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.