Intervals and sets of numbers: corrected math exercises in 2nd grade.

The math exercises on intervals and sets of numbers in the second grade are important. To fully understand this chapter, you need to do regular exercises. Thus, intervals are sets of numbers. An interval can be defined using absolute values to specify the lower and upper limits of the interval.

Exercise series on Intervals and sets of numbers

Exercise 1:

Copy and complete the table below:

Statement

Interval

Graphical representation

-1\leq\,\,x<3 x \in
4>x>0 x \in
-7\geq\,\,x>\,-8 x \in
x\in\,\mathbb{R}^+ x \in
x\neq\,5 x \in

Exercise 2:

Translate into interval form :

1) y > – 3 and y < 4 2) y > – 3 or y < 4

3) y\leq\,\,\frac{1}{3} and y\leq\,\,\frac{1}{2} 4) y\leq\,\,\frac{1}{3} or y\leq\,\,\frac{1}{2}

Exercise 3:

Complete with the symbols \in or \notin:

1) 7 … ] 0 ; 7 [

2) 5,9 … ] 5,8 ; +∞ [

3) – 0,25 … ] – 0,3 ; – 0,2 [ … ] 1 ; 2 ]

4) – 0,199 … ] – 0,2 ; – 0,19 [

5) \pi…. [ 3,14 ; 3,141 [

Exercise 4:

True or false?

1) If x ∈ [ 6.7 ; +∞ [ then x ∈ [ 6 ; +∞ [.

2) If x ∈ ] – 3 ; 4 [ then x ∈ [ – 2 ; 5 [.

3) If x ∉ [ – 5 ; 2[ then x ∈ ] -\infty; – 3 [ ∪ [ 2 ; +∞[.

4) The interval ] 0 ; 4[ is included in [ 0 ; 4 [.

5) \mathbb{N}\,\subset\,\mathbb{Q}^+.

6) If x\,\notin\,\mathbb{Q} then x\,\notin\,D.

Exercise 5:

Simplify the following notations where possible.
A = [ – 5 ; 7[ ∪ [ – 2 ; 12 [
B = [ 0 ; +∞ [ ∪ ] – 2 ; +∞ [
C = ] -∞ ; 0 [ ∪ [ 0 ; +∞ [
D = ] -∞ ; 4/3 [ ∩ [ – 10 ; 10 ]
E = [ – 4 ; [ ∪ ] \frac{1}{2}; 10]

Exercise 6:

Plot I and J on a graduated line, then determine I ∩ J and I ∪ J.

1) I = [ 2 ; 5.5 ] and J = ] 1 ; 3 ].

2) I = [ – 1 ; +∞ [ and J = ] -2 ; 3 ].

3) I = ] – 1 ; 3 ] and J = [ – \sqrt{2}; \pi ].

4) I\,=\,\mathbb{R}^- and J\,=\,\mathbb{R}^+.

5) I = {1 ; 2 ; 3 ; 4} and J = [ – 5 ; 5 ].

Exercise 7:

We consider graduated lines on which we have marked sets of numbers.

Give the corresponding interval.

Interval and set of numbers

Exercise 8:

Represent on a graduated line and describe, using an interval, each set of real numbers x such that :

a) 0\leq\,\,x\leq\,\,3 b) -2<x<1

c) x\leq\,\,9 d) x>-3,5

Exercise 9:

Represent on a graduated line each of the following intervals.

a) %5D1,6%5D b) %5B-0,5;3,2%5D

c) %5D-\infty;2%5D d) %5B0;+\infty%5B

Exercise 10:

Write the inequalities verified by the reals x for each of the following cases.

a) x\in%5B0;1,2%5D b) x\in%5D-\frac{5}{3};3%5D

c) x\in%5B4,73;+\infty%5B d) x\in\,%5D-\infty;0%5B

Exercise 11:

Copy and complete with the signs \in and \notin.

a) 1,4...%5B0;7%5D b) -\pi...%5D-3;-1%5B

c) 6...%5B\frac{7}{3};+\infty%5B d) -3...\,%5D-\infty;-3,5%5B

Exercise 12:

Without a calculator, tell if \frac{2}{3} belongs to the following intervals.

a) %5B0;\frac{4}{5}%5D b) %5B\frac{3}{5};1%5D c) %5B\frac{1}{3};\frac{2}{5}%5D

Exercise 13:

Let I=%5B-6;8%5D and J=%5D2;100%5B.

Say whether each of the following numbers belongs to I, J, I\cap\,J, I\cup\,J.

a) – 10 b) – 6 c) – 0,5 d) 2

e) 8,1 f) 99,9 g) 1 000 h) 0

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