Tuesday, 21 April 2020

S-L1 Algebra Practice

ALGEBRA

(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       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) – (4u– 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.  143- 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) – (4u– 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 3a x (2a)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) y x (y)4   

(b) (xy)0   


4.  Evaluate the following without using calculator
(a)  815/4  
(b)  1000 -2/3   

5.  Solve  45x   = 512


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