PLC Papers Created For:

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1 PLC Papers Created For: Josh Angles and linear graphs

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

3 y d x (2) Question 2 Which of these are linear functions? Circle your answer(s) y = 7 3x y = x 4 y = x x + 3y = 5 y = x (2) Total /10

4 Plotting straight line graphs 1 Grade 3 Objective: Plot graphs of straight-lines in the coordinate plane Question 1

5 Question 2 (1) (Total: 3 marks)

6 Question 3 (1) (Total: 3 marks) Total Mark /10

7 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, L 1, drawn on a grid. A straight line, L 2, is parallel to the straight line L 1 and passes through the point (0, 5). Find an equation of the straight line L 2. (3 marks)

8 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

9 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 D 62 º y º E F 64 º G DE is parallel to FG. Diagram NOT accurately drawn (i) Find the size of the angle marked y. (ii) Give a reason for your answer (Total 2 marks)

10 Question 2 (Total 2 marks)

11 Question 3

12 Question 4 y = Total /10

13 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)

14 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)

15 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 /10 (Total 3 marks)

16 PLC Papers Created For: Josh Angles and linear graphs

17 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 a y B1 line with positive gradient B1 intercept indicated x -3 (2) B1 line with negative gradient B1 intercept indicated y b 10 x (2) y c 4 B1 line with positive gradient B1 intercept indicated x (2)

18 d y B1 line with negative gradient B1 intercept indicated 0 x (2) Question 2 Which of these are linear functions? Circle your answer(s) y = 7 3x y = x 4 y = x x + 3y = 5 y = x B1 for any three B2 for all four correct answers (2) Total /10

19 Plotting straight line graphs 1 Grade 3 Solutions Objective: Plot graphs of straight-lines in the coordinate plane Question 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

20 Question B2 for all 3 values correct in table B1 for 2 values correct A1 for correct line from x = -2 to x = 2 (1) (Total: 3 marks)

21 Question B2 for all 3 values correct in table B1 for 2 values correct A1 for correct line from x = -1 to x = 3 (1) (Total: 3 marks) Total /10

22 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, L 1, drawn on a grid. A straight line, L 2, is parallel to the straight line L 1 and passes through the point (0, 5). Find an equation of the straight line L 2. 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)

23 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 To get from B to C, across -6 (3 TIMES THE A TO B DISTANCE), 4x3-12 Q= = 16 A1 M1 M1 (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

24 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 D 62 º y º E F 64 º G DE is parallel to FG. Diagram NOT accurately drawn (i) Find the size of the angle marked y. (ii) Give a reason for your answer. 64 A1... Alternate angles are equal. A1.... (Total 2 marks)

25 Question Alternate angles are equal hence r = 72 Corresponding angles are equal & Angles on a straight line adds up to 180 therefore s = = 55 No reasons required 72 A1 55 A1 (Total 2 marks)

26 Question A1 Angles on straight line adds up to = 130 A1 50 A1 Alternate angles are equal. A1

27 Question 4 y = y = 120 A1 Corresponding angles are equal A1 OR Accept: co-interior angles add up to 180 therefore = 120 A1 Total /10

28 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)

29 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) (A1) (A1) (A1) (Total 4 marks)

30 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