Math Unit 1 test/ chapter review

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words, equations, tables, and graphs

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ordered pairs and relations

Commutative properties

words The order in which numbers are added or multiplied does not change the sum or product. symbols For any numbers a and b, a+b=b+a For any numbers a and b, a*b=b*a Examples 6+9=9+6 4*7=7*4 15=15 28=28

Algebraic Espression

3 + c words three dollars more than the cost of a sandwich. ( when it says THAN you need to flip the expression) Variable Let c represent the cost of a sandwich Expression c+3

Antonia bought a video game system for $323.96. She paid in 12 equal installments. About how much did she pay.

323.96/12=29.99. Antonia paid $29.99 for each payment.

Evaluate each expression if r=1, s=5, and t=8

6s+2t=46 r+(40-3t)=7 6*5+2*8 1+(40-3*8) 30+2*8 1+(40-24) 30+16 1+6 46 7

Equation

An equation always contains an equal sign. For example, 60t is an expression, but d=60t is an equation

Where numbers go on a graph.

If you had a number like (1 , 7) then the 1 would go onto the x axis and the 7 would go one the y axis.

Algebra

It's a branch of mathematics that uses symbols. A variable is often used in algebra. A variable is a letter or symbol used to represent an unknown value. Any letter can be used as a variable.

A Plan For problem solving: Understand

Know what the problem is asking you, Ask "What facts do I know?", Ask,"what do I need to find out?", and Ask "is there enough information to solve the problem? Is there extra information?"

A Plan For Problem Solving: Plan

Reread the problem to identify relevant facts, Determine how the facts relate to one another, Make a plan a choose a strategy for solving it, Estimate what you think the answer should be.

A Plan For Problem Solving: Check

Reread the problem. Is there another why to solve it?, Examine your answer carefully,If your answer is not reasonable, make a new plan and solve the problem another way.

The gas tank of Tyrell,s truck holds 19.8 gallons. When the tank is empty, Tyrell fills it with gas that costs $3.65 per gallon. About how much will it cost to fill the tank?

So if it's $3.65 per gallon you would need to do 19.8 times 3.65 because there is 19.8 gallons and 1 gallon would cost $3.65 so he would pay $72.27 if he needed to fill his tank all the way back up.

Domain and Range

So the Domain is also known as the x axis and the x axis goes horizontal. And the Range is also known as the y axis and the y axis is vertical.

Number Properties

additive identity Words: When 0is added to any number, the sum is the number Symbols: For any number a, a+0=0+a=a Examples: 5+0=5 0+5+5 Multiplicative identity Words: When any number is multiplied by 1, the product is the number. Symbols: For any number a, a*1=1*a=a Examples: 8*1=8 1*8=8 Multiplicative property of zero Words When any number is multiplied by 0, the product is 0 symbols: For any number a, a*0=0*a=0 Examples: 3*0=0 0*3=0

5[11-(7+5)/4]

first you do 7+5=12 then do 12/4=3 then 11-3=8 last 5[8]=40. So the answer is 40 5[11-(7+5)/4] 5[11-12/4] 5[11-3] 5[8] 40

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Variables and expressions

Naming properties

(2 * 8) * 5 = 2 * (8 * 5) assoc. Prop. of * 4 + (9 + 2) = (4 + 9) +2 assoc. Prop. of + 5k * 1 = 5k Mult. Ident.

properties

(9 + 7) + 3 = 3 + (9 + 7) Comm. Prop of +

Translating a phrase into a algebraic expression

24 / s twenty-four pieces of candy divided among some students. 24/s 12 f the number of inches in any number of feet 12f

60-15 ------ 2+7

60-15=45 45 ------- ------ =5 2+7=9 9

Describe the graph of all possible points, (x,y) if y=0

All of the number would be on the x axis.

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Properties of numbers

Test Form 3A

Test review sheet

A Plan For Problem Solving: Solve

Use your plan to solve the problem, If your plan doesn't work, revise it or make a new plan.

ordered pairs

in mathematics, a coordinate system or coordinate plane is used to locate points. The coordinate system is formed by the intersection of two number lines that meet at right angles at their zero points. An ordered pair of numbers is used to locate any point on a coordinate plane. The first number is called the x-coordinate, and the second number is called the y-coordinate.

Associative property

words the way in which numbers are grouped when added or multiplied does not change the sum or product. symbols For any numbers a,b,and c, (a+b)+c=a+(b+c) For any numbers a,b,and c (a*b)*c=a*(b*c) Examples (3+6)+1=3+(6+1) (5*9)*2=5*(9*2) 9+1=3+7 42*2=5*18 10=10 90=90

Jenna picked the game card shown. Make a table for four different domain values and write and algebraic expression for the rule. Then state the domain and range of the relation.

x 3n-1 y D: {3,6,8,9} The rule is 3n-1 R: {8,17,23,26} 3 3*3-1 8 6 3*6-1 17 8 3*8-1 23 9 3*9-1 26

The Planet Mercury takes 56.6 Earth days to rotate once about its axis. About how many times do it rotate about its axis during one Earth year?

I year is 365 days then you need to that divide by 56.6 because that's how many Earth days it it takes to go around its axis so you would go around its axis about 6 times because you also need to estimate instead of giving an exact answer.

Each ticket at the school musical costs $8

Number of total D: {4,7,9,12} tickets cost ($) R: {32,56,72,96} 4 32 7 56 9 72 12 96

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Plan For Problem Solving

Rectangle ABCD has vertices A(3 , 2), B(5, 2) C(5, 2). What are the coordinates of point D?

So you would draw a graph and put all of the points on the graph you know and to find the last one you need to put the point on the graph where it completes it and connects the rest of them to make a Rectangle.

Order of Operations

Step 1: Simplify the expressions inside grouping symbols. Step 2: Multiply and/or divide in order from left to right Step 3: Add and/or subtract in order from left to right

Variables

The letter x is often used as a variable. 5m means 5*m ab means a*b y -- means y/3 3

A birthday party at the skating rink costs $45 to reserve a party area and $4.50 per guest for skating and skate rental. How much will a party cost if you invite: a. 5 guests b. 9 guests c. 25 guests

a. 5 guests= 45+(4.50x5)=$67.50 b. 9 guests= 45+(4.50x9)=$85.50 c. 25 guests= 45+(4.50x25)=$157.50

Subsitition Property of Equality

Words If two quantities are equal, than one quantity can be replaced by the other symbols For all numbers a and b, if a=b, then a may be replaced by b

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Words and Expresions

Multiple representations

Words, equations, tables, and graphs can be used to represent relations. An equation is a mathematical sentence stating that two quantities are equal. Relations are often written as equations with two variables--one to represent domain values and one to represent range values.

Express {(2,4), (0,3), (1,4), (1,1)} as a table.

X: 2 0 1 1 D: {2, 0, 1, 1} Y: 4 3 4 1 R: {4, 3, 4, 1}

To evaluate and expression

You find its numerical value. If an expression has more than one operation, use the order of operations. The order of operations are the rules to follow when evaluating an expression with more than one operation. These rules ensure that numerical expressions have only one value.

The total amount of money if you have nine dollars and twelve dollars

You would do 9+12 because total means to add and in the problem the numbers are 9 and 12.

Numerical expresions

contain a combination of numbers and operations such as addition, subtraction, multiplication, and division.