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
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 + a2. 4ab + 2b
3. ab + 2ab
4. 3a2b + 6b
5. 2a + 3b
6. 3ab - ab
7. a + a
(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
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
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