2. Solve These Equations. Some Will Require Rearrangement Before Factorising

Basic Skills & Straight Line

1. Solve (a) x2 – 9x + 8 = 0 (b) x2 + 19x + 18 = 0 (c) x2 – 9x + 18 = 0 (d) x2 + 3x  18 = 0 (e) x2 – 3x  18 = 0 (f) x2 – 9x + 20 = 0 (g) x2 + 4x  21 = 0 (h) x2 – 4x  32 = 0 (i) x2 – 13x + 36 = 0

2. Solve these equations. Some will require rearrangement before factorising. (a) x2 + 12x + 27 = 0 (b) x2  x = 2 (c) x2 + 36 = 15x (d) x2 – 6x = 7 (e) x2 + 54 = 15x (f) x(x + 4) = 45 (g) x(x – 12) = 13 (h) x(x + 5) = 24 (i) 10x – 11 = x2 (j) 44 – 15x = x2 (k) x(x – 5) + 2(x – 14) = 0 (l) x(x + 6) – 8(5x – 8) = 0 (m) x(x + 29) – 9(x – 2) = 4x + 3

3. Solve the following pairs of simultaneous equations: (a) 2x  y  8 (b) 4x  y  21 (c) 2x  y  6 3x  2y  5 3x  3y  12 4x  3y  22 (d) x  5y  8 (e) 4x  2y  8 (f) 3x  2y  7 3x  2y  11 x  3y  2 5x  4y  12 (g) 6x  7y  13 (h) 8x  3y  27 (i) 5x  2y  6 3x  2y  1 2x  5y  1 3x 10y  26 4. Find the angles which the lines joining the following pairs of points make with the positive direction of OX. (a) (0 , 0) , (1 , 1) (b) (2 , 2) , (4 , 4) (c) (0 , 0) , (1 , 3 ) (d) (0 , 0) , ( 3 , 1) (e) (3 , 4) , (5 , 6) (f) (3 , 6) , (5 , 4)

5. Find the equations of the lines through the following points, with the given gradients. (a) (2 , 3) , 4 (b) (1 , 1) , 2 (c) (0 , 4) , 2 (d) (4 , 1) , 2 (e) (3 , 3) , 1 (f) (4 , 2) , ½

6. Find the equations of the lines through the following points, parallel to the given lines. (a) (1 , 2) , y = 6x – 4 (b) (5 , 2) , x + y = 5 (c) (1 , 0) , x – y = 0 (d) (3 , 2) , 2x + 3y + 4 = 0

7. Find the equations of the lines through the following pairs of points: (a) (3 , 4) , (1 , 2) (b) (0 , 1) , (5 , 2) (c) (1 , 3) , (4 , 0) (d) (0 , 0) , (2 , 3) (e) (1 , 4) , (3 , 6) (f) (5 , 2) , (8 , 1)

8. P is the point (4 , 0), Q is (0 , 3) and R is (5 , 1). Given that PQRS is a parallelogram, obtain the equations of RS and PS.