1.
The grid below shows the graph of y = x2 + 3x – 2
y = x 2 + 3x –2
10
9
8
7
6
5
4
3
2
1
–7
–6
–5
–4
–3
–2
–1 O
1
2
3
4
5
6
7
–1
–2
–3
–4
–5
(a)
By drawing an appropriate straight line on the graph solve the equation
x2 + 3x – 3 = 0
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Answer ………………………………..
(2)
The Robert Smyth School
1
(b)
By drawing an appropriate straight line on the graph solve the equation
x2 + 2x – 1 = 0
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Answer ………………….……………..
(3)
(Total 5 marks)
2.
The graph of y = x2 – 4x + 8 is shown below.
y
14
13
12
11
10
9
8
7
6
5
4
3
2
1
–1
O
1
2
3
4
5
x
–1
–2
The Robert Smyth School
2
(a)
(i)
By drawing the graph of an appropriate straight line, solve the equation
x2 – 4x + 8 = 3x – 2
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Answer ..........................................................................
(3)
(ii)
Hence, or otherwise, solve x2 – 7x + 10 = 0
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Answer ..........................................................................
(1)
(b)
The graph of y = x2 – 4x + 8 is to be used to solve the equation x2 – 5x + 4 = 0
What straight line graph would need to be drawn?
(You do not need to draw it, just state its equation.)
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Answer y = ...................................................................
(2)
(Total 6 marks)
3.
The grid shows the graph of
The Robert Smyth School
y = x2 + 2x – 5
3
y
4
2
–4
–3
–2
–1
O
1
2
x
–2
–4
–6
The Robert Smyth School
4
By drawing an appropriate straight line, solve the equation x2 + 2x – 5 = x – 1
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Answer ......................................................................
(Total 3 marks)
4.
(a)
Complete the table of values for y = x2 – 2x – 3.
x
y
–2
–1
0
1
2
0
–3
–4
–3
3
4
5
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.....................................................................................................................................
(2)
The Robert Smyth School
5
(b)
On the grid below, draw the graph y = x2– 2x – 3
for values of x between –2 and +4.
y
5
4
3
2
1
–2
–1
O
1
2
3
4
x
–1
–2
–3
–4
(2)
(c)
Write down the solutions of x2– 2x – 3 = 0
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Answer ..................................................................
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6
(1)
(d)
By drawing an appropriate linear graph, write down the solutions of
x2 – x – 4 = 0
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Answer ..................................................................
(3)
(Total 8 marks)
1.
(a)
(b)
Line y= 1 drawn or points on curve
Accept y = 1 written in body of script.
M1
0.8, –3.8 (±0.1)
A1
Attempt to split equation into
x2 + 3x – 2 = ax + b
Or x2 + 3x – 2 -(x2 + 2x – 1)
Or x2 + 3x – 2 + ax + b = x2 + 2x – 1
Ml
Line (y = x – 1) drawn
A1
0.4, –2.4 (±0.1)
f.t. on their line if Ml awarded,
e.g. y = x + 1(1, –3), y = 1 – x(0.6 (0.7), –4.6
(–4.7)),y = –1 –x(0.2, –4.2)
Alf.t
[5]
2.
(a)
(i)
(ii)
(b)
y = 3x – 2 plotted
must draw correct line
M1
x = 2, x = 5
A1 for each, must be correct
answers...no ft.
coordinates given ... lose 1 mark
A2
x = 2, x = 5
must have both solutions (ft answers
from part (a) earns 1 mark)
B1
x2 – 4x +8 = x + 4
allow one slip in manipulation
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M1
7
y=x+4
A1
Straight line to be clearly stated
[6]
3.
Attempt at y = x – 1
‘m’ or ‘c’ correct (y = –1 scores M0)
Table of values seen with at least one pair correct, with attempt
at line, earns M1
M1
Correct ruled line
A1
– 2.6 ≤ x ≤ – 2.5
and 1.5 ≤ x ≤ 1.6
A1ft
ft their line, two solutions only, tolerance of
± 0.05
[3]
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4.
(a)
(b)
(c)
x = –2, y = 5
B1
x = 3, y = 0
B1
Plot points
B1
Join with smooth curve
B1
x = 3, –1
B1
Accept (3,0), (–1,0)
(d)
x2 – 2x – 3 = –x + 1
Or subtraction:
M1
x2 – 2x – 3 – (x2 – x – 4)
Draw y = 1 – x
Draw line (not y = k)
x = 2.6 to 2.5 and –1.6 to –1.5
Inclusive
B1 ft
A1
[8]
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