2: Decimals

Question 1

Place value

Answer 1

Depends on its location within the number (Ex. Units, tens, hundreds, thousands)

Question 2

10^0

Answer 2

1 (Ones)

Question 3

10^-1

Answer 3

0.1 (Tenths)

Question 4

How to multiply decimals

Answer 4

Count all the digits to the right of the decimal point - then multiply normally, ignoring the decimals. Put the same number of decimal places in the product.

Question 5

Absolute Value

Answer 5

The POSITIVE value of the expression within the absolute value brackets. Inside the brackets can be positive or negative but the absolute value is always positive.

Question 6

What are the three guessing strategies?

Answer 6

1) Identical twins (Both answers simplify to the same thing so either or is sufficient or neither are)
2) Cannibal (One statement completely incorporates the other)
3) C-Trap (Then don’t answer C or E)

Question 7

0 Exponent (Raised to any power)

Answer 7

0 raised to any power equals 0

Question 8

1 Exponent (Raised to any power)

Answer 8

1 raised to any power equals 1

Question 9

(-1)^Odd

Answer 9

Any negative number to the power of an odd number will be a NEGATIVE number

Question 10

(-1)^Even

Answer 10

Any negative number to the power of an even number will be a POSITIVE number

Question 11

Base fraction negative (-) Exponent

Answer 11

If the base fraction is negative, then raising it to either an even or odd power makes the fraction LARGER

Raising to an even power turns the fraction positive (Positive fraction is larger than a negative one)

When raising negative base to an odd power it actually becomes less negative or closer to 0

Question 12

What does a negative exponent mean?

Answer 12

General rule: Something with a negative exponent is just “one over” the same thing with a positive exponent.

Question 13

How many solutions in x^2

Answer 13

2 - Positive and negative

Question 14

How many solutions in the square root of x

Answer 14

1 - You can only square root a positive number therefore, x must be positive. Although if you take the square root of an equation with a squared variable than you would get positive and negative……

Question 15

When to Test Cases

Answer 15

Data sufficiency (When the problem allows multiple possible values for the unknowns - Try to get different answers)

Problem solving (When the program asks a must be or could be question)

Question 16

When to Choose Smart Numbers

Answer 16

Problem solving only

The variable expression or relative values. The problem never gives real numbers.

Question 17

When to Work Backwards

Answer 17

Problem solving only

Real numbers in the answers that you can try