SAT SUBJECT TEST MATH LEVEL 1
TOPICS IN ARITHMETIC
The absolute value of a number a, denoted |a|, is the distance between a and 0 on the number line. Since 4 is 4 units to the right of 0 on the number line and –4 is 4 units to the left of 0, both have an absolute value of 4:
• |4| = 4
• |–4| = 4
Since 4 and –4 are the only numbers that are 4 units from 0, if |x| = 4, then x = 4 or x = –4. If |x| < 4, then x is less than 4 units from 0, which means –4 < x < 4. If |x| > 4, then x is more than 4 units from 0, which means either that x < –4 or x > 4.
The absolute value of a number is never negative.
Key Fact A2
If b is a positive number, then
These results are displayed graphically on the three number lines below.
|x| = b
|x| < b
|x| > b
Given any two numbers x and y, you can always find their sum (x + y), difference (x – y), product (xy), and quotient (x y)—with your calculator, whenever necessary—except that you may never divide by zero. For example, 4 0 is meaningless. If you attempt to divide by 0 on your calculator, you will get an error message.