 256−3

4

D. Solve :-

16. 256𝑥2 − 169 = 0 17. 35𝑥2 = 𝑥 + 12 18. 𝑥2 −5𝑥

3=

2

3

E. Express in the form (𝑥 + 𝑝)2 + q or 𝑞 − (𝑥 + 𝑝)2

19. 𝑥2 + 8𝑥 − 13 20. 𝑥2 − 3𝑥 + 4 21. −𝑥2 − 10𝑥 + 3

Non-Calculator Algebra - Wikispaces Algebra... · · 2016-11-14Non-Calculator Algebra Exercise...

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Transcript of Non-Calculator Algebra - Wikispaces Algebra... · · 2016-11-14Non-Calculator Algebra Exercise...