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Standard FormReverse PercentagesSpeed and DensityReal Life and Distance Time GraphsExpanding and Factorising QuadraticsSolving QuadraticsDrawing Quadratic GraphsDrawing Other Graphs: Cubic/Reciprocal

Tests

Test ATest BTest CTest D

Stage 8 Test C

Question 1

Dawn drove from London to Birmingham. She made one stop at a service station.

Here is part of Dawn's travel graph.

A travel graph showing distance from London in miles against time. The y-axis is labeled 'Distance from London (miles)' and ranges from 0 to 120 in increments of 20. The x-axis is labeled 'Time' and shows hours from 10 00 to 14 00. The graph consists of three segments: a line from (10 00, 0) to (11 30, 60), a horizontal line from (11 30, 60) to (12 00, 60), and a line from (12 00, 60) to (12 45, 90).

TimeDistance from London (miles)
10 000
11 3060
12 0060
12 4590
a.

For how many minutes did Dawn stop at the service station?

[1]
b.

What was Dawn's average speed between London and the service station?

[2]
Question 2

In a sale, the normal price of a car is reduced by 30%. The sale price of the car is £5950

Work out the normal price of the car.

[2]
Question 3
a.

Write 3.71 × 10-5 as an ordinary number.

[1]
b.

Write 9 million in standard form.

[1]
c.

Calculate (4.3×105)×(3.5×10−2)(4.3 \times 10^5) \times (3.5 \times 10^{-2})(4.3×105)×(3.5×10−2) Give your answer in standard form.

[2]
Question 4

Expand and simplify (4x−3)(x−2)(4x - 3)(x - 2)(4x−3)(x−2)

[2]
Question 5

Andrew ran 3.1 miles in 17 minutes and 25 seconds.

He assumes he can run 8 miles at the same speed.

Work out how long it would take Andrew to run 8 miles.

Give your answer in minutes and seconds to the nearest second.

[4]
Question 6

Solve b2−10b+24=0b^2 - 10b + 24 = 0b2−10b+24=0

[3]
Question 7

Here is the graph of y=6−2x−x2y = 6 - 2x - x^2y=6−2x−x2

Graph of the quadratic function y = 6 - 2x - x^2. The graph is a downward-opening parabola on a coordinate plane. The x-axis ranges from -6 to 6 with major grid lines every 2 units and minor grid lines every 1 unit. The y-axis ranges from -6 to 8 with major grid lines every 2 units and minor grid lines every 1 unit. The parabola has its vertex at (-1, 7). It crosses the x-axis at x = -4 and x = 2. It crosses the y-axis at y = 6. The origin is labeled O.

a.

Write down the turning point of the graph y=6−2x−x2y = 6 - 2x - x^2y=6−2x−x2

[1]
b.

Use the graph to find the roots of the equation x2+2x=6x^2 + 2x = 6x2+2x=6

[2]
Question 8
a.

Complete the table of values for y=x3+x−2y = x^3 + x - 2y=x3+x−2

xxx-2-1012
yyy
[2]
b.

On the grid, draw the graph of y=x3+x−2y = x^3 + x - 2y=x3+x−2

A Cartesian coordinate system with a grid. The x-axis is labeled 'x' and has tick marks at -2, -1, 0, 1, and 2. The y-axis is labeled 'y' and has tick marks at -12, -8, -4, 4, 8, and 12. The origin is labeled 'O'. The grid consists of 16x16 small squares.

[2]