Indices and Algebra

Index Laws I

100

Simplify 2a³ x 3a²

6a⁵

200

Simplify the following expression 

(3x^3)^2

9x⁶

300

Simplify the following expression 

(m^2/4)^3

m^6/64

400

Simplify the following expression:

(x^3y^4 * x^2y)/(x^8y^3

y^2/x^3

500

Simplify the following:

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

48a^10b^16

Index Laws II

100

Simplify 3a⁰

3

200

Simplify the following expression:

5x^-3

5/x^3

300

Simplify the following:

(3(x^2)^-2)/((3x)^3

1/(9x^7)

400

Simplify the following:

5x^0y + y(3x^4y^3)^0

6y

500

Simplify the following:

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

64/(24a^2b^2)

Expanding

100

Expand the following expression:

2t(t + 4)

2t² + 8t

200

Expand the following expression:

x(3x + 5)

3x²+5x

300

Expand and simplify the following expression:

7g² + 4 - 3g(4g + 5) 

4 - 15g

400

Expand and simplify the following expression:

2x(2x - 6y)+6y(2x - 6y)

4x² - 36y²

500

Expand and simplify the following expression:

4a(4a + 5b)+ 5b(4a+5b)

16a² + 40ab + 25b²

Factorising

100

Factorise the following expression:

4n³ + 10n

2n(2n² + 5)

200

Factorise the following expression:

6ab³ + 15ab 

3ab(2b² + 5)

300

Factorise the following expression:   

45fg⁵h⁴ - 36f²g⁴ +18fg²h

9fg²(5g³h⁴ - 4fg² + 2h)

400

Factorise the following expression by grouping:

a(a+3b)+3c(a+3b)

(a + 3c)(a + 3b)

500

Factorise the following expression by grouping:

4p(3p²+7)-7(3p²+7)

(4p - 7)(3p² + 7)

Scientific Notation

100

Write the following number in scientific notation:

8 956 600 000

8.956 x 10⁹

200

Is the following number written in scientific notation?

73.6 x 10^-8

No

300

Write the following number in decimal form:

3.86 x 10^-3

0.00386

400

Without a calculator, evaluate (2 x 10⁵) x (4 x 10^-7). Leave your answer in scientific notation.

8 x 10^-2

500

The land size of a country is approximately 110 600 square meters and its population is approximately 16 million. Determine the number of square meters per person living in this country, giving your answer in scientific notation.

6.91 x 10^-3 m² per person  

Sig Fig

100

How many significant figures is 0.00304 ?

3

200

Write 32 452 000 in scientific notation with 3 sf

3.25 x 10⁷

300

Write 0.039274 to 2sf in scientific notation

3.9 x 10^-2

400

Write 25 years in hours, in scientific notation to 3 sf.

(365.25 days in a year)

2.19 x 10⁵

500

Write 432 nanoseconds in seconds. To 3 sf in scientific notation.

There are 10⁹ nanoseconds in a second

4.32 x 10^-7