PLC Papers Created For: Daniel Inequalities
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) -2-1 0 1 2 3-1 0 1 2 3 4 (4)
(c) Which of these inequalities (a) or (b) has the most integer solutions?. (1) Total /10
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)
Question 3 Solve. 9(2 + 3x) < 72 (3) Total /10
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 = 2 + 5 have been drawn on the grid. Use the graphs to solve the simultaneous equations = 3 and = 2 + 5. =. =. (Total 1 mark) Question 2. Solve the simultaneous equations 2 + 3 = 31 3 + 6 = 57 =. =. (Total 3 marks)
Question 3. Solve the simultaneous equations 4 + 7 = 68 9 2 = 11 =. =. (Total 3 marks) Question 4. Solve, by substitution, the simultaneous equations + = 4 = 2 + 10 =. =. (Total 3 marks) TOTAL /10
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)
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)
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)
PLC Papers Created For: Daniel Inequalities
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 > -2-1 0 1 2 3-3 -2-1 0 1 (2) Question 2-3 n < 2 n is an integer -3-2 -1 0 1 2 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) -2-1 0 1 2 3-1 0 1 2 3 4-2 x < 3 (M1 A1) 0 < x 3 (M1 A1) (4)
(c) Which of these inequalities (a) or (b) has the most integer solutions? (a) B1. (1) Total /10
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 - 12 2x + 2 < -12 (M1) 2x < -14 (M1) x < -7 (b) Write down the largest integer that satisfies 3x + 2 < x - 12-8 (B1) (3) (1)
Question 3 Solve. 9(2 + 3x) < 72 18 + 27x < 72 (M1) 27x < 54 (M1) x < 2 (3) Total /10
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 = 2 + 5 have been drawn on the grid. Use the graphs to solve the simultaneous equations = 3 and = 2 + 5. = 1. = 3. (Total 1 mark) Question 2. Solve the simultaneous equations 2 + 3 = 31 3 + 6 = 57 4 + 6 = 62 = 5 (M1) 10 + 3 = 31 3 = 21 = 7
=. =. (Total 3 marks) Question 3. Solve the simultaneous equations 8 + 14 = 136 4 + 7 = 68 9 2 = 11 63 14 = 77 71 = 213 = 3 (M1) 12 + 7 = 68 7 = 56 = 8 =. =. (Total 3 marks) Question 4. Solve, by substitution, the simultaneous equations + = 4 = 2 + 10 + 2 + 10 = 4 (M1) 3 + 10 = 4 3 = 6 = 2 2 + = 4 = 6 =. =. (Total 3 marks) TOTAL /10
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)
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 1 4 + 2 (M1) (Total 4 marks)
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