Math Emsat 1+2

Question 1

What’s a rational number?

Answer 1

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.

Question 2

Which numbers are rational numbers?

Answer 2

Whole numbers, such as 2
Terminating decimal numbers, such as 2.583
Recurring decimal numbers, such as 2.121212…
Perfect square/cube numbers

Question 3

Which numbers are irrational?

Answer 3

Non-terminating numbers, such as pi (3.14159…)
Non-perfect square/cube numbers

Question 4

Irrational no. + Irrational no. =

Answer 4

Irrational number

Question 5

Irrational no. + Rational no. =

Answer 5

Irrational no.

Question 6

Rational no. + Rational no. =

Answer 6

Rational number

I believe

Question 7

What are the two conditions that make an equation undefined?

Answer 7

1. Any number divided by 0, such as 2/0
2. Any square rooted negative number, such as sqrt-2

Question 8

How do you find out what value makes an quotient expression undefined?

Answer 8

Solve for x by making the denominator equal to zero

Question 9

What’s an example of a quadratic equation?

Answer 9

x^2+2x+2=0

Question 10

What’s an example of a cubic equation?

Answer 10

x^3+5x^2+x+8=0

Question 11

What’s an example of a linear equation?

Answer 11

3x-1=0

Question 12

What are the two ways to write (a+b)^2 ?

Answer 12

1. (a+b)(a+b) (Simplified)
2. a^2+2ab+b^2 (Expanded)

Question 13

What must you do when you are asked to solve/expand?

Answer 13

Find the value of a given number; solve all the way through is possible

Question 14

What must you do when you’re asked to simplify?

Answer 14

Do not solve all the way through; (a+b)(a+b)

Question 15

What are the two ways to write
(a-b)^2 ?

Answer 15

1. (a-b)(a-b) (Simplify)
2. a-2ab+b^2 (Solve/expand)

Question 16

How do you simplify a^2-b^2?

Answer 16

1. (a-b)(a+b)

There is no second way for expand/solve because it turns out to be the

same

Question 17

What do you do if you have a interchanged numnbers in the numerator and denimonator and want to cancel?

Answer 17

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!

Question 18

What’s an easy way to find the simplification of quotient polynomial question without solving? (Multiple choice)

Answer 18

Choose a number other than 0 or 1, plug it into the quotient polynomial, and save the answer. Then plug in the number into

Question 19

How do you solve for X on the calculator?

First way, when it doesn’t equal to 0

Answer 19

1. To type X on the calculator, press alpha, and press ‘)’
2. To type =, press alpha, then calc
3. To get the value of X, press shift, calc, then =

Question 20

What equations can be solved using the second calculator method?

Answer 20

Quadratic, cubic, and linear equations

Question 21

How do you solve using the second calculator method?

When X=0 or you can make it as so.

Answer 21

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)

Question 22

How do you factor to find the zeros?

Answer 22

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!

Question 23

What’s an integer?

Answer 23

A whole number (a number that isn’t a fraction)

Question 24

What does this expression become?
-(4x^3+5x-6)

Answer 24

-4x^3-5x+6

Question 25

What are the three universal polynomial identities?

Answer 25

1. (a+b)^2 = (a+b)(a+b) <- Simplify
   a^2+ab+b^2 <- Expand
2. (a-b)^2 = (a-b)(a-b) <- Simplify
   a^-2ab+b^2 <- Expand
3. a^2+b^2 = (a+b)(a-b)

Question 26

Solve no. 2 of Chapter 2

Notes

Answer 26

Answer: a

Question 27

How do you solve no. 2 of Ch 2 normally?

Answer 27

1. Use the universal identities to simplify the numerator and denominator
2. Multiply one of the four parts by -1 in order to switch the positions of its numbers
3. Cancel what you can and use the same method to get rid of the -1
4. Choose answer