Stage 8 Test D

Question 1

Write 3.4 × 10⁶ as an ordinary number.

[1]

Write 0.007 in standard form.

[1]

Question 2

A car travels a distance of 235 miles in 4 hours and 20 minutes.
Work out the average speed of the car, in miles per hour.
Give your answer to 1 decimal place.

[2]

Question 3

The value of a litre of petrol increased by 4%.
A litre of petrol then cost £1.30

Work out the price of a litre of petrol before the increase.

[2]

Question 4

A block exerts a force of 126 Newtons on the ground.
The block has an area of 3 m².

Work out the pressure on the ground.


$pressure=forcearea\displaystyle \text{pressure} = \frac{\text{force}}{\text{area}}$
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[1]

Question 5

Here is the graph of $y = x^2 + 2x - 5$

Write down the turning point of the graph $y = x^2 + 2x - 5$

[1]

Use the graph to find the roots of the equation $x^2 + 2x - 5 = 2$

[2]

Question 6

Emily drove to the beach. She stayed at the beach and then she drove back home. Here is Emily's travel graph.

Time	Distance from home (miles)
14:00	0
14:30	34
16:00	34
16:45	0

For how many minutes did Emily stay at the beach?

[1]

What was Emily's average speed on her journey on the way back from the beach?

[2]

Question 7

Solve $x^2 - x - 42 = 0$

[3]

Question 8

A large rock has a weight of 1.42 × 10⁴ grams.
Find, in standard form, the weight of 18 of these large rocks.

[2]

Question 9

Expand and simplify $(a - 5) (a - 5)$

[2]

Factorise $b^2 - 121$

[1]