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mathematics UK Year 10 Mathematics (KS4)
 
Solved problems for the chapter:
 

Numbers and number lines

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Detailed solution steps are available at:
 
https://en.openprof.com/wb/chapter:numbers_and_number_lines/3542/


Example 1.
Determine the correctness of the statement.

    
Example 2.
Determine the correctness of the statement.

    
3.
Determine the correctness of the statement.

    
4.
Determine the correctness of the statement.

    
5.
Determine the correctness of the statement.

    
6.
Indicate the order of calculation in parentheses in the given statement.

    
7.

Write out the sets of the intervals below and present it on a number line:


    
8.

Write out the sets of the intervals below and present it on a number line:


    

9.

Write out the set of the interval below and present it on a number line:


    
10.

Write out the sets of the interval below and present it on a number line:


    
11.

Write down the sets of all non-negative real numbers less than and present it on a number line.

    
12.

Given that set A includes set of real numbers less than , and set B includes the set of negative real numbers greater than :


  • Write out the intervals of each of the given set and represent each of them on a number line.


  • Write out the union and the intersection of the sets A and B and present them on a number line.


  • Write out the intervals of sets of A-B and B-A.

    
13.

Write out the intersection of the intervals below:


    
14.

Write out the intersection of the intervals below:


    
15.

Write out the intersection of the intervals below:


    
16.

Write out the intersection of the intervals below:


    
17.

Write out the union of the intervals below:


    
18.

Write out the union of the intervals below:


    

19.

Write out the union of the intervals below:


    
20.

Write out the union of the intervals bellows:


    
21.

Write out the union of the interval below:


    
22.

Draw a point on the number line that represents the number .

    
23.

Draw a point on the number line that represents the number .

    
24.

Draw a point on the number line that represents the number .

    
25.

Draw a point on the number line that represents the number .

    
26.

Draw a point on the number line that represents the number .

    
27.

Draw a point on the number line that represents the number .

    
28.

Draw a point on the number line that represents the number .

    

29.

State whether each of the following statements are correct or incorrect?


  • - 2 is a natural number.


  • is a real number.


  • is an irrational number.


  • is a rational number.

    
30.

Is Andreana right when he says, "On a number line, we always draw the smaller number to the left of the larger one."

    
31.

Draw a diagram of subsets of real numbers and insert the numbers below in the appropriate subset.


    
32.

Arrange the given numbers in ascending order and show them on the number line.


    
33.

Write down the additive inverse of the numbers below and illustrates them on the number line.


    
34.

Calculate the absolute values ​​of the following numbers: