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(p+4) = 18

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

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

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

a) x=±9

b) x=$\pm\sqrt{23}$

c) x= ±3

7F) Solve the following equations

a) x²=81

b) x²=23

c) 3x²=27

a) 0

b) 1

c) 2

7F) State the number of solutions

a) x²=-3

b) x²=0

c) x²=7

a) 22

b) 17

7G) Apply the formula for a rectangle’s perimeter P=2l+2w

a) P when l=7 and w=4

b) L when P=40 and w=3

a) a=b/b+1

b) a=-b

c) a= $\sqrt{k-y}$

7G) rearrange to make a the subject

a) ab+a =b

b) 1/a + 1/b=0

c) 4(g-a)=5a-3

d) k=a²+y

a) 118

b) 119

7H) The sum of three consecutive numbers is 357

a) use an equation to find the smallest of the numbers

b) What is the average of these numbers.

2 litres in the first jug.

7H) One jug has an unknown quantity of water.  A second jug has 2 litres of water.  One third of the contents of the jug are transferred into the second jug, then one quarter of the contents of the second jug are transferred to the first jug.  After which the two jugs contain the same amount of water.  How much water was initially in the first jug? Answer as x litres in the first jug

CORRECT

9A) Cartesian Plane

Plot these points and label them

a) A(2,3) b) B(0,4) c) C(-1,2.5)

(2,4)

9A) The midpoint of a line segment is the point that cuts the segment in half. Find the midpoint of the line segment joining these pairs of points.

(1,3) and (3,5)

square root of 52

9A) Find the distance between these pairs of points.

(0,0) and (0,10) use the formula below

d = sqrt((x2 - x1)^2 + (y2 - y1)^2) paste into google to find out definition

CORRECT

9B) For the rule y=2x-1, construct a table and draw a graph

Yes, No

9B) Decide if the points (1,3) and (-2,-3) lie on the graph of y=3x

y=3x-2

9B) Find a rule for this table