# Summer Math Exercises. For students who are entering. Pre-Calculus

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1 Summer Math Eercises For students who are entering Pre-Calculus

2 It has been discovered that idle students lose learning over the summer months. To help you succeed net fall and perhaps to help you learn some lessons that you did not learn the first time through we have prepared the following packet of math eercises to be completed over the summer. It is clear that most students do not want to spend their entire summer doing math work. Based on how fast or slow you work, you may find that you only need to do math a few days a week. Working on this packet will be most effective if you do work throughout the summer so try not to skip weeks. You may use the following chart to get an idea of how often you might need to work problems: For eample, if your student worked on math for 60 minutes per session and took 2 minutes per problem, he or she could complete 30 problems a day. That would equate to only about 7 sessions of working math problems over the summer. At the other end of the spectrum, if a student wanted to work only 30 minutes a time and took on average 5 minutes to complete each problem, he or she would only get 6 problems done during a session and would have to do about 36 sessions to complete the work (i.e., math work about every other day during the summer break). Note that it should not take a student who has previously learned the material more than an average of 5 minutes to work a problem. This work is MANDATORY for CCHS students. Please follow these guidelines: Complete this packet of eercises and bring the completed work to the first day of classes so you will get credit. Use PENCIL and write legibly. Do all your work on separate sheets of paper. Identify each section with a header (e.g, Lesson.) and number each problem. Please circle your answers. Into Pre-Calc Problems: 26 Min/Day Min/Prob Prob/Day Sessions

3 Assignment for students entering Pre-Calculus Lessons No of Probs Problems Assigned Date Completed every 3rd every 3rd every 3rd every 3rd every 3rd every 3rd every 3rd every 3rd every 3rd every 3rd every 3rd every 3rd every 3rd every 3rd every 3rd, every 3rd every 3rd every 3rd every 3rd every 3rd Assess every 3rd,29,32,35,38 26

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5 . For use with Lesson.: Operations with Integers Evaluate the epression Topic Identify the property that is illustrated by the given statement Admission Prices The admission prices to an amusement park are \$27 for adults, \$6 for children, and \$8 for senior citizens. There are 6 adults, 3 children and 2 senior citizens in your group. Write an epression to represent the total admission cost for your group. Find the total cost. 43. Pizza Party You and 3 friends buy a pizza for \$0 including ta, plus a delivery fee of \$2. Write and solve an epression to find C, the cost per person. Algebra 2 7

6 .2 For use with Lesson.2: Operations with Rational Numbers Add or subtract Find the reciprocal of each number Topic Multiply or divide Evaluate the epression Fishing You went trout fishing. You caught trout with the lengths (in inches) of 82 and 9 5 3, 0 2, 83 4, 95 6, 0 3, 2. Find the average length of the trout you caught. 32. Gasoline Prices Last week the price of gasoline was \$.25 per gallon. This week the price of gasoline is \$.33 per gallon. What is the change in the price per gallon of gasoline? Algebra 2 3

7 .3 For use with Lesson.3: Square Root Concepts Find all square roots of the number or write no square roots. Check the results by squaring each root Topic Evaluate the epression ± Approimate the square roots ± 225 ± Geometry Use the Pythagorean theorem (a 2 b 2 c 2 ) to find the missing side length of the given right triangle c 3 b c a 24 8 Algebra 2

8 .4 For use with Lesson.4: Simplifying Square Roots Simplify the epression using the product property Simplify the epression using the quotient property. Rationalize the denominator when necessary Topic Simplify the epression Area Your square bedroom has an area of 28 square feet. Find the length of one wall. Geometry Find the radius of the circle with the given area. The area of a circle is A r A 44 in A 208 cm 2 r r Algebra 2 23

9 2. For use before Lesson 2.: Evaluating Epressions Name the operation indicated by the epression s r 30 Write a variable epression for the verbal phrase times 6. m plus divided by n minus t Evaluate the epression for the given value of the variable when 5 0. b 6 when b 24 y. when y m 45 when m 58 Evaluate the epression when a 2, b 6, and c a b b 4. ac 5. 3a 4b 6. 25c 2 b a 7. c ab 8. ab 3 c a a 0.3b 0.05c 2 a 3 b Topic Perimeter The perimeter of a rectangle is equal to 2l 2w, where l is the length and w is the width. Find the perimeter of the rectangle at the right. Dimensions are in inches. = 6.7 w = Area The area of a triangle is equal to 2 bh, where b is the length of the base and h is the height. h = 0.2 Find the area of the triangle at the right. Dimensions are in centimeters. b = Average Speed The average speed (in miles per hour) is given by the formula Average speed Distance d Find the average speed of a car that traveled 80 miles Time t. in 3 hours. Algebra 2 29

10 2.2 For use with Lesson 2.2: Simplifying Epressions Simplify the epression by combining like terms y 9y y p 3.p 9. 3 w 4 w n 6 2n 2. a 3a Find the sum or difference using the vertical or horizontal format. 3. 5y 2 6y 2 4y m 3 7m 5 4m 2 6m n n Topic 2 Simplify the epression by using the distributive property and combining like terms a 4 5a Geometry Write an epression modeling the area of the large rectangle as the product of its length and width. Then write another epression modeling this area as the sum of the areas of the two smaller rectangles. Simplify each epression Algebra 2

11 2.3 For use with Lesson 2.3: Properties of Powers Evaluate the epression Simplify the epression. The simplified epression should have no negative eponents y y a y yz 3 y 2 z y y 2 2y y 2 a 3 a y a y 2 y 2 y 6 2 b 5 b 7 Topic Geometry The volume of a sphere is given by V 4 3 r 3, where r is the radius and is approimately 3.4. What is the volume of the sphere at the right in terms of a? 2a Algebra 2 39

12 2.4 For use with Lesson 2.4: Simplifying Epressions with Powers Multiply using the distributive property y 2y y y 6y 3 2y 8. 0a a 2 3a y 4y 2 2 y 3 y 5b 3 9b 2 8b 2 Simplify the product y y. 4 3 y y 5y2 2y y 4. 2y 5. 4y y 2 y 3 36a 8 b 2 ab 6 2 y 2 y 3 6 ab y y 2 Topic 2 Rewrite in scientific notation , ,452, ,000,000, ,4 Evaluate the epression. Write the result in scientific notation Size of Earth Earth has a radius of about miles. Use the equation V 4 3 r 3 to find Earth s volume. 44 Algebra 2

13 3. For use with Lesson 3.: Solving Equations State the inverse.. Add Subtract Multiply by Divide by Divide by 6. Subtract Add Multiply by Subtract Solve the equation y p b 5 5. a p r 5 6 y 4 4 a b 3 c 7 5 Find the measure of each angle in A (45 ) B (47 23) (2 44) C ABC. C A (50 ) ( 5 9 ) (3) B Topic Find the Numbers The sum of two numbers is 45. The second number is twice the first number. Find the two numbers. Algebra 2 5

14 3.2 For use with Lesson 3.2: Solving Inequalities Solve the inequality.. 8 < < 3 y a b > > 52. 9y < a 4. b 5. 0 > < y < z > a y 2 7 > 20 9 c n 7 0 z 4 2 c < > 0.8 Geometry Write and solve an inequality for the value of. 25. Area > 24 square meters 26. Area < 36 square meters 6 m 9 m 27. Area 42 square feet 28. Area 56 square inches 2 ft 8 in. Topic Bowling Tournament After two games of bowling, Carla has a total score of 475. To win the tournament, she needs a total score of 684 or higher. Let represent the score she needs for her third game to win the tournament. Write and solve an inequality for. What is the lowest score she can get for her third game and win the tournament? Algebra 2 57

15 3.3 For use with Lesson 3.3: Solving Multi-Step Equations and Inequalities Solve the equation if possible b 5b c 4 5c 2 2c n 4 4 0n n n a 2 5a 4 Solve the inequality y > < > y > 6 2y m m Solve the equation if possible t n < > y 2 6 2m 2 24 Solve the absolute-value equation or inequality if possible n 0 m < y t > r.58 Topic 3 Algebra 2 63

16 3.4 For use with Lesson 3.4: Writing and Solving Proportions Tell whether the proportion is True or False Solve the proportion w c 6 r r In Eercises 9 22, pairs of similar triangles are shown. Find the missing lengths of the sides f e = m w 4 2w c = b = 2 a = 3 2 b = 3 2 d a = 2 5 d e c = 2 f = Topic 3 b = 4 c f = 5 c = 2 b = 3 2 c = 4 a = 3 e = 7 f d a d = Bruce traveled 345 miles in his car on 5 gallons of gasoline. How far will he be able to travel with a full tank of 8 gallons? 24. Trisha earned \$5.75 in 3 hours at her part-time job. How much would she earn for working 5 hours? Algebra 2 69

17 4. For use with Lesson 4.: Plotting Points Write the ordered pairs that correspond to the points labeled A, B, C, and D in the coordinate plane.. y 2. y 3. A B y C B D C A D A C B D 4. y 5. y 6. y A C B B D A A D B D C C Plot and label the ordered pairs in a coordinate plane. 7. A 0, 2, B, 3, C 4, 0 8. A 6, 3, B 0, 0, C 3, 3 9. A 2, 4, B 0, 5, C 2, 2 0. A 4, 0, B 6, 3, C 5,. A 3, 8, B 0, 7, C 0, 0 2. A 6, 6, B, 3, C 2, 4 3. A 0, 2.5, B.5, 3, C 3, A 2, 0, B 23 4, 2 3, C 3, Plot the triangle with vertices at A 5, 8, B 2, 3, and C 3, 4 in a coordinate plane. 6. Plot the parallelogram with vertices at A 5, 3, B 2, 9, C 5, 9, and D 2, 3 in a coordinate plane. Without plotting the point, tell whether it is in Quadrant, Quadrant 2, Quadrant 3, or Quadrant , , , , , 8 22., 23. 4, , 3 True or False? Determine whether the statement is true or false. 25. In the ordered pair 6, 8, 6 is the -coordinate. 26. The point 0, 4 is in Quadrant Each point in a coordinate plane corresponds to an ordered pair of real numbers. Topic 4 Algebra 2 75

18 4.2 For use with Lesson 4.2: Slope-Intercept Form of a Linear Equation Find the slope and y-intercept of the graph of the equation.. y 5 2. y y y y 8. y y y Graph the equation. 3. y 2 4. y y 4 7. y y y y y 6 y y 2 0 y 5 y 3 2 y 3 4 Write the equation in slope-intercept form. Then graph the equation. 22. y y y y y 2 4 y 3 0 Match the equation with its graph. A. y B. y C. y y 29. y 30. y 2 Snowstorm In Eercises 3 and 32, snow fell at a rate of inch per 3 hour. Before the snowstorm began, there were already 5 inches of snow on the ground. The equation y 2 models the depth y 3 5 of snow on the ground after hours. Topic 4 3. What is the slope of y 2 What is the y-intercept? 3 5? 32. Graph the amount of snow on the ground during the snowstorm. 80 Algebra 2

19 4.3 For use with Lesson 4.3: Quick Graphs Using Intercepts Use the graph to find the -intercept and y-intercept of the line.. y 2. y 3. y Find the -intercept of the graph of the equation. 4. 2y y y y Find the y-intercept of the graph of the equation. 0. y 3. y y y y 8 6 5y 30 y y 8 Graph the line with the given intercepts. 6. -intercept: intercept: intercept: 7 y-intercept: 2 y-intercept: 6 y-intercept: 3 Find the -intercept and the y-intercept of the line. Graph the equation. Label the points where the line crosses the aes. 9. y y y y y y y y 2 2 9y 36 Topic 4 Fundraiser In Eercises 28 3, use the following information. The girls softball team is having a spaghetti dinner to raise money for new uniforms. By selling tickets for the dinner, the team hopes to raise \$600. Let represent the number of adult tickets they sell at \$6 each, and let y represent the number of student tickets they sell at \$3 each. 28. Graph the linear function 6 3y What is the -intercept? What does it represent in this situation? 30. What is the y-intercept? What does it represent in this situation? 3. What are three possible numbers of adult and student tickets to sell that will make the softball team reach its goal? 84 Algebra 2

20 4.4 For use with Lesson 4.4: Nonlinear Equations Find the coordinates of the verte of the graph.. y y y y Sketch the graph of the function. Label the verte. 7. y 2 8. y y y y y y y y 20. y y y y 2 4 y 2 3 y y y 4 2 Sketch the graph of the function. y y y 2 4 y 4 y y y 5 y 6 y Basketball In Eercises 3 and 32, use the following information. You throw a basketball whose path can be modeled by y , where represents time (in seconds) and y represents the height of the basketball (in feet). 3. What is the maimum height that the basketball reaches? 32. In how many seconds will the basketball hit the ground if no one catches it? Topic 4 Algebra 2 89

21 5. For use with Lesson 5.: Common Monomial Factors Find the greatest common factor. Topic 5. 6, , , , , y 4, 56 4 y y 5, 5y y, 8 2 y y 2, 5y 3 Find the greatest common factor and factor it out of the epression Simplify the epression and then factor the greatest common factor out of the epression y 4 6 4y 8 Algebra 2 95

22 Topic 5 LESSON 5.2 For use with Lesson 5.2: Factoring 2 b c Match the trinomial with the correct factorization A B C D. 4 3 Choose the correct factorization. If neither is correct, find the correct factorization A. 6 8 A. 2 5 A. B. 4 2 B. 5 2 B Factor the trinomial Algebra 2

23 5.3 For use with Lesson 5.3: Factoring a 2 b c Match the trinomial with the correct factorization A B C D. 3 8 Choose the correct factorization. If neither is correct, find the correct factorization A. 3 6 A A. 4 5 B B. 6 3 B Factor the trinomial Topic 5 Algebra 2 05

24 Topic 5 LESSON 5.4 Factor the epression. For use with Lesson 5.4: Factoring Special Cases y y y 2 Factor the epression Factor the epression. Tell which special product factoring pattern you used y 2 Factor the epression completely Algebra 2

25 Topic 5 TOPIC 5 Cumulative Assessment For use after Topics 5 Evaluate the epression. Write your answer in simpliest form Simplify the epression Evaluate the epression when 4 and y 3. 2y y Simplify the epression. 5 2 y y y 3 5 y y y 5 Solve the equation or inequality < y 3 6a4 b 2 4a 0 b Solve the proportion Plot the triangle with the given vertices in a coordinate plane. 28. A 2, 4, B 5,, C 4, 29. A 4, 8, B 2, 8, C 2, Find the slope, -intercept, and y-intercept of the graph of the equation. Then graph the equation. 30. y y y 6 Factor the epression Algebra 2

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