Course 3 Math, Trimester 1 Benchmark Study Guide

Solve: -3(2x + 1) = -4x - 6 - 18x - 12

-15/16

Change to Scientific notation: (3.2x10^4)*(4x10^6)

1.28x10^11 (You multiply the numbers, getting 12.8, you multiply the ten powers getting 10^10 then you convert it back into Scientific notation by moving the decimal to the left 1 place value)

When dividing exponential #s with the same base, you subtract the exponents.

2^5/2^7 =2^(5-7)=2^(-2)

(4 x^4 y^2)^3

4^3 x^(4 times 3) y^(2 times 3) = 64 x^12 y^6

In scientific notation, large numbers get positive exponents with the ten power and itty bitty numbers get negative exponents with the ten power.

60,000 = 6x(10^4) , 0.006 = 6x10^(-3)

Rational Number

A number that can be written as a fraction, decimal or repeating decimal. Square roots are rational if the number being square rooted is a square number.

What does it mean for an equation to have infinite solutions?

Any x value will work, an equation equal to itself or a number equal to itself and is TRUE will be expected as the answer such as: 2x + 3 = 2x + 3, or 4 = 4, or 0 = 0.

A linear equation with no solution should have a variable on each side (the same letter), and when you move the variables to the same side (using addition or subtraction) the variables will___________________

Cancel out or add to zero, leaving us with numbers that are different on each side.

When solving equations you should first:

Distribute and combine like terms on each side of the equal sign.

When asked "How many times greater is...?" you will be using what operation to solve?

Division

2^(-1) gives you a negative number, true or false?

False, negative exponents change expressions to fractions, they do not make a positive into a negative or a negative into a positive.

Negative exponents always represent a:

Fraction

When you solve a square root equation you get a positive and a negative.

Given the equation x^2 = 49, when you square root both sides, the answers of x = 7 and x = -7 are both expected.

When you cube root a cubic equation you only get one solution.

If x^3 = 8 then x = 2, if y^3 = -27, then y = -3.

Square root of 3, Rational or irrational?

Not rational, 3 is not a square number from our list.

Square root of 25, rational or irrational?

Rational, 25 is a square number and the square root of 25 is 5. Since 5 is a whole number it also is rational.

Equivalent equations have the same _________________

Solution. You have to solve both equations and the solutions that match are equivalent equations.

What is the first step in solving this equation? 2 - 4x = 9

Subtract 2 from both sides: solution is -7/4 or -1 & 3/4

Estimating the square root of 27.

The square numbers surrounding 27 are 25 and 36. The square root of 25 is 5 and the square root of 36 is 6. Since 27 is in between 25 and 36, the square root of 27 is between 5 and 6.

What does it mean for an equation to have no solution?

There is no value for x which will check correctly with the answer. An answer that doesn't make any sense and is FALSE such as 4 = 5, -6 = 2, or 0 = 8 would give you an answer of no solution.

How do you square root a fraction?

You square root the numerator and then the denominator, then simplify any fraction left.