13 c and d can be difficult because they B1 2 B1 for identifying some examples with a valid reason M contain minus signs; errors are often made when combining minus signs. x t x), In substituting = into = –3 –2(3 – B2 B1 for clear identification of one typical error with one a common error is to assume 3 is – –3 equation. 0. z In substituting = into = a typical x –3 error is to assume a negative divided B1 for another typical error by a negative gives a negative answer. A suggestion to avoid these errors is to remember that when multiplying or B1 B1 for a satisfactory suggestion dividing with positive and negative numbers, same signs means positive, different signs means negative. 4 14 The similarities are that both include an B1 2 B1 for clear explanation of similarities M equals sign and both require the manipulation of terms. The difference is that in solving an B1 B1 for clear explanation of differences equation you reach a numerical answer, but in rearranging you still have a formula. 2 15 B1 2 B1 for identifying the first error M In line 2 Phillip has initially x2 x(x rearranged + 2x 3 to + 2) – – 3 when he should have factorised it as (x + 3)(x 1). – He has incorrectly simplified in line 3. B1 B1 for identifying the second error He should have factorised (x2 9) to – (x + 3)(x 3). – Philip has cancelled incorrectly just by B1 B1 for a clear explanation of the errors made looking at the different numbers and not realising that you can only cancel a number on both numerator and denominator if it is a factor of the complete expression. 3
13 c and d can be difficult because they contain minus signs; errors are often made when combining minus signs. In substituting x = –3 into t = –2(3 – x), a common error is to assume 3 – –3 is 0. In substituting x = –3 into z = a typical error is to assume a negative divided by a negative gives a negative answer. A suggestion to avoid these errors is to remember that when multiplying or dividing with positive and negative numbers, same signs means positive, different signs means negative. B1 B2 B1 2 B1 for identifying some examples with a valid reason B1 for clear identification of one typical error with one equation. B1 for another typical error B1 for a satisfactory suggestion M 4 14 The similarities are that both include an equals sign and both require the manipulation of terms. The difference is that in solving an equation you reach a numerical answer, but in rearranging you still have a formula. B1 B1 2 B1 for clear explanation of similarities B1 for clear explanation of differences M 2 15 In line 2 Phillip has initially rearranged x2 + 2x – 3 to x(x + 2) – 3 when he should have factorised it as (x + 3)(x – 1). He has incorrectly simplified in line 3. He should have factorised (x2 – 9) to (x + 3)(x – 3). Philip has cancelled incorrectly just by looking at the different numbers and not realising that you can only cancel a number on both numerator and denominator if it is a factor of the complete expression. B1 B1 B1 2 B1 for identifying the first error B1 for identifying the second error B1 for a clear explanation of the errors made M 3
Higher_Skills_Algebra_MarkScheme_AQA.docx