Algebra

a) 36

b) 676

c) t

5A) extension

this expression has 26 terms, one for each letter of the alphabet.

a+4b+9c+16d+25e+...

a)what is the coefficient of f

b) what is the coefficient of z

c) which pronumeral has a coefficent of 400

b) T

c) F

d) T

e) F

5A) 12

If x is a positive number classify these as true or false

b) x is always smaller than x+2

c) x is always smaller than x^2

d) 1-x is always less than 4-x

e) x-3 is always a positive number

a)5(3) or 5*3

= 15

b)5(3)^2 + 2(6) + 3

= 5(9) +12 +3

= 45 + 15

= 60

5B) Substitute x=3 and y=6 to evaluate the following expressions

a) 5x

b) 5x^2 + 2y + x

No

5B) Are x - 3 and 3 - x equivalent expressions

a) L

b) N

c) N

5C) Classify the following pairs as like terms (L) or unlike terms (N)

a) 3pq and -3qp

b) 5st^2 and 3s^2t

c) 8a^2b and 9b^2a

7x

5C) Simplify 8x - 3x + 2x by combining like terms

15x^2yz

5D) Simplify 3xy*5xz

= xy/z

5D) Simplify 8x^2y/8xz

a) =8x-4xy

b) =-56-16y

5G) expand

a) 4x(2-y)

b) -8(7+2y)

a) = 6b + 15 + 3b

= 9b+15

b) = 12xy +14x -7xy

= 5xy +14x

5G) expand and simplify

a) 3(2b+5)+3b

b) 12xy + 7x(2-y)

a) 26a/15

b) 9k/10

c) 13x^2/3

5E) Simplify

a) 4a/3 + 2a/5

b) 6k/5 - 3k/10

c) 4x + x/3

a) 3(2x + 5)

b) 6a(2 +3b)

c) 7(3x - 2y)

5H) Factorise

a) 6x + 15

b) 12a + 18ab

c) 21x - 4y

a) 5

b) 6a

c) 3x

5H) Find HCF of

a) 20 and 35

b) 18a and 24ab

c) 12x and 15x^2

= (y-2)(3y+7)

5H) Factorise by removing a common factor

3y(y - z) + 7(y - 2)

= x(y + 3) +2(y + 3)

= (y+3)(2 + x)

5H) Factorise by removing common factor or using the separate brackets.

xy +3x +2y +6

a) coefficient

b) constant

General knowledge)

in the term 6xy + 25

a) six is the _______ of x and y

b) 25 is the _______ term

a) x^2-5x-30

b) x^2-7x-7

Multiplying factors)

a)(x+8)(x-2)

b)(x-9)(x+2)

a) 6ab/35

b) 4x/x-2

5F) Simplify

a) 2a/5 * 3b/7

b) 12x + 24/x-2 * x/3x + 6

a) (x+1)(x+4)

b) (x-2)(x-1)

c) (x-7)(x+3)

Factorise)

a) x^2 + 5x +4

b) x^2 -3x +2

c) x^2 -4x -21

a) x-5/x

b) y+3/5

Factorise fractions)

a) x^2 -25/x^2 +5x

b) y^2 -9/5y-15

a) 4k

b) 40 + 70n

5I) Write an expression for

a) The total cost, in dollars, of k bottles if each bottle costs $4

b)The total cost, in dollars, of hiring a plumber for n hours if they charge a $40 call out fee and $70 per hour

a) 5^12

b) x^7

c) 10^3

d) 5x^4/2

5J) Use index law to simplify the following:

a) 5^3 * 5^7 * 5^2

b)x^3 *x^4

c) 10^8/10^5

d) 10x^6/4x^2

a) 2

b) 1

5K) Simplify the following using index laws

a) 10^0 +5^0

b) (4x)^0 * (8xy)^0

a) 2^15

b) 25x^6

5K) simplify the following

a) (2^3)^5

b) (5x^3)^2

a) 1/b^4

b) 3y^2/x^4

c) 5x^3

Negative indices) Express using positive indices

a) b^-4

b) 3x^-4y^2

c) 5/x^-3

a) 2/a^2b

b) n^7/2m^7

Negative indices) Express using positive indices

a) 2a^3b^2/a^5b^3

b) 4m^-2n^3/8m^5n^-4

a) x=20

b) u=5

c) x=6

7A) Solve the equations algebraically

a) x-4=16

b) 2u+7=17

c) 40-3x=22

a) k=24.5

b) n=13

7A) Write equations and solve for the pronumerals

a) The number k is doubled and the result is 52

b) Akira works n hours earning $12 per hour. The total she earned was $156.

a) x=6

b) y=3

c) x=10

7C) Solve the following algebraically

a) 4x/3=8

b) 4y+15/9=9

c) 4 + 5x/2=29

a) t=3

b) x=2

c) u=4

7D) Solve the following

a) 7t+4 = 5t +10

b) 6x+4=22-3x

c) 2u=7u-20

a) p=2

b) q=2

c) x=7

d) k=8

7E) Solve the following equations by first expanding brackets

a) 3(+4) = 18

b) -12(3q +5) =-132

c) 4(2x-5) + 3x=57

d) 2(3k +1) = 5(2k-6)