Year 9 Mathematics Advanced Revision

Numbers of Any Magnitude

100

Round 4.747568 to 4 significant figures.

4.748

200

A crowd of approximately 87 000 attended the grand final. What is this number in scientific notation?

8.7 x 10⁴

300

Toby's mass is 68.4kg. What is the absolute error of his mass?

Precision = 100g

Absolute Error = 1/2 x Precision = 1/2 x 100g = 50g

400

State the limits of accuracy for a distance measured to be 13.45 km.

Precision = 0.01 km

Absolute Error = 1/2 x precision = 1/2 x 0.01 = 0.005 km

Upper Bound = 13.45 + 0.005 = 13.455 km

Lower Bound = 13.45 - 0.005 = 13.445 km

500

Find the percentage error for a measurement of 55 kg.

Precision = 1 kg

Absolute Error = 1/2 x precision = 1/2 x 1 = 0.5 kg

Percentage Error = absolute error / measurement = 0.5 / 55 = 0.91%

600

Convert 3218941207 to scientific notation, rounding to four significant figures.

3.219 x 10⁹

700

Evaluate 

(2.6xx10^6)+(7.1xx10^5)

Give your answer in scientific notation. 

3.31 x 10⁶

Indices

100

Simplify

3^3+19^0

Express your answer as a basic numeral.

27

200

Simplify 

27x^3y^6 ÷9xy^2

3x^2y^4

300

Simplify

(10m^5n^4)/(2m^2n)

5m³n³

400

Simplify

(x^9xxx^-2)/x^3

x⁴

500

Simplify

6/(y^3z^3)xxz/(2y)

3/(y^4z^2)

600

Simplify 

(y^(-3)xxy^7)^3

y¹²

700

Simplify

25xx5^3xx5^6

Express your answer with a base of 5.

5¹¹

Algebraic Techniques

100

Simplify 

3x+5+4x-2

7x+3

200

Simplify

(2a)/5+a/10

a/2

300

Simplify 

(6y)/9÷(2y)/6

2

400

Expand

-2(3x-4)

-6x + 8

500

Simplify 

3(2a+5)-4(a+3)

2a + 3

600

Factorise 

5m^2+2m

m(5m+2)

Quadratic Expressions

100

Expand 

(3x-2)(x+4)

3x^2+10x-8

200

Expand 

(2x+3)^2

4x^2+12x+9

300

Expand 

(2y-1)(2y+1)

4y² - 1

400

Factorise 

9b^2-25

(3b+5)(3b-5)

500

Factorise 

(8x+6)-x(8x+6)

(8x+6)(1-x)

600

Factorise 

x^2+5x-36

(x-4)(x+9)