Algebra and Index 9core

Adding/subtracting

100

2x + 4x - x

5x

200

3b + 4a - 2b - a

b + 3a

300

10x² - 12x + 3x² - 8x³

13x² - 12x - 8x³

400

-2x + xy + 2x - 2xy

-xy

times/divide

100

2y * 3x

6xy

200

2a * 3b * 4c

24abc

300

10r * 3w * r

30r²w

400

3x²y/12xy

x/4

substitution

100

Solve 2a + 1 where a = 3

7

200

4a + b where a = 2 and b = 4

4*2 + 4 

= 8 + 4 

= 12

300

10ab - 4b where a = 3 and b= 2

10*3*2 - 4*2

= 60 - 8

= 52

400

Goal = 6 and point = 1

Team A scored 3g + 6p

Team B scored 4g + p

Which team won?

Team A = 3*6 + 6 = 24

Team B = 4*6 + p = 25

Therefore, team B won

Index laws

100

a³ x a⁴

a⁷

200

b⁶ / b³

b³

300

(23 + 2ab)⁰

1

400

(y³)⁴

y¹²

other

100

The coefficient of b is:    3ab + 4a + 2b – 7.

2

200

Mark buys 6 hamburgers.  If the cost of each hamburger is $x, an expression for the total cost of the hamburgers is

6x

300

Expand 2(x+4)

2x + 8

400

Factorise 8xy + 10y

2y(4x + 5)