REVISION HOMEWORK

ADOLYGU GWAITH CARTREF

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Dosbarth:_____________________________

Target Target Practice Met

Identify equations of lines parallel and perpendicular to a given line and Interpret straight line graphs

1

Recognise, quadratic, reciprocal and cubic graphs 2Solving equations graphically – intersection of straight line and curve or two curves

3

Calculate the Gradient of a curve at a given point by drawing a tangent

4

Area under a graph between limits, using the trapezium rule

4

GRAPHS OF FUNCTIONS

HIGHER TIER

%

MARK

Classwork Questions

1. Write down the equation of a line, which is parallel to the graph of 2 y=6 x−7 and passes through the point (0,-4) [2]

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1. [1]

(b) On the graph paper below, draw the graph of y=2 x3−3 for values of x between -2 and 2

(c) Draw the graph of y=x+4 and write down the coordinates of the points of intersection of y=2x3−3 with the line y=x+4. [3]

(d) Find an estimate for the gradient of the graph at the point when x = 1 [3]

GCSE Revision Homework Questions

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3. The table shows some of the values of y=3 x2+x−5 for values of x from -3 to 3.(a) Complete the table by finding the value of y for x = -2. [1]

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(b) On the graph paper below, draw the graph of y=3 x2+x−5 for x between -3 and 3. [3]

(c) Draw the line y = 11 on your graph paper and write down the x – values of the points where your two graphs intersect. [2]

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(c) Use the trapezium rule with 7 strips to find the area enclosed by the x axis between the curvex = -1.5 and x =2. [4]

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5. The graph of y=x3−5 x2−12 x+36 for values of x between x = -4 and x = 7, has been drawn below

(a) Use the graph to solve the equation x3−5 x2−12 x+36=0 [1]

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6. The table shows some of the values of y=x3+6 x2−x−27 for values of x from -6 to 3.

7. The graph of y=−x3+2 x2+11 x−12 is shown below.

(a) By drawing an appropriate line on the graph solve the equation −x3+2 x2+x−12=0 [3]

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(b) Find an estimate of the gradient of the curve y=−x3+2 x2+11 x−12 when x = 1 [3]………………………………………………………………………………………………………………………………………………..

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8. A cyclist travels a 20km route starting at 12.00 from Glenfall and reaching Newfield at 14.00. The following diagram is a distance-time graph for the journey.

Use the graph to estimate the speed in km/h of the cyclist at 12.30

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Target Practice

1. Here is the equation of a line. 3y = 12x + 21 (a) Write down the equation of a line parallel to the line above, which passes through the point (-4,0)

(b) Write down the equation of a line perpendicular to the line 3y = 12x + 21

2. Use the axes given below to sketch the following.(a) y = x2 y [1]

(b) y = - x2 [1]

(c) y = x3 [1]

3.

[3]

4. The table shows some of the values of y=8−5 x−2 x2 for values of x from - 2 to 4(a)Complete the table by finding the value of y for x = -1. [1]

x -4 -3 -2 -1 0 1 2y -4 5 10 8 1 -10

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(b) On the graph paper below.Draw the graph of y=8−5 x−2 x2 for values of x between – 2 and 4. [2]

(c) Find an estimate of the gradient of the curve y=8−5 x−2 x2 when x = - 2 [3]………………………………………………………………………………………………………………………………………………..

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(d) Use the trapezium rule with ordinates x = -3, x = -2, x = -1, x = 0, x = 1 to find the area of the region enclosed by the curve y=8−5 x−2 x2 and the x -axis between the values x = - 3 and x = 1. [4]

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