## OCCT practice study guide

What is the definition of p.e.m.d.a.s? Parentheses, exponents, multiplication, division, addition, and subtraction.
How many pounds are in a ton? 2,000
How many feet are in a yard? 3
How many yards are in a mile? 1,760
How many faces does a triangular pyramid have? 5
How many vertices does a rectangular prism have? 8
How many edges does a cube have? 12
What is the definition of diameter? The distance across a circle through its center.
What is the definition of radius? The distance from the center of a circle to any point of the circle.
What is the definiition of area? The number of square units needed to cover a surface.
How do you find the perimiter? Add all of the sides togeather.
Kierstynn went the store to get apples, she bought 5 times 8 divided by 10 subtracted by 2. How many apples did she buy? Kierstynn bought 2 apples
What doespie stand for? 3.14

## OCCT pracice study guide

What is the definition of: formula? An equation that shows a relationship among certain quantities.
What is the formula for area of a rectangle? Length x Width.
What is the formula for volume of a cube? Length x Width x Height.
What is the definition of: angle? Two rays with a common point form an angle.
What is the tool used for measuring angles? A protractor.
What does an acute angle have to have to be acute? A measure of 0-89 degrees.
What does an obtuse angle have to have to be obtuse? A measure of 91-180 degrees.
What does a right angle have to have to be a right angle? A measure of exactly 90 degrees.
If two angles are exactly the same, what are they called? Congruent angles.
What is volume? The amount of space that a three-dimensional figure contains. Volume is measured in cubic units.
The volume of a square with measures: 5, 7, and 8 would be what? 280 cubic units.
What does perfect square mean? A number that is the square of an integer. For example, 25 is a perfect square since 25 = 5 to the second power.
What is the number that makes 64 a perfect square? 8 x 8 = 64, so, 8 is the number that makes 64 a perfect square.
What is a percent? A percent is a number expressed in relation to 100, represented by the symbol %.
What is 76% written as a fraction? 76/100. That will reduce down to 19/25.
What is 7 x 6(9+5)-12? 588.
In this pattern, what are the next 2 munbers? 76, 82, 83, 89, 90.. The next two numbers are 96, and 97.
How many quarts are in a gallon? 4 quarts = 1 gallon.
How many pints are in a quart? 2 pints = 1 quart.
How many cups are in a pint? 2 cups = 1 pint.

## CDFMS 7th Geo Vocab

Term Definition
complementary angles two angles with a sum of 90 degrees.
congruent two figures that have lengths and angle measurements of the same size
equilateral triangle a triangle that has all three sides congruent.
isosceles triangles triangles that have at least two congruent sides
parallelogram a figure that is a quadrilateral with both pairs of opposite sides parallel and opposite sides congruent
reflection a type of transformation involving a flip of the graphed figure
rhombus a quadrilateral that has opposite sides parallel, all four sides congruent, and not all angles equal
scalene triangle triangles that have no congruent sides
similar figures that have congruent corresponding angles and proportional corresponding sides
supplementary angles two angles with a sum that equals 180 degrees
transformation a change in position, size, or shape of a figure on a coordinate plane.
translation a type of transformation involving a slide of the graphed figure
trapezoid a quadrilateral with exactly one set of parallel sides
proportion an equation that states that two ratios are equal
corresponding angles have the same position in two different similar figures and are congruent
ratio a comparison of two numbers
corresponding sides have the same position in two different similar figures and are proportional
unit cost the cost for one unit of measure
cross products a method that can be used to determine if two ratios are equal

## Expressions and Equations vocabulary for 6th grade math

Term Definition
Addition Property of Equality If you add the same number to each side of an equation, the two sides remain equal. For any numbers a, b, and c, if a = b, then a + c = b + c. Example: If x = 3, then x + 5 = 3 + 5.
*Associative Property The way in which three numbers are grouped when they are added or multiplied does not change their sum or product.
Example:: (2 + 3) + 4 = 2 + (3 + 4) or (2 x 3) x 5 = 2 x (3 x 5)
coefficient The numerical factor of a term.
*Division Property of Equality If you divide each side of an equation by the same nonzero number, the two sides remain equal.
Division Property of Inequality When you divide each side of an inequality by a negative number, the inequality symbol must be reversed for the inequality to remain true.
equation A mathematical sentence stating that two expressions are equal.
Example: 3 x (7 + 8) = 9 x 5
*equivalent equation Equations that have the same solution.
Inequality An open sentence that uses symbols to compare two expressions with less than, greater than, less than or equal to, greater than or equal to.
*Multiplicative Property of Equality If you multiply each side of an equation by the same nonzero number, the two sides remain equal. For any numbers a, b, and c, if a = b, then a(c) = b(c). Example: If x = 3, then 5x = 3(5).
solution A replacement value for the variable in an open sentence. A value for the variable that makes an equation true. Example: The solution of 12 = x + 7 is 5.
Subtraction Property of Equality If you subtract the same nonzero number from each side of an equation, the two sides remain equal. For any numbers a, b, and c, if a = b, then a – c = b – c.
Example: if x = 3, then x – 2 = 3 – 2.
Multiplicative Property of Inequality When you multiply each side of an inequality by a negative number, the inequality symbol must be reversed for the inequality to remain true.
Addition Property of Inequality If you add the same number to each side of an inequality, the inequality remains true.
two-step equation An equation having two operations.
two-step inequality An inequality that contains two operations.

8 x 3
6 x 4
12 + 12
23 + 1
34 – 10
13 + 11
12 x 2
14 + 10
25 – 1
36 – 12
24 x 1
15 + 9
26 – 2
39 – 15
24/ 1
16 + 8
27 – 3
40 – 16
48/ 2
17 + 7
28 – 4
42 – 18
72/ 3
18 + 6
29 – 5
44 – 20
96/ 4
19 + 5
30 – 6
45 – 21
120/ 5
20 + 4
31 – 7
46 – 22
144/ 6
21 + 3
32 – 8
48 – 24
192/ 8
22 + 2
33 – 9

13 squared 169
2 cubed 8
3 cubed 27
4 cubed 64
5 cubed 125
6 cubed 216
7 cubed 343
8 cubed 512
9 cubed 729
10 cubed 10000

## Tips needed to solve complex numbers

How are a set of complex numbers defined when including the imaginary unit? the imaginary unit can written as i
what is the value of imaginary i when in squared form? when in form i squared is equal to -1
To multiply square roots what must we do first? to multiply square roots you must write each numerator in the form of the imaginary unit i
what is complex number standard form? a+bi
In the equation a+bi are a and b real numbers? yes
Complex numbers are equal when? a=c and b=d
Can(a+c) be added to (b-d) in a complex number equation? No, only (a+c) or (a-c) can be combined or subtracted because they are both real numbers. Only(b+d)or(b-d) can be combined or subtracted because they are alike in terms.
How should complex numbers be multiplied? they should be handled like binomials
What is used to divide complex numbers? Complex conjugates
what is form of complex numbers? (a+bi) or (a-bi)
What is (a+bi)(a-bi) when being treated as a binomial? a squared added to b squared
what is the main goal when dividing complex numbers? you want to eliminate the imaginary unit in the denominator.
How can division problems be checked? you can always see if you have the right answer by multiplying your products.

## Area

Term Definition
Base of a parallelogram This can be any one side.
Altitude Segment that is perpendicular to the base.
Height Length of the altitude.
Base of a triangle This can be any one side.
Height of a trapezoid Perpendicular distance between bases.
Radius of a regular polygon Distance from the center to a vertex.
Apothem Perpendicular distance from center to a side.
Semicircle Half Circle
Minor arc Smaller than a half circle.
Major arc Larger than a half circle.
Arc length Fraction of the circumference.

## Module 16 – Solving Quadratic Equations by Completing the Square

Solve the equation by completing the square
x^2+10x+22=0
To solve a quadratic equation by completing the square add a constant to both sides of the equation so that the remaining trinomial is a perfect square trinomial.
The coefficient of x^2 term of the quadratic equation must be equal to 1 in order to determine the constant to be added to both sides of the equation.
Is the leading coefficient equal to 1?

x^2+10x+22=0

yes or no?

If you answered yes, you are correct!! :))
Rewrite the equation with the constant by itself on the right side of the equation.
x^2+10x+22=0
Subtract 22 from both sides

X^2+10x=-22

Now take 1/2 of the numerical coefficient of the x-term and square it.
x term is equal to 10x
1/2* (10) = 5
now square it
(5)^2 = 25
Add the constant 25 to both sides of the equation to form a perfect square trinomial on the left side of the equation as the square of a binomial
x^2+10x=-22
Now add 25 to both sides…

x^2=10x=25=-22+25

Now factor the left side

x^2=10x=25=-22+25

It should look like this:

(x+5)^2= -22+25

Now, simplify the right side of the equation
(x+5)^2= -22+25
Which should look like this:

(x+5)^2= 3

The square root property is stated as…. If x^2=a where a is a real number then x=+/-va
Use the square root property. Remember that the value on the right can be positive or negative. Solve for x. (x+5)^2 = 3
x+5+=/-v3
x+5=v3 or x+5= -v3

x= -5+v3, -5-v3

Congrats you made it through!! ðŸ™‚

13×1 13
13×2 26
13×3 39
13×4 52
13×5 65
13×6 78
13×7 91
13×8 104
13×9 117
13×10 130
13×11 143
13×12 156
13×13 169
14×1 14
14×2 28
14×3 42
14×4 56
14×5 70
14×6 84
14×7 98
14×8 112
14×9 126
14×10 140
14×11 154
14×12 168
14×13 182
14×14 196
15×1 15
15×2 30
15×3 45
15×4 60
15×5 75
15×6 90
15×7 105
15×8 120
15×9 135
15×10 150
15×11 165
15×12 180
15×13 195
15×14 210
15×15 225