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1 Integers & Absolute Value Represent the following as an integer: 1. a loss of 2 hours 2. a gain of 4 ounces degrees below normal 4. spending $25 Evaluate: = = = = Review: Integer Operations Evaluate the following: = = (-10) = 4. 3 (-6) = 5. 7 x -6 = x -12 = = =

2 Order of Operations 1. What do you use for the order of operations? Simplify the following: 2. (8 2) ( ) (2 + 3) Evaluating Expressions Evaluate the following: 1. x(3 + y) z if x = 6, y = 4, and z = x 2 4x + 5 if x = a 5b if a = -7 and b = 3

3 Properties Name the Property Used: (3 + 8) = 5 + (8 + 3) = = 8 4. (5 3) 2 = 5 (3 2) 5. 6(8 3) = = =0 Review! Simplify the following: (5 + 4 ) 7 4. Evaluate a b, if a = -4 and b = 10 Properties: x 1 = 3x 6. 4(xy) = 4(yx) = 0

4 One-Step Equations Solve the following equations: 1. x 5 = y = = m p = k = w = 18 3 Translating Expressions & Equations Translate the following expressions: 1. Five more than 3 times a number. 2. The quotient of twice a number and less than z. Translate the following equations: 4. The product of 6 and a number is subtracted from a number is more than 3 times a number is 18.

5 Fraction, Decimal, Percent Complete the following chart: Fraction Decimal Percent More Fraction, Decimal, & Percent Complete the following chart: Fraction Decimal Percent % %

6 Scientific Notation Convert to standard form: Convert to scientific notation: ,078 Comparing & Ordering Numbers Order the following from least to greatest: , 5%, 0.005, 5 10, ,, , 4%

7 Adding & Subtracting Fractions Add or Subtract the following fractions. Write in your answer in simplest form Multiplying & Dividing Fractions Multiply or Divide the following fractions. Write your answer in simplest form

8 Fraction Application Find the perimeter and area of the following: Rational Equations Solve the following equations: 1. b = x 2 = x 3. 1 y = 3 4. =

9 Exponents Find the value of each expression: Rewrite the expression using exponents: 7. a b b c a b Square Roots 1. Which is not a perfect square? A. 1 B. 81 C. 16 D. 50 Find the following: Between which two whole numbers do the following square roots lie?

10 The Real Numbers Name the smallest subset of Real Numbers that contains the following: π The Real Numbers True or False? If false, give an example. 1. Real Numbers can be both Rational and Irrational. 2. All Integers are Rational. 3. All Rational Numbers are Natural Numbers. 4. All Whole Numbers are Natural Numbers.

11 Ratios 1. In a computer lab, there are 15 desktop computers, 7 laptop computers, and 5 printers. What is the ratio of printers to desktop computers? Simplify your answer. 2. In classroom, there are 12 boys and 16 girls. What is the ratio of girls to total number of students? Simplify your answer. Simplifying Ratios Simplify the ratios below: 1. 6 doctors to 27 patients wins to 16 losses Simplify the ratios by converting to the same unit. 1. 8in 3ft 2. 2min 300s 3. 7gal 10 qt 4. 8m 60 cm

12 Unit Rates 1. Cady stamped 250 envelopes in 10 minutes. How many envelopes per minute did she stamp? 2. It took Max 5 minutes to type 410 words. How many words per minute does Max type? 3. Ciera s car used 5 gallons to drive 135 miles. How many miles per gallon does her car get? Unit Rates: Price/ Quantity Use unit rates to find the better deal: oz box of cereal for $4.89 or a 21-oz box of cereal for $ a pack of 6 pens for $4.74 or a pack of 15 pens for $12.72

13 Rate of Change The table below shows the temperature recorded every hour. Week Weight What is the rate of change from week 0 3? 2. What is the rate of change from week 3 7? Proportions Do the following ratios form proportions? 1. 12, , Solve the following proportions: x = = y

14 Proportion Word Problems 1. A car on a racetrack drove 96 miles in 60 minutes. How far did it drive in 10 minutes? 2. If recycling 2,000 pounds of paper saves 17 trees, how many trees are saved when 5,000 pounds of paper are recycled? Scale Drawings & Maps 1. A scale on a map uses ½ inch = 15 miles. If Austin and Houston are 6¾ inches apart, what is their actual distance? 2. The blueprint for a new swimming pool uses the scale ¾ inch = 2 feet. If the actual dimensions of the pool will be 8 feet wide by 12 feet long, find the dimensions of the pool on the blueprint.

15 Similar Polygons Find the missing side: Indirect Measure 1. A fence post s shadow is 8 feet tall and a tree s shadow is 16 feet tall. If the fence post is 9 feet tall, how tall is the tree? 2. A tower casts a 30-foot shadow. At the same time, a person 6½ feet tall casts a 4-foot shadow. How tall is the tower?

16 Dilations 1. Triangle ABC has the following coordinates: A(0, -4) B(-2, 4) and C(2, 6) a. Find the new coordinates using a scale factor of 3. b. Find the new coordinates using a scale factor of A 18 inch banner is to be dilated by a scale factor of 8/3. What will the new size of banner? How many feet is this? Percents Write as a percent: Write as a decimal and fraction % 6. 5%

17 The Percent Proportion is what percent of 186? 2. What is 55% of 134? is 5% of what number? Percent Proportion Word Problems 1. At East Middle, 60% of the students voted in an election. If there are 1500 students, how many voted? 2. Eleven of the 48 members of the football team are on the field. What percent of the members are playing? 3. On the written part of her driving test, Sara got 84% of the questions right. If Sara got 63 questions right, how many total questions were on the test?

18 Discount & Mark-Up 1. A $ skateboard is on sale for 30% off. Find the final price. 2. How much would a $75 video game be with 8.25% sales tax? 3. Find the final price of a $149 ipod with a 10% discount and 5% sales tax. Percent of Change 1. Find the percent of discount when a $1200 TV sells for $ What is the mark-up rate on a $120 watch that sells for $160? 3. On the first season of The Biggest Loser, Ryan went from 311 lbs to 208 lbs by the end of the season. Find his percent weight loss.

19 Simple Interest 1. Suppose $1,250 is placed in a savings account for 2 years. Find the interest earned if the rate is 4.5% 2. A savings account starts with $575. Find the total amount in the account after 2 ½ years if the interest rate is 4.25% Finding Missing Angles Find all missing angles. Identify the angle pair as complementary, supplementary, or vertical x x x x

20 More with Angles 1. Angles A and B are complementary. If m A = 35, find m B. 2. Angles C and D are supplementary. If m C = 65, find m D. 3. Angles X and Y are vertical. If m X = 110, find m Y. Parallel Lines & Angles Use the diagram below to give an example of each type of angles Alternate Interior Angles and 2. Alternate Exterior Angles and 3. Vertical Angles and 4. If m 7 = 135, complete the diagram with all missing angles.

21 Pythagorean Theorem Determine whether the side lengths could represent a right triangle: 1. 8 in, 15 in, 17 in 2. 5 in, 10 in, 12 in Find the missing side Pythagorean Theorem Word Problems 1. A pool table is 8 feet long and 4 feet wide. What is the length of the diagonal? 2. A 16 foot ladder leaning against a wall. The bottom of the ladder is 8 feet from the base of the wall. How far up the wall does the ladder reach? 3. Tara drives 22 miles north then 11 miles east. How far is she from starting point?

22 Quadrilaterals Find the missing measure: x x 60 Classify the type of quadrilateral: More Quadrilaterals True or False? Be able to explain. 1. All trapezoids are quadrilaterals. 2. All rhombi are parallelograms. 3. All rectangles are squares. 4. All parallelograms are rectangles.

23 Congruent Polygons 1. What does it mean if polygons are congruent? 2. If quadrilateral ABCD is congruent to quadrilateral FGHJ, find each measure. B C 70 D 50 A H 18 cm J G F 27 cm a. AB b. BC c. m G d. m H Transformations Describe what happens with each transformation: 1. Reflection 2. Translation 3. Rotation 4. Dilation

24 Area Formulas Find the area of the following shapes: in. 15 in. 9 in Finding Missing Measures Use the area formula to find the missing measure: 1. Find the height of a triangle with a base of 6.4 meters and an area of 22.4 square meters. 2. A trapezoid has an area of 108 square feet. If the lengths of the bases are 10 feet and 14 feet, find the height.

25 Application Problem The deck shown is constructed in the shape of a trapezoid. You would like to waterproof the deck with a sealant. If one bottle of sealant covers 400 square feet, how many bottles will you need? Area & Circumference of Circles 1. Find the area and circumference of the following circle: 20 cm 2. The circumference of a circle is 37.7 meters. Approximate its radius.

26 Complex Figures Find the area of the figures below: Prisms & Pyramids Classify the following figures. Then, identify the number of faces, edges, and vertices

27 Volume of Prisms & Cylinders Find the volume of the following figures: Finding Missing Measures 1. A cylinder has a volume of 225 cm 3 and a radius of 6 centimeters. Find the height of the cylinder. 2. A sandbox is 8 feet long, 6 feet wide, and 1.5 feet deep. The volume of sand in the box is 36ft 3. How deep is the sand?

28 Volume of Pyramids & Cones Find the volume of the following figures: yd 15 yd 9 yd 2. Surface Area of Prisms & Cylinders Find the surface area of the following figures: 1. 4 ft 12 ft 7 ft 2. 7 yd 8 yd

29 Application Problem Sara s Dad built her a new sandbox: 1.5 ft 8 ft 6 ft 1. He decided to paint the box purple. If one can of paint covers 30 ft 2, how many cans will he need? 2. To fill the box with sand, one bag fills 10 ft 3, how many bags will he need? Surface Area of Pyramids & Cones Find the surface area of the following figures: ft 12 ft

30 Simple Probability Using a standard 6-sided number cube, find: 1. P(even) 2. P(greater than 4) 3. P(perfect square) 4. P(7) There are 2 green, 6 red, and 4 blue marbles in a jar, find: 5. P(blue) 6. P(red or green) 7. P(not red) 8. P(yellow) The Counting Principle 1. A dime is tossed 3 times. Use the counting principle to find the total number of outcomes. 2. Suppose a letter of the alphabet is selected and 2 coins are tossed. Use the counting principle to find all possible outcomes. 3. Find the total number of outcomes if a card is chosen at random from a deck of 52 cards, and a number cube is rolled.

31 Factorials & Permutations Evaluate the following: 1. 8! 2. 13! 9! 3. What is a permutation? 4. How many 5-digit passwords can be made from the digits 1 9? 5. How many ways can 3 picture frames be arranged on a shelf? Combinations 1. How are combinations different from permutations? 2. How many 4-member groups can be selected from 18 students? 3. There are 8 different fruits at The Smoothie Shop. If you can choose 2, how many different smoothies can you make?

32 Permutations vs. Combinations Determine permutation or combination, then solve: 1. Total number of ways to choose two people from 8 to present a project. 2. Total number of ways to arrange 3 books on a shelf. 3. Total number of ways to award first, second, and third place winners out of 18 people. Compound Probability 1. If a die is rolled twice, find P(5, then perfect square) 2. What is the probability of tossing a coin 3 times and getting heads each time? There are 4 red, 6 green, and 5 blue pencils in a jar. Once a pencil is selected, it is NOT replaced. Find each probability. 3. P(red, then blue) 4. P(not red, then red) 5. P(green, then green)

33 Theoretical vs. Experimental Probability Mark spun the spinner 20 times and got the following results: Red 3, Yellow 7, Orange 4, Green 5, Purple 1 1. Theoretically, what is the probability of spinning green? 2. Based on Mark s experiment, what is the probability of spinning green? 3. Based on the experimental probability, how many times can Mark expect to spin green with after 300 spins? Mean, Median, Mode, Range Find the mean, median, mode & range of the following data sets: 1. 9, 5, 15, 8, 20 Mean= Median= Mode(s)= Range = 2. 36, 38, 33, 34, 32, 30, 34, 35 Mean= Median= Mode(s)= Range = 3. Rosemary s math grades are 90, 98, 96, 94, and 85. What must her sixth grade be so that her average is 92? A. 92 B. 91 C. 89 D. 86

34 Box-and- Whisker Plots Answer the questions given the following diagram. Stem & Leaf Plots 1. What is the median? 2. What is the lower and upper quartile? 3. What is the range? 4. What is the interquartile range? 5. What percent of the data is greater than 2? Find the mean, median, mode, and range of the stem-and-leaf plot

35 Matrices Let X =! ', Y = ( and Z =! 9 0 ' What are the dimensions of Matrix Y? Find the following: 2. X + Z 2. Y + Z 3. -2Y Combining Like Terms Simplify by Combining Like Terms: x x 7 3x p 1 9p h h

36 Distributing Simplify by Distributing: 1. 4(x + 4) 2. 2(w 8) 3. -8(v 7) 4. -3(y + 9) 5. 6(2x + 4) 6. -4(7x 1) Simplifying Expressions Simplify by distributing and combining like terms: 1. -4(x + 2) 3x 2. 2(-2b + 1) + 9b 3. 10(x 2) x (10x 3) + 12x + 5

37 One-Step Equations Review! 1. x + 4 = = w y = y = k = = -5n 8 Two-Step Equations 1. 6p 5 = = 2b + 17 y c = = = m n =

38 Translating & Solving Equations 1. The product of 4 and a number increased by 9 is Eight less than three times a number is The quotient of a number and -7, minus 4 is -11. Multi-Step Equations 1. 5x x = x 10x = (x + 4) = (x + 3) = -6

39 Equations Review 1. -5x + 7 = (x 1) = (x + 2) 3x = (x 2) (x + 5) = 17 Variables On Both Sides 1. -2x + 20 = 5x a + 10 = 5a 3. 2x + 8 = -3x k + 20 = 9k 4

40 Inequalities Translate the following: 1. x is less than or equal to 4 2. x is at least 18 Solve the following: x 3. 2x + 5 > x 5. -3x + 8 > More with Inequalities Determine which value could be a solution: 1. 3x + 5 >17 A. 2 B. 3 C. 4 D x 1 < 7 A. 0 B. 1 C. 2 D. 3

41 Multi-Step Inequalities 1. 6x 5 8x x 6 > 3(2x + 7) Relations 1. What is a relation? 2. Given the relation: {(6, 1), (5, 0), (4, -1), (3, -2), (5, -3)} a. What is the domain? b. What is the range?

42 Functions 1. What is the range of the function y = 2x 3 when the domain is {-1, 0, 1, 2}? 2. Find the range of the function y = 1 x + 1 if the 4 domain is {-8, -4, 0} Function Tables 1. Given the equation y = x y x 4, complete the table Determine the domain and range of the points.

43 Slope 1. How do you find slope given a graph? Find the slope between the following points: Graphing by Slope- Intercept Graph the following functions using y = mx + b 1. y = 1 x 2 2. y = 2x 4 3. y = -x y = 3 x 1 5

44 Slope- Intercept Application The repair shop charges $79 for a new muffler plus $40 per hour of labor. 1. Write an equation to represent the total cost of replacing a muffler. 2. What is the independent variable? 3. If Karen s total cost was $159, find the number of labor hours.

3. Jean got 12 hits out of 16 times at bat. Express this rate as a fraction in simplest form.

$3. Jean got 12 hits out of 16 times at bat. Express this rate as a fraction in simplest form.$ Express each ratio as a fraction in simplest form. (6.1) 2 nd Semester Pre-Algebra Practice Exam 1. 10 girls out of 24 students 2. 18 ounces to 3 cups (1 cup = 8 ounces) 3. Jean got 12 hits out of 16 times