S-L1 Algebra Practice

ALGEBRA

Recap

Simplify

1) a + a                              1a)  2a + 3a  

2) 2a + a                            2a)  2a - 5a

3) 2a - a                             3a)  -a + 4a

4) a - a                               4a)  2a - 2a

5) a - 0                               5a)  4a - 4a

6) 0 - a                               6a)  0 - 7a

7) 2a + 3a - a                     7a)  6a +a - a

8) 5a - 2a + a                     8a) -9a + 6a

9) 2a + a - a - 2a                9a)  2a + a + 3a + 2a

10) 2a + 2a + 3b               10a) a + b + 2a + 2b 

11) 2a - a - b + 2b             11a)  -a + b -2a - 4b

12) 3a + 2a - b                  12a)   a - a + b - b

13) 1 x a                            13a) 2 x a 

14) 0 x a                            14a) 2a x b x 0

15) 1 x -a                           15a) -2a x 0

16) a x a                            16a)  a x -a

17) 2a x a                          17a)  -2a x -a

18) a x 3a                          18a) -a x 3a

(1) Notations, Addition/Subtraction of Linear Expression

(A) Write the algebraic expression for the following:

1.   Add 2x and y and 5
2.   Subtract 2w from 34
3.   Product of 21 and g
4.   Divide 6 by n
5.   Sum of 7, 2p and q

6.   Sally had x books. Her friend gives her 2 books. How many books does she have?

7.   A box has x cookies. How many cookies are there in 12 such boxes?

(B) Simplify:

1. 4y + 2x -y + x

2. 5x - 3y - y - 2x

3. 7x + y - 3y - 4y + x

4. 2x + y - x - y - x

(C) Simplify:

1.   3ab + a
2.   4ab + 2b
3.   ab + 2ab

4.   3a²b + 6b

5.   2a +   3b

       5.       5
6.   3ab - ab

         8     4
7.   a + a

      2    2

8.   a + a

            3

(D). Simplification of Linear Expression

1.    Express each of the following as two separate terms.

a.    2x – 7      b.   15x – 8

            4                      10

2. Simplify the following

a.    x+ x        b. -3x + 2x     c.  3(y -1 )  + 5(2y – 3)

       2    5            4       6               8                  12

3.  Lily is 5x years old. Annie is 2(x – 1)/5 years old. Find the sum and difference of Lily and Annie.

(2) Expansion of 2 linear Expressions/Extract Common Factors

1. Expand the followings:

a.   4 ( x + y)

b.   (2x + y) 

          4

c.  3(2x - 3y)

2. Simplify the following:

a. -8 + 4y – 4y² -2 + y²

b. (-3u² + 5u – 8) – (4u² – 6u + 5)

c.  -6(-3y² + 3y + 1) – 4(2y2 – 2y – 9)

3.  Subtract the sum of -3(n² – 2n +5) and 2(-6n2 + n + 2) from 4(-3n² -3n – 1)

4.  Car X travels at a speed of (2x² + 5x – 7) km/h for 4 hours. Car Y travels at a speed of (x² – 2x + 9) km/h for 3 hours. Which car has covered more distance? By how many km more?

5.  Expand        a. (5m + n)(7m + 3)

                         b. (2m – 5n)(2m + 5n)

                         c.  –c(-6c – d)(-4y + 3z)

                         d. (2p + 5q – 9)(4p – 5q)

6.  Expand and simplify

a.  (2p – q)(2p + 3q) – (p + q)(p – 5q)

b.  (2p + q)(3x – 2y) + (p – 2q)(3x + 4y)

7. Expand each of the following.

a. (12p + 1/3q)2

b.(5a -3b)2

c.  (11p – 8q)(11p + 8q)

d.  (3u – 4v)² – (2u + 9v)(2u +9v)

8. Expand (x + 1/x)². If x² + 1/x² = 7, and x > 0, find the value of

a. x + 1/x 

b. (x + 1/x)²

(3) Factorisation

1.  Factorise each of the following expressions

a.  a² + 15a + 44

b.  21 – 4b – b2

c.  9q2 + 30q + 25

d.  4 – 2d – 12d2

e.  (3x – 4)(2x – 5) + 8(2x – 5)

f.   (3x – 4)2 – (2x + a)2

g.  y + 24yz – 81yz2

2.  Factorise

a.  p² + 8pq + 16q2

b.  s²t² – 16st + 64

c.  45x² – 320y²

3.  Find the value of

a.  143² - 142²

b.  √200.5 ² – 199.5 ²

c.   13.5 ² – 6.5 ²

4.  Factorise

a.  100 – y² + 6yz – 9z²

b.   3x² – 48x

5. Factorise

a.  (a + 3b)x + (a + 3b)y

b.  m(3p – q) – 2n(3p – q)

c.  10px + 15qz + 8py + 12qy

d.  36ax – 63ay – 4bx + 7by

e.  54p2 – 6p – s + 9ps

f.  21 mx – 7kx – 2ky + 6my

Expansion and Factorisation of algebraic expression

1.  Simplify the following:

a. -8 + 4y – 4y² -2 + y²

b. (-3u² + 5u – 8) – (4u² – 6u + 5)

c.  -6(-3y² + 3y + 1) – 4(2y2 – 2y – 9)

2.  Subtract the sum of -3(n² – 2n +5) and 2(-6n2 + n + 2) from 4(-3n² -3n – 1)

3.  Car X travels at a speed of (2x² + 5x – 7) km/h for 4 hours. Car Y travels at a speed of (x² – 2x + 9) km/h for 3 hours. Which car has covered more distance? By how many km more?

4.  Expand     a. (5m + n)(7m + 3)

                         b. (2m – 5n)(2m + 5n)

                         c.  –c(-6c – d)(-4y + 3z)

                         d. (2p + 5q – 9)(4p – 5q)

5.  Expand and simplify

a.  (2p – q)(2p + 3q) – (p + q)(p – 5q)

b.  (2p + q)(3x – 2y) + (p – 2q)(3x + 4y)

Exercise 1

1. Factorise bx - 2by + 3ax - 6ay

2. Simplify -4(x - 2) + 8x

3. Write    2     +   4        as a fraction in its simplest form.

            (x+1)²     x + 1

4. Simplify 3a²  x (2a² )⁴   

5. Simplify 5a³  ÷  25a  

                  2         8

Exercise 2

1. Simplify 3(2x - 5) + 8x

2. Find the value of -5y - 2 = 3

3.  Simplify the following, expressing your answers with positive indices

(a) y²  x (y² )⁴   

(b) (xy)⁰   

4.  Evaluate the following without using calculator

(a)  81^5/4  

(b)  1000 ^-2/3   

5.  Solve  4^5x   = 512

Answers

Recap

1.  a + a = 2a                                   1a) 2a + 3a = 5a

2.  2a + a = 3a                                 2a) 2a - 5a = -3a

3.  2a - a = a                                    3a) -a + 4a = 3a

4.   a - a = 0                                     4a) 2a - 2a = 0

5.   a - 0 = a                                     5a) 4a - 4a = 0

6.   0 - a = -a                                    6a) 0 - 7a = -7a

7.  2a + 3a - a = 5a - a = 4a             7a) 6a + a - a = 6a

8.  2a + 3a - a = 3a + a = 4a            8a) -9a + 6a = -3a

9.  2a - a -a - 2a = 3a - a - 2a = 0     9a) 8a

10. 2a + 2a + 3b = 4a + 3b             10a) 3a + 3b

11. 2a - a -b + 2b = a + b                11a) -3a - 3b

12. 3a + 2a - b = 5a - b                   12a) 0

13. a x a = a                                    13a) 2a

14. 0 x a = 0                                    14a) 0

15. 1 x -a = -a                                  15a) 0

16. a x a = a^2                                 16a) -a^2

17. 2a x a = 2 a^2                            17a) 2a^2

18. a x 3a = 3a^2                             18a) -3a^2

C4.   3a²b + 6b   Step 1 : Take out common factors 3b

        3b(a² + 2)    Step 2 : bracket

5.   2a +   3b        Step 1 : Take out common factors 1/5

       5        5

       1 (2a + 3b)    Step 2 : bracket

       5