Initial Diagnostic Audit - Unit F2: Algebraic Concepts
Section F2.1 - Simplifying Expressions

Simplify each of the expressions below.
1.
4a + 5a – 2a =         
2.
3a – b – 4a + 4b =         
Remove the brackets from each of these expressions.
3.
2(3x – 4) =         
4.
x(x + 1) =         
5. Simplify
2(3x – 4y) – 3(x + 5y) =         
Section F2.2 - Simple Equations

Solve each of the following equations for x.
6. x + 7 = 9      x =
7. 3x = 36      x =
8.
x
 = 5      x =
4
9. x – 12 = -4      x =
10. 7x = -21      x =
Section F2.3 - Solving Linear Equations
11. 2x + 7 = 13      x =
12. 4x - 5 = 19      x =
13.
x
  – 4 = 5      x =
3
14. 3(x – 1) = 21      x =
15. 4x – 2 = 8 – 6x      x =
Section F2.4 - Algebraic Manipulation

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

Make x the subject of each of the following formula, where a, b and c are constants.
16.
2x + a = x – b             
17.
3(x – a) = 2(b + x)             
18.
ax – c = 3x + b   (a 3)             
19.
a =  
3x
b – x
   (a -3)             
20.
x
a
   =  
x + b
c
   (a c)             
Section F2.5 - Algebraic Fractions

When completing this section, use fractions and conventional algebraic notation to avoid using × and ÷ symbols in your answers
21.
Express  
x
3
   +  
x
6
   as a single fraction.             
22.
Express  
5y
7
   +  
8y
7
   as a single fraction.          
23.
Express  
2
x
   +  
1
x + 1
   as a single fraction.          
24. Combine the fractions below into a single fraction.

5
x – 2
   –  
1
x
    =          
25. Simplify the expressions below, giving your answer as a single fraction.

3
2x – 1
   +  
4
3x – 1
    =          

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Produced by Russell Geach for CIMT - April 2013