Sec 1 Maths Coordinates and linear graphs worksheet with answers

A free Sec 1 Maths worksheet on coordinates and linear graphs: 8 questions, 30 marks, short questions first and then structured ones, in the school exam style. The answers and full worked solutions are on the last page.

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Sec 1 Maths worksheet: Coordinates and linear graphs

Total: 30 marksSuggested time: 45 minutes

Name: ______________________________Class: ____________ Date: ____________

Answer all questions. Show all your working. Give non-exact answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless the question says otherwise.

Section A

The graph shows the taxi fare, $

y

, for a trip of

x

km. Use the graph to find the fare for a trip of

10

km.

Answer[1]

State whether the gradient of the line shown is positive, negative, zero or not defined.

Answer[1]

ABCD

is a rectangle. The points

A

B

and

C

are shown. Find the coordinates of

D

Answer[2]

Write down the coordinates of the point

E

Answer[2]

(a)Complete the table of values for

y = -4x - 5

Answer (a)[3]

(b)Complete the table of values for

4x - y = -7

Answer (b)[3]

Section B

(a)The graph shows the height,

y

cm, of a candle

x

hours after it is lit. The candle burns at a steady rate. Find this rate, in cm per hour.

Answer (a)[2]

(b)Complete the table of values for

4x - y = -5

Answer (b)[3]

(a)The line passes through the points

A

and

B

shown. Find its gradient.

Answer (a)[2]

(b)The graph shows the taxi fare, $

y

, for a trip of

x

km. Assuming that the line continues in the same way, find the fare for a trip of

15

km.

Answer (b)[3]

(a)

P

is the point

(-1, -4)

and

Q

is the point

(2, -4)

. Find the length of

PQ

Answer (a)units[1]

(b)The graph shows the length,

y

cm, of a spring when a mass of

x

kg hangs from it. Use the graph to find the length of the spring when a mass of

6

kg hangs from it.

Answer (b)[1]

(c)(i)Complete the table of values for

y = 2x - 4

Answer (c)(i)[3]

(c)(ii)Complete the table of values for

4x + y = 2

Answer (c)(ii)[3]

END OF PAPER

Answers and worked solutions

Question 1

Answer: Fare: $

23

[1]

Fare: $

23

Question 2

Answer: POSITIVE[1]

The line goes up from left to right.So the gradient is positive.

Question 3

Answer: So

D(-2, 1)

.[2]

Across:

2 - 2 = 0

Up:

1 - (-5) = 6

x = -2

y = 1

D(-2, 1)

Question 4

Answer: So

E(-3, 4)

.[2]

x = -3

y = 4

E(-3, 4)

Question 5

(a)Answer:

y = -17

[3]

When

x = -2

y = -4(-2) - 5

y = 3

When

x = -1

y = -4(-1) - 5

y = -1

When

x = 3

y = -4(3) - 5

y = -17

(b)Answer:

y = 19

[3]

-y = -4x - 7

y = 4x + 7

When

x = -2

y = 4(-2) + 7

y = -1

When

x = 1

y = 4(1) + 7

y = 11

When

x = 3

y = 4(3) + 7

y = 19

Question 6

(a)Answer: Rate:

3

cm per hour[2]

The line goes from

(0, 30)

(10, 0)

.Rise:

0 - 30 = -30

; run:

10 - 0 = 10

\text{Gradient} = \dfrac{-30}{10}

\phantom{\text{Gradient}} = -3

Rate:

3

cm per hour

(b)Answer:

y = 21

[3]

-y = -4x - 5

y = 4x + 5

When

x = -1

y = 4(-1) + 5

y = 1

When

x = 0

y = 4(0) + 5

y = 5

When

x = 4

y = 4(4) + 5

y = 21

Question 7

(a)Answer:

m = 2

[2]

A(-5, -5)

and

B(-3, -1)

Rise:

-1 - (-5) = 4

Run:

-3 - (-5) = 2

m = \dfrac{4}{2}

m = 2

(b)Answer: Fare: $

18

[3]

\text{Start} = 3

The line goes from

(0, 3)

(10, 13)

.Rise:

13 - 3 = 10

; run:

10 - 0 = 10

\text{Rate} = 1

3 + 1 \times 15 = 18

Fare: $

18

Question 8

(a)Answer:

PQ = 3

units[1]

P and Q have the same y-coordinate, so PQ is horizontal.

\mathstrut 2 - (-1) =

3

units

PQ = 3

units

(b)Answer: Length:

30

cm[1]

Length:

30

(c)(i)Answer:

y = -2

[3]

When

x = -2

y = 2(-2) - 4

y = -8

When

x = 0

y = 2(0) - 4

y = -4

When

x = 1

y = 2(1) - 4

y = -2

(c)(ii)Answer:

y = -2

[3]

y = -4x + 2

When

x = -1

y = -4(-1) + 2

y = 6

When

x = 0

y = -4(0) + 2

y = 2

When

x = 1

y = -4(1) + 2

y = -2

Practice questions by skill

Sec 1 Maths Coordinates and linear graphs worksheet with answers

In the print window, choose Save as PDF to download it.

Need the formulas first? Read the Coordinates and linear graphs notes. Or practise it online with step-by-step help when you get one wrong.

Answers and worked solutions

Question 1

Answer: Fare: $

23

[1]

Fare: $

23

Question 2

Answer: POSITIVE[1]

The line goes up from left to right.So the gradient is positive.

Question 3

Answer: So

D(-2, 1)

.[2]

Across:

2 - 2 = 0

Up:

1 - (-5) = 6

x = -2

y = 1

D(-2, 1)

Question 4

Answer: So

E(-3, 4)

.[2]

x = -3

y = 4

E(-3, 4)

Question 5

(a)Answer:

y = -17

[3]

When

x = -2

y = -4(-2) - 5

y = 3

When

x = -1

y = -4(-1) - 5

y = -1

When

x = 3

y = -4(3) - 5

y = -17

(b)Answer:

y = 19

[3]

-y = -4x - 7

y = 4x + 7

When

x = -2

y = 4(-2) + 7

y = -1

When

x = 1

y = 4(1) + 7

y = 11

When

x = 3

y = 4(3) + 7

y = 19

Question 6

(a)Answer: Rate:

3

cm per hour[2]

The line goes from

(0, 30)

(10, 0)

.Rise:

0 - 30 = -30

; run:

10 - 0 = 10

\text{Gradient} = \dfrac{-30}{10}

\phantom{\text{Gradient}} = -3

Rate:

3

cm per hour

(b)Answer:

y = 21

[3]

-y = -4x - 5

y = 4x + 5

When

x = -1

y = 4(-1) + 5

y = 1

When

x = 0

y = 4(0) + 5

y = 5

When

x = 4

y = 4(4) + 5

y = 21

Question 7

(a)Answer:

m = 2

[2]

A(-5, -5)

and

B(-3, -1)

Rise:

-1 - (-5) = 4

Run:

-3 - (-5) = 2

m = \dfrac{4}{2}

m = 2

(b)Answer: Fare: $

18

[3]

\text{Start} = 3

The line goes from

(0, 3)

(10, 13)

.Rise:

13 - 3 = 10

; run:

10 - 0 = 10

\text{Rate} = 1

3 + 1 \times 15 = 18

Fare: $

18

Question 8

(a)Answer:

PQ = 3

units[1]

P and Q have the same y-coordinate, so PQ is horizontal.

\mathstrut 2 - (-1) =

3

units

PQ = 3

units

(b)Answer: Length:

30

cm[1]

Length:

30

(c)(i)Answer:

y = -2

[3]

When

x = -2

y = 2(-2) - 4

y = -8

When

x = 0

y = 2(0) - 4

y = -4

When

x = 1

y = 2(1) - 4

y = -2

(c)(ii)Answer:

y = -2

[3]

y = -4x + 2

When

x = -1

y = -4(-1) + 2

y = 6

When

x = 0

y = -4(0) + 2

y = 2

When

x = 1

y = -4(1) + 2

y = -2