Functional QuestionHigher(Algebra 2)

For the week beginning ….

The diagram shows the cross-section of a river bed, ABCDE. Not drawn accurately

          BD is the surface of the river.          C is the midpoint of the river.          A and E are points on the river bank that are 1 metre above the river

surface.Taking the origin at B, metre as 1 unit on bothaxes and the river surface as the x-axis, the curve ABCDE can be represented by theequation

                             

                        

                       

(a)     Show that the depth of the river at the mid-point C is 2 metres. (3)

(b)     Show that the distance AE is approximately 12.25 metres. (5)

(Total 8 marks) (b)     Show that the distance AE is approximately 12.25 metres (5)(Total 8 marks)

(a)     2x(x – 10) = 0M1 – Method mark

          River ( x = ) 10 ( m wide)A1 – Accuracy marks are awarded when following on from a correct method

          When  x = 5,           y = (50 – 100) ÷ 25 = –2A1 – Accuracy marks are awarded when following on from a correct method

(b)     2x2 – 20x = 25M1 – Method mark

          2x2 – 20x – 25 = 0M1 – Method mark          Use quadratic formula, completing the square to solve equationAllow one error but not wrong formulaM1- Method mark          x = –1.123 or 11.123A1 – Accuracy marks are awarded when following on from a correct method

          AE = 1.123 + 11.123 ≈ 12.25 mNB error with – b gives 1.123 and – 11.123Allow last A1A1 – Accuracy marks are awarded when following on from a correct method

 

 

This question was the second least successful question on the paper. There were very few fully correct answers. The majority of scripts were blank. Candidates had little idea of how to relate the x and y values. In part (a), few realised that y had to be put equal to zero. It was often put equal to 25. A few candidates started with y = –2 which was accepted as a method providing it led to x = 5 and that x = 10 was then tested to give y = 0. Very few who tried this method gained full marks. Several also began with y = 2 which led nowhere. In part (b), substituting  = 12.25 was the most frequent error. The few that put the equation equal to 1 often obtained a quadratic expression but then failed to solve it correctly

Common Mistakes – what did the examiners say?