Download Topic 2c (foundation) – Homework on Pictograms

The Robert Smyth School
Mathematics Faculty
Y10 Topic 9
Quadratics
Innovation & excellence
Name:
HW1 – Grade C
Drawing Quadratic Graphs
1.
(a)
Complete the table of values for y = x2 – 3
x
–3
y
–2
–1
0
1
1
–2
–3
–2
2
Teacher
Assessment
3
6
.....................................................................................................................................
(1)
(b)
On the grid draw the graph of y = x2 – 3 for values of x from –3 to +3
y
6
5
4
3
2
1
–3
–2
–1
O
1
2
x
3
–1
–2
–3
–4
(2)
(c)
Use the graph to solve the equation x2 – 3 = 0
Answer ....................................
(2)
(d)
Write down the values of x at the points where the line y = 2 crosses your graph.
.....................................................................................................................................
Answer .............................. and ..............................
(2) (Total 7 marks)
The Robert Smyth School
1
The Robert Smyth School
Mathematics Faculty
Y10 Topic 9
Quadratics
Innovation & excellence
2.
(a)
Complete the table for the equation y = x2 – 2x + 2
x
–1
0
1
2
3
y
(1)
(b)
On the grid below draw the graph of y = x2 – 2x + 2 for –1 < x < 3.
y
5
4
3
2
1
–1
0
1
2
3
4 x
(2)
(c)
Use your graph to find the values of x when y = 3.
…….……..……….…..…..……………………………….…………………..……..
…….……..……….…..…..……………………………….…………………..……..
(1)
The Robert Smyth School
2
The Robert Smyth School
Mathematics Faculty
Y10 Topic 9
Quadratics
Innovation & excellence
3.
(a)
Complete this table of values for y = (2 + x)(3 – x)
x
–2
y
–1
0
1
2
3
4
6
6
4
0
4
……………...........………………………….....…………………………………….
……………...........………………………….....…………………………………….
(2)
(b)
On the grid, draw the graph of y = (2 + x)(3 – x) for values of x from –2 to + 4.
y
7
6
5
4
3
2
1
–2
–1
O
1
2
3
4
x
–1
–2
–3
–4
–5
–6
–7
(2)
(Total 4 marks)
The Robert Smyth School
3
The Robert Smyth School
Mathematics Faculty
Y10 Topic 9
Quadratics
Innovation & excellence
4.
(a)
Complete the table of values for y = 2x2– 5x
x
–2
–1
0
1
2
y
18
7
0
–3
–2
3
4
12
(1)
(b)
On the grid below, draw the graph of y = 2x2 – 5x for
values of x between –2 and +4.
y
18
16
14
12
10
8
6
4
2
–2
–1
O
1
2
3
4
–2
x
(2)
–4
(c)
Write down the value of x for which y has a minimum value.
Answer x=.....................................................
(1) (Total 4 marks)
Success:
The Robert Smyth School
Target:
4
The Robert Smyth School
Mathematics Faculty
Y10 Topic 9
Quadratics
Innovation & excellence
HW2 – Grade B
Solving quadratic equations by drawing quadratic graphs
1.
(a)
Teacher
Assessment
Complete the table for the graph of y = x2 – 3x + 1.
x
–1
y
0
1
2
1
–1
–1
3
4
5
.....................................................................................................................................
.....................................................................................................................................
(2)
(b)
On the grid below, draw the graph of y = x2 – 3x + 1 for values of x from –1 to + 4.
y
5
4
3
2
1
–1
1
2
3
4
x
–1
–2
(2)
(c)
Use your graph to solve the equation x2 – 3x + 1 = 0.
.....................................................................................................................................
Answer .............................. and ...............................
(2)
(Total 6 marks)
The Robert Smyth School
5
The Robert Smyth School
Mathematics Faculty
Y10 Topic 9
Quadratics
Innovation & excellence
2.
(a)
Complete the table of values for y = x2 – 4x – 1.
x
–1
y
0
1
–1
–4
2
3
4
5
–4
–1
4
......................................................................................................................................
......................................................................................................................................
(2)
(b)
On the grid, draw the graph of y = x2 – 4x – 1 for values of x from –1 to +5.
y
5
4
3
2
1
–2
–1 O
1
2
3
4
5
6
x
–1
–2
–3
–4
–5
–6
(2)
(c)
Use your graph to solve the equation
x2 – 4x – 1 = 0.
Answer ........................... and ...................................
(2)
(Total 6 marks)
The Robert Smyth School
6
The Robert Smyth School
Mathematics Faculty
Y10 Topic 9
Quadratics
Innovation & excellence
3.
(a)
Complete the table of values for y = 2x2 – 4x – 1
x
–2
y
15
–1
0
1
–1
2
3
–1
5
(2)
(b)
2
On the grid below, draw the graph of y = 2x – 4x – 1 for values of x from – 2 to +3.
y
(2)
15
14
(c) An approximate solution of the equation
2x2 – 4x – 1 = 0 is x = 2.2
13
12
11
(i) Explain how you can find this from the
graph.
10
..............................................................................
9
..............................................................................
8
…………………………………………………
7
…………………………………………………
(1)
6
(ii) Use your graph to write down another
solution of this equation.
5
4
Answer x = ...............................................
(1)
(Total 6 marks)
3
2
1
–2
–1
O
1
2
3
x
–1
–2
–3
Success:
The Robert Smyth School
Target:
7
The Robert Smyth School
Mathematics Faculty
Y10 Topic 9
Quadratics
Innovation & excellence
HW3 – Grade A/A*
Solving equations using intersecting graphs
1.
Teacher
Assessment
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
……….............…............……...................…………….....…………........................
……….............…............……...................…………….....…………........................
(b)
Answer ……………………………….. (2)
By drawing an appropriate straight line on the graph solve the equation
x2 + 2x – 1 = 0
……….............…............……...................…………….....…………........................
……….............…............……...................…………….....…………........................
……….............…............……...................…………….....…………........................
The Robert Smyth School
8
Answer ………………….……………..
(3) (Total 5 marks)
The Robert Smyth School
Mathematics Faculty
Y10 Topic 9
Quadratics
Innovation & excellence
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
(a)
(i)
–2
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)
The Robert Smyth School
9
The Robert Smyth School
Mathematics Faculty
Y10 Topic 9
Quadratics
Innovation & excellence
(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) (Total 6 marks)
3.
The grid shows the graph of
y = x2 + 2x – 5
y
4
2
–4
–3
–2
–1
O
1
x
2
–2
–4
–6
By drawing an appropriate straight line, solve the equation x2 + 2x – 5 = x – 1
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
Answer ......................................................................
(Total 3 marks)
The Robert Smyth School
10
The Robert Smyth School
Mathematics Faculty
Y10 Topic 9
Quadratics
Innovation & excellence
4.
(a) Complete the table of values for y = x2 – 2x – 3.
–2
x
y
–1
0
1
2
0
–3
–4
–3
3
4
5
(2)
(b)
2
On the grid below, draw the graph y = x – 2x – 3
for values of x between –2 and +4.
y
(2)
5
(c) Write down the solutions of
x2– 2x – 3 = 0
4
.................................................................
Answer ........................................
3
(1)
(d) By drawing an appropriate linear
graph, write down the solutions of
2
x2 – x – 4 = 0
.................................................................
1
………………………………………….
………………………………………….
–2
–1
O
1
2
3
4
x
………………………………………….
………………………………………….
–1
………………………………………….
………………………………………….
–2
………………………………………….
–3
Answer..........................................
(3)
(Total 8 marks)
–4
Success:
The Robert Smyth School
Target:
11