Spotsylvania -Math 8 SOL Review Booklet 2014-2015.docx

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SOL Review Booklet

2014-2015

Math 8

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SOL 8.1 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.

8

3

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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.

HINTS & NOTES

How to simplify numeric expressions:

G Perform operations with Grouping symbols (parentheses, brackets, absolute value) E Simplify Exponents

MD Perform all Multiplication and Division (in order from left to right) AS Perform all Addition and Subtraction (in order from left to right)

PRACTICE

0

3

64

2

22 



11. What is the value of the expression shown?

12. What is the value of 4(6 + 2)2? 64

160 256 1,024

13. Identify each expression that is equivalent to 24.

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

HINTS & NOTES

How to simplify numeric expressions:

G

E

MD

AS

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

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SOL 8.2

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

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; , π Subset – smaller or more specific group within a set Example: The Integers are a subset of the Rational Numbers “Contained in” – EVERYTHING is a subset of the bigger group

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

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5. Which number in this list is NOT an integer?

6. Which number is an irrational number?

10 499

7. Which of the following sets of numbers contain the number ?

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The student will

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

8

5.

12

5 p

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PRACTICE

100 %

$

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SOL 8.3 (CONTINUED) The student will

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

5. At a water park, $8 buys 15 tickets. Sue is going to spend $96 on tickets. How many tickets will her $96 buy? 12

18 120 180

6. Dora bought a total of 48 cupcakes. Each cupcake cost $0.55, including tax. Of the cupcakes she bought, were vanilla cupcakes. What was the total cost of only the vanilla cupcakes? $6.60

$9.90 $16.50 $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? $42.71

$44.71 $46.71 $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? 10%

12% 70% 90%

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

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? 1 ft

1.5 ft 2 ft 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? $675

$3,375 $19,125 $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? $270

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

1. What is the value of 3(x2 - 4x) when x =5? 5

15 30 55

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

if a=4,b=3,and c=-2? 20

18 14 9

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

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

4. What is the value of when ? 16

20 32 50

18 21 39

6. If and , what is the value of ? 12

4 -72 -144

6 9 12

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

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 Exponents

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Determine whether a given number is a perfect square; and

Find the two consecutive whole numbers between which a square root lies.

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PRACTICE

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The student will

Verify by measuring and describe the relationships among vertical angles, adjacent angles, supplementary angles, and complementary angles; and Measure angles of less than 360 .⁰

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Verify by measuring and describe the relationships among vertical angles, adjacent angles, supplementary angles, and complementary angles; and Measure angles of less than 360 .⁰

PRACTICE

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The student will

Investigate and solve practical problems involving volume and surface area of prisms, cylinders, cones, and pyramids; and Describe how changing one measured attribute of a figure affects the volume and surface area.

PRACTICE HINTS & NOTES

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

Rectangular Prism: V = lwh Triangular Prism: V = Bh

Cylinder: V = πr 2h Cone: V = πr 2h Pyramid: V = Bh

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

Rectangular Prism: SA = 2lw + 2lh + 2wh Triangular Prism: SA = hp + 2B

Cylinder: SA = 2πrh + 2πr 2 Cone: SA = πrl + πr 2 Pyramid: SA = ½l p + B

Where: V = volume SA = surface area B = area of the base l = length or slant height w = width

h = height r = radius

p = perimeter of the base

A. 15.7 in3

B. 19.7 in3

C. 31.4 in3

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Investigate and solve practical problems involving volume and surface area of prisms, cylinders, cones, and pyramids; and Describe how changing one measured attribute of a figure affects the volume and surface area.

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The student will

Apply transformations to plane figures; and Identify applications of transformations

A transformation is a change in the position, shape, or size of a figure. The original figure you start with is called a pre-image.

The figure you end with is called the image.

There are 4 types of transformations:

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. Reflections are transformations that flip a figure over a line. This line is called the line of reflection.

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

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.

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Apply transformations to plane figures; and Identify applications of transformations

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

PRACTICE HINTS & NOTES Dimensional Figures

1-D: Length 2-D: Length and width 3-D: Length, width and depth

Parts of a Cube

Vertex – Corner where three sides meet. Face – Flat part of a cube.

Edge – Part where two faces meet. 3-D Views:

Front – Part that faces you.

Top – Looking down on the object (bird’s eye view) Side – Tilted part (profile view)

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Verify the Pythagorean Theorem; and Apply the Pythagorean Theorem

Pythagorean Theorem: leg2 + leg2 = hypotenuse2 Can only be applied to right triangles.

The hypotenuse of a right triangle is always opposite the right angle.

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

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!

What is the perimeter of this figure?

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SOL 8.12

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

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

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?

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? 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?

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? PRACTICE

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.

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

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The student will

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

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

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

PRACTICE

HINTS & NOTES

Remember the Rule of 5. You can represent relationships in several ways. Manipulatives

Pictures Tables Graphs 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.

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

Identify properties of operations used to solve an equation.

1. What is the solution of this equation?

C. 1 D.

2. What value of x makes this equation true?

36C. 16 17 D. 9

3. What is the solution to ?

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

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: Addition and Subtraction 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: is less than is greater than is less than or equal to 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’snot true, shade the other side. Properties Distributive Property Identity Properties Inverse Properties The dots:

o ¿ open dot / circle

o ≤ closed dot

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The student will

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

Identify properties of operations used to solve an equation.

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SOL 8.16

The student will graph a linear equation in two variables.

PRACTICE HINTS & NOTES Testing strategies:

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! 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!

What is the missing y-value?

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

5. What is the range of for the domain of {2, 8}?

6.

Determine the independent and dependent variable in each situation.

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.

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 needed r = the length of the road

Which is the independent variable? PRACTICE

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.