48 a B1 2 B1 for a correct inequality M For example, 2x > 10 B1 B1 for clear explanation of how to solve the inequality x Divide both sides by 2 to get > 5. chosen B1 B1 for explanation about circles at the end of each line b We show the solution with a line and a B1 circle at each end point. B1 for clear explanation differentiating between solid A solid circle means that the solution and open circles includes the end point; an open circle means that the solution does not include the end point. For example: B1 B1 for use of a clear diagram to support the explanation The top diagram shows 2. It has a x ≤ solid circle at the end point = 2 x because that is part of the solution. The bottom diagram shows > 1, it has x an open circle at the end point = 1 x because = 1 is not part of the solution. x B1 B1 for a full, clear explanation showing both aspects of Starting with an equation 10 > 4 x – the circles and solving by adding to both sides gives x x. the solution 6 > x This can also be given as < 6 (1) ….. c B2 x Consider again 10 > 4. – B1 for clear explanation This time multiply throughout by –1. Keeping the inequality sign the same B1 for using an example in a way that illustrates the gives: principle x + > -4 –10 x Add 10 to each side to give > 10 4. – This gives the solution as > 6 (2) x ….. But comparing this with equation (1) we see that the signs are the other way round, this illustrates that when we multiplied through by a negative number, we should have changed the sign from > to <. 8
48 a b c For example, 2x > 10 Divide both sides by 2 to get x > 5. We show the solution with a line and a circle at each end point. A solid circle means that the solution includes the end point; an open circle means that the solution does not include the end point. For example: The top diagram shows x ≤ 2. It has a solid circle at the end point x = 2 because that is part of the solution. The bottom diagram shows x > 1, it has an open circle at the end point x = 1 because x = 1 is not part of the solution. Starting with an equation 10 – x > 4 and solving by adding x to both sides gives the solution 6 > x. This can also be given as x < 6 ….. (1) Consider again 10 – x > 4. This time multiply throughout by –1. Keeping the inequality sign the same gives: –10 + x > -4 Add 10 to each side to give x > 10 – 4. This gives the solution as x > 6 ….. (2) But comparing this with equation (1) we see that the signs are the other way round, this illustrates that when we multiplied through by a negative number, we should have changed the sign from > to <. B1 B1 B1 B1 B1 B1 B2 2 B1 for a correct inequality B1 for clear explanation of how to solve the inequality chosen B1 for explanation about circles at the end of each line B1 for clear explanation differentiating between solid and open circles B1 for use of a clear diagram to support the explanation B1 for a full, clear explanation showing both aspects of the circles B1 for clear explanation B1 for using an example in a way that illustrates the principle M 8
Higher_Skills_Algebra_MarkScheme_AQA.docx