Absolute value: math exercises in 2nd grade corrected in PDF.

The absolute value of a number allows us to consider a number without taking into account its sign. More precisely, if a number x is positive, then the absolute value of x is x. However, if x is negative, then the absolute value of x is its opposite, i.e. -x. With second grade math exercises on absolute value, you will develop new skills.

Exercise series on absolute value

Exercise 1:

Solve in the following equations and inequations:

a) | 2 – x | < 4

b) | 6 – 2 x | = 3

c) | x + 2 | > 3

d) | x + 2 | < | x + 3 |

e) | x3 – 1 | + p > 0

f) 3 < | x + 2 | < 4

g) | 4 – 12 x + 9 | = 4

h) | 3 x + 1 | + | 1 – x | > 3

i) | 1 + | =2x

Exercise 2:


a) %7C-4%7C b) %7C3,8%7C c) %7C-\frac{100}{3}%7C

d) %7C5-6%7C e) %7C\sqrt{17}-2%7C f) %7C2-\sqrt{17}%7C

Exercise 3:

Without a calculator, simplify :

a) %7C4%7C+%7C-3%7C b) %7C1,2%7C-%7C-1,2%7C

c) \frac{%7C5-8%7C-3}{2} d) 2%7C4-10%7C+%7C7-5%7C

Exercise 4:

1.a) On a graduated line, place the numbers 5 and \frac{1}{3}.

b) Calculate the distance between 5 and \frac{1}{3}.

2. Repeat question 1. with 3 and -\frac{4}{5}.

3. Repeat question 1. with -1 and -\frac{4}{5}.

Exercise 5:

Using an absolute value, write the distance between :

a) \frac{125}{3} and 2. b) \sqrt{2} and 5

c) – 5 and \frac{12}{5} d) \pi and 4

Exercise 6:

without calculator, simplify :

a) %7C5-\pi%7C b) %7C8-\frac{2}{3}%7C c) %7C2-\frac{9}{2}%7C

d) %7C-1-8%7C e) %7C-5-\pi%7C f) %7C\frac{1}{2}+6%7C

Exercise 7:

In the same way that %7Cx-3%7C represents the distance between the real number x and 3,

express in terms of distance :

a) %7Cx-100%7C b) %7Cx-\frac{1}{3}%7C

c) %7Cx+5%7C d) %7C1,35,-x%7C

e) %7C-7-x%7C f) %7C\pi-x%7C

Exercise 8:

Determine the set, in interval form, of real numbers x verifying :

a) %7C%7Cx-10%7C\leq\,\,1 b) %7Cx-2,5%7C\leq\,\,0,2 c) %7Cx-\frac{1}{2}%7C\leq\,\,\frac{5}{2}

Exercise 9:

Consider an interval [a ; b] with a and b two real numbers.

The center of the interval [a ; b] is the number c=\frac{a+b}{2}
and radius of the interval [a ; b] the number r=\frac{b-a}{2}.
Graphically, we have :
Absolute value

1. a) Calculate the center and radius of [2; 6].

b) Translate |x – 4| in terms of the distance between two real numbers.
c) Copy and complete: x\in%5B2;6%5D\Leftrightarrow\,%7Cx-4%7C\leq\,\,...

2. In the same way, copy and complete :
a) x\in%5B1;25%5D\Leftrightarrow\,%7Cx-13%7C\leq\,\,....
b) x\in%5B6;20%5D\Leftrightarrow\,%7Cx-...%7C\leq\,\,...
c) x\in%5B1,2;3%5D\Leftrightarrow\,%7Cx-...%7C\leq\,\,...

Exercise 10:

Write an inequality verified by x and using an absolute value in the following cases.

a) x\in\,%5B-4;5%5D b) x\in\,%5B0;1,1%5D a) x\in\,%5B\,\frac{1}{3};\frac{2}{3}%5D

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