Algebra Review

Factorizing

100

4 - 3p - p² = 0

(p - 1)(p + 4) so p=1 or p=-4

200

x² - 5x - 36 = 0

(x + 4)(x - 9) so x=-4 or x=9

300

2x² + 7x - 4 =0

(2x - 1)(x + 4) so x=1/2 or -4

400

Solve the quadratic equation. 2/x-1 + 3/x+1 = 1

x = 0 or 5

500

x(x - 3) = x + 21

(x + 3)(x - 7) so x= -3 or 7

Completing the square

100

Write the following in the form (x + h)² + k

x² + 5x - 5

(x + 2.5)² - 11.25

200

Solve the equations. Give your answer to 2 decimal places. x² + 10x - 12 = 0

x = 1.08 or -11.08

300

Solve the equation correct to 3 significant figures 1/x+4 - 2/x+5 = 4

x = -3.83 or -5.43

400

Give your solution in surd form (Square root). x² - 6x - 2 = 0

x = 3 +/- square root 11

500

Solve the equation. Give answer to 2 decimal places 6x² - 3x - 2 = 0

x = 0.88 or -0.38

Quadratic Formula

100

solve the equations. Give solutions correct to 3 significant figures. x² + 4x + 2 = 0

x = -0.586 or -3.41

200

Solve the equation. Give answer to 3 significant figures 5x² - 9x + 2 = 0

x = 1.54 or 0.260

300

Solve the equation. Give answers to 3 significant figures x(2x + 3) = 4 - 7x

x = 0.372 or -5.37

400

Solve the quadratic equation. 2/x+1 + 4/3x-1 = 3

x = 1 or -5/9

500

The length of a rectangular wall is 5m greater than the height of the wall. The area of the wall is 16m squared. What is the length of the wall?

7.22m

Simultaneous Equations (1)

100

4x + 6y = 5 and 3x + 4y = 4

y = -0.5 and x = 2

200

Solve the simultaneous equations 5x - y = -4 and y = 2x + 1

x=-1 and y=-1

300

Mrs. Naidu bought $155 in groceries. She paid her bill with $5 and $20 notes using a total of 13 notes. Calculate how many of each type of note were used?

seven $5 and six $20

400

Solve the simultaneous equations 2y = 4x² - 7 and y = 6x

(3.5, 21) and (-0.5, -3)

500

Solve the simultaneous equations x² + y² = 34 and y = 1 + 2x

(2.2, 5.4) and (-3, -5)

Simultaneous Equations (2)

100

Solve the simultaneous equations y=2x and x + y = 3  

x=1 y=2

200

Solve the simultaneous equations y = 3 - x² and y = 5 - 3x

(1,2) (2,-1)

300

Solve the simultaneous equations x² + 4y = 7 and 2y + x = 2

(3, -0.5) (-1, 1.5)

400

Solve the simultaneous equations by graphing x² + y² = 25 and y = 2x + 1

(1.8, 4.7) and (-2.6, -4.3)

500

Solve the simultaneous equation by graphing. x² + y² = 49 and x + y = 5

(6.8, -1.8) and ( -1.8, 6.8)