PLC Papers

Created For:

Josh

Angles and linear graphs

PiXL PLC 2017 Certification

Graphs of Linear Functions 1 Grade 4

Objective: Recognise, sketch and interpret graphs of linear functions.

Question 1

Sketch the graph of each function, clearly indicating the y-intercept.

a) y = 5x -3 b) y = 10 – 2x c) 2y = 4x + 8 d) y = -3x

y

a

x

(2)

y

b

x

(2)

y

c

x

(2)

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y

d

x

(2)

Question 2

Which of these are linear functions? Circle your answer(s)

y = 7 – 3x

y = x 4 y = x2 + 4 2x + 3y = 5 y = x

(2)

Total /10

Plotting straight line graphs 1 Grade 3

Objective: Plot graphs of straight-lines in the coordinate plane

Question 1

Question 2

(1)

(Total: 3 marks)

Question 3

(1)

(Total: 3 marks)

Total Mark /10

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Using the equation of a straight line 1 Grade 4

Objective: Identify and interpret gradients and intercepts of linear functions, both algebraically and graphically

Question 1

The diagram shows a straight line, L1, drawn on a grid.

A straight line, L2, is parallel to the straight line L1 and passes through the point (0, −5).

Find an equation of the straight line L2.

(3 marks)

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Question 2

The points A, B and C lie on a straight line.

The coordinates of A are (9, 0). The coordinates of B are (7, 4). The coordinates of C are (1, q).

Work out the value of q.

(3 marks)

Question 3

The straight line L has equation y = 3x – 4

(a) Write down an equation of the line parallel to L which passes through the origin.

(2 marks)

(b) Find an equation of the straight line that passes through (0, 5) and is parallel to L.

(2 marks)

Total marks / 10

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Alternate & corresponding angles 1 Grade 4

Objective: Apply the properties of angles and a point, angles on a straight line, vertically opposite angles, alternate angles and corresponding angles

Question 1

DE is parallel to FG.

(i) Find the size of the angle marked y°.

..........................

(ii) Give a reason for your answer.

.......................................................................................................................... .

(Total 2 marks)

D

F

E

G

62 º º

64 º

Diagram NOT accurately drawn

�

y

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Question 2

(Total 2 marks)

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Question 3

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Question 4 y =

Total /10

PiXL PLC 2017 Certification

Represent linear inequalities 1 Grade 6 Objective: Represent the solution of a linear inequality in two variables on a number line, using set notation and on a graph

Question 1.

The graph shows the region that represents the inequalities � < 3, � < �, and � + � > 12 by shading the unwanted regions.

a) In the dataset listed below, circle the points that satisfy all three inequalities.

{ (4,8), (7,4), (5,6), (4,7), (5,5)}

b) If the inequality � < � were to be changed to � ≤ �, what would the fully correct dataset be?

………………………

(Total 3 marks)

PiXL PLC 2017 Certification

Question 2.

The dataset shown below lists the complete integer solution set to three inequalities.

{ (1,3), (1,4), (2,4) }

Plot the points on the given axes and determine the three inequalities for which they are the complete integer solution set.

………………………

(Total 4 marks)

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Question 3.

a) Represent the solution to the inequalities � > � + 2, � + � ≤ 5 and � > 0.5 graphically on the grid below by shading the unwanted regions.

………………………

(Total 3 marks)

Total /10

PLC Papers

Created For:

Josh

Angles and linear graphs

PiXL PLC 2017 Certification

Graphs of Linear Functions 1 Grade 4 Solutions

Objective: Recognise, sketch and interpret graphs of linear functions.

Question 1

Sketch the graph of each function, clearly indicating the y-intercept.

a) y = 5x -3 b) y = 10 – 2x c) 2y = 4x + 8 d) y = -3x

y B1 line with positive gradient

a B1 intercept indicated

x

-3

(2)

B1 line with negative gradient B1 intercept indicated

y

b 10

x

(2)

y B1 line with positive gradient B1 intercept indicated

c 4

x

(2)

PiXL PLC 2017 Certification

y B1 line with negative gradient B1 intercept indicated

d

0 x

(2)

Question 2

Which of these are linear functions? Circle your answer(s)

y = 7 – 3x

y = x 4 y = x2 + 4 2x + 3y = 5 y = x B1 for any three

B2 for all four correct answers

(2)

Total /10

PiXL PLC 2017 Certification

Plotting straight line graphs 1 Grade 3 Solutions

Objective: Plot graphs of straight-lines in the coordinate plane

Question 1

-4 -2 8

B2 for all 3 values correct in table

B1 for 2 values correct

M1 ft for plotting at least 2

correct points

A1 for correct line from x = -2 to

x = 2

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Question 2

(1)

(Total: 3 marks)

B2 for all 3 values correct in table

B1 for 2 values correct

A1 for correct line from x = -2 to

x = 2

-5 3 7

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Question 3

(1)

(Total: 3 marks)

Total /10

-4 11 6

B2 for all 3 values correct in table

B1 for 2 values correct

A1 for correct line from x = -1 to

x = 3

PiXL PLC 2017 Certification

Using the equation of a straight line 1 Grade 4 SOLUTIONS

Objective: Identify and interpret gradients and intercepts of linear functions, both algebraically and graphically

Question 1

The diagram shows a straight line, L1, drawn on a grid.

A straight line, L2, is parallel to the straight line L1 and passes through the point (0, −5).

Find an equation of the straight line L2.

The gradient is 2/4=0.5 M1

Y=mx+c, substitute in information given with m=0.5 and c=-5 M1

Y=0.5x-5 A1

(3 marks)

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Question 2

The points A, B and C lie on a straight line.

The coordinates of A are (9, 0). The coordinates of B are (7, 4). The coordinates of C are (1, q).

Work out the value of q.

Gradient of line from B and A: -4/2=-2

To get from A to B, across -2 and up 4 M1

To get from B to C, across -6 (3 TIMES THE A TO B DISTANCE), 4x3- 12 M1

Q= 4 + 12 = 16 A1

(3 marks)

Question 3

The straight line L has equation y = 3x – 4

(a) Write down an equation of the line parallel to L which passes through the origin.

y=3x M1 for same gradient and M1 for +0 for intersect.

(2 marks)

(b) Find an equation of the straight line that passes through (0, 5) and is parallel to L.

y=3x+5 M1 for same gradient and M1 for +5 for intersect.

(2 marks)

Total marks / 10

PiXL PLC 2017 Certification

Alternate & corresponding angles 1 Grade 4 SOLUTIONS

Objective: Apply the properties of angles and a point, angles on a straight line, vertically opposite angles, alternate angles and corresponding angles

Question 1

DE is parallel to FG.

(i) Find the size of the angle marked y°.

..........................

(ii) Give a reason for your answer.

.......................................................................................................................... .

(Total 2 marks)

D

F

E

G

62 º º

64 º

Diagram NOT accurately drawn

�

64 ° A1

Alternate angles are equal. A1

y

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Question 2

(Total 2 marks)

72 ° A1 55 ° A1

• Alternate angles are equal hence r = 72°

• Corresponding angles are equal & Angles on a straight line adds up to 180

therefore s = 180- 125= 55 °

No reasons required

125°

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Question 3

130 ° A1

Angles on straight line adds up to 180° A1

180 – 50 = 130°

50 ° A1

Alternate angles are equal. A1

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Question 4 y =

Total /10

y = 120 ° A1

Corresponding angles are equal A1

OR

Accept:

co-interior angles add up to 180 ° therefore 180 – 60 = 120 A1

PiXL PLC 2017 Certification

Represent linear inequalities 1 Grade 6 SOLUTIONS Objective: Represent the solution of a linear inequality in two variables on a number line, using set notation and on a graph

Question 1.

The graph shows the region that represents the inequalities � < 3, � < �, and � + � > 12 by shading the unwanted regions.

a) In the dataset listed below, circle the points that satisfy all three inequalities.

{ (4,8), (7,4), (5,6), (4,7), (5,5)} (A1)

b) If the inequality � < � were to be changed to � ≤ �, what would the fully correct dataset be?

{(4,4), (4,5), (4,6), (4,7), (5,5), (5,6)} (A2)

………………………

(Total 3 marks)

PiXL PLC 2017 Certification

Question 2.

The dataset shown below lists the complete integer solution set to three inequalities.

{ (1,3), (1,4), (2,4) }

Plot the points on the given axes and determine the three inequalities for which they are the complete integer solution set.

Plotting (1,3), (1,4) and (2,4) correctly (M1)

� ≥ 1 (A1)

� ≤ 4 (A1)

� ≥ � + 2 (A1)

………………………

(Total 4 marks)

PiXL PLC 2017 Certification

Question 3.

a) Represent the solution to the inequalities � > � + 2, � + � ≤ 5 and � > 0.5 graphically on the grid below by shading the unwanted regions.

(A3)

………………………

(Total 3 marks)

Total /10