Year 9 Algebra

Scientific Notation

100

Write the following as Scientific Notation:

131 000 000

1.31 x 10⁸

200

What is the following in Scientific Notation:

0.0009042

9.042 x 10^-4

300

(9 x 10⁹) + (3 x 10⁷)

9.03 x 10⁹

400

The Length and Width of a farm is 

L= 3.1 x 10⁴ m

W= 2 x 10³ m 

What is the area for this farm?

6.2 x 10⁷

500

What is the volume of a cube if it has a width of 

3 x 10⁶ cm ?

2.7 x 10¹⁹

Index Laws 1, 2 & 3

100

Simplify:

y² x y x y⁴

y⁷

200

25w³ / 5w

5w²

300

7⁰ + 8⁰ =

1 + 1 = 2

400

(4a^2b * 9a^3b^2)/(3ab)

12a⁴b²

500

(5a^2b^7)/(9a^3b) * (9a^4b^2)/(5a^2b^7)

ab

Index Laws 4 & 5

100

(4a²)³

4³a⁶   or   64a⁶

200

((3n^3)/(2m^4))^3

(3^3n^9)/(2^3m^12)  or (27n^9)/(8m^12)

300

((2x³)²)⁴

2⁸x²⁴   or 256x²⁴

400

((2m^3n)^3)/(m^4)

2³mn³  or 8mn³

500

(-3(2^4a^4b^3)^3)/(-2^3a^2b)^4

3a⁷b⁵

Factorising Binomials

100

Factorise the following expression:

3x + 6

3(x + 2)

200

Write the factorised for for the following expression:

10z + 25

5(2z + 5)

300

Factorise the following expression:

-12 - 16f

-4(3 + 4f)  or  4(-3 - 4f)

400

Factorise the following:

14jn + 10n

2n(7j + 5)

500

Simplify and then factorise the following:

2(x + 1) + 5(x +1)

7(x + 1)

Expanding Double Brackets

100

(x + 2)(x + 5)

x² + 7x + 10

200

(x - 6)(x + 2)

x² -4x - 12

300

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

6x² - x - 2

400

(xy - yz)(z + 3x)

-2xyz + 3x²y - yz² 

500

(4x - 3y)(3x - 4y)

12x² - 25xy + 12y²