Download 1 - NCETM

1.
The graph y = x2 – 2x – 4 is drawn below for values of x between –3 and +4.
y
12
10
8
6
4
2
–3
–2
–1
0
1
2
3
4 x
–2
–4
–6
(a)
Using the graph, find the solutions of x2 – 2x – 4 = 0, giving your answers to 1
decimal place.
Answer ............................................
(1)
(b)
By drawing an appropriate linear graph, write down the solutions of
x2 – 3x – 2 = 0
.....................…………………………………………………………………………
Answer ............................................
(3)
The Robert Smyth School
1
2.
The graph of y = 2x2 – x – 2 is drawn below.
y
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
–2
–1
O
1
2
3
4
x
–1
–2
–3
(a)
Write down the solutions of 2x2 – x – 2 = 0.
Answer .........................................................................
(2)
(b)
By drawing an appropriate linear graph, write down the solutions of
2x2 – 4x – 3 = 0
......................................................................................................................................
Answer .........................................................................
(3)
The Robert Smyth School
2
3.
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
……….............…............……...................…………….....…………........................
Answer ………………………………..
(2)
(b)
By drawing an appropriate straight line on the graph solve the equation
x2 + 2x – 1 = 0
……….............…............……...................…………….....…………........................
……….............…............……...................…………….....…………........................
……….............…............……...................…………….....…………........................
Answer ………………….……………..
(3)
The Robert Smyth School
3
4.
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
O
–1
1
2
3
4
5
x
–1
–2
(a)
(i)
By drawing the graph of an appropriate straight line, solve the equation
x2 – 4x + 8 = 3x – 2
Answer ..........................................................................
(3)
(ii)
Hence, or otherwise, solve x2 – 7x + 10 = 0
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.)
.....................................................................................................................................
Answer y = ...................................................................
(2)
The Robert Smyth School
4