Numbers And Operations

Question 1

Natural number

Answer 1

Greater than 0 and has no decimals or fractions attached.

Question 2

Whole number

Answer 2

Natural numbers and the number 0

Question 3

Integers

Answer 3

Positive and negative natural numbers and 0

Question 4

Rational number

Answer 4

Can be represented as a fraction.

Question 5

Irrational number

Answer 5

Cannot be represented as a fraction. Never ends or resolves into a repeating pattern.

Question 6

Real number

Answer 6

Can be represented by a point on a number line.

Question 7

Imaginary number

Answer 7

Imaginary numbers produce a negative value when squared.

Question 8

Complex number

Answer 8

All imaginary numbers are complex. Real numbers. A + Bi

Question 9

Factor

Answer 9

All numbers that can multiply together to make the number

Question 10

Composite number

Answer 10

More than two factors. Example: 6. Factors 1, 6, 3, 2

Question 11

Commutative property

Answer 11

An operation if order doesn’t matter when performing the operation

For example: (-2)(3) = (3)(-2)

Question 12

Associative property

Answer 12

An operation if elements can be regrouped without changing the result.

For example: -3 + (-5 + 4) = (-3 + -5) + 4

Question 13

Distributive property

Answer 13

A product of sums can be written as a sum of products.

For example: a(b+c) = ab + ac

Question 14

FOIL

Answer 14

First, Outer, Inner, Last

Useful way to remember the distributive property

Question 15

Identity element

Answer 15

The identity element for multiplication on real numbers is 1 (a x 1) = a

For addition is 0 (a + 0) = a

Question 16

Inverse element

Answer 16

Addition : -a because a + (-a)=0

Multiplication: 1/à because a*1/a=a

Question 17

Closed number system

Answer 17

An operation on two elements of the system results in another element of that system.

For example: integers during addition, multiplication, subtracting, but not division. Dividing two integers could result in a rational number that is not an integer.

Question 18

Conjugate

Answer 18

where you change the sign (+ to −, or − to +) in the middle of two terms.

Examples:
• from 3x + 1 to 3x − 1
• from 2z − 7 to 2z + 7
• from a − b to a + b

Question 19

Complex conjugate

Answer 19

the number with an equal real part and an imaginary part equal in magnitude but opposite in sign.

4+7i is 4 - 7i.

Question 20

Adding complex numbers

Answer 20

simply add the real parts and add the imaginary parts. For example:
(3+4i)+(6−10i)
= (3+6)+(4−10)i
= 9−6i

Question 21

Subtracting complex numbers

Answer 21

we simply subtract the real parts and subtract the imaginary parts. For example:
=(3+4i)−(6−10i)
=(3−6)+(4−(−10))i
=−3+14i
​

Question 22

Multiplying complex numbers

Answer 22

we perform a multiplication similar to how we expand the parentheses in binomial products:
(a+b)(c+d)=ac+ad+bc+bd

Unlike regular binomial multiplication, with complex numbers we also consider the fact that
i^2=−1

Question 23

2⋅(−3+4i)

Answer 23

2⋅(−3+4i)
=2⋅(−3)+2⋅4i
=−6+8i

Question 24

3i⋅(1−5i)

Answer 24

3i⋅(1−5i)
=3i⋅1+3i⋅(−5)i
=3i−15i ^2
=3i−15(−1)
=15+3i
​

Question 25

(2+3i)⋅(1−5i)

Answer 25

=2⋅1+2⋅(−5)i+3i⋅1+3i⋅(−5)i
=2−10i+3i−15i ^2
=2−7i−15(−1)
=17−7i

Question 26

Scientific notation

Answer 26

Learn how to add and subtract in scientific notation

Question 27

Absolute value

Answer 27

The distance the number is from zero

|-2| = 2

Question 28

metric system mnemonic device: King Henry Drinks Under Dark Chocolate Moon

Answer 28

Kilo
Hecto
Deca
Unit
Deci
Centi
Milli

Question 29

Factorial

Answer 29

N is denoted by n! and is equal to 1x2x3x4x….xn.

0! And 1! = 1

Question 30

Find the whole in a ratio

Answer 30

Add the values in the ratio

Ex: 2:3, whole is 5

Question 31

Proportion

Answer 31

An equation that states two ratios are equal

A/B = C/D where a and d terms are the extremes, and the b and c are the means

Question 32

Radicals

Answer 32

Expressed as b square root of a. B is callled the index and a is the radicand

Used to indicate inverse operation of an exponent: finding the base which can be raised to b to yield a.

For example, 3 square root 125 is equal to 5 because 5x5x5=125

Question 33

Matrix

Answer 33

Rectangular arrangement of numbers into rows (horizontal set of numbers) and columns (vertical set of numbers)

Question 34

Rows (matrix)

Answer 34

Horizontal set of numbers

Question 35

Columns (matrix)

Answer 35

Vertical set of numbers

Question 36

Square matrix

Answer 36

Same number of rows and columns

Question 37

Dimensions of a matrix

Answer 37

M x N

M= number of rows
N= number of columns

Question 38

Determinants of a matrix

Answer 38

Written as det(A) or |A| is a value calculated by manipulating elements of a square matrix.

Question 39

Identity matrices (I)

Answer 39

A square matrix with values of 1 forming a diagonal from the upper left corner to the bottom right corner; the rest of the elements are 0

Question 40

Inverse matrix (A ^-1)

Answer 40

A square matrix that, when multiplied by the original matrix, results in the identity matrix (A x A^-1 = 1)

Question 41

Arithmetic series

Answer 41

The sum of an artithmetic sequence

Question 42

Geometric series

Answer 42

The sum of geometric sequence

Question 43

Arithmetic growth

Answer 43

Constant growth, meaning that the difference between any one term in the series and the next consecutive term will be the same constant. This constant is called the common difference.

To list the terms in the sequence, one can just add or subtract the same number repeatedly.

Question 44

Recursive definition

Answer 44

Next term = current term + common difference

Question 45

Geometric sequence

Answer 45

Similar to an arithmetic sequence, but with multiplication instead of addition

Question 46

Converge (infinite geometric sequence)

Answer 46

If the infinite terms of the sequence add up to a finite number

Question 47

Diverge (infinite geometric sequence)

Answer 47

If the infinite terms of the sequence add up to an infinite number