Number and algebra: Linear and non-linear relationships
Chapter 15: Coordinates and the Cartesian plane
Test B
Name: ___________________________
FLUENCY
Mark
1
1
On the map shown above the square in which the Sands Caravan Park is located is:
A J9
B H8
C F6
D K9
E G11
Answer: B
© John Wiley & Sons Australia, Ltd 2011
1
Maths Quest 7
Chapter 15: Coordinates and the Cartesian plane
Test B
2
2
Give grid references for each of the following.
(a) Tasmania
(b) Kalgoorlie
Answer:
(a) Tasmania E1
(b) Kalgoorlie C2
© John Wiley & Sons Australia, Ltd 2011
2
Maths Quest 7
Chapter 15: Coordinates and the Cartesian plane
Test B
3
3
Study the map above. In which square would you find:
(a) Little Billabong
(b) Dudalcooma Swamp
(c) Albury/Wodonga (2 squares).
Answers:
(a) J3
(b) F2
(c) F5 and F6
© John Wiley & Sons Australia, Ltd 2011
3
Maths Quest 7
Chapter 15: Coordinates and the Cartesian plane
Test B
2
4
Write the coordinates of H and M.
Answer:
H (5, 2), M (0, 6)
5
The pair of coordinates which have the same y-coordinates are:
A (1, 2) and (2, 1)
B (4, 7) and (4, 3)
C (5, 9) and (3, 8)
D (7, 3) and (7, 7)
E (2, 8) and (4, 8)
1
Answer: E
© John Wiley & Sons Australia, Ltd 2011
4
Maths Quest 7
6
Chapter 15: Coordinates and the Cartesian plane
Place the following points on a Cartesian plane.
A (1, 4)
B (3, 0)
C (2, 3)
D (5, 1)
E (1, 4)
F
(1, 3)
G (0, 2)
H (0, 4)
I
(2, 2)
J
(3, 0)
K (1, 5)
Test B
3
Answer:
© John Wiley & Sons Australia, Ltd 2011
5
Maths Quest 7
7
Chapter 15: Coordinates and the Cartesian plane
Write down the coordinates of the points A to K marked on the Cartesian plane below.
Test B
3
Answer:
A (1, 1)
B (0, 2)
C (2, 4)
D (1, 5)
E (2, 1)
F (4, 0)
G (3, 2)
H (3, 3)
I (5, 2)
J (1, 0)
K (4, 4)
© John Wiley & Sons Australia, Ltd 2011
6
Maths Quest 7
8
Chapter 15: Coordinates and the Cartesian plane
Plot the following points on a Cartesian plane.
(a)
x
–3
–2
–1
0
1
2
3
y
–2
0
2
4
6
8
10
x
–3
–2
–1
0
1
2
3
y
9
7
5
3
1
–1
–3
Test B
4
(b)
Answer:
(a)
(b)
9
For the tables in question 8 complete, find the y-coordinate when x = 4.
2
Answer:
(a) (4, 12)
(b) (4, –5)
© John Wiley & Sons Australia, Ltd 2011
7
Maths Quest 7
10
Chapter 15: Coordinates and the Cartesian plane
State the next point in each linear pattern.
(a) (3, 20) (2, 10) (1, 0) (0, 10) (1, 20) (2,30)
(b) (3, 8) (2, 4) (1,0) (0, 4) (1, 8) (2, 12)
Test B
2
Answer:
(a) (3, 40)
(b) (3, 16)
UNDERSTANDING
2
11
Connect the following points on the Cartesian plane above and state the shape which is
formed.
(1, 0) (1, 5) (5, 5) (5, 0) (1, 0)
Answer:
Square
© John Wiley & Sons Australia, Ltd 2011
8
Maths Quest 7
Chapter 15: Coordinates and the Cartesian plane
Test B
2
12
Connect the following points on the Cartesian plane above and state the shape that is
formed.
(1, 2) (3, 5) (6, 5) (4, 2) (1, 2)
Answer:
Parallelogram
13
Do each of the following sets of points lie on a straight line?
(a) (–1, 5), (0, 7), (1, 9), (2, 11)
(b) (–3, 3), (–2, 1), (–1, –1), (0, –3), (1, –5)
2
Answer:
(a) Yes
(b) Yes
© John Wiley & Sons Australia, Ltd 2011
9
Maths Quest 7
14
Chapter 15: Coordinates and the Cartesian plane
Imagine a line is drawn through the points below. Complete the following points that
would also be on the line.
Test B
2
(a) (0.5, ___)
(b) (___, –6)
Answer:
(a) (0.5, –1.5)
(b) (–4, –6)
15
Complete the following table for using rule y = 5x – 1.
x
–2
–1
0
1
2
y
–11
Answer:
x
–2
y
–11
–1
–6
0
–1
1
4
2
2
9
REASONING
16
There are five points each with the same y-coordinate. A line is drawn through these five
points.
(a) Is this line vertical or horizontal?
(b) Which axis will the line be parallel to?
2
Answer:
(a) horizontal
(b) x-axis
17
A straight line goes through the points (–1, 2) and the origin.
(a) List two points that it would go through the 4th quadrant.
(b) Explain how you answered part (a).
4
Answer:
(a) Many answers are possible. Eg (1, –2) and (2, –4).
(b) If the line goes through (–1, 2) and (0, 0) then for every 1 unit it moves right it also
moves 2 units down.
0 + 1 = 1 and 0 – 2 = –2
1 + 1 = 2 and –2 – 2 = –4
So it also goes through the points (1, –2) and (2, –4).
© John Wiley & Sons Australia, Ltd 2011
10
Maths Quest 7
18
Chapter 15: Coordinates and the Cartesian plane
Describe two variables that have a negative linear relationship. Meaning that as one
variable increases by a constant amount the other variable decreases by a constant
amount. Explain your answer.
Test B
2
Answer:
Different answers are possible.
For example, the number of pencils purchased and the amount remaining in your wallet.
If pencils cost $ 1 each and we start with $10 in the wallet then we could have the points
(0, 10), (1, 9), (2, 8), (3, 7), … which when graphed would form a straight line.
PROBLEM SOLVING
19
The following graph shows the time taken by Lucy to swim 100 m freestyle each day for
a week.
3
(a) How long did Lucy take to swim 100 m on Wednesday?
(b) What is the difference between Lucy’s time on Monday and her time on Friday?
(c) Overall Lucy’s times appear to be improving. Is it possible for her times to improve
at a genrally constant rate for a number of weeks? Discuss.
Answer:
(a)
(b)
(c)
35 seconds
37 – 28 = 9 seconds
Lucy’s times could improve at a constant rate over a number of days but after a
few weeks it would be likely that her times would plateau.
© John Wiley & Sons Australia, Ltd 2011
11
Maths Quest 7
20
Chapter 15: Coordinates and the Cartesian plane
Jack works in a newsagent to earn extra pocket money. He is paid $85 a week plus $1
for every newspaper he sells.
(a) Copy and complete the table to show how much money Jack would be paid if he
sold 0 to 6 newspapers per week.
Newspapers (N )
Money $ (M )
0
85
1
2
3
4
5
Test B
6
6
(b) Plot the points in your table on a Cartesian plane.
(c) Do the points form a linear graph?
(d) Predict how much Jack would be paid if he delivered 20 newspapers in a week.
Answer:
(a)
Newspapers (N )
Money $ (M )
0
1
2
3
4
5
6
85 86 87 88 89 90 91
(b)
(c) Yes
(d) $85 + $20 = $105
© John Wiley & Sons Australia, Ltd 2011
12