7th Math Final Review

7th Math Final Review

By Dijonnae Robinson

The real number system flows upward. A natural number is also a whole number. integer, and rational number. A Rational Number is not always an integer, whole number or natural number. ​

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Unit 1: Just Be Rational

Real Number System

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Multiple Choice

Which Venn Diagram best represents the relationship among integers, natural numbers, rational numbers, and whole numbers? 

• F

• G

• H

• J

Numbers that are in the opposite position on the number line are opposite numbers.

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The distance a number is from 0 on a number line is the absolute value. Remember distance can never be negative. So your absolute value will also be positive.​

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Unit 1: Just Be Rational

Opposite Numbers & Absolute Value

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Multiple Choice

What is the opposite of 4?

• -4

• $$\frac{1}{4}$$  

• 4

• $$-\frac{1}{4}$$  

Multiple Choice

What is the absolute value of 4?

• -4

• $$\frac{1}{4}$$  

• 4

• $$-\frac{1}{4}$$  

​To simplify rationals you need to first identify the largest number that divides both the numerator and denominator (Greatest Common Factor) then divided both the numerator and denominator by the GCF to arrive at the lowest term.

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You can also repeatedly divide the numerator and denominator by 2, 3, or 5 until the numerator and denominator have no other factors in common other than 1. ​

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Unit 1: Just Be Rational

Simplifying Fractions​

Multiple Choice

What is $$\frac{8}{12}$$  in its most reduced term

• $$\frac{8}{12}$$  

• $$\frac{4}{6}$$  

• $$\frac{2}{3}$$  

To convert a rational to a mixed number First divide the numerator by the denominator. Then write down the whole number answer and finally write down the remainder above the denominator. ​

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Unit 1: Just Be Rational

Converting An Improper Fraction to a Mixed Number

Multiple Choice

Which answer represents $$\frac{7}{4}$$  as a mixed number?

• $$1\frac{3}{4}$$  

• $$2\frac{1}{4}$$  

• $$1\frac{1}{2}$$  

​To convert a mixed number to a rational first multiply the denominator by the whole number. Then add the answer to the numerator. Finally, write down the answer over the denominator. ​

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Unit 1: Just Be Rational

Converting An Mixed Number to An Improper Fraction

Multiple Choice

Which rational represents $$4\frac{2}{5}$$  ?

• $$\frac{24}{5}$$  

• $$\frac{23}{5}$$

• $$\frac{22}{5}$$  

When adding or subtracting rationals first convert any mixed numbers or whole numbers to a rational. Then find a common denominator by finding the LCM. then add or subtract the numerators and keep the same common denominator. Always check to see if simplifying is needed.

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Unit 1: Just Be Rational

Adding/Subtracting Fractions

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Multiple Choice

What is the sum of $$1\frac{3}{4}\ +\ 1\frac{1}{3}$$  ?

• $$3\frac{1}{2}$$   

• $$2\frac{4}{7}$$  

• $$3\frac{1}{12}$$  

• $$2\frac{1}{12}$$  

​When adding or subtracting decimals you need to line them up by place value. Put any zeros as filler for empty spaces if needed. Then drop your decimal down to your answer. Add or subtract like normal. ​

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Unit 1: Just Be Rational

Adding/Subtracting Decimals

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Multiple Choice

What is the sum of 65.371 + 34.5 ?

•    98.871   

• 99.871 

•  100.817

• 101.718 

​To multiply fractions you do not need a common denominator. Convert all mixed and whole numbers to rationals. Multiply your numerators, then multiply your denominators. Simplify as needed. ​

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Unit 1: Just Be Rational

Multiplying Fractions

Multiple Choice

What is the product of $$3\frac{1}{2}\ \times\ 12$$  ?

• 42

• $$36\ \frac{1}{2}$$  

• 24

• $$18\ \frac{1}{2}$$  

​When multiplying decimals you do not line up by place value. Stack the longer number on top. Multiply like normal. Then count the number of decimal spots and swing your answer in that many times.

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Unit 1: Just Be Rational

Multiplying Decimals

Multiple Choice

What is the product of .83 x 4 ?

• 332

• 33.2

• 3.32

• .332 

​When dividing fractions convert your mixed and whole numbers into rationals. Then perform Keep Change Flip (KCF). After you will multiply your numerators, multiply your denominators and reduced if needed. ​​

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Unit 1: Just Be Rational

Dividing Fractions

Multiple Choice

What is the quotient of $$1\frac{1}{2}\ \div\ \frac{1}{6}$$  ?

• $$\frac{1}{9}$$  

• 12

• $$\frac{1}{12}$$  

• 9

​Make sure your divisor is a whole number and move your dividend the same amount of times you moved your divisor. Bring the decimal up to the quotient and Divide like normal.

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Unit 1: Just Be Rational

Dividing Decimals

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Multiple Choice

What is the quotient of $$23.155\ \div\ 0.5$$  ?

• 45.32

• 46.31

• 47.3 

• 48

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​When adding integers of the same sign you add them and take the sign they both have.

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W​hen adding integers with different sign subtract them and take the sign of the bigger number

Unit 1: Just Be Rational

Adding/Subtracting Integers​

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Multiple Choice

What is the sum of -10 + 5 = ?

• -5

• $$-\frac{1}{5}$$  

• 5 

• $$\frac{1}{5}$$  

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​When Multiplying or Dividing with same sign your answer will be positive.

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When Multiplying or Dividing with different sign your answer will be negative.

Unit 1: Just Be Rational

Multiplying/ Dividing Integers

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Multiple Choice

What is the quotient of $$-25\ \div\ 5$$  ?

• -5

• $$-\frac{1}{5}$$  

• 5 

• $$\frac{1}{5}$$  

​When converting a fraction to a decimal divide the numerator by the denominator.

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​When converting a decimal to a percent multiply the decimal by 100 (which is the same as moving the decimal to the right twice).

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When converting a percent to a fraction put the percent over 100 and simplify.

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When converting a percent to a decimal divide by 100 (which is the same as moving the decimal to the left twice). ​

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Unit 2: CONSTANTly CHANGEing

Converting Rationals

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Multiple Choice

Which answer choice shows .52 as a percent?

• .52%

• 5.2% 

• 52%

Multiple Choice

Which answer choice shows .52 as a simplified fraction?

• $$\frac{26}{50}$$  

• $$\frac{13}{25}$$  

• $$\frac{52}{100}$$  

Multiple Choice

Which answer choice shows $$\frac{1}{4}$$   as a decimal?

• .25 

• .24 

• .23 

​A ratio is a comparison between two things. Make sure to always label a ratio so you know what you are comparing. ​ You must write ratios in the order asked. There are part to whole and part to part ratios. You write ratios in word, colon and fractional form.

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Unit 2: CONSTANTly CHANGEing

Ratios

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Multiple Choice

What is the ratio of soccer balls to basketballs?

• 6 to 3

• 3 to 5

• 3 to 6

• 5 to 3

​A proportion is two ratios set equal to one another. There are various methods to solve proportions. Simplify the ratios, find the scale factor, cross-product or convert to decimals.​

Unit 2: CONSTANTly CHANGEing

Proportions

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Multiple Choice

The ratio of the number of boys to the number of girls in a choir is 5 to 4. There are 60 girls in the choir. How many boys are in the choir?

• 80

• 48

• 61

• 75

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​Rates are a ratio that compares different units of measure.

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Unit rate is a rate that compares a quantity of one to the other.

Unit 2: CONSTANTly CHANGEing

Rate & Unit Rate

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Multiple Choice

A car travels 240 miles in 4 hours. How many miles did the car travel per hour?

• 80

• 70

• 60

• 50

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​​When solving percent proportions always start by writing down your formula. The number closer to "is" will be your part/numerator. The number closer to "of" is your whole/denominator. Your percent will always go over 100. After the set uo you sovle like a proportion. ​

Unit 2: CONSTANTly CHANGEing

Percent Proportions

Multiple Choice

What is 75% of 4?

• 2

• 3

• 4

• 5

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​When solving a percent change you first want to write down your formula. They find the amount of change by subtracting the original from the new. ​After setting up your formula divide and multiply by 100.​

Unit 2: CONSTANTly CHANGEing

Percent Change

Multiple Choice

The price of a sweater was reduced from $20 to $12. By what percentage was the price of the sweater reduced?

• 8%

• 80%

• 40%

• 60%

​ Tax is a percent of the purchase price and is an amount paid in addition to the purchase price.

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Tip, or gratuity, is a small amount of money in return for service.

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The amount a store increases the price of an item by is called the markup.

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​Discount is the amount by which the regular price of an item is reduced. The sale price is the regular price minus the discount.

Unit 2: CONSTANTly CHANGEing

Tax, Tip & Discount

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Multiple Choice

$320 flatscreen TV is on sale for 5% off. Determine the sales price of the TV.

• $160

• $304

• $16

• $320

Multiple Choice

Josiah went to the barber to get his haircut. It cost $18 for the haircut. Josiah tipped the barber 20%. What was the total cost of the haircut including the tip?

• $3.60

• $20.00

• $14.40

• $21.60

​Constant of Proportionality is the constant value (K) relating two things that rise or fall together.

Unit 2: CONSTANTly CHANGEing

Constant of Proportionality

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Multiple Choice

What is the constant of proportionality (K) in the graph?

• 1

• 2

• 3

• 4

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​Similar Figures are same shape but different size. They have corresponding sides that are proportion. Similar Figures are increased or decreased by a scale factor.

Unit 3: Proportions SHAPE Our Thinkning

Similar Figures

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Multiple Choice

Find the missing side length (x) in the similar triangles

• 5

• 10

• 15

• 20

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​Scale Drawings is a picture or model of a real-life item. Scale Drawings are scaled down ( divided) by a scale factor or scaled up ( multiplied) by a scale factor. Scale Drawings are proportion to the real-life item.

Unit 3: Proportions SHAPE Our Thinkning

Scale Drawings

Multiple Choice

Julie is constructing a scale model of her room. The rectangular room is 10 inches by 8 inches. If 1 inch represents 2 feet of the actual room, what is the area of Julie’s room in inches?

• $$310\ in^2$$  

• $$320\ in^2$$  

• $$330\ in^2$$  

• $$340\ in^2$$  

A Dilation is a transformation in which an image is enlarged or reduced. ​An Enlargement will have a scale factor larger than 1. A Reduction will have a scale factor less than 1. ​

Unit 3: Proportions SHAPE Our Thinkning

Dilations

Multiple Choice

Is the screen on your new TV an Enlargement or a Reduction?

•  Enlargement

• Reduction 

Measurement Conversions are changing one measurement into the equivalent value of another measurment.

Unit 3: Proportions SHAPE Our Thinkning

Measurement Conversions

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Multiple Choice

John rode 2 kilometers on his bike. His sister Sally rode 3000 meters on her bike. Who rode the farthest and how much farther did they ride

• John rode further by 1 km.

• Sally rode further by 1 km.

• John rode further by 2 km.

• Sally rode further by 2 km.

​Probability is ​about how likely an event is to happen.

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An event is certain if it has a probability of 1.

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An event is impossible to happen if it has a probability of 0. ​

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A Sample Space is the set of all possible outcomes for an event. ​

Unit 4: What Are The Chances?

Probability

Multiple Choice

Nabiha has 5 pink bows, 1 blue bow, and 4 purple bows in a box. She will randomly choose 1 bow from the box. What is the probability Nabiha will choose a purple bow?

• $$\frac{1}{2}$$  

• $$\frac{2}{5}$$  

• $$\frac{1}{10}$$  

• $$\frac{3}{5}$$  

​A simple event is an event that only has a single possible outcome.

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For example, tossing a coin. ​

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Unit 4: What Are The Chances?

Simple Events

Compound Events

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​A compound event is an event that only has several possible outcomes. A compound event refers to the probability of one event then another happening.

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For example, rolling a 3 on the dice and spinning a red on a spinner.

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Multiple Choice

The probability of rain on Monday is 0.1. The probability of rain on Tuesday is 0.8. What is the probability of rain on both Monday and Tuesday?

• .8 

• .08 

• 8 

• 80 

Theoretical Probability is what is expected to happen based on mathematics. ​

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Unit 4: What Are The Chances?

Theoretical Probability

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Experimental Probability

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Experimental Probability is what actually happenes based on an experiment. ​

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​There are various ways to represent linear equations. Slope-Intercept form is y=mx+b. Where m = slope and b = y-intercept.

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Unit 5: Solve And Solve Again

Parts of a Linear Equation

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Unit 5: Solve And Solve Again

Solving Two-Step Equations & Inequalities

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​​The steps for solving equations and inequalities are the same. ​

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Remember that 5x = 5 multiplied by x and x/2 means x divided by 2. ​

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First, undo your addition and subtraction. Then undo your multiplication and division. ​ ​ The inverse of addition is subtraction. The inverse of subtraction is addition. The inverse of multiplication is division. The inverse of division is multiplication. ​

Inequalities

Parts of a circle

Circumference & Area of a Cirlce

Area of 2D Shapes

​Composite figures are made up of other shapes such as triangles, rectangles, and semi-circles.

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To find the area of composite figures first decompose the shape into shapes you can find the area of Then​ find the area of the shapes. Last, add up all the area of the shapes to find the area of the composite figure.

Unit 6: Getting In Shape

Area of Composite Figures

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Multiple Choice

What is the area of the composite figure?

• 42.28

• 36

• 20.28

• 6.28

​Total Surface Area is the sum of the areas of the faces and bases of a 3D Shape.

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L​ateral Surface Area is the area of the faces of a 3D Shape. NO BASES

Unit 6: Getting In Shape

Lateral Surface Area & Total Surface Area

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Multiple Choice

Find the Total Surface Area of the prism.

• $$150.88\ cm^2$$  

• $$75.08\ cm^2$$  

• $$45.88\ cm^2$$  

Multiple Choice

Find the Lateral Surface Area of the prism.

• $$120\ cm^2$$  

• $$240\ cm^2$$  

• $$360\ cm^2$$  

Unit 7: Turn Up The Volume

Volume of a Prism & Pyramid

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​Where B = area of the base.

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Prisms & Pyramids get their name from their base. So a triangular prisms base is a triangle​

Fill in the Blanks

Fill in the Blanks

Population with Surveying for Data​

Multiple Choice

Jose wants to know the favorite sport of students at

his high school. He surveyed 20 boys in the locker

room after football practice.

What is the population of the scenario above?

• Jose

• Jose's High School

• 20 Boys in the locker room after football practice

Multiple Choice

Jose wants to know the favorite sport of students at

his high school. He surveyed 20 boys in the locker

room after football practice.

Is the sample population from Jose's survey biased or random?

• Biased, because his population is not represented fairly

• Random, because his population is represented fairly.