1. Functional Question Higher (Algebra 2) For the week beginning ….

2. 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 both axes and the river surface as the x-axis, the curve ABCDE can be represented by the equation (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)

3. (a) 2x(x – 10) = 0 M1 – 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 = –2 A1 – Accuracy marks are awarded when following on from a correct method (b) 2x2 – 20x = 25 M1 – Method mark 2x2 – 20x – 25 = 0 M1 – Method mark Use quadratic formula, completing the square to solve equation Allow one error but not wrong formula M1- Method mark x = –1.123 or 11.123 A1 – Accuracy marks are awarded when following on from a correct method AE = 1.123 + 11.123 ≈ 12.25 m NB error with – b gives 1.123 and – 11.123 Allow last A1 A1 – Accuracy marks are awarded when following on from a correct method

4. 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?