Initial Diagnostic Audit - Unit B2: Number Classification and Bases

Do NOT use a calculator for any questions in the audit unless specifically told otherwise
Section B2.1 - Number Classification
1. Select all of the numbers below that are irrational numbers.
2
3
√
2
0.55
22
π
2. Select all of the numbers below that are recurring decimals.
1
11
1
10
1
9
1
8
1
7
3.
Write 0.375 as a rational number of the form  
m
   when n ≠ 0 and m and n are integers
n
with no common factors (except 1).

0.375 =   
  
4.
Given that a = 1 + 
√
2
   and b = 1 –  
√
2
 , is

(a) a + b rational or irrational?

(b) ab rational or irrational?

Section B2.2 - Binary Numbers
Convert the binary numbers to base 10.
5. 1111 =
6. 10101010 =
Convert the base 10 numbers to binary numbers.
7. 45 =
8. 1000 =
9. What is the difference between the base 10 number 11111 and the binary number 11111?
Give your answer in base 10.
Section B2.3 - Adding and Subtracting Binary Numbers

Calculate these binary number sums, giving your answers in binary.
10. 1111 + 1010 =
11. 1000 + 1000 + 1000 =
12. 1111 - 1010 =
13. 11000 - 1101 =
14. Below are 3 binary numbers. Add together the two smallest of these numbers.
101101       110000      100111
Give your answer in base 10.
Section B2.4 - Multiplying Binary Numbers

Calculate these binary numbers, giving your answers in binary.
15. 11 × 11 =
16. 1101 × 100 =
17. 10100 ÷ 10 =
18. 11(101 + 101) =
19. 1011(10001 – 1000) =
Section B2.5 - Other Bases

Convert each of the following numbers to base 10.
20. 454 in base 6 =
21. 1203 in base 5 =
Write each of the following base 10 numbers in the base stated.
22. 521 in base 4 =
23. 1000 in base 5 =
24. Carry out the following calculation in base 7
105 + 5
giving your answer in base 10.

Marking your audit and producing your report

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Produced by Russell Geach for CIMT - January 2013