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(Forming Equations, Substitution, Operations with –ve numbers ) 2x Grade B 3x Area = 150 cm2 x+5 Grade A x+3 Area = 26 cm2 Grade A* The area of the shape is 25 cm2. a) Show that 6x2 + 17x – 39 = 0 b) Calculate the length of the shortest side EFSMaths Solving Problems with Quadratics Forming Equations (Application) Grade B-A* Algebra is usually used to write equations so that we can solve them for a particular variable GCSE A* Q1 GCSE A* Q2 Diagram NOT accurately drawn x+2 The diagram shows a 6-sided shape. All the corners are right angles. All the measurements are given in centimetres. x–5 2x – 7 x+6 3x The diagram shows a trapezium. The lengths of three of the sides of the trapezium are x – 5, x + 2 and x + 6. All measurements are given in centimetres. 3x + 4 x The area of the trapezium is 36 cm2. Diagram NOT accurately drawn (a) (4) (b) The area of the shape is 85 cm2. (a) Show that 9x2 – 17x – 85 = 0 (i) Solve the equation x2 – x – 56 = 0 ………………… Hence find the length of the shortest side of the trapezium. (3) (b) Show that x2 – x – 56 = 0 Solve 9x2 – 17x – 85 = 0 …………………… cm Give your solutions correct to 3 significant figures. x = ........... or x = ................... (ii) (4) (Total 8 marks) GCSE A* Q3 Diagram NOT accurately drawn Hence, work out the length of the shortest side of the 6-sided shape. x 2x ................................. cm (4) (Total 7 marks) 20 The diagram shows a trapezium. The area of the trapezium is 400 cm2. (a) Show that x2 + 20x = 400 (2) (b) Find the value of x. Give your answer correct to 3 decimal places. ..................................... (3) (Total 5 marks)