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SOL Review Booklet2016-2017

Math 8Sterling Middle School

Adapted from Spotsylvania County Schools

HINTS & NOTES

How to simplify numeric expressions:

GE

MDAS

Step 1: Perform operations with grouping symbols (parenthesis and brackets).

Step 2: Simplify exponents.

Step 3: Perform all multiplication and division (in order from left to right)

Step 4: Perform all addition and subtraction (in order from left to right).

4. Which list is ordered from least to greatest?

A.13, 35,30 % ,3×10−2

B.35, 13,30 % ,3×10−2

C. 3×10−2 ,30 % , 13, 35

D.13,30 % ,3×10−2 , 3

5

5. Arrange the numbers from greatest to least.

9.1×102 918 % 18302

920.0

6. Arrange the numbers from least to greatest.65 % 2

36.04×10−1 6.40

1. Identify each number between 1.7×100 and 195%.

1.8×1011 7

818.5 7

4

2. What is 102,000,000 expressed in scientific notation?

A. 1.02 x 109

B. 1.02 x 108

C. 1.02 x 107

D. 1.02 x 106

3. Which statement is true?

A. 0.09 >

78

B. 6% < 0.09

C.

78 < 8.0 x 10-3

D. 8.0 x 10-3 > 6%

PRACTICE

HINTS & NOTES To write a number in scientific notation, you write the number as two factors.

o Move the decimal to the left or right to make a factor between 1 and 10.o The exponent will be the number of places that you moved the decimal.

Example: 25,000,000 = 2.5 x 107

Example: .000345 = 3.4 x 10-4

To write a number in standard form, you move the decimal point to the left or right as many places as the exponent indicates. Put 0 in any space. Positive exponents indicate a number greater than 1. Negative exponents will make a number less than 1.

o Example: 3.4 x 105 = 340,000o Example: 5.8 x 10-3 = .0058

Steps for ordering numbers:o Change all of the numbers to decimals.o Remember to look for the order that the questions asks. (L →G or G→L)

To change a fraction to a decimal → divide the numerator (top number) by the denominator (bottom number).

Example:

38 = 0.375

To change a percent to a decimal →move the decimal two places to the lefto Example: 78% = 0.78

Ascending means numbers are increasing (moving left to right on the number line).

Descending means numbers are decreasing (moving right to left on the number line).

SOL 8.1The student will

a) simplify numerical expressions involving positive exponents, using rational numbers, order of operations, and properties of operations with real numbers; and

b) compare and order decimals, fractions, percents, and numbers written in scientific notation.

11. What is the value of the expression shown?|−4−20|

8+√121

12. What is the value of 4(6 + 2)2?A. 64B. 160C. 256D. 1,024

13. Identify each expression that is equivalent to 24.

18+32

23 ∙3

(2+3 ) ∙4

4+4 ∙5

36÷2+6

14. According to the order of operations, what should be performed first to simplify the expression.

10+18÷6+3 ∙2

A. 10+18B. 6+3C. 3 ∙2D. 18÷6

7. According to the order of operations, whichoperation should be performed first to simplify theexpression?

12 + 2 • 52 – 1

A. 12 + 2B. 5 – 1C. 2 • 52

D. 52

8. Which value is equivalent to

22−23

√64−30?

A. 2B. 14C. 16D. 30

9. What is the value of (4 – 2)2 + 4 -1?

A. 7B. 9C. 15D. 17

10. What is the value of the expression shown?√225

5+|−10+6|

PRACTICE

HINTS & NOTES How to simplify numeric expressions:

G Perform operations with Grouping symbols (parentheses, brackets, absolute value)E Simplify ExponentsMD Perform all Multiplication and Division (in order from left to right)AS Perform all Addition and Subtraction (in order from left to right)

SOL 8.1 (CONTINUED)The student will

a) simplify numerical expressions involving positive exponents, using rational numbers, order of operations, and properties of operations with real numbers; and

b) compare and order decimals, fractions, percents, and numbers written in scientific notation.

PRACTICE

5. Which number in this list is NOT an integer?124,−42 ,√25 ,−4.8

A.124

B. −42

C. √25D. −4.8

6. Which number is an irrational number?A. −√9B. −¿10C. 5.499D. √17

7. Which of the following sets of numbers contain the

number −13 ?

Integers Real Numbers

Rational Numbers Whole Numbers

Irrational Numbers Natural Numbers

8. Identify each classification of the real number system that can describe the set of numbers shown.

{−√36 ,35 % ,2 }

Real Natural

Whole Integer

Irrational Rational

1. Which of the following does not contain the number 24?

A. IntegersB. Whole NumbersC. Natural NumbersD. Irrational Numbers

2. Which of the following is not a rational number?

A. -0.75B. 0

C. √16D. √13

3. What subset of the real number system is completely contained in the Whole Numbers?

A. NaturalB. IntegerC. RationalD. Irrational

4. The set of whole numbers is not a subset of -

A. irrational numbersB. integersC. rational numbersD. real numbers

HINTS & NOTES Natural: “counting numbers”; 1, 2, 3, … Whole: the Natural numbers plus 0; 0, 1, 2, 3, … Integers: Whole numbers and their opposites; …, -2, -1, 0, 1, 2, … Rational: Numbers that can be written as a ratio; decimals end or

repeat; ½, ¼, 5, -2, 0 Irrational: Decimals that never end and never repeat; √13, π Subset – smaller or more specific group within a set

o Example: The Integers are a subset of the Rational Numbers “Contained in” – EVERYTHING is a subset of the bigger group

o Example: The Natural numbers are completely contained in the Whole numbers

SOL 8.2The student will describe orally and in writing the relationship between the subsets of the real number system.

Rational

Integers

Whole

Natural

Irrational

Real

3.

4. A librarian knows that 45% of the books currently checked out will NOT be returned on the due date. The library has a total of 5,040 books. How many of the library’s books will be returned on the due date?

HINTS & NOTES Set up a proportion with two equal fractions with similar information, cross multiply and divide to solve

the equation.

Percent Proportion

x$=%

100 Change a percent to a decimal and multiply: Move the decimal place two places to the left.

o Ex: 5.5% is 0.055 or 1% is 0.01 Tax: Find the % tax in $ by MULTIPLYING the $ times the % as a decimal. ADD to original amount. Tip: Find the % tip in $ by MULTIPLYING the $ times the % as a decimal. ADD to original amount. Mark-Up: Find the % mark-up in $ by MULTIPLYING the $ times the % as a decimal. ADD to original

amount. Sales/Discount: Find the % in $ by MULTIPLYING the $ times the % as a decimal. SUBTRACT from the

original amount Interest: I = prt, where p is the _______ amount ($), r is the ______ (%), and t is the _______ (years). Checkbook Vocabulary:

o Credit/Deposit = ________ o Debit/Withdraw = ________

Percent Increase/Decrease (change):o new value - old value x 100

old value

PRACTICE

1. Manuel can paint 5 pictures in 12.5 hours. At this rate, which proportion can be used to find p, the number of pictures Manuel can paint in 8 hours?

A.

58=20 .5

p

B.

58= p

20 .5

C.

512 .5

= 8p

D.

512 .5

= p8

2. Xavier saved money to purchase a bike that originally cost $250, not including tax. The store discounted the bike by 20%. What is the discounted price he will pay for the bike, not including tax?

A. $200 B. $230 C. $270 D. $280


a) Solve practical problems involving rational numbers, percents, ratios, and proportions; andb) Determine the percent increase or decrease for a given situation.

PRACTICE

10. Susan’s checkbook had a balance of $22.05 on April 1. On April 5, she wrote a check for $106.30 to the auto repair shop. On April 7, she wrote a check in the amount of $310.00 for rent. On April 9, her dad sent her $95.00 to deposit into her account. What is the balance of Susan’s account after this deposit?

11. Jane bought a new sweater. It was priced at $32.00 and there was a 25% discount. Jane gave the cashier $40. What was her change?

12. If a pole 9 feet tall casts a shadow of 3 feet, how long of a shadow would a 6 foot man cast?

A. 1 ftB. 1.5 ftC. 2 ftD. 2.5 ft

13. Don buys a car for $22,500. Don gets a loan for 5 years with an interest rate of 3% per year. How much total interest will Don pay over the five years?

A. $675B. $3,375C. $19,125D. $25,875

14. While shopping at a store, Billy found a $900 television that was on sale at a discount rate of 30%. What is the amount of discount?

A. $270B. $630C. $870D. $1170

5. At a water park, $8 buys 15 tickets. Sue is going to spend $96 on tickets. How many tickets will her $96 buy?

A. 12B. 18C. 120D. 180

6. Dora bought a total of 48 cupcakes. Each cupcake cost $0.55, including tax. Of the cupcakes she bought, 38 were vanilla cupcakes. What was the total cost of

only the vanilla cupcakes?A. $6.60B. $9.90C. $16.50D. $26.40

7. Emil bought a camera for $268.26, including tax. He made a down payment of $12.00 and paid the balance in 6 equal monthly payments. What was Emil’s monthly payment for this camera?

A. $42.71B. $44.71C. $46.71D. $56.71

8. A food company reduced the amount of salt in one of their food products from 700 milligrams to 630 milligrams. What is the percent decrease in the amount of salt in this food product?

A. 10%B. 12%C. 70%D. 90%

9. Kaylee caught 9 insects for her science project in the first week. She caught 13 insects in the second week. What is the percent increase in the number of insects Kaylee caught from the first week to the second week? Round your answer to the nearest whole number.


c) Solve practical problems involving rational numbers, percents, ratios, and proportions; andd) Determine the percent increase or decrease for a given situation.

HINTS & NOTES Substitution: Replace the variable with the appropriate given value. Follow the order of operations.

G Perform operations with Grouping symbols (parentheses, brackets, absolute value)E Simplify ExponentsMD Perform all Multiplication and Division (in order from left to right)AS Perform all Addition and Subtraction (in order from left to right)

PRACTICE

5. What is the value of x3+ x2+x when x=3?A. 9B. 18C. 21D. 39

6. If x=2 and t=4, what is the value of 18

(x3−4 )(t2+8)?

A. 12B. 4C. -72D. -144

7. What is the value of 83n3 when n=3

2 ?

A. 4B. 6C. 9D. 12

8. Identify each expression that has a value of 53 when given the corresponding replacement set.

a3+13bwhen a=3and b=2

10b2 ∙ 12+a3

when a=2 and b=3

a2+1 ∙ b2 when a=4 and b=6

3a+4 b2

2 when a=2 and b=5

5+a2 ∙ b+8 when a=2 and b=5

1. What is the value of 3(x2 - 4x) when x =5?A. 5B. 15C. 30D. 55

2. What is the value of the expression 5(a + b) - 3(b + c)

if a=4,b=3,and c=-2?A. 20 B. 18C. 14D. 9

3. What is the value of the following when b = 2?

3 b + 3(b - 4) b2 - b

4. What is the value of 2(5−a)2+7a when a=2?A. 16B. 20C. 32D. 50

SOL 8.4The student will apply the order of operations to evaluate algebraic expressions for given replacement values of

the variables.

5. Place the √23 where it belongs on a number line.

6. What is −√324?

7. Which pair of numbers are both between 6 and 7?A. √30 and √42B. √36 and √49C. √37 and √50D. √42 and √48

8. Which statement best describes √50?A. Exactly 7B. Exactly 25C. Between 7 and 8D. Between 24 and 26

HINTS & NOTES Perfect Square: is the product of an integer and itself.

Ex.: 52 = 102 = 152 = 122 =

Square Root: is the base which when multiplied by itself is equal to the original number.

Ex: √64 = √81 = -√400 = √1 = Estimating Square Roots: Identify the two consecutive whole numbers between which square root of a

given whole number lies.

Ex. √21o Determine the two perfect squares that 21 falls between.o Take the square root of the two perfect squareso Answer.o Example

√21 16 & 25

√16 & √25 4 & 5

PRACTICE

1. Which of the following numbers is a perfect square?

A. 36B. 28C. 22D. 14

2. Between which two whole numbers is √33 ?A. 32 and 34B. 16 and 17C. 6 and 7D. 5 and 6

3. Which number is a perfect square?A. 2B. 5C. 25D. 52

4. Which has a value between -2 and -3?

A. -√21

B. -√8C. -√3D. -√2


a) Determine whether a given number is a perfect square; andb) Find the two consecutive whole numbers between which a square root lies.

HINTS & NOTES Vertical angles: Angles directly opposite that are congruent.

Complementary angles: Two Angles are Complementary if they add up to ______ degrees (a Right Angle). Complementary think Corner.

Supplementary angles: Two angles are Supplementary if they add up to ________ degrees (straight line). Supplementary think Straight Line.

Reflex angles: Angles that measure between 180 and 360 degrees.

Adjacent angles: any two non-overlapping angles that share a common side and a common vertex.

2. Which pair of angles is supplementary?1. In which diagram do <1 and <2 appear to be vertical angles?

PRACTICE


c) Verify by measuring and describe the relationships among vertical angles, adjacent angles, supplementary angles, and complementary angles; and

d) Measure angles of less than 360⁰.

7. Which statement is true?

A. Angle 2 and angle 4 are vertical angles.B. Angle 3 and angle 6 are complementary angles.C. Angle 1 and angle 2 are supplementary angles.D. Angle 1 and angle 5 are complementary angles.

8. Which is the closest to the measure of <WXY?

A. 45⁰B. 55⁰C. 135⁰D. 145⁰

9. In the figure shown, m<1=(4 x+12)⁰ and m<2=(6 x+8)⁰.

What is m < 1?A. 20⁰B. 40⁰C. 50⁰D. 76⁰

3. Which of the following could be the measurements of two supplementary angles?

A. 7⁰ and 83⁰B. 83⁰ and 83⁰C. 97⁰ and 83⁰D. 117⁰ and 83⁰

4. Look at the angles.

Identify each angle that is adjacent to Angle 2.

Angle 1 Angle 3 Angle 4 Angle 5

5. In this figure, m<1=(15 x−5)⁰ and m<2=(10 x+35)⁰.

What is m<1?A. 31⁰B. 65⁰C. 85⁰D. 115⁰

6. Label each angle with its measure.

127⁰

PRACTICE


e) Verify by measuring and describe the relationships among vertical angles, adjacent angles, supplementary angles, and complementary angles; and

f) Measure angles of less than 360⁰.

3. The volume of a square-based pyramid is 588 cubic inches. The height of this pyramid is 9 inches. What is the area of the base of this pyramid?

4. What is the total surface area and volume of this prism?

Surface Area =Volume =

5. Which is closest to the volume of this cylinder?

1. What is the volume of a square-based pyramid with base side lengths of 16 meters, a slant height of 17 meters, and a height of 15 meters?

A. 1280 m3

B. 1360 m3

C. 1450 m3

D. 2040 m3

2. Which is the closest to the surface area of the cone with dimensions as shown?

A. 66 sq in.B. 75 sq in.C. 113 sq in.D. 207 sq in.

HINTS & NOTES Volume is the number of unit cubes, or cubic units, needed to fill a solid figure. (filling a box)

o Formulas:Rectangular Prism: V = lwhTriangular Prism: V = BhCylinder: V = πr 2h

Cone: V = 13πr 2h

Pyramid: V = 13Bh

Surface Area is the sum of the areas of its surfaces. (wrapping a box)o Formulas:

Rectangular Prism: SA = 2lw + 2lh + 2whTriangular Prism: SA = hp + 2BCylinder: SA = 2πrh + 2πr 2

Cone: SA = πrl + πr 2

Pyramid: SA = ½l p + B

PRACTICE


a) Investigate and solve practical problems involving volume and surface area of prisms, cylinders, cones, and pyramids; and

b) Describe how changing one measured attribute of a figure affects the volume and surface area.

Where:V = volumeSA = surface areaB = area of the basel = length or slant heightw = widthh = heightr = radiusp = perimeter of the base

A. 15.7 in3

B. 19.7 in3

C. 31.4 in3

D. 78.5 in3

9. Josh has two rectangular prisms. The length of the second prism is 10 times the length of the first prism. The heights and widths of the two prisms are the same. Which best describes the volume of the second prism?

A. The volume is 10 times the volume of the first prism.

B. The volume is 30 times the volume of the first prism.

C. The volume is 100 times the volume of the first prism.

D. The volume is 1,000 times the volume of the first prism.

10. If a rectangular prism has a length of 3 feet, a width of 4 feet, and a height of 5 feet and you double the width, what will happen to the volume and surface area?

11. Two triangular prisms show have bases with the same area.

The Volume of prism N can be found by multiplying the volume of prism M by what scale factor?

A.15

B. 3C. 5D. 8

6. What is the surface area of a rectangular prism with the dimensions shown?

A. 7 sq in.B. 14 sq in.C. 18 sq in.D. 25 sq in.

7. What is the volume of the cube?

A. 144 m3

B. 432 m3

C. 864 m3

D. 1,728 m3

8. Raymond needs to cover the entire surface are of this square-based pyramid with paper.

What is the minimum amount of paper he will need?A. 276 sq ftB. 408 sq ftC. 528 sq ftD. 672 sq ft

PRACTICE


c) Investigate and solve practical problems involving volume and surface area of prisms, cylinders, cones, and pyramids; and

d) Describe how changing one measured attribute of a figure affects the volume and surface area.

3. Dwight drew a line segment on a coordinate grid. He plans to reflect the line segment over the y-axis.Graph the new line segment.

4. A figure was rotated 180⁰ clockwise about the origin.

Which is most likely the new figure?

A. B. C.

1. Which grid shows only a translation of the shaded polygon to create the unshaded polygon?

2. One piece of stained glass is transformed three times.

What transformation was used to create this section of stained glass window?

A. TranslationB. ReflectionC. RotationD. Dilation

HINTS & NOTES A transformation is a change in the position, shape, or size of a figure.

o The original figure you start with is called a pre-image.o The figure you end with is called the image.

There are 4 types of transformations:o Rotations are transformations that turn a figure about a fixed point called the center of rotation.

The angle of rotation is the number of degrees the figure rotates.o Reflections are transformations that flip a figure over a line. This line is called the line of

reflection.o Translations are transformations that move each point of a figure the same distance in the same

direction.o Dilations are transformations that create similar figures of larger or smaller sizes. The ratio of the

pre-image and the image is called the scale factor. A dilation with a scale factor greater than 1 is called an enlargement. A dilation with a scale factor less than 1 is called a reduction.

PRACTICE


a) Apply transformations to plane figures; andb) Identify applications of transformations

7. What type of transformation has occurred?

A. DilationB. RotationC. ReflectionD. Translation

8. What type of transformation has occurred?

A. TranslationB. Reflection across the y-axisC. Reflection across the x-axisD. Rotation 90⁰ clockwise around the origin

9. Look at the transformation of polygon A to polygon A’. Polygon A was rotated counterclockwise how many degrees?

5. What are the new coordinates of point B after ∆ ABC is translated 2 units down and 3 units to the left?

6. Dilate the pre-image using a scale factor of 3. Draw the new image.

PRACTICE


c) Apply transformations to plane figures; andd) Identify applications of transformations

3. A three-dimensional figure is constructed using identical cubes. Three views of this figure are shown.

Which could be this three-dimensional figure?

4. Identify each three-dimensional figure that could be represented by these three views.

1. The front view of a three-dimensional figure using identical cubes is shown.

Identify each three-dimensional figure that has this front view.

2. A figure has the bottom and left-side views shown, and its front view is shaded. Which represents the figure?

A. C.

B. D.

HINTS & NOTES Dimensional Figures

o 1-D: Lengtho 2-D: Length and widtho 3-D: Length, width and depth

Parts of a Cubeo Vertex – Corner where three sides meet.o Face – Flat part of a cube.o Edge – Part where two faces meet.

3-D Views:o Front – Part that faces you.o Top – Looking down on the object (bird’s eye view)o Side – Tilted part (profile view)o Bottom – Opposite of top. Looking up at the object.

PRACTICE

SOL 8.9The student will construct a three-dimensional model, given the top or bottom, side, and front views.

4. For the rectangle shown, which equation can be used to find the value of x?

5. A wire connects to the top of a flagpole to the ground as shown.

Which is the closest to the height, h, of the flagpole?A. 3.2 mB. 5.0 mC. 8.7 mD. 11.2 m

6. Mr. Malone plans to construct a walkway through his rectangular garden, as shown in the drawing.

What is the closest value of w?A. 22 ft B. 21 ft C. 15 ft D. 11 ft

1. Which group of three side lengths could form a right triangle?

A. 5 ft, 12 ft, 13 ftB. 7 ft, 11 ft, 14 ftC. 15 ft, 20 ft, 22 ftD. 18 ft, 34 ft, 39 ft

2. Which of the following equations is represented by the figure?

A. 32 + 42 = 72

B. 32 + 42 = 52

C. 32 + 52 = 82

D. 42 + 52 = 92

3. These triangles are not drawn to scale. Which triangle is a right triangle?

A. C.

B. D.

A. (x+5)2=122

B. 52+x2=122

C. 52+122=x2

D. 5+12=x2

HINTS & NOTES Pythagorean Theorem: leg2 + leg2 = hypotenuse2 Can only be applied to right triangles. The hypotenuse of a right triangle is always opposite the right angle.

The longest side of a right triangle is always the hypotenuse. The legs of a right triangle are always adjacent (next to) the right angle; they form the right angle.

Three numbers will form a right triangle if a2+b2=c2 and c is the biggest number.

PRACTICE


a) Verify the Pythagorean Theorem; andb) Apply the Pythagorean Theorem

4. Calculate the area and perimeter of the following shape.

5. Find the area of the shaded region.

6. Spotsylvania County has to pay for maintenance on the football field. They need to replant sod, which costs $3.50 per meter squared. How much will it cost to sod the field?

1. What is the area of this polygon?

A. 77 sq cmB. 86 sq cmC. 96 sq cmD. 108 sq cm

2. This figure is formed by a square and an isosceles trapezoid.

3. The net of square-based pyramid is shown.

What is the area of this net?

What is the perimeter of this net?

HINTS & NOTES Perimeter of a polygon is the distance around the figure. The area of any composite figure is based upon knowing how to find the area of the composite parts such

as triangles and rectangles. An estimate of the area of a composite figure can be made by subdividing the polygon into triangles,

rectangles, squares, trapezoids and semicircles, estimating their areas, and adding the areas together. Remember to use your formula sheet if you don’t remember the area and perimeter formulas!

PRACTICE

SOL 8.11The student will solve practical area and perimeter problems involving composite plane figures.

What is the perimeter of this figure?

A. 19 in.B. 34 in.C. 39 in.D. 44 in.

HINTS & NOTES Two events are either dependent or independent. If the outcome of one event does not influence the occurrence of the other event, they are called

independent. If the outcome of one event does influence the occurrence of the other event, they are called dependent.

o With dependent events, your denominator will decrease with each occurrence. You will multiply the individual probabilities whether it is independent or dependent :

P(A and B) = P(A)∙P(B)

PRACTICE

4. Eric and Sue will randomly select from a treat bag containing 6 lollipops and 4 gumballs.

Eric will select a treat, replace it, and then select a second treat.

Sue will select a treat, not replace it, and then select a second treat.

Calculate each probability. Who has the greater probability of selecting 1 lollipop and then 1 gumball?

5. A bag contains 6 red marbles, 8 blue marbles, and 6 white marbles. If one marble is selected at random from the bag and NOT replaced, what is the probability that it will be blue and then blue?

A.4

25

B.750

C.34

D.1495

6. There are 8 brownies and 4 cookies. Each student may have one dessert. You choose one, then the next person picks one. What type of event is this?

7. In an experiment, you are asked to roll a die and flip a coin. What type of even is this?

1. Two fair coins are flipped at the same time. What is the probability that both display tails?

A.18

B.14

C.13

D.12

2. A box contains 9 new light bulbs and 6 used light bulbs. Each light bulb is the same size and shape. Meredith will randomly select 2 light bulbs from the box without replacement. What is the probability Meredith will select a new light bulb and then a used light bulb?

A.1

54

B.2

15

C.6

25

D.9

35

3. Cynthia has 14 roses in a vase. 2 yellow roses 5 pink roses 3 white roses 4 red roses

Cynthia will randomly select 2 roses from the vase with no replacement. What is the probability that Cynthia will select a red rose and then a pink rose?

SOL 8.12The student will determine the probability of independent and dependent events with and without replacement.

HINTS & NOTES Scatterplots: two related sets of data are graphed as points to display correlations (trends).

Positive Trend Negative Trend No Trend

3. The graph shows the number of text messages two students sent each day for 4 days.

Based on the graph, which statement is true?A. On Day 2 and Day 3, the total number of text

messages sent by Paul was 4 more than the total number of text messages sent by Kala.

B. The total number of text messages sent by Kala was the same as the total number sent by Paul for these four days.

C. The mean number of text messages Kala sent on Day 2 and Day 4 was exactly 4.5.

D. Kala sent fewer text messages than Paul on Day 3 and Day 4 combined.

4. The circle graph displays the items sold at the football concession stand. The concession stand sold a total of 450 items. How many more nachos were purchased than popcorn?

1. The hourly wages of the 25 employees at a restaurant are shown.

Based on the graph, what is the mean hourly wage of the 25 employees at this restaurant?A. $11.75 B. $9.36 C. $9.00 D. $8.56

2. The graph shows Anna’s height on each of her last five birthdays.

Based on the graph, between which two consecutive years was the increase in Anna’s height the greatest?

A. Between 8 and 9 yearsB. Between 9 and 10 yearsC. Between 10 and 11 yearsD. Between 11 and 12 years

PRACTICE


a) Make comparisons, predictions, and inferences, using information displayed in graphs; andb) Construct and analyze scatterplots.

7. The following scatterplot shows the scores several students received in math and music classes last semester.

Which statement best describes the relationship in the scatterplot?

A. As the math score decreases, the music score increases.

B. As the math score increases, the music score decreases.

C. As the math score decreases, the music score does not change.

D. As the math score increases, the music score increases.

8. Which of these best describes the relationship of data shown on this scatterplot?

A. Constant relationshipB. Negative relationshipC. Positive relationshipD. No relationship

5. The scatterplot shows the relationship between Marvin’s age and the time it took him to run a mile.

Which statement best describes the relationship between Marvin’s age and the time it takes him to run a mile?

A. As Marvin’s age increased, the time it took him to run a mile increased.

B. As Marvin’s age increased, the time it took him to run a mile decreased.

C. As Marvin’s age increased, the time it took him to run a mile remains constant.

D. There is no relationship between Marvin’s age and the time it took him to run a mile.

6. Mr. Robert took a survey of his sixth period class to determine what breeds of dogs the students have as pets. The results are shown in this graph.

What percentage of the dogs owned by Mr. Robert’s class are a beagle or a terrier?

PRACTICE


c) Make comparisons, predictions, and inferences, using information displayed in graphs; andd) Construct and analyze scatterplots.

3. Which of these equations represents the table of values?

4. Margaret has $200 in her savings account. She will deposit $50 into this account each week and will make no withdrawals. Which table represents this situation, excluding interest?

1. Which best represents y=x−1?

2. Which table contains only points that lie on the

line represented by y=23x−6?

HINTS & NOTES Remember the Rule of 5. You can represent relationships in several ways.

o Manipulativeso Pictureso Tables o Graphs o Rules

Remember when you are graphing ordered pairs, you move left or right on the x-axis first, then up or down on the y-axis.

Test taking strategies: If you have to match a table to an equation, substitute the x and y values until you make a

match. If you have to match a table to a graph, be sure to check all ordered pairs you are given. If you have to match an equation to a graph, create a table of at least 3 x-values, substitute

them in to get the y-values, then match your ordered pairs to the correct graph. If you have to match a graph to an equation, make a list of the ordered pairs from each

graph then substitute them into the equation until you find a match.

PRACTICE

SOL 8.14The student will make connections between any two representations (tables, graphs, words, and rules) of a given

relationship.

A. y=−xB. y=x+7C. y=3 x+3D. y=2x+6

4. Which graph best represents the solution to

78≥ 1

4x+ 1

2?

HINTS & NOTES Remember to solve equations or inequalities you MUST maintain balance (what you do to one side of the

equation has to be done to the other side of the equation). Don’t forget to FLIP the inequality sign if you multiply or divide by a negative when solving inequalities. Inverse Operations:

o Addition and Subtractiono Multiplication and Division

Don’t forget your integer operation rules. Use your calculator to check your work! Test taking strategy: If all else fails, PLUG And CHUG, substitute each answer choice into the equation

until you find the one that works!Graphing Inequalities

The symbols:o ¿ is less thano ¿ is greater thano ≤ is less than or equal too ≥ is greater than or equal to

Shade the part of the number line that contains the numbers that make the inequality true. Pick a number and check it in the inequality…if it’s a true statement, shade it!; if it’s not true, shade the other side.

Properties Distributive Property Identity Properties Inverse Properties

PRACTICE

1. What is the solution of this equation?x=5 x+6

A.−32 C. 1

B. −1 D. 32

2. What value of x makes this equation true?5 x+8+3 x=26+6 x

A. 36 C. 16B. 17 D. 9

3. What is the solution to n+4

2−3=13?

A. n = 4 C. n = 16B. n = 14 D. n = 28


a) Solve multistep linear equations in one variable with the variable on one and two sides of the equation;b) Solve two-step linear inequalities and graph the results on a number line; and

c) Identify properties of operations used to solve an equation.

The dots:o ¿ open dot / circleo ¿ open dot / circleo ≤ closed dot o ≥ closed dot

9. The first six steps used to solve an equation are shown.

Between which two steps does the zero property of multiplication justify the work?

A. Steps 2 and 3B. Steps 3 and 4C. Steps 4 and 5D. Steps 5 and 6

10. Eric solved the equation x−3=10 as shown.

What property justifies Eric’s work from Step 2 to Step 3?

11. Which is one value of the set of x that makes the following true?

−6>−4 x−18A. -21B. -5C. -10D. -21

5. What is the solution to this inequality?1.6≥0.8x+4

A. −3≥ xB. −3≤xC. 7≥ xD. 7≤ x

6. Solve this inequality for x.

2< x4+5

7. Identify each equation that illustrates the commutative property of multiplication.

8. Martha wrote the first step in solving an equation.

4 x+ (x+2 )=27 Step 1: (4 x+x )+2=27

Which property justifies this step?A. Associative property of multiplicationB. Commutative property of additionC. Associative property of additionD. Distributive property

PRACTICE


d) Solve multistep linear equations in one variable with the variable on one and two sides of the equation;e) Solve two-step linear inequalities and graph the results on a number line; and

f) Identify properties of operations used to solve an equation.

3. Which graph appears to contain all the ordered pairs in this relation?

4. Alana is creating a table of values to graph the equation 2 x+3 y=9.

5. Using the graph of the line, fill in the missing values in each ordered pair in the table: -6, -2, 0, 2, 4

1. Which line appears to contain both ordered pairs shown in this table?

2. Which line appears to be a graph of the equation shown?

y=−2x−1

HINTS & NOTES Testing strategies:

o If given a table with coordinates to match with a graph, draw a graph on scratch paper and plot the points and then choose the graph that matches!

o If given a graph and asked to choose a table that matches, write down all the points in the graph and then choose the table that matches!

PRACTICE

SOL 8.16The student will graph a linear equation in two variables.

What is the missing y-value?A. -5B. -1C. 1D. 5

1. What is the range of this relation?

2. What is the greatest value in the range of y=−5x+3 for the domain {-2, 0, 1, 3}?

A. 3B. 8C. 13D. 18

3. Which relation has a domain of {3, 5, 8}?A. {(5, 1), (3, 4), (8, 2), (3, 3)}B. {(3, 2), (5, 1), (8, 3), (1, 4)}C. {(2, 8), (1, 3), (3, 5)}D. {(3, 8), (5, 3), (3, 5)}

4. What are the domain and range of this function?

HINTS & NOTES Domain: All the VALUES of x, or the independent variable. Range: All the VALUES of y, or the dependent variable. Independent Variable: “I Change”; usually associated with the x-axis. Dependent Variable: This depends on the independent variable; usually associated with the y-axis.

PRACTICE

5. What is the range of y=−3x+1 for the domain of {2, 8}?

6. Determine the independent and dependent variable in each situation.

a) Sarah has hired a contractor to replace the windows in her house. The more people that work, the less time it takes to install the windows.

b) Leon sells ice cream cones in the park. He has observed that when the outside temperature exceeds ninety degrees, he sells more ice cream cones.

7. A team from the Department of Public Works is painting lines on the freeway. The number of hours needed to finish the project depends on the length of the road that needs to be lined.

h = the number of hours neededr = the length of the road

Which is the independent variable?

SOL 8.17The student will identify the domain, range, independent variable, or dependent variable in a given situation.

A. {1, 2, 4, 6}B. {1, 2, 4, 5}C. {1, 2, 4, 5, 6}D. {0, 1, 2, 3, 4, 5, 6}

loudoun county public schools / overview · web viewa) simplify numerical expressions involving...

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