Y8 Algebraic Equations

Expanding

100

Expand

-(3x - 2y + z)

-3x+2y-z

200

Expand and simplify

5(p+7) + 2p - 9

7p+26

300

Expand and simplify

3(x+8) + 7(x-9)

10x-39

400

Expand and simplify

5(x+3) - 4(x-7)

x+43

500

Expand and simplify

9m(m+7n) - 3m(2n+3m)

57mn

Factorising

100

Factorise

15a + 10

5(3a+2)

200

Factorise

-3x + 6 + 9x²

-3(x - 2 - 3x)

300

Factorise

4xd + 14d²

2d(2x+7d)

400

²Factorise

-4a²b + 8a³bc

-4a²b(1 - 2ac)

500

Find the perimeter of a triangle with edge lengths 2b+a, 5a-b and 2a+3b then factorise the answer.

4(2a+b)

Solving

100

Solve

3m + 2 = 4

m = 2/3

200

Solve

20 - 7x = 6x - 6

x = 2

300

Solve

2(2x + 1) = 3(x - 4)

x = -14

400

Solve

(7c+4) = 11
    8

c = 12

500

Solve

(x + 7) = x + 7
    6

x = -7

Substitution + Simple Quadratics

100

Solve

x² = 100

x = +-10

200

In the formula v = u + at find v if u=8, a=4 and t=-2.

v = 0

300

Solve

9x² = 25

x = +- 5/3

400

If C = E/R find E if C = -5 and R = 7.

E = -35

500

Solve to 1 decimal place

7x² - 3 = 4x² + 12

x = 2.2

Word Problems

100

I think of a certain number, double it and subtract 3. The result is 17. Find the number.

x = 10

200

The product of a certain number and 5 is divided by 9. The result is 10. Find the number.

x = 18

300

The length of a rectangle is twice its breadth. If the perimeter is 72m, find the dimensions of the rectangle.

12m and 24m 

400

Sarah is x years old.
Tom is 3 years older than Sarah.
Dave is twice as old as Sarah.
Their ages sum to 51.
Find their ages

Sarah = 16

Tom = 19

Dave = 32

500

The sum of two numbers is 25. One of the numbers exceeds the other by 9. Find the numbers.

8 and 17