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Index law

100

Simplify:

(a²)³ x a²

a⁸

200

Simplify:

y²/y⁸

1/y⁶

300

p² x p⁷/(p³)²

p³

400

Simplify:

(2a/3b³)⁴

16a⁴/81b¹²

500

Simplify:

(3n^-2)^-1 x 2(ab)^-1

2n²/3ab

Solving Equations

100

Solve for x:

-2x+14=44

x=-15

200

Solve for x:

3(x-2)-x=12

x=9

300

Solve for x:

(x-1)/3=6/2

x=10

400

solve for x:

5x+2=3x+14

x=6

500

Solve for x:

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

x=1.857

scientific Notation

100

Express in scientific notation:

259

2.59 x 10²

200

Express in scientific notation:

0.259

2.59 x 10^-1

300

Express in scientific notation:

0.0000407

4.07 x10^-5

400

Write as ordinary decimal number:

7.8 x 10⁴

78000.0

500

Write as an ordinary decimal number:

4.33 x 10^-7

0.000000433

Algebraic Expansion

100

Expand and Simplify:

a(a+2)+2a(3a-2)

7a²-2a

200

Expand and simplify:

2a(a²-3a+1)

2a³-6a²+2a

300

Expand and simplify:

(x+5)²

x²+10x+25

400

Expand and simplify:

(2x-3)(x+5)

2x²+7x-15

500

Expand and simplify:

5-2(x+3)²

-2x²-12x-13

Factorising

100

Fully factorise:

-2x²-4x

-2x(x+2)

200

Fully factorise:

x²-4

(x-2)(x+2)

300

(x+2)²-9

(x+5)(x-1)

400

Fully factorise:

25-(x-2)²

(x+3)(7-x)

500

Fully factorise:

3x²-18x+27

3(x-3)²