Constructing and using tangents - Higher tier only test questions - GCSE Maths Numeracy (WJEC) Revision

1

A straight line graph. The x axis is numbered from 0 to 16, the y axis is numbered from 0 to 10

What is the gradient of the graph?

0.4

2.5

0.8

2

A concave up graph. The x axis is numbered from -5 to 5, the y axis from 0 to 35. A tangent passes the curve at point A, and through the x axis at 1, 0

What is the gradient of point A? The tangent has been drawn to help you.

3

0.27

3.75

3

If you find the gradient of a velocity-time graph, what are you calculating?

Acceleration

Velocity

Distance

4

A concave up graph. The x axis is numbered from 0 to 100, the y axis from 0 to 12. A tangent passes the curve at point A, and through the x axis at 20, 0

What is the gradient of the curve at A?

10

0.1

0.08

5

This graph shows a journey. Find the acceleration at Time = 8 seconds of the speed boat. The tangent has been drawn for you.

A curved line graph. The x axis is numbered from 0 to 14, the y axis is numbered from 0 to 7. A tangent passes along part of the curve, and through the y axis at 7

Acceleration = \(-\frac {2} {7}~{m/s}{^2}\)

Acceleration = \(-{3.5}~{m/s}{^2}\)

Acceleration = \(\frac{2} {7}~{m/s}{^2}\)

6

A straight line graph. The x axis is labelled 'time' and numbered from 0 to 6, the y axis is labelled 'velocity' and numbered from 0 to 120

What is the distance travelled in the first four seconds on the journey?

Distance = 360 m

Distance = 160 m

Distance = 320 m

7

A velocity-time graph of a train's journey. The x axis is numbered from 0 to 10, the y axis from 0 to 100. The 3 stages of the journey are labelled 'A', 'B', and 'C'

This is the velocity-time graph of a train’s journey. What is the distance travelled during stage A of the train’s journey, where the train is accelerating?

160 m

240 m

120 m

8

This is the velocity-time graph of a train’s journey. What is the total distance travelled by the train?

160 m

400 m

520 m

9

A concave down graph. The x axis is numbered from -4 to 4, the y axis is numbered from -2 to 4

A 2 row table labelled x and y. x has values 0, 1, 2, 3, and 4. y has values 0, 1, 1.5, 1.7, and 2

Use the information from the graph and the table to estimate the area bounded by the curve, the x-axis and the line y = 4.

Area = 10.4

Area = 5.2

Area = 4.7

10

Using the Trapezium rule estimate the distance travelled in the first 20 seconds of this journey?

A curved line graph. The x axis, labelled 'time in seconds', is numbered from 0 to 20. The y axis, labelled 'velocity in metres per second', is numbered from 0 to 80

860 m

1720 m

840 m