Initial Diagnostic Audit - Unit F5: Solving Equations
Section F5.1 - Algebraic Fractions

When completing this section, use fractions and conventional algebraic notation to avoid using × and ÷ symbols in your answers

Expand the following.
1. Simplify
x8
x2
   =         
2. Simplify
x2 + x
x3 + x2
   =         
3. Simplify
x3 – x2
x2
   =         
4. Simplify
x2 – 16
x2 – 6x + 8
   =         
5. Simplify
x2
x + 1
   +  
x
x + 1
   =         
Section F5.2 - Algebraic Fractions and Quadratic Equations
6. The equation

x
x – 2
   –  
x
x + 2
   =  
4
3

can be wrritten in the form

x2 + ax + b = 0

where a and b are integers.

(a) What is the value of a?a =

(b) What is the value of b?b =

(c) Hence solve the original equation.x = or x =

7. Solve this equation

4
x
   +  
3
10 – x
   = 2

x = or x =

Section F5.3 - Algebraic Solution of Simultaneous Equations - One Linear and One Quadratic
8. Solve the simultaneous equations:

y = x2 – 4
y = 3x

x = and y =
or
x = and y =

9. Solve the simultaneous equations:

x + 2y = 2
x2 + 8y = 8

x = and y =
or
x = and y =


10.		 What is the number of points that the line y = 4 – x intersects the circle x2 + y2 = 22?
Number of points of intersection =

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Produced by Russell Geach for CIMT - May 2013