Download Year 12 Algebra Revision

Year 12 Algebra Revision
1.
Solve the following equations:
a) 4x2 – 12x = 0
b) (2x – 3)(x + 4) = 0
c) 2x – 1 = -1
d) x2 + 3x – 13 = 0
x
2.
Complete the square for: x2 – 4x – 5
3.
Sketch the following graphs showing the vertex and intercepts:
a) y = x2 – 9
b) y = (x – 2)2 – 1
c) y = x2 + x – 6
4.
Find the point of intersection of the graphs with equations:
y = -x2 – 5x + 3 and y = x2 + 3x + 11
5.
Simplify fully:
a) 3x + 1
+
5
c)
5
x–3
+
2x
3
3
x+1
b) 2x2 – 10x × x2 – 1
2x
x+1
d)
3x – 2
x+1
-
2x + 3
x–1
6.
Complete the square for: 2x2 + 6x – 4
7.
Find in the form of ax2 + bx + c the equation of the quadratic whose graph:
passes through ( -1 , 4 ) and touches the x axis at -2.
8.
Find the equations of these graphs:
a)
b)
9.
Complete the square for: 2 x 2  6 x  4 and state the coordinates of the
vertex of the graph.
10.
Factorise:
6 x 2  5 x  21