Note: Award 4 without any working. 12(a) 1 state recurrence relation 1 2 (b) 2 knows how to find limit 3 #2.2 3.89 < 4 so the expectation is 3 process limit incorrect. #2.2 compare and state conclusion Note: The only answer that should be awarded 1 is above. This would include the fractional equivalent of 0·1. 13 1 prepares to differentiate 1 2 2 differentiates first term correctly 3 3 differentiates second term correctly 14 (a) 1 differentiates 1 2 substitutes 2 (b) #2.2 explaining a solution #2.2 tangent at is parallel to x-axis 15 1 differentiates correctly 1 2 2 finds gradient 3 3 finds y 4 4 equation of tangent 16 #2.1 begins to differentiate and equates to #2.1 zero 1 finds derivative 1 2 finds 2 x-value 3 justifies nature = min and 3 nature table or 2nd derivative communicates findings
Note: Award 4 without any working. 12(a) (b) 1 state recurrence relation 2 knows how to find limit 3 process limit #2.2 compare and state conclusion 1 2 3 #2.2 3.89 < 4 so the expectation is incorrect. Note: The only answer that should be awarded 1 is above. This would include the fractional equivalent of 0·1. 13 1 prepares to differentiate 2 differentiates first term correctly 3 differentiates second term correctly 1 2 3 14 (a) (b) 1 differentiates 2 substitutes #2.2 explaining a solution 1 2 #2.2 tangent at is parallel to x-axis 15 1 differentiates correctly 2 finds gradient 3 finds y 4 equation of tangent 1 2 3 4 16 #2.1 begins to differentiate and equates to zero 1 finds derivative 2 finds x-value 3 justifies nature = min and communicates findings #2.1 1 2 3 nature table or 2nd derivative
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