A free Year 10 maths test

Put 3.1 × 10⁴, 4.2 × 10^-1, 8.6 × 10³ and 5.7 × 10^-2 in order from smallest to largest.

• AA: 3.1 × 10⁴, 8.6 × 10³, 4.2 × 10^-1, 5.7 × 10^-2
• BB: 5.7 × 10^-2, 4.2 × 10^-1, 8.6 × 10³, 3.1 × 10⁴
• CC: 4.2 × 10^-1, 5.7 × 10^-2, 8.6 × 10³, 3.1 × 10⁴
• DD: 3.1 × 10⁴, 4.2 × 10^-1, 5.7 × 10^-2, 8.6 × 10³

Amara earns $1600 a week and takes 2 weeks of leave with 17.5% leave loading. What is Amara's total holiday pay?

• AA: $3760.00
• BB: $3480.00
• CC: $560.00
• DD: $3200.00

Which is ¹⁄₁₂₅ written with a negative index?

• AA: 5^-3
• BB: 5³
• CC: 3^-5
• DD: -5³

Expand and simplify (2x + 1)(x + 4).

• AA: 3x + 5
• BB: 2x² + 9x + 5
• CC: 2x² + 4
• DD: 2x² + 9x + 4

Buses hold 24 students each. Solving 24n = 300 gives n = 12.5. How many buses does a school need for 300 students?

• AA: 12.5
• BB: 12
• CC: 13
• DD: 7200

Find the distance between (0, -3) and (5, 4), correct to 1 decimal place. Use the table of square roots.

• AA: 4.9
• BB: 12
• CC: 8.6
• DD: 74

The graph of the cost C of hiring a bike against the hours h passes through (0, 8) and (3, 20). What does the point (0, 8) tell you?

• AA: Each hour of riding costs $8
• BB: An $8 fee is paid before any riding
• CC: Riding for 3 hours costs $8
• DD: The bike can be hired for up to 8 hours

Which curve rises most steeply for x greater than 0?

• AA: y = 5^x
• BB: y = 2^x
• CC: y = 1^x
• DD: y = 0.5^x

A ramp rises 2 m over a horizontal run of 15 m. Which equation gives the angle θ between the ramp and the ground?

• AA: sin θ = ²⁄₁₅
• BB: cos θ = ²⁄₁₅
• CC: tan θ = ¹⁵⁄₂
• DD: tan θ = ²⁄₁₅

The bearing of A from B is 240°T. What is the bearing of B from A?

• AA: 240°T
• BB: 120°T
• CC: 060°T
• DD: 420°T

A trough is half a cylinder with a radius of 25 cm and a length of 100 cm. Take pi as 3.14. How many litres does it hold?

• AA: 98125
• BB: 98.125
• CC: 196.25
• DD: 981.25

A rectangle 3 cm by 5 cm is enlarged by a scale factor of 3. What is the area of the enlarged rectangle, in cm²?

• AA: 15
• BB: 45
• CC: 48
• DD: 135

A park is 3 cm by 2 cm on a map with a scale of 1:5000. What is the real area of the park?

• AA: 250 m²
• BB: 500 m²
• CC: 3 m²
• DD: 15 000 m²

The table gives the five-number summaries of two classes' test marks. Which statement is correct?

• AA: Class 9B has the higher median and the smaller IQR
• BB: Class 9B has the higher median and the larger IQR
• CC: Class 9A has the higher median and the larger IQR
• DD: Class 9A has the higher median and the smaller IQR

Ten marks have a mean of 65 and a standard deviation of 4. A new mark of 20 is added. What happens to the mean and the standard deviation?

• AA: Both stay the same
• BB: The mean stays the same and the standard deviation goes up
• CC: The mean goes down and the standard deviation goes up
• DD: The mean goes down and the standard deviation goes down

Students in a study practised for between 1 and 8 hours. Using the line of best fit to predict the score for 15 hours of practice is an example of what?

• AA: interpolation
• BB: extrapolation
• CC: a cause and effect link
• DD: an outlier

A bag holds 4 red and 2 blue counters. Two are taken without replacement. What is the probability both are the same colour?

• AA: ⁷⁄₁₅
• BB: ²⁄₇₅
• CC: ⁵⁄₉
• DD: ²⁄₅

The first traffic light on a route is green with a chance of 0.6 and the second with a chance of 0.7, independently. What is the chance that exactly one light is green?

• AA: 0.18
• BB: 0.46
• CC: 0.42
• DD: 1.3

Ayla spins a spinner 20 times and gets 9 reds. Dev spins the same spinner 400 times and gets 112 reds. Which is the better estimate of the probability of red?

• AA: 0.45, from Ayla's 20 spins
• BB: 0.5, because red either happens or it does not
• CC: 0.28, from Dev's 400 spins
• DD: 112, from Dev's 400 spins