Chapter 17 Revision
1
(a) On squared paper, draw the co-ordinate grid with axes between –6 and 6.
(b) Plot the following points and join them up in the order given.
E(4, 5),
F(6, –3),
G(–5, –3),
H(–1, 5)
(c) What is the name of the shape you have drawn?
(d) Describe the lines that join H to E and G to F.
2
For each line segment, write down the co-ordinates of both end points.
3
Draw a co-ordinate grid with both the x-axis and the y-axis with values between –6 and
6. On your grid draw the lines
4
(a) x = 3
(b) x = 6
(c) x = –5
(d) y = 5
(e) y = –1
(f) y = –4
What are the equations of the lines that represent
(a) the x-axis (b) the y-axis?
5
(a) Construct a table of results for each linear equation, using the range of x
values shown.
i)
y = x, using x values of 0, 3 and 6
ii) y = 2x, using x values of 0, 2 and 3.
iii) y = 3x, using x values of 0, 1 and 2.
© Pearson Education Limited 2009
1
(b) Draw a co-ordinate grid with x and y values between 0 and 6. Plot these points and
draw the straight lines.
(c) What do you notice about the three lines you have drawn?
(d) What effect does increasing the value of the number in front of x have?
6
(a) Construct the appropriate table of results for the following linear equations.
(i) y = 2x + 2
(ii) y = 2x – 4
(iii) y = 2x +
1
2
(b) Draw the three lines on the same co-ordinate grid.
(c) What do you notice about the three lines you have drawn?
7
Look at the following equations of straight lines. In each case write down the gradient of
the line.
(a) y = 20x – 10
8
10
11
y = –3x + 4
(c) y = 5 – 2x
(d) y = –7x
Rearrange the following equations to make y the subject. In each case write down the
gradient of the line.
(a) y = 4x – 9
9
(b)
(b)
4x = y – 6
(c) –2x = 4 – y
(d) y – x – 1 = 0
Without plotting these straight lines, identify all the lines that are parallel to the line
y = 2x – 3.
(a) y = 3x – 2
(b)
y = 4x – 6
(c) y = – 3 + 2x
(d) y + 2 = 3x
(e)
3 = 2x – y
(f) 2y = 4x – 6
Write down the following equations in the form of y = mx + c. For each line, state the
gradient and the y-intercept values.
(a) 4y = 4x – 8
(b)
6y = 18x + 36
(c) 7y = 21x
(d) 8y = 16 – 32x
(e) 3y + 12x = 9
(f)
5x – 5y = 35
(g) 8 – 2y = 14x
(h) 8y = 0
(i) 12x + 6y = –18
(j)
y–x–1=0
Rearrange the following into linear equations in the form y = mx + c.
Express both m and c as fractions.
(a) 2y = 5x – 7
(b)
3y = 4x + 8
(c) 5y = 7x – 8
(d) 10y = –4x – 5
(e) 6y + 4x = 3
(f)
3y – 2x = –1
(g) 4x + 5y = –3
(h) x + 6y – 3 = 0
(i) 6 – 8x = 10y
2
© Pearson Education Limited 2009
12
For each of the following graphs
(a) make a table of values
(b) plot the points
(c) join the points with a smooth curve
(d) state the line of symmetry.
(i)
y = x2 for x values –3 < x < 3
(ii)
y = x2 + 3x for x values –3 < x < 3
(iii) y = x2 + x + 1 for x values –4 < x < 3
13
Draw the curve y = 2x² – x in the range x = –2 to x = 3. Now draw the line y = 6. Solve
the equation 2x² – x = 6 by noting the two points of intersection.
14
(a) Draw the graph of y = x² – 3x + 3 by creating a table of values for values of between
–2 and 5.
(b) Solve the equation x² – 3x + 3 = 7.
15
Copy and complete the table that converts litres into pints.
litres
0
pints
0
5
10
17.5
(a) Draw a conversion graph for this data.
(b) One gallon is the same as eight pints. How many litres is this equivalent to?
16
This table shows the conversion between m2 and cm2.
m2
0
cm2
0
2
5
25 000
(a) Complete the table and draw the area conversion graph.
(b) What do you notice about this particular graph?
(c) What is this shape called?
(d) What is 3.7 m2 approximately equivalent to in cm2?
© Pearson Education Limited 2009
3
17
Benito walks 3 km home after school every day at 3.40pm. He always visits the local
sweet shop 1.25 km from the school, which takes him 15 mins. He spends 10 mins
inside the shop before continuing his journey and arriving home at 4.25pm. Draw a
distance-time graph for Benito's journey and work out
(a) his speed from school to the shop
(b) his speed from the shop to home
(c) his speed for the whole journey.
Give your answers in km/h.
4
© Pearson Education Limited 2009