Edexcel GCSE Maths

Topic Questions

Estimating Gradients & Areas under Graphs

1
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3 marks

The distance-time graph shows information about part of a car journey.

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Use the graph to estimate the speed of the car at time 5 seconds.

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2a
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3 marks

Karol runs in a race.

The graph shows her speed, in metres per second, t seconds after the start of the race.

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Calculate an estimate for the gradient of the graph when t space equals space 4
You must show how you get your answer.

2b
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2 marks

Describe fully what your answer to part (a) represents.

2c
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1 mark

Explain why your answer to part (a) is only an estimate.

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3a
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2 marks

The graph shows information about the velocity of a parachutist after jumping from a plane.

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By drawing a suitable tangent, find an estimate of the gradient of the curve after 3 seconds.

3b
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1 mark

Interpret the value of the gradient.

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4a
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2 marks

The graph shows the temperature of a fish tank over the first 6 hours after a heater is added.

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By drawing a suitable tangent, find an estimate of the gradient of the curve when h = 3.

4b
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1 mark

Interpret the value of the gradient.

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5a
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2 marks

A fish bowl is being filled with water.
The graph shows how the diameter of the surface of the water changes with time.

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Find an estimate for the gradient at t = 10.

5b
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1 mark

Give an interpretation of the gradient.

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6a
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1 mark

The diagram shows parts of the graphs of y=f(x) and y=g(x)

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Write down the value of x where the gradient of the curve y=g(x) is zero.

6b
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2 marks

Calculate an estimate for the gradient of the curve y = f(x) at the point on the curve where x = 4.

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7a
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2 marks

The diagram shows part of the graph of y space equals space x to the power of 2 space end exponent long dash space 2 x space plus space 3

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By drawing a suitable straight line, use your graph to find estimates for the solutions of x squared space long dash space 3 x space long dash space 1 space equals space 0

7b
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3 marks

P is the point on the graph of y space equals space x squared space long dash space 2 x space plus space 3 where x space equals space 2

Calculate an estimate for the gradient of the graph at the point P.

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8a
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2 marks

The curve space y space equals space x cubed long dash space 3 x long dash 2 spaceis shown on the grid.

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Write down the co-ordinates of the points where the gradient of the curve is zero.

8b
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1 mark

Write down the range of values of x when the gradient of the curve is negative.

8c
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2 marks

Find an estimate of the gradient of the curve when x = 2.

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9
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3 marks

Part of the curve with equation y space equals space straight f left parenthesis x right parenthesis is shown on the grid.

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Find an estimate for the gradient of the curve at the point where x space equals space 2
Show your working clearly.

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10a
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2 marks

A and B are points on a curve.

A is left parenthesis 2 comma space 7 right parenthesis space   B is left parenthesis 12 comma space 0 right parenthesis

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Work out the instantaneous rate of change of y with respect to x at point A.

10b
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1 mark

The average rate of change of space y spacewith respect to x between points A and B is worked out.

Which statement is correct?
Tick one box.

begin mathsize 26px style square end style It is positive.
begin mathsize 26px style square end style It is zero.
begin mathsize 26px style square end style It is negative.
size 26px square You cannot tell if it is positive or negative.

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11a
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3 marks

The speed-time graph shows 20 seconds of a car journey.

Harry wants to estimate the distance the car travels in this time.

He uses a triangle and a trapezium, as shown, to estimate the area under the graph.

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Complete Harry’s method to estimate the distance the car travels.

.......................m

11b
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1 mark

For this journey, which of these is true for Harry’s method?
Tick one box.

begin mathsize 26px style square end style      It works out an overestimate of the distance

size 26px square        It works out an underestimate of the distance

size 26px square      It could work out an overestimate or an underestimate of the distance

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12a
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1 mark

A container is filled with water in 5 seconds.
The graph shows the depth of water, d cm, at time t seconds.

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The water flows into the container at a constant rate.

Which diagram represents the container?
Circle the correct letter.

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12b
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2 marks

Use the graph to estimate the rate at which the depth of water is increasing at 3 seconds.

You must show your working.

.....................cm/s

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13
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2 marks

A ball is thrown from a point 6 metres above the ground.

The graph shows the height of the ball above the ground, in metres.

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Estimate the speed of the ball, in m/s, after 1 second.

You must show your working.

...............................m/s

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14
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4 marks

The graph shows the distance travelled by a particle over 8 seconds.

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Estimate the speed of the particle at 5 seconds.

................................................... m/s

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15
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3 marks

The graph shows the speed, v metres per second (m/s), of a car at time t seconds.

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Use the graph to estimate the acceleration at t = 7.

...................................................m/s2

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