YEAR 9 MATHS EXAM

Indices

100

Write 2 × 𝑎 × 𝑎 × 𝑎 × 𝑏 × 3 × 𝑏 × 𝑎 × 𝑏 in index form

6a⁴b³

200

Simplify (2⁵)³ x 2^-4

2¹¹

300

Simplify 4x³y^-2 x (-2x^-1y⁵)

-8x²y³

400

Simplify and express with positive indices:
a^-3b² x a⁵b^-4 

a² / b²

500

Express 0.000643 in scientific notation to 3 significant figures

6.43 x 10^-4

Probability

100

A die is rolled 2 times. Probability of rolling a 3 both times?

1/36

200

A card is drawn from a deck. Probability it is a red king or a black queen?

1/13

300

Dora rolls a spinner numbered 0–4. What’s the probability of rolling an even number?

3/5

400

Two students are selected from Adam, Brenda, Caroline, Darren. Probability at least one is Brenda?

1/2

500

Spinner #1: 0,1,2,3. Spinner #2: 0,1,1,2,3,3. Probability of 2 and then 3?

1/12

Geometry

100

Which angles are complementary: 27° & 63° or 71° & 109°?

27° & 63°

200

Clock shows 2:30. Reflex angle between hands?

255°

300

Two similar triangles. Triangle 1 side = 8, triangle 2 corresponding side = 12. Scale factor = ?

1.5

400

Angle sum of one octagon?

1080°

500

Two triangles are similar. Triangle ABC has sides AB = 9 cm, AC = 12 cm, BC = 15 cm. Triangle DEF has side DE = 6 cm corresponding to AB. Find the lengths of sides DF and EF.  

DF= 8cm
EF= 10cm

Algebra

100

Simplify 3x²y - 5xy² + 2x²y + 4xy²

5x²y - xy²

200

Factorise 12x² - 18x

6x(2x-3)

300

Expand and simplify

(x-5)(x+7)

x² + 2x - 35

400

Factorise 16x² - 81y²

(4x - 9y)(4x + 9y)

500

Solve x² - 11x + 28 = 0

x = 4,7

Mixed

100

Simplify m⁴ x m^-6

m^-2

200

Venn diagram: Fishing = 30, Surfing = 20, Both = 10. Probability person likes fishing but not surfing?

1/2

300

Which congruence test proves triangles are congruent if two angles and included side match?

ASA

400

Dora spins first spinner 0,1,2,3; second spinner 0,1,1,2,3,3. How many different products are possible?

7

500

Simplify (3x²y³)² / 9xy

x³y⁵