Math Emsat 1+2 Flashcards
What’s a rational number?
A rational number is a number that is expressed as the ratio of two integers, where the denominator should not be equal to zero.
An integer is a whole number.
Which numbers are rational numbers?
Whole numbers, such as 2
Terminating decimal numbers, such as 2.583
Recurring decimal numbers, such as 2.121212…
Perfect square/cube numbers
Which numbers are irrational?
Non-terminating numbers, such as pi (3.14159…)
Non-perfect square/cube numbers
Irrational no. + Irrational no. =
Irrational number
Irrational no. + Rational no. =
Irrational no.
Rational no. + Rational no. =
Rational number
I believe
What are the two conditions that make an equation undefined?
- Any number divided by 0, such as 2/0
- Any square rooted negative number, such as sqrt-2
How do you find out what value makes an quotient expression undefined?
Solve for x by making the denominator equal to zero
What’s an example of a quadratic equation?
x^2+2x+2=0
What’s an example of a cubic equation?
x^3+5x^2+x+8=0
What’s an example of a linear equation?
3x-1=0
What are the two ways to write (a+b)^2 ?
- (a+b)(a+b) (Simplified)
- a^2+2ab+b^2 (Expanded)
What must you do when you are asked to solve/expand?
Find the value of a given number; solve all the way through is possible
What must you do when you’re asked to simplify?
Do not solve all the way through; (a+b)(a+b)
What are the two ways to write
(a-b)^2 ?
- (a-b)(a-b) (Simplify)
- a-2ab+b^2 (Solve/expand)
How do you simplify a^2-b^2?
- (a-b)(a+b)
There is no second way for expand/solve because it turns out to be the
same
What do you do if you have a interchanged numnbers in the numerator and denimonator and want to cancel?
Choose one of the exchanged numbers, either denominator or numerator and multiply it by -1. That changes their places.
Ex: (x-4)/(4-x) -> -1(4-x)/(4-x)
The places change but the signs don’t!
What’s an easy way to find the simplification of quotient polynomial question without solving? (Multiple choice)
Choose a number other than 0 or 1, plug it into the quotient polynomial, and save the answer. Then plug in the number into
How do you solve for X on the calculator?
First way, when it doesn’t equal to 0
- To type X on the calculator, press alpha, and press ‘)’
- To type =, press alpha, then calc
- To get the value of X, press shift, calc, then =
What equations can be solved using the second calculator method?
Quadratic, cubic, and linear equations
How do you solve using the second calculator method?
When X=0 or you can make it as so.
Alpha mode 5, select the polynomial, enter the values without X but with their respective signs, simplify the answer if necessary (don’t forget to check S->D for)
How do you factor to find the zeros?
Find the X’s by using the calc (Shift, Mode, 5, 1-4), then make each X equal to zero and move the zero to the other side. Then find the answer that matches what you got.
You can skip the factoring step… just look at the numbers!
What’s an integer?
A whole number (a number that isn’t a fraction)
What does this expression become?
-(4x^3+5x-6)
-4x^3-5x+6
