A- Level Topic Review s1

A– LEVEL TOPIC REVIEW unit C1 expanding, factorising and quadratics

1. Expand the brackets and simplify the following expressions: a) (2x- 5)( x + 2) b) (x2 + 2 x + 3)(2 x - 5) c) (x + 3)2 d) (x + 3)3 (6 marks)

2. Solve the following equations by factorisation: a) x2 +4 x + 3 = 0 b) x2 -2 x - 3 = 0 c) 2x2 + 3 x - 5 = 0 d) 3x3- 7 x 2 - 6 x = 0 e) 4x2 - 9 = 0 (10 marks)

3. Use the quadratic formula to solve the following equations, giving your answers correct to 3 decimal places: a) x2 +5 x + 1 = 0 b) 2x2 - 3 x - 4 = 0 (6 marks)

4. Solve the following equations by the method of completing the square, leaving your answers in an exact form: a) x2 +6 x - 2 = 0 b) 2x2 - 3 x - 7 = 0 (6 marks)

5. Sketch the curves a) y= x2 -6 x + 5 b) y=5 x - 2 x2 Mark clearly on your sketches the coordinates of the points where the curve crosses the axes, and the coordinates of the turning points, which you should find by completing the square. (8 marks)

6. a) Given the identity (px+ 2)2 = 9 x 2 + qx + 4 , where p and q are positive integers, find the values of p and q. (2 marks) b) Express 4x2 - 12 x + 11 in the form a( x+ b )2 + c and hence write down: (3 marks) (i) the minimum value of 4x2 - 12 x + 11. (1 mark) 1 (ii) the maximum value of . (1 mark) 4x2 - 12 x + 11

7. Solve the inequalities: a) x2 +5 x + 6 > 0 b) 2x2 + x 6 c) (x - 2)2 9 (7 marks) A– LEVEL TOPIC REVIEW : ANSWERS unit C1 expanding, factorising and quadratics

1. a) 2x2 - x - 10 A1 5. a) axes (1, 0) (5, 0) (0, 5) M1A1 b) 2x3- x 2 - 4 x - 15 A1 turning point (3, –4) A1 2 U-shape G1 c) x+6 x + 9 M1A1 b) axes (0, 0) (2.5, 0) A1 d) x3+9 x 2 + 27 x + 27 M1A1 5, 25 turning point ( 4 8 ) M1A1 2. a) (x+ 3)( x + 1) = 0� x - - 3, 1 M1A1 upside down U-shape G1 b) (x- 3)( x + 1) = 0� x - 3, 1 M1A1 2 2 5 6. a) p x+4 px + 4 M1 c) (2x+ 5)( x - 1) = 0� x - 2 ,1 M1A1

2 p=3, q = 12 A1 d) x(3 x+ 2)( x - 3) = 0� x - 0,3 ,3 2 M1A1 b) 4( x- 3 x) + 11 M1 3 3 e) (2x+ 3)(2 x - 3) = 0� x - , M1A1 4轾 (x -3 )2 - 9 + 11 2 2 臌 2 4 A1 3 2 4(x -2 ) + 2 A1 -5� 25 4 3. a) = -0.209, - 4.791 M1A2 (i) 2 M1 2 1 (ii) 2 A1 3� 9 32 b) =2.351, - 0.851 M1A2 4 7. a) (x+ 2)( x + 3) > 0 M1 x< -3, x > - 2 4. a) (x + 3)2 = 11 M1 A1 b) (2x- 3)( x + 2) 0 M1 x = -3 11 A1 ＃ 3 2 3 7 -2 x 2 A1 b) x-2 x - 2 = 0 M1 c) x2 -4 x - 5 0 M1 (x -3 )2 - 9 - 7 = 0 A1 4 16 2 (x- 5)( x + 1) 0 M1 (x -3 )2 = 65 M1 4 16 x� 1, x 5 A1 3 65 x = A1 4