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1 PLC Papers Created For: Daniel Inequalities
2 Inequalities on number lines 1 Grade 4 Objective: Represent the solution of a linear inequality on a number line. Question 1 Draw diagrams to represent these inequalities. (a) x 3 (b) x > -2 (2) Question 2-3 n < 2 n is an integer Write down all the possible values of n and represent these values on a number line. (3) Question 3 Write down the inequality that is represented by each diagram below. (a) (b) (4)
3 (c) Which of these inequalities (a) or (b) has the most integer solutions?. (1) Total /10
4 Solve linear inequalities one variable 1 Grade 5 Objective: Solve linear inequalities in one variable Question 1 Solve. (a) 5x 1 > 14 (2) (b) Write down the smallest integer that satisfies 5x - 1 > 14 (1) Question 2 Solve. (a) 3x + 2 < x - 12 (b) Write down the largest integer that satisfies 3x + 2 < x - 12 (3) (1)
5 Question 3 Solve. 9(2 + 3x) < 72 (3) Total /10
6 Simultaneous equations (linear) 1 Grade 6 Objective: Form and/or solve simultaneous equations Question 1. The graphs of the straight lines with equations = 3 and = have been drawn on the grid. Use the graphs to solve the simultaneous equations = 3 and = =. =. (Total 1 mark) Question 2. Solve the simultaneous equations = = 57 =. =. (Total 3 marks)
7 Question 3. Solve the simultaneous equations = = 11 =. =. (Total 3 marks) Question 4. Solve, by substitution, the simultaneous equations + = 4 = =. =. (Total 3 marks) TOTAL /10
8 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)
9 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)
10 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)
11 PLC Papers Created For: Daniel Inequalities
12 Inequalities on number lines 1 Grade 4 Solutions Objective: Represent the solution of a linear inequality on a number line. Question 1 Draw diagrams to represent these inequalities. (a) x 3 (b) x > (2) Question 2-3 n < 2 n is an integer Write down all the possible values of n and represent these values on a number line. -3, -2, -1, 0, 1 (M1 A1) (3) Question 3 Write down the inequality that is represented by each diagram below. (a) (b) x < 3 (M1 A1) 0 < x 3 (M1 A1) (4)
13 (c) Which of these inequalities (a) or (b) has the most integer solutions? (a) B1. (1) Total /10
14 Solve linear inequalities one variable 1 Grade 5 Solutions Objective: Solve linear inequalities in one variable Question 1 Solve. (a) 5x 1 > 14 5x > 15 (M1) x > 3 (2) (b) Write down the smallest integer that satisfies 5x - 1 > 14 4 (B1) (1) Question 2 Solve. (a) 3x + 2 < x x + 2 < -12 (M1) 2x < -14 (M1) x < -7 (b) Write down the largest integer that satisfies 3x + 2 < x (B1) (3) (1)
15 Question 3 Solve. 9(2 + 3x) < x < 72 (M1) 27x < 54 (M1) x < 2 (3) Total /10
16 Simultaneous equations (linear) 1 Grade 6 SOLUTIONS Objective: Form and/or solve simultaneous equations Question 1. The graphs of the straight lines with equations = 3 and = have been drawn on the grid. Use the graphs to solve the simultaneous equations = 3 and = = 1. = 3. (Total 1 mark) Question 2. Solve the simultaneous equations = = = 62 = 5 (M1) = 31 3 = 21 = 7
17 =. =. (Total 3 marks) Question 3. Solve the simultaneous equations = = = = = 213 = 3 (M1) = 68 7 = 56 = 8 =. =. (Total 3 marks) Question 4. Solve, by substitution, the simultaneous equations + = 4 = = 4 (M1) = 4 3 = 6 = = 4 = 6 =. =. (Total 3 marks) TOTAL /10
18 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)} 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)
19 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) (Total 4 marks)
20 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
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