MYP Standard Mathematics 1.6 Absolute Value Questionbank

For any non-zero real number ${x}$, simplify the following expression:

A swimming pool manager maintains the pH level of the water at a target of $7.4$. An automated alarm is triggered if the absolute difference between the actual pH and the target is strictly greater than $0.2$. Which of the following pH levels will trigger the alarm?

Fill in the blank: For any real numbers $a$ and $b$, the identity property for multiplication is $|ab| = \_\_\_\_\_\_$.

Using the piecewise definition of absolute value, rewrite the function $f(x) = |x - 10|$ specifically for the domain where ${x < 10}$.

Simplify the expression:

$3x^2$

3x

3|x|

-3x

7.30

7.25

7.59

7.61

$|a||b|$

$|a| + |b|$

$-|ab|$

$(ab)^2$

x - 10

10 - x

-x - 10

x + 10

$-6|b^4|$

$6|b|$

$6b^4$

$-6b^4$