tutoring@otterbee.com, Chris

1

Facts to Memorize

Contents Imaginary Numbers ................................................................................................................................... 2

Divisibility Rules ........................................................................................................................................ 3

Squares to 400 .......................................................................................................................................... 4

Primes to 100 and Not Primes .................................................................................................................. 5

Odds and Evens ......................................................................................................................................... 6

Positives and Negatives ............................................................................................................................ 7

Order of Operations .................................................................................................................................. 8

Divide by Zero ........................................................................................................................................... 9

Triangle Types ......................................................................................................................................... 10

Triangle Properties .................................................................................................................................. 11

Pythagorean Theorem for Right Triangles .............................................................................................. 12

3D Pythagorean Theorem for Rectangular Solids ................................................................................... 13

Special Right Triangles: Look at Angles ................................................................................................... 14

Special Right Triangles: Look at Sides ..................................................................................................... 15

Circle Properties ...................................................................................................................................... 16

Circle Tangents ........................................................................................................................................ 17

Circles: Arc Length and Sector ................................................................................................................ 18

Circles: Inscribed vs. Circumscribed ........................................................................................................ 19

Perfect Square Factoring......................................................................................................................... 20

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2

Imaginary Numbers

is an imaginary number and will never appear on the test.

is a real number and might appear on the test.

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3

Divisibility Rules Divide by 2 Even number. Ends in 0,2,4,6, or 8.

Divide by 3 Digits added together can be divided by 3.

Divide by 4 Last 2 digits are divisible by 4.

Divide by 5 Ends in 0 or 5.

Divide by 6 Even number AND digits added together can be divided by 3.

Divide by 7 Just divide the number by 7.

Divide by 8 Last 3 digits are divisible by 8.

Divide by 9 Digits added together can be divided by 9.

Divide by 10 Ends in 0.

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4

Squares to 400

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5

Primes to 100 and Not Primes 2

3

5

7

11

13

17

19

23

29

31

37

41

43

47

53

59

61

67

71

73

79

83

89

97

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6

Odds and Evens No real need to memorize these. Just pick numbers.

Addition and Subtraction

Multiplication

Division: You will probably not see questions like these on the test.

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7

Positives and Negatives Addition

Subtraction

Multiplication

Division

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8

Order of Operations Parentheses

Exponent

Multiply and Divide

Add and Subtract

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9

Divide by Zero

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10

Triangle Types Equilateral Triangle: All 3 sides are equal.

Isosceles Triangle: 2 sides are equal.

Scalene Triangle: No sides are equal.

Right Triangle: 90o angle.

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11

Triangle Properties

Side 1

Base

Height

Angle 1 Angle 1

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12

Pythagorean Theorem for Right Triangles

Side 1

Sid

e 2

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13

3D Pythagorean Theorem for Rectangular Solids

Side 1

Sid

e 3

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14

Special Right Triangles: Look at Angles 30o-60o-90o Half of an Equilateral Triangle

45o-45o-90o Half of a Square

Side

Side

Sid

e 30O

60O 90O

90O

45O

45O

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15

Special Right Triangles: Look at Sides 3-4-5

5-12-13

Side * 4

Sid

e *

3

Sid

e *

5

Side * 12

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16

Circle Properties

Diameter

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17

Circle Tangents

90O

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18

Circles: Arc Length and Sector

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19

Circles: Inscribed vs. Circumscribed These circles are inscribed.

These circles circumscribe the other shapes.

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20

Perfect Square Factoring

1) ( )( ) ( )

2) ( )( ) ( )

3) ( )( ) NO

4) NO NO

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21

Quadrilaterals Quadrilateral: ANY four sided figure.

Trapezoid: A quadrilateral with two parallel sides.

Parallelograms: A trapezoid with opposite sides that are parallel and of equal length.

Rhombus: A parallelogram with ALL equal sides.

Rectangle: A parallelogram with 90O angles.

Square: A rhombus with 90O angles or a rectangle with ALL equal sides.

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22

Quadrilaterals

Rectangle

Square

Quadrilateral

Parallelogram

Trapezoid

Rhombus

Two parallel sides.

Opposite sides are parallel

and of equal length.

ALL sides are equal. ALL angles are 90O.

All sides are equal and

ALL angles are 90O.

ANY four sided figure.