California High School Exit Examination. Mathematics Released Test Questions

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1 alifornia High School Eit Eamination Mathematics Released Test Questions alifornia epartment of Education Januar 008

2 Mathematics Released Test Questions Introduction ll alifornia public school students must satisf the alifornia High School Eit Eamination (HSEE) requirement, as well as all other state and local requirements, in order to receive a high school diploma. The HSEE is divided into two parts: English-language arts and mathematics. ll questions on the HSEE are evaluated b committees of content eperts, including alifornia educators, teachers, and administrators, to ensure the questions appropriateness for measuring the designated alifornia academic content standards in English-language arts and mathematics. In addition to content, all items are reviewed and approved to ensure their adherence to the principles of fairness and to ensure no bias eists with respect to characteristics such as gender, ethnicit, and language. This document combines released test questions that have appeared on the mathematics part of the HSEE since the school ear, and contains new test questions from the school ear. similar document for English-language arts is also available. The questions are grouped b strand (e.g., Number Sense). t the beginning of each strand section is a list of the specific standards assessed on the HSEE. Following a group of questions is a table that gives the correct answer for each question, the content standard each question is measuring, and the ear each question originall appeared on the HSEE. The following table lists each strand, the number of items that appear on the eam, and the number of released test questions that appear in this document. NUMER OF NUMER OF STRN QUESTIONS RELESE ON EXM TEST QUESTIONS Number Sense (NS) 5 Statistics, ata nalsis, and Probabilit (PS) 8 lgebra and Functions (F) 7 Measurement and Geometr (MG) 7 Mathematical Reasoning (MR) 8 lgebra I () 5 TOTL In selecting test questions for release, three criteria are used: () the questions adequatel cover the content standards assessed on the HSEE; () the questions demonstrate a range of difficult; and () the questions present a variet of was each standard can be assessed. These released test questions do not reflect all of the was the standards ma be assessed. Released test questions will not appear on future tests. For more information about the HSEE, visit the E s Web site at based on performance on released test questions. opright 007 b the alifornia epartment of Education.

3 Mathematics Released Test Questions NUMER SENSE The following ten alifornia mathematics academic content standards from the Number Sense strand are assessed on the HSEE b test questions and are represented in this booklet b 5 released test questions. These questions represent onl a few of the was in which these standards ma be assessed on the HSEE. GRE 7 NUMER SENSE Standard Set.0 Students know the properties of, and compute with, rational numbers epressed in a variet of forms:. Read, write, and compare rational numbers in scientific notation (positive and negative powers of 0) with approimate numbers using scientific notation.. dd, subtract, multipl, and divide rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole-number powers.. onvert fractions to decimals and percents and use these representations in estimations, computations, and applications.. alculate the percentage of increases and decreases of a quantit..7 Solve problems that involve discounts, markups, commissions, and profit, and compute simple and compound interest. Standard Set.0 Students use eponents, powers, and roots, and use eponents in working with fractions:. Understand negative whole-number eponents. Multipl and divide epressions involving eponents with a common base.. dd and subtract fractions b using factoring to find common denominators.. Multipl, divide, and simplif rational numbers b using eponent rules.. Use the inverse relationship between raising to a power and etracting the root of a perfect square integer; for an integer that is not square, determine without a calculator the two integers between which its square root lies and eplain wh..5 Understand the meaning of the absolute value of a number; interpret the absolute value as the distance of the number from zero on a number line; and determine the absolute value of real numbers. based on performance on released test questions. opright 007 b the alifornia epartment of Education.

4 Number Sense. The radius of the earth s orbit is 50,000,000,000 meters. What is this number in scientific notation? M = =.00 0,00. Which epression represents in scientific notation? M000 M095. The five members of a band are getting new outfits. Shirts cost $ each, pants cost $9 each, and boots cost $9 a pair. What is the total cost of the new outfits for all of the members? $90 $95 $50 $ Which of the following numerical epressions results in a negative number? ( 7) + ( ) ( ) + (7) () + (7) () + ( 7) + () 7. One hundred is multiplied b a number between 0 and. The answer has to be less than 0. between 0 and 50 but not 5. between 0 and 00 but not 50. between 0 and 00. M008 M00 M0075 M00 based on performance on released test questions. opright 007 b the alifornia epartment of Education.

5 Number Sense 8. John uses of a cup of oats per serving to make oatmeal. How man cups of oats does he need to make servings?. What number equals 8? M If Frea makes of her 5 free throws in a basketball game, what is her free throw shooting percentage? 0% 0% 80% 90% 0. Some students attend school 80 of the 5 das in a ear. bout what part of the ear do the attend school? 8% 50% 75% 80% M05 M00 M0007. The cost of an afternoon movie ticket last ear was $.00. This ear an afternoon movie ticket costs $5.00. What is the percent increase of the ticket from last ear to this ear? 0% 0% 5% 0%. The weekl sales of a magazine increased from 500,000 to 00,000. what percentage did the magazine sales increase? 7% 0% 8% 0%. Traditions lothing Store is having a sale. Shirts that were regularl priced at $0 are on sale for $7. What is the percentage of decrease in the price of the shirts? % 5% 8% 85% M058 M M080 based on performance on released test questions. opright 007 b the alifornia epartment of Education.

6 Number Sense 5. Sall puts $00.00 in a bank account. Each ear the account earns 8% simple interest. How much interest will be earned in three ears? $.00 $.00 $8.00 $0.00 M09 9. salesperson at a clothing store earns a % commission on all sales. How much commission does the salesperson earn on $00 sale? $ $5 $0 $50 a M070. pair of jeans regularl sells for $.00. The are on sale for 5% off. What is the sale price of the jeans? $.00 $8.00 $0.00 $ plaer regularl sells for $80. It is on sale for 0% off. What is the sale price of the plaer? $ $0 $ $9 8. Jana bought a car for $00 and later sold it for a 0% profit. How much did Jana sell the car for? $0 $90 $50 $70 M0870 M05 M Which number equals ( )? = Which of the following is equivalent to 7 i 7? M005 M08 M79 5 based on performance on released test questions. opright 007 b the alifornia epartment of Education.

7 Number Sense. Which fraction is equivalent to 5 + 7? Which of the following is the prime factored form of the lowest common denominator 7 8 of +? M7. 8 ( ) = 0 7. i = What is i? 8 5 M00 M0 M08 M09 5. What is? 9. What is the value of i 5 0? 7 M55 0. The square root of 50 is between 0 and. and. and. M50 and. M0 based on performance on released test questions. opright 007 b the alifornia epartment of Education.

8 Number Sense. The square of a whole number is between 500 and 00. The number must be between 0 and 5. 5 and 0. 0 and 5. 5 and Which number has the greatest absolute value? M795 M00. etween which two integers is the value of? and 7 7 and 8 8 and 9 9 and 0 M059. If =, what is the value of? or 0 or 0 or 9 or 9 M0. What is the absolute value of? M07 7 based on performance on released test questions. opright 007 b the alifornia epartment of Education.

9 Number Sense Question Number orrect nswer Standard School Year of Eam 7NS NS NS NS NS NS NS NS NS NS NS NS NS NS NS NS NS NS NS NS NS NS NS NS NS NS NS NS NS NS NS NS NS NS NS based on performance on released test questions. opright 007 b the alifornia epartment of Education.

10 Mathematics Released Test Questions STTISTIS, T NLYSIS, N PROILITY The following seven alifornia mathematics academic content standards from the Statistics, ata nalsis, and Probabilit strand are assessed on the HSEE b test questions and are represented in this booklet b 8 released test questions. These questions represent onl a few of the was in which these standards ma be assessed on the HSEE. GRE STTISTIS, T NLYSIS, N PROILITY Standard Set.0 Students compute and analze statistical measurements for data sets:. ompute the range, mean, median, and mode of data sets.* Standard Set.0 Students use data samples of a population and describe the characteristics and limitations of the samples:.5 Identif claims based on statistical data and, in simple cases, evaluate the validit of the claims. Standard Set.0 Students determine theoretical and eperimental probabilities and use these to make predictions about events:. Represent all possible outcomes for compound events in an organized wa (e.g., tables, grids, tree diagrams) and epress the theoretical probabilit of each outcome.. Represent probabilities as ratios, proportions, decimals between 0 and, and percentages between 0 and 00 and verif that the probabilities computed are reasonable; know that if P is the probabilit of an event, - P is the probabilit of an event not occurring..5 Understand the difference between independent and dependent events. GRE 7 STTISTIS, T NLYSIS, N PROILITY Standard Set.0 Students collect, organize, and represent data sets that have one or more variables and identif relationships among variables within a data set b hand and through the use of an electronic spreadsheet software program:. Know various forms of displa for data sets, including a stem-and-leaf plot or bo-and- whisker plot; use the forms to displa a single set of data or to compare two sets of data.*. Represent two numerical variables on a scatterplot and informall describe how the data points are distributed and an apparent relationship that eists between the two variables (e.g., between time spent on homework and grade level). * The crossed-out portion of this standard is not assessed on the HSEE, but is still included in grade-level standards. 9 based on performance on released test questions. opright 007 b the alifornia epartment of Education.

11 Statistics, ata nalsis, and Probabilit. onald priced si personal ompact isc () plaers. The prices are shown below. $.00, $.00, $.00, $9.00, $5.00, $.00 What is the median price? $.00 $.00 $7.00 $0.00 M09 9. The bo below shows the number of kilowatt-hours of electricit used last month at each of the houses on Harris Street. 0, 570, 570, 590, 50, 0, 590, 590, 580 What is the mode of these data? M8 7. Rico s first three test scores in biolog were 5, 90, and 7. What was his mean score? M07 0. The Smithburg town librar wanted to see what tpes of books were borrowed most often. Home Repair 7% Msteries 0% 8. The chart below shows the mathematics test scores of three students. Parisa Test 7 Mathematics Test Scores Test 8 Test 0 Test Other % Romance % rt % Science Fiction 8% Hector harles hildren s % What is Hector s mean score? M00 ccording to the circle graph shown above more hildren s books were borrowed than Romance and Science Fiction combined. more than half of the books borrowed were hildren s, Msteries, and rt combined. more Msteries were borrowed than rt and Science Fiction combined. more than half of the books borrowed were Romance, Msteries, and Science Fiction combined. 0 M0 based on performance on released test questions. opright 007 b the alifornia epartment of Education.

12 Statistics, ata nalsis, and Probabilit. Three-fourths of the members of a club attended a meeting. Ten of those attending the meeting were female. Which one of the following questions can be answered with the information given? How man males are in the club? How man females are in the club? How man male members of the club attended the meeting? How man female members of the club did not attend the meeting?. The number of games won over four ears for three teams is shown on the graph below. Number of Games Won Games Won Year Year Year Year Team Team Team M00. The table below shows the number of real estate transactions b tpe for a cit. Real Estate Transactions Tpe of Propert Sold Number of Sales Single-Famil Residence 57 ondo/townhouse 7 Mobile Home Multi-Famil ommercial 5 Land 55 Total 5 ased on the information in the table, which statement is true? More than half of the sales were singlefamil residences. More sales occurred for land than in all other areas combined. The number of condo/townhouse sales was more than 0% of the total sales. The number of mobile home and multifamil sales combined was twice the number of commercial sales. M0 Which statement is true based on this information? Team alwas came in second. Team had the best average overall. Team alwas won more games than Team. Team won more games each ear than in the previous ear. M000 based on performance on released test questions. opright 007 b the alifornia epartment of Education.

13 Statistics, ata nalsis, and Probabilit. To get home from work, urtis must get on one of the three highwas that leave the cit. He then has a choice of four different roads that lead to his house. In the diagram below, each letter represents a highwa, and each number represents a road. Road Highwa If urtis randoml chooses a route to travel home, what is the probabilit that he will travel Highwa and Road? 5. The table below shows all of the possible outcomes when flipping three fair coins at the same time. First Second Third oin oin oin H H H H H T H T H H T T T H H T H T T T H T T T Which of the following statements must be true? The probabilit that eactl two coins have the same outcome is. The probabilit of getting eactl one tail is higher than getting eactl two tails. The probabilit of getting at least one head is higher than the probabilit of getting at least one tail. The probabilit that all of the coins will land on heads is the same as the probabilit that all of the coins will land on tails. M M05 based on performance on released test questions. opright 007 b the alifornia epartment of Education.

14 Statistics, ata nalsis, and Probabilit. armen wants to bu a new car. Her choices are a -door or a -door, a convertible top or a hard top, and red, white, or black. Which of the following tree diagrams represents all the possible choices for the car? H R W R W R H W R H W R W R W H H R W R W R W R W M000 based on performance on released test questions. opright 007 b the alifornia epartment of Education.

15 Statistics, ata nalsis, and Probabilit 7. restaurant is advertising -item combination specials that must include a main dish, a vegetable, and a drink. Lunch Specials Main ish Vegetable rink hicken roccoli Water RE LUE YELLOW GREEN eef arrots Peas orn Soft drink Milk How man -item combinations include a soft drink and corn? 8 8. bucket contains bottles of apple juice, bottles of orange juice, bottles of tomato juice, and 8 bottles of water. If Kira randoml selects a bottle, what is the probabilit that she will select a drink other than water? M78 9. The spinner shown above is fair. What is the probabilit that the spinner will NOT stop on red if ou spin it one time? 50. Fran has s in a bo: countr, rock, dance, and classical. If she takes out one without looking, what is the probabilit that she will pick a rock or countr? 5% 50% 75% 00% M0009 M05 M79 based on performance on released test questions. opright 007 b the alifornia epartment of Education.

16 Statistics, ata nalsis, and Probabilit 5. These 8 cards are placed face down and shuffled. 5. Mr. Gulati is holding five cards numbered through 5. He has asked five students to each randoml pick a card to see who goes first in a game. Whoever picks the card numbered 5 goes first. Juanita picks first, gets the card numbered, and keeps the card. What is the probabilit that Yoko will get the card numbered 5 if she picks second? If eatrice turns over onl one card, what is the probabilit she will get a card with a number less than? M bag contained four green balls, three red balls, and two purple balls. Jason removed one purple ball from the bag and did NOT put the ball back in the bag. He then randoml removed another ball from the bag. What is the probabilit that the second ball Jason removed was purple? 9 M M based on performance on released test questions. opright 007 b the alifornia epartment of Education.

17 Statistics, ata nalsis, and Probabilit 5. nna has the letter tiles below in a bag. S T T I S T I S She reached in the bag and pulled out an S. She then put the tile back in the bag. If nna randoml selects a tile from the bag, what is the probabilit she will select an S again? 0% 5% 0% F 5% 0% The circle graph shown above represents the distribution of the grades of 0 students in a certain geometr class. How man students received s or s? M5 M0000 based on performance on released test questions. opright 007 b the alifornia epartment of Education.

18 Statistics, ata nalsis, and Probabilit 8 Speed of Four Runners in a 00-Meter ash 57. The graph below represents the closing price of a share of a certain stock for each da of a week. Speed (meters per second) 7 5 Value in ollars st nd rd th place place place place Runners 5. ased on the bar graph shown above, which of the following conclusions is true? Everone ran faster than meters per second. The best possible rate for the 00-meter dash is 5 meters per second. The first-place runner was four times as fast as the fourth-place runner. The second-place and third-place runners were closest in time to one another. M Monda Tuesda Wednesda Thursda Frida Which da had the greatest increase in the value of this stock over that of the previous da? Tuesda Wednesda Thursda Frida M based on performance on released test questions. opright 007 b the alifornia epartment of Education.

19 Statistics, ata nalsis, and Probabilit 58. The students at a high school were asked to name their favorite tpe of art. The table below shows the results of the surve. rt Surve Tpe of rt Number of Students Painting 7 rawing 709 Sculpture 9 Other 05 Which circle graph EST shows these data? Sculpture 5% 5% Other Sculpture 0% 0% Other rawing 5% 5% Painting Painting 5% 5% rawing Sculpture Other 5% 5% Sculpture Other 0% 0% 5% rawing 5% 5% 5% rawing Painting Painting M05 8 based on performance on released test questions. opright 007 b the alifornia epartment of Education.

20 Statistics, ata nalsis, and Probabilit 59. The Venn diagram below shows the number of girls on the soccer and track teams at a high school. 8 Soccer Track ost per Ticket (in dollars) Ticket Prices to Funland Number of Tickets Purchased How man girls are on both the soccer and track teams? 9 55 M 0. The cost of a ticket to Funland varies according to the season. Which of the following conclusions about the number of tickets purchased and the cost per ticket is EST supported b the scatterplot above? The cost per ticket increases as the number of tickets purchased increases. The cost per ticket is unchanged as the number of tickets purchased increases. The cost per ticket decreases as the number of tickets purchased increases. There is no relationship between the cost per ticket and the number of tickets purchased. M008 9 based on performance on released test questions. opright 007 b the alifornia epartment of Education.

21 Statistics, ata nalsis, and Probabilit. Which scatterplot shows a negative correlation? Number of ooks Number of Students 50 Miles riven Number of People Price per Person Number of People 50 ost of all (cents) Number of Minutes M05 0 based on performance on released test questions. opright 007 b the alifornia epartment of Education.

22 Statistics, ata nalsis, and Probabilit. The scatterplot below shows the time cheese has been aging and the amount of lactic acid present in the cheese. Lactic cid (parts per thousand) Lactic cid in heese ge of heese (das) Which statement is MOST strongl supported b the scatterplot? The longer cheese ages, the more lactic acid is present. The longer cheese ages, the less lactic acid is present. The amount of lactic acid present remains constant as cheese ages. No relationship eists between the time cheese ages and the amount of lactic acid present.. The scatterplot below shows the ages of some children and the distance each child lives from school. istance (miles) istance from School ge (ears) Which statement EST describes the relationship between age and distance from school? s age increases, the distance from school increases. s age increases, the distance from school decreases. s age increases, the distance from school remains constant. There is no relationship between age and distance from school. M055 M077 based on performance on released test questions. opright 007 b the alifornia epartment of Education.

23 Statistics, ata nalsis, and Probabilit Question Number orrect nswer Standard School Year of Eam PS PS PS PS PS PS PS PS PS PS PS PS PS PS PS PS PS PS PS PS PS PS PS PS PS PS PS PS based on performance on released test questions. opright 007 b the alifornia epartment of Education.

24 Mathematics Released Test Questions LGER N FUNTIONS The following ten alifornia mathematics academic content standards from the lgebra and Functions strand are assessed on the HSEE b 7 test questions and are represented in this booklet b released test questions. These questions represent onl a few of the was in which these standards ma be assessed on the HSEE. GRE 7 LGER N FUNTIONS Standard Set.0 Students epress quantitative relationships b using algebraic terminolog, epressions, equations, inequalities, and graphs:. Use variables and appropriate operations to write an epression, an equation, an inequalit, or a sstem of equations or inequalities that represents a verbal description (e.g., three less than a number, half as large as area ).. Use the correct order of operations to evaluate algebraic epressions such as ( + 5)..5 Represent quantitative relationships graphicall and interpret the meaning of a specific part of a graph in the situation represented b the graph. Standard Set.0 Students interpret and evaluate epressions involving integer powers and simple roots:. Interpret positive whole-number powers as repeated multiplication and negative whole-number powers as repeated division or multiplication b the multiplicative inverse. Simplif and evaluate epressions that include eponents.. Multipl and divide monomials; etend the process of taking powers and etracting roots to monomials when the latter results in a monomial with an integer eponent. Standard Set.0 Students graph and interpret linear and some nonlinear functions:. Graph functions of the form = n and = n and use in solving problems.. Graph linear functions, noting that the vertical change (change in -value) per unit of horizontal change (change in -value) is alwas the same and know that the ratio ( rise over run ) is called the slope of a graph.. Plot the values of quantities whose ratios are alwas the same (e.g., cost to the number of an item, feet to inches, circumference to diameter of a circle). Fit a line to the plot and understand that the slope of the line equals the quantities. Standard Set.0 Students solve simple linear equations and inequalities over the rational numbers:. Solve two-step linear equations and inequalities in one variable over the rational numbers, interpret the solution or solutions in the contet from which the arose, and verif the reasonableness of the results.. Solve multistep problems involving rate, average speed, distance, and time or a direct variation. based on performance on released test questions. opright 007 b the alifornia epartment of Education.

25 lgebra and Functions. Which of the following inequalities represents the statement, number,, decreased b is less than or equal to 9? < 9 M t a local bookstore, books that normall cost b dollars are on sale for 0 dollars off the normal price. How man dollars does it cost to bu books on sale? b 0 b + 0 ( b 0 ( b +0 ) ) M shopkeeper has kilograms of tea in stock. He sells 5 kilograms and then receives a new shipment weighing kilograms. Which epression represents the weight of the tea he now has? ivide a number b 5 and add to the result. The answer is 9. Which of the following equations matches these statements? n = n + = = n n + = 9 5 M000 M If n = and =, then n ( ) = 7 0 hk + 9. If h = and k =, then = What is the value of ( 5 ) when = 7? M000 M0005 ( + ) M9 based on performance on released test questions. opright 007 b the alifornia epartment of Education.

26 lgebra and Functions istance (kilometers) ar ar Time (hours) 7. fter three hours of travel, ar is about how man kilometers ahead of ar? The cost of a long distance call charged b each of two telephone companies is shown on the graph below. ost ($) ompan ompan M The graph below compares the weight of an object on Earth to its weight on the Moon. Weight on the Moon (pounds) n Object s Weight on the Moon Weight on Earth (pounds) What is the approimate weight on the Moon of an astronaut who weighs 0 pounds on Earth? 5 pounds 0 pounds 5 pounds 0 pounds M Minutes ompan is less epensive than ompan for all calls. minute calls onl. calls less than minutes. calls longer than minutes. M080 5 based on performance on released test questions. opright 007 b the alifornia epartment of Education.

27 lgebra and Functions 7. m works as a computer consultant. She charges $0 per hour for her work. Which graph shows the relationship between the number of hours m works and the amount of mone she charges for her work? Total mount harged (dollars) Total mount harged (dollars) Hours Worked 0 5 Hours Worked Total mount harged (dollars) Total mount harged (dollars) Hours Worked 0 5 Hours Worked M9 based on performance on released test questions. opright 007 b the alifornia epartment of Education.

28 lgebra and Functions 75. = 79. Simplif the epression shown below. 9 ( ) 7. What does 5 equal when =? M0879 abc abc 5 abc abc 5 ( abc )( 7ab c ) M Which epression is equivalent to 7 abi 7bc? abc 9 ab c 9 abc abc M87 M Which of the following is equivalent to ( )( )( + )? ( ) ( + ) ( )( + ) ( ) ( + ) M = M007 7 based on performance on released test questions. opright 007 b the alifornia epartment of Education.

29 8. Which of the following is the graph of =? alifornia High School Eit Eamination lgebra and Functions M00 8 based on performance on released test questions. opright 007 b the alifornia epartment of Education.

30 lgebra and Functions 8. Which of the following could be the graph of =? M000 9 based on performance on released test questions. opright 007 b the alifornia epartment of Education.

31 lgebra and Functions 8. Which graph represents the function =? M 0 based on performance on released test questions. opright 007 b the alifornia epartment of Education.

32 lgebra and Functions 8. Which equation EST represents the part of the graph shown below? 8. The slope of the line shown below is. d = 75. = 75. =. 75 =. 75 M070 0 What is the value of d? 9 M What is the slope of the line shown in the graph above? M055 based on performance on released test questions. opright 007 b the alifornia epartment of Education.

33 lgebra and Functions 87. What is the equation of the graph shown below? What is the slope of the line below? (5, 5) (, ) 0 = = + = + = M005 M0077 based on performance on released test questions. opright 007 b the alifornia epartment of Education.

34 lgebra and Functions 89. Mario drives 500 miles ever month. Which line plot correctl represents Mario s total miles driven over a period of si months? Total Miles Total Miles Month 0 5 Month Total Miles Total Miles Month 0 5 Month M5 based on performance on released test questions. opright 007 b the alifornia epartment of Education.

35 lgebra and Functions 90. The graph below shows Francine s electric bill for different months. What is the price per kilowatt-hour of Francine s electricit? 9. Solve for. = 7 Monthl Electric ill 5 $70 $0 November ecember 5 M077 ost $50 $0 $0 $0 $0 0 $0.5 $0.0 $.50 $ September 00 October 00 Kilowatt-hours 500 M08 9. In the inequalit + $ 0, 000 $ 70, 000, represents the salar of an emploee in a school district. Which phrase most accuratel describes the emploee s salar? t least $0,000 t most $0,000 Less than $0,000 More than $0, Solve for n. n < n < n < 5 n < 7 n + <7 M The owner of an apple orchard ships apples in boes that weigh kilograms (kg) when empt. The average apple weighs 0.5 kg, and the total weight of a bo filled with apples is kg. How man apples are packed in each bo? M07 M0 based on performance on released test questions. opright 007 b the alifornia epartment of Education.

36 lgebra and Functions 95. rad bought a $ binder and several packs of paper that cost $0.0 each. If his total was $.0, how man packs of paper did rad bu? 98. Sara can ride her biccle miles in 5 minutes. t this rate, how man miles can she ride her biccle in 50 minutes? M77 M 9. Stephanie is reading a 5-page book. uring the past 7 das she has read 8 pages. If she continues reading at the same rate, how man more das will it take her to complete the book? Lisa tped a 000-word essa at an average rate of 0 words per minute. If she started tping at :0 p.m. and did not take an breaks, at what time did Lisa finish tping the essa? :0 p.m. :50 p.m. 7:00 p.m. 7:0 p.m. M5 M Robert s to car travels at 0 centimeters per second (cm/sec) at high speed and 5 cm/sec at low speed. If the car travels for 5 seconds at high speed and then 0 seconds at low speed, what distance would the car have traveled? 050 cm 00 cm 5 cm 75 cm M078 5 based on performance on released test questions. opright 007 b the alifornia epartment of Education.

37 lgebra and Functions Question Number orrect nswer Standard School Year of Eam 7F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F based on performance on released test questions. opright 007 b the alifornia epartment of Education.

38 Measurement and Geometr MESUREMENT N GEOMETRY The following ten alifornia mathematics academic content standards from the Measurement and Geometr strand are assessed on the HSEE b 7 test questions and are represented in this booklet b released test questions. These questions represent onl a few of the was in which these standards ma be assessed on the HSEE. GRE 7 MESUREMENT N GEOMETRY Standard Set.0 Students choose appropriate units of measure and use ratios to convert within and between measurement sstems to solve problems:. ompare weights, capacities, geometric measures, times, and temperatures within and between measurement sstems (e.g., miles per hour and feet per second, cubic inches to cubic centimeters).. onstruct and read drawings and models made to scale.. Use measures epressed as rates (e.g., speed, densit) and measures epressed as products (e.g., person-das) to solve problems; check the units of the solutions; and use dimensional analsis to check the reasonableness of the answer. Standard Set.0 Students compute the perimeter, area, and volume of common geometric objects and use the results to find measures of less common objects. The know how perimeter, area and volume are affected b changes of scale:. Use formulas routinel for finding the perimeter and area of basic twodimensional figures and the surface area and volume of basic threedimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and clinders.. Estimate and compute the area of more comple or irregular two- and threedimensional figures b breaking the figures down into more basic geometric objects.. ompute the length of the perimeter, the surface area of the faces, and the volume of a three-dimensional object built from rectangular solids. Understand that when the lengths of all dimensions are multiplied b a scale factor, the surface area is multiplied b the square of the scale factor and volume is multiplied b the cube of the scale factor.. Relate the changes in measurement with a change of scale to the units used (e.g., square inches, cubic feet) and to conversions between units ( square foot = square inches or [ ft ] = [ in ], cubic inch is approimatel.8 cubic centimeters or [ in ] = [.8 cm ]). 7 based on performance on released test questions. opright 007 b the alifornia epartment of Education.

39 Measurement and Geometr Standard Set.0 Students know the Pthagorean theorem and deepen their understanding of plane and solid geometric shapes b constructing figures that meet given conditions and b identifing attributes of figures:. Understand and use coordinate graphs to plot simple figures, determine lengths and areas related to them, and determine their image under translations and reflections.. Know and understand the Pthagorean theorem and its converse and use it to find the length of the missing side of a right triangle and the lengths of other line segments and, in some situations, empiricall verif the Pthagorean theorem b direct measurement.. emonstrate an understanding of conditions that indicate two geometrical figures are congruent and what congruence means about the relationships between the sides and angles of the two figures. 00. One millimeter is of a meter. 000 of a meter meters. 000 meters. 0. bo is two meters tall. bout how tall is the bo in feet (ft) and inches (in.)? ( meter 9 inches ) 5 ft 0 in. 5 ft in. ft 0 in. ft in. M00 M007 8 based on performance on released test questions. opright 007 b the alifornia epartment of Education.

40 Measurement and Geometr 0. Juanita eercised for one hour. How man seconds did Juanita eercise? 0 0 0,00 0. The actual width (w) of a rectangle is 8 centimeters (cm). Use the scale drawing of the rectangle to find the actual length (l).. cm w l. cm 0. If Jill is driving at 5 miles per hour, what is her approimate speed in kilometers per hour?( mile. kilometers ) 0 7 M007 cm cm cm 5 cm M0087 M5 9 based on performance on released test questions. opright 007 b the alifornia epartment of Education.

41 Mathematics Released Test Questions 05. The scale drawing of the basketball court shown below is drawn using a scale of inch (in.) = feet (ft). in. in. What is the length, in feet, of the basketball court? 90 ft 0 ft ft 0 ft M0 0 based on performance on released test questions. opright 007 b the alifornia epartment of Education.

42 Measurement and Geometr 0. Javier is using a ruler and a map to measure the distance from Henle to Sailport. 07. scale drawing of a horse is shown below. Mt. Roger Seaside Henle urton Sailport? in entimeters (cm) The actual distance from Henle to Sailport is 0 kilometers (km). What scale was used to create the map? = 8 inches cm = km cm = km cm = 5 km cm = 0 km M9 What is the actual height of the horse, in inches (in.), from the hoof to the top of the head? M00 based on performance on released test questions. opright 007 b the alifornia epartment of Education.

43 Measurement and Geometr 08. Sit miles per hour is the same rate as which of the following? mile per minute mile per second miles per minute 0 miles per second 09. everl ran si miles at the speed of four miles per hour. How long did it take her to run that distance? hr hrs hrs hrs 0. Marcus can tpe about words per minute. If he tpes at this rate for 0 minutes without stopping, about how man words will he tpe? M07 M00. landscaper estimates that landscaping a new park will take person 8 hours. If people work on the job and the each work -hour das, how man das are needed to complete the job? 8 M5. In the figure above, the radius of the inscribed circle is inches (in.). What is the perimeter of square? π in. π in. in. 8 in. M0 M09 based on performance on released test questions. opright 007 b the alifornia epartment of Education.

44 Measurement and Geometr ft 8 ft 05 ft ft 0 feet. The largest possible circle is to be cut from a 0-foot square board. What will be the approimate area, in square feet, of the remaining board (shaded region)? ( = πr and π. ) rectangular pool feet b 8 feet is on a rectangular lot 05 feet b feet. The rest of the lot is grass. pproimatel how man square feet is grass?,00,800,000 8,000 M00 M000 9 in. 8 5 in. 5 in. 5. What is the area of the triangle shown above? square units 0 square units 88 square units 0 square units. What is the volume of the shoebo shown above in cubic inches (in. )? M09 M000 based on performance on released test questions. opright 007 b the alifornia epartment of Education.

45 Measurement and Geometr 7. What is the area, in square units, of trapezoid QRST shown below? = h ( b + b ) 7 R S 5 Q 8 V 0 T 9. In the figure shown above, all the corners form right angles. What is the area of the figure in square units? M M What is the area of the shaded region in the figure shown below? 8. One-inch cubes are stacked as shown in the drawing below. cm cm { in. { { in. What is the total surface area? 9 in. 9 in. in. 8 in. in. cm cm 8 cm cm cm cm M08 M08 based on performance on released test questions. opright 007 b the alifornia epartment of Education.

46 Measurement and Geometr. right triangle is removed from a rectangle as shown in the figure below. Find the area of the remaining part of the rectangle.. The short stairwa shown below is made of solid concrete. The height and width of each step is 0 inches (in.). The length is 0 inches. in. in. 0 in. 0 in. 8 in. 8 in. 0 in. 0 in. 0 in. in. 8 in. 5 in. in. What is the volume, in cubic inches, of the concrete used to create this stairwa? M0990 M009. In the figure below, ever angle is a right angle onni has two similar rectangular boes. The dimensions of bo are twice those of bo. How man times greater is the volume of bo than the volume of bo? 8 9 M0 What is the area, in square units, of the figure? M based on performance on released test questions. opright 007 b the alifornia epartment of Education.

47 Measurement and Geometr 5. Gina is painting the rectangular tool chest shown in the diagram below. 7. The width of the rectangle shown below is inches (in.). The length is feet (ft). in. in. ft in. 0 in. If Gina paints onl the outside of the tool chest, what is the total surface area, in square inches ( in. ), she will paint? M0. The object below is made of ten rectangular prisms, each with dimensions of 5 centimeters (cm) b cm b cm. What is the volume, in cubic centimeters, of the object? What is the area of the rectangle in square inches? 0 M0 8. One cubic inch is approimatel equal to.8 cubic centimeters. pproimatel how man cubic centimeters are there in cubic inches? cm cm cm 9. rectangular field is feet long and 0 feet wide. How man acres is the field? ( acre =,50 square feet ) M M0 M98 based on performance on released test questions. opright 007 b the alifornia epartment of Education.

48 Measurement and Geometr 0 R S T 0. Which of the following triangles R S T is the image of triangle RST that results from reflecting triangle RST across the -ais? T T 0 R S 0 R S S 0 R T S 0 R T M08 7 based on performance on released test questions. opright 007 b the alifornia epartment of Education.

49 Measurement and Geometr. The points (, ), (, ), (, ), and (5, ) are the vertices of a polgon. What tpe of polgon is formed b these points? Triangle Trapezoid Parallelogram Pentagon. The graph of rectangle is shown below. 0 What is the area, in square units, of rectangle? 0 M078. clothing compan created the following diagram for a vest. E F To show the other side of the vest, the compan will reflect the drawing across the -ais. What will be the coordinates of after the reflection? ( 7, ) 7 (, ) (, 7) (, 7) M00 M0 8 based on performance on released test questions. opright 007 b the alifornia epartment of Education.

50 Measurement and Geometr. What is the value of in the right triangle shown below? 5 feet feet 8 feet feet 8 feet 5 feet M08. What is the value of in the triangle shown above? N km 7 km 9 M0 Home 5. The club members hiked kilometers north and kilometers east, but then went directl home as shown b the dotted line. How far did the travel to get home? km 5 km km 7 km M000 9 based on performance on released test questions. opright 007 b the alifornia epartment of Education.

51 Measurement and Geometr 7. In the drawing below, the figure formed b the squares with sides that are labeled,, and z is a right triangle. 8. Which figure is congruent to the figure shown above? z Which equation is true for all values of,, and z? + = z + = z i = z = z M550 M based on performance on released test questions. opright 007 b the alifornia epartment of Education.

52 Measurement and Geometr 9. In the diagram below, heagon LMNPQR is congruent to heagon STUVWX. R L Q M P N 0. If triangles EFG and JKL are congruent, then which two segments MUST be congruent? E F S T X U W V G Which side is the same length as MN? NP TU UV WX L J M09 K EF and JK EF and JL FG and JK FG and JL M5 5 based on performance on released test questions. opright 007 b the alifornia epartment of Education.

53 Measurement and Geometr Question Number orrect nswer Standard School Year of Eam 00 7MG MG MG MG MG MG MG MG MG MG MG MG MG MG MG MG MG MG MG MG MG MG MG MG MG MG MG MG MG MG MG MG MG MG MG MG MG MG MG MG MG based on performance on released test questions. opright 007 b the alifornia epartment of Education.

54 Mathematics Released Test Questions MTHEMTIL RESONING The following si alifornia mathematics academic content standards from the Mathematical Reasoning strand are assessed on the HSEE b 8 test questions and are represented in this booklet b released test questions. These questions represent onl a few of the was in which these standards ma be assessed on the HSEE. NOTE: Each question in this strand also addresses a standard in one of the other five strands and is classified b that strand for purposes of reporting student scores. For eample, the first question in the following set is classified as 7MR. and also 7MG.. Standard Set.0 GRE 7 MTHEMTIL RESONING Students make decisions about how to approach problems:. nalze problems b identifing relationships, distinguishing relevant from irrelevant information, identifing missing information, sequencing and prioritizing information, and observing patterns.. Formulate and justif mathematical conjectures based on a general description of the mathematical question or problem posed. Standard Set.0 Students use strategies, skills, and concepts in finding solutions:. Use estimation to verif the reasonableness of calculated results.. Estimate unknown quantities graphicall and solve for them b using logical reasoning and arithmetic and algebraic techniques.. Make and test conjectures b using both inductive and deductive reasoning. Standard Set.0 Students determine a solution is complete and move beond a particular problem b generalizing to other situations:. evelop generalizations of the results obtained and the strategies used and appl them to new problem situations. 5 based on performance on released test questions. opright 007 b the alifornia epartment of Education.

55 Mathematical Reasoning. hris drove 00 kilometers from San Francisco to Santa ruz in hours and 0 minutes. What computation will give hris average speed, in kilometers per hour?. ivide 00 b.5. ivide 00 b.. Multipl 00 b.5. Multipl 00 b.. M0 flower shop deliver van traveled these distances during one week: 0., 7.8, 9., 8.7, and 5. miles. How man gallons of gas were used b the deliver van during this week? E What additional information is needed to find the area of parallelogram? = bh ( ) Length of Length of Length of E Perimeter of the parallelogram M000. What other information is needed in order to solve this problem? The average speed traveled in miles per hour The cost of gasoline per gallon The average number of miles per gallon for the van The number of different deliveries the van made 5. If n is an odd number, which of the following is true about n +? It is an odd number. It is an even number. It is a prime number. It is the same number as n. M0055 M008. shipping compan has 5 offices that shipped 0,000 packages last week. The offices were open das and used 80,000 kilowatt-hours of electricit. Which pieces of information given above are necessar to find the average number of packages shipped per da last week? the number of offices and the number of packages the number of packages and the amount of electricit used the number of packages and the number of das open during the week the number of das open during the week and the amount of electricit used M058 5 based on performance on released test questions. opright 007 b the alifornia epartment of Education.

56 Mathematical Reasoning. The table below shows the flight times from San Francisco (S.F.) to New York (N.Y.). Leave S.F. Time rrive N.Y. Time 8:0.M. :50 P.M. :00 noon 8:5 P.M. :0 P.M. :0 P.M. 9:5 P.M. 5:50.M. Which flight takes the longest? The flight leaving at 8:0.M. The flight leaving at :00 noon The flight leaving at :0 P.M. The flight leaving at 9:5 P.M. 7. If a is a positive number and b is a negative number, which epression is alwas positive? a b a + b a b a b M Use the addition problems below to answer the question. + = = = = 8 ased on this pattern, what is the sum of ? M5 M08 55 based on performance on released test questions. opright 007 b the alifornia epartment of Education.

57 Mathematical Reasoning 9. The table below shows the number of visitors to a natural histor museum during a -da period. a Number of Visitors Frida 597 Saturda 5 Sunda Monda 5 Which epression would give the EST estimate of the total number of visitors during this period? Which is the EST estimate of i79? 900 9,000 90, ,000 M M Marcus plans to bu a ompact isc () that has a regular price of $.99. It is on sale for 0% off, but Marcus will have to pa 7% sales ta. Which is the MOST reasonable estimate of the total cost of the including ta? $.50 $.50 $.50 $ The temperature on a mountain peak was 7 degrees Fahrenheit ( F ) at :00 p.m. 8:00 p.m., the temperature had dropped to 0 F. If the temperature continued to drop at about the same rate, which is the EST estimate of the temperature at :00 p.m.? 0 F F 0 F 9F 5. Sall paid $.89 for 5 plums. bout how man plums would she get for $0? M89 M05 M50 5 based on performance on released test questions. opright 007 b the alifornia epartment of Education.

58 Mathematical Reasoning 5. The graph below shows the value of Whistler ompan stock at the end of ever other ear from 99 to 000. Stock Value ($) Whistler ompan Stock Value Year From this graph, which of the following was the most probable value of Whistler ompan stock at the end of 99? $0 $ $0 $0 M based on performance on released test questions. opright 007 b the alifornia epartment of Education.