REVISION HOMEWORK
ADOLYGU GWAITH CARTREF
Enw: _____________________________
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]
2.
3.
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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4.
(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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