Question | Answer |
---|---|

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

Question | Answer |
---|---|

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. |

## Facts to help with 24 game

Question | Answer |
---|---|

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 |

## perfect square roots

Question | Answer |
---|---|

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

Question | Answer |
---|---|

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

Question | Answer |
---|---|

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™‚ |

## Multiplication Facts 13’s, 14’s, 15’s

Question | Answer |
---|---|

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 |