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GED Math Practice Test Learner Resource A Draft (NSSAL) C. David Pilmer ©2015 (Last Updated: June 2015) This resource is the intellectual property of the Adult Education Division of the Nova Scotia Department of Labour and Advanced Education. The following are permitted to use and reproduce this resource for classroom purposes. NS CLO instructors delivering GED Math curriculum within the Nova Scotia Adult Learning Program Canadian public school teachers delivering public school curriculum Canadian nonprofit tuition-free adult basic education programs The following are not permitted to use or reproduce this resource without the written authorization of the Adult Education Division of the Nova Scotia Department of Labour and Advanced Education. Upgrading programs at post-secondary institutions Core programs at post-secondary institutions Public or private schools outside of Canada Basic adult education programs outside of Canada Individuals, not including teachers or instructors, are permitted to use this resource for their own learning. They are not permitted to make multiple copies of the resource for distribution. Nor are they permitted to use this resource under the direction of a teacher or instructor at an unauthorized learning institution. Acknowledgments The Adult Education Division would like to thank the following ALP instructors for piloting this resource and offering suggestions during its development. Patrick Carruthers (EHCL) Andre Davey (Metroworks) Shannon Davis (YCLN) Marcia Franklin (DLN) Florence MacEachern (ACALA) Sheri MacNeil (DALA) Dale Taylor (Metroworks) Phil van den Hevvel (DLN) Table of Contents Introduction for Instructors ………………………………………………………………….. ii Word Problems: Whole Numbers and Money ………………………….…………………… Proportional Reasoning ……………………………………………………………………… Statistics and Probability …………………………………………………………..………… Measurement …………………………………………………………………………….…... Graphs and Functions ………………………………………………………………………… Algebra ……………………………………………………………..………...…………….... Geometry and Trigonometry …………………………………………………………….…... 1 11 18 25 31 38 42 Answers ……………………………………………………………………………………… 45 NSSAL ©2015 i Draft C. D. Pilmer Introduction for Instructors This learner resource, which is an adaption of the GED Math Customized Practice Resource, is designed so that learners can experience a variety of “true” GED math practice test questions (i.e. multi-step, multi-concept problem solving questions). The original GED Math customized resource, which comes in a MS Word version, allows instructors to create a variety of customized GED practice tests. The only limitation with this resource is that instructors need to devote some of their preparation time to create these customized tests. One of the course development team members (Andre Davey from Metroworks) suggested that we take the customized practice instructor resource and break it into three student resources (i.e. GED Math Practice Test Learner Resource A, B, and C). So that is what we did. A learner receives the complete resource and is either assigned all the questions in the booklet or specific questions; this is at the discretion of the instructor. These three resources, like the GED Math Prep Plus resource and its accompanying videos, should be given to the learners in the last six to seven weeks of their 16-week GED Math Prep course. We recommend this practice because almost all questions are multi-step and multi-concept questions. NSSAL ©2015 ii Draft C. D. Pilmer Word Problems: Whole Numbers and Money 1A You are given the following statement. Lana has 4 keys on her key chain, and Ajay has 20 keys on his key chain. Which one of the four following responses is incorrect based on the information provided in the statement above? (a) Ajay has 16 more keys than Lana (b) Lana has one-fourth the number of keys as compared to Ajay. (c) Ajay has 5 times as many keys as Lana (d) Lana and Ajay have a total of 24 keys. 2A Two brothers, Bashir and Kadeer, started a three month exercise program. The brothers devoted 2 hours a day to this program, 7 days a week. Bashir originally weighed 205 pounds but dropped 10 pounds over the three month period such that his new weight was 195 pounds. Kadeer lost 8 pounds over that same period, going from 195 pounds to 187 pounds. How much weight did Bashir lose during this exercise program? (a) 10 (b) 7 (c) 8 (d) 2 3A You are given the following statement. Dan is 52 years old. Genevieve is 48 years old. Based on this, we can say that Dan is 4 years older than Genevieve. Which one of the following statements is an incorrect reworking of the statement above? (a) Genevieve, who is 48 years old, is younger than Dan, who is 52 years old, by 4 years. (b) There is a 4 year difference between Genevieve and Dan's ages. If Genevieve is younger and 48 years old, then Dan must be 52 years old. (c) If Genevieve was born 4 years after Dan and she is 48 years old, then Dan must be 52 years old. (d) Dan is younger than Genevieve by 4 years. If he is 52 years old, then Genevieve is 48 years old. 4A To the right you have been given four numbers. Three of those four numbers can be filled into the statement below such that the statement makes sense. Ryan, who prefers running, ran for _____ minutes and biked for _____ minutes. That means he trained for a total of _____ minutes. In what order should three of those four amounts be inserted into the statement? (a) 40, 30, 70 (b) 30, 40, 70 (c) 30, 20, 40 (d) 20, 30, 70 5A Identify the only statement that makes total sense. (a) At the age of 10 years, a particular boy is 5 feet tall. That means that at 20 years, he should be 10 feet tall? (b) Roommates, who are renting a small apartment, agree to buy a $600 flat screen television (after taxes) and share the cost equally. That means that each of the 60 roommates must pay $10. (c) Rajani ran 6 kilometres per day over 7 days. In that period of time she ran a total of 42 kilometres. (d) Kendrick is 31 years old, and Marcus is 37 years old. That means that Marcus is 6 years younger than Kendrick. NSSAL ©2015 3 40 70 20 30 Draft C. D. Pilmer 6A The expression 5 7 is (a) equal to 12 (b) between 8 and 9 (c) between 4 and 5 (d) between 9 and 10 7A Find the value of the following expression: (a) 19 (b) 15 (c) 29 (d) 21 8A The local elementary school has 600 students, and the local middle school has 300 students. Combined the two schools have 30 teachers. How many more students are at the elementary school compared to the middle school? 2 2 2 3 5 3 25 2 3 __________ 9A Lisa used a 200 ml container to fill a larger container. She used the 200 ml container six times, but on the last pour she could only add 150 ml of the 200 ml. How many millilitres can the larger container hold? __________ 10A Two towns looked at the new construction that occurred in their areas over the last year. During that time apartments, singled detached houses (i.e. single family homes), semi-detached houses (i.e. duplexes), and row houses were built. The number of each type of building for the two towns is shown in the circle graphs below. Town A Town B Look at the total number of single detached and semi-detached homes built in each of these towns. How many more of these houses were built in Town A compared to Town B? __________ NSSAL ©2015 4 Draft C. D. Pilmer 11A Angela works from 9 a.m. until 5 p.m. (with a paid lunch break). If she makes $10 per hour, how much will she make, before deductions, in a 5-day work week? (a) $350 (b) $375 (c) $400 (d) $450 12A You need to purchase 12 cubic yards of topsoil. The company supplying the soil charges $20 per cubic yard of soil plus a trucking fee of $55. Before taxes, how much will it cost to purchase and have the soil dropped off at your property? (a) $295 (b) $345 (c) $680 (d) $900 13A Four roommates decide to share the following monthly expenses equally: rent - $945, electric - $130, and water - $45. Which expression below represents how much each roommate had to contribute to the monthly expenses? (a) 4 945 130 45 (b) (c) (d) 14A 945 130 45 4 945 130 45 4 4 945 130 45 Tyrus goes to a fast food restaurant. His bill before taxes is $12.70. The tax on the meal is $1.91. If Tyrus pays with a $10 and $5 bill, which one of these expressions represents the change he will receive? (a) 10 5 12.70 1.91 (b) 12.70 1.91 10 5 (c) 12.70 1.91 10 5 (d) 15A Sasha wishes to join the local gym, and has two payment options from which to choose. The first option allows her to make monthly payments of $90. The other option is a one-year membership where she makes two payments of $480 – one at the beginning of the year, and the other six months later. Assuming that Sasha is going to use the gym for one year, which expression represents her savings using the second payment option compared to the first payment option? 480 90 (a) 2 12 480 90 (b) 12 2 (c) 12 480 2 90 (d) NSSAL ©2015 12.70 1.91 10 5 12 90 2 480 5 Draft C. D. Pilmer 16A To the right, you have an input output table. You input one number and another number is generated (i.e. the output number). Which of the four rules listed below describes the relationship between the input and output number in this case? (a) output 2 input +5 Input 9 4 6 Output 23 8 14 (b) output 2 input +2 (c) output 4 input 10 (d) output 3 input 4 17A Donna is a waitress at a local restaurant, where on average she serves 8 tables per hour. She earns $11 each hour and keeps all her tips, which average $5.00 per table. How much money could Donna expect to earn between 11:00 a.m. and 2:00 p.m.? $__________ 18A A local restaurant needs flyers to advertise its business. A printing company gives the following costs. Basic set-up charge First 300 flyers Extra flyers above the 300 Cost $25 $12 per 100 flyers $8 per 100 flyers If the restaurant needs 500 flyers, what is the cost? $_________ 19A Both Sandra and Monique work from 9 a.m. until 5 p.m. (with a paid lunch) at the same retail store. Sandra makes $13 per hour and Monique makes $11 per hour. How much more does Sandra make compared to Monique in five days of work? $__________ NSSAL ©2015 6 Draft C. D. Pilmer 20A The table below shows the pay rates of three employees. The employees are paid the regular rate for the number of hours up to 40 and are paid the overtime rate for the number of extra hours they work over 40. There is also a bar graph showing the number of hours worked by each employee in a specific week. Employee regular overtime Kennedy $12/hour $18/hour Chopra $14/hour $21/hour Theriault $20/hour $30/hour Kennedy Chopra Theriault 38 39 40 41 42 43 44 45 46 47 48 49 50 51 hours w orked How much more did Theriault earn than Kennedy in this specific week? $_________ 21A The average precipitation for three Canadian cities over three months is shown in the table below. St. John’s Newfoundland Charlottetown P.E.I. Toronto Ontario June 89 mm 83 mm 63 mm July 83 mm 73 mm 81 mm August 113 mm 93 mm 67 mm What is the difference in the combined average precipitation between St John’s and Toronto for the months of July and August? __________ mm NSSAL ©2015 7 Draft C. D. Pilmer 22A The daytime high temperatures in Celsius for three cities over five days are shown in the graph below. (a) How much warmer in terms of the daytime high is it in City C on day 2 compared to City A on day 5? __________ oC (b) What is the median temperature for City B during this five day interval? __________ oC 23A There are three candidates for mayor in a municipal election. The following chart shows the election results for all four polling stations, but it is missing one number. Candice Spencer Manish Shah Stuart Knockwood Spoiled Ballots Candidates Polling Station 1 53 47 39 3 Polling Station 2 28 42 32 4 Polling Station 3 ? 39 49 2 Polling Station 4 41 24 29 3 If 470 citizens cast votes in the municipal election and they are each only permitted to vote for one candidate, which of the candidates won the election? (a) Candice Spencer (b) Manish Shah (c) Stuart Knockwood (d) Not enough information is supplied. NSSAL ©2015 8 Draft C. D. Pilmer 24A Nashi is ordering three T-shirts for $14.95 each (before taxes) and one blouse for $32.95 (before taxes) from a catalog. The shipping charges (before taxes) are listed in the table below. Price Range for Total Order $0.01 to $20 $20.01 to $40 $40.01 to $70 $70.01 to $110 Over $110 Standard Shipping (7 to 10 business days) $5.95 $7.95 $10.95 $13.95 $16.95 Priority Shipping (3 to 5 business days) $9.95 $12.95 $16.95 $21.95 $25.95 Same Day Shipping (next business day) $15.95 $20.95 $26.95 $32.95 $38.95 What is the total cost of Nashi’s purchase (before taxes) if she uses Priority shipping? $__________ 25A The following chart shows how Dave has been slowly raising the price over the last four years of the three identical apartments that he rents out in his triplex. Year Rental Price of Each Apartment 2011 $825 per month 2012 $835 per month 2013 $859 per month 2014 $879 per month 2015 $895 per month How much more money per year does he bring in for renting the three apartments in 2015 compared to 2013? $__________ 26A At Mike’s Bike Shop, 30 fewer bikes were sold in April than in May. The total number of bikes sold in April and May at the shop is less than the 115 bikes sold in June. What is the maximum number of bikes that could have been sold in April? __________ bikes NSSAL ©2015 9 Draft C. D. Pilmer 27A The local home décor store can make customized window blinds. The following chart shows the different options and prices. Width of Blinds Type 24 inches to 35 inches Vinyl Blinds Aluminum Blinds Wood Blinds Vinyl Blinds Aluminum Blinds Wood Blinds Vinyl Blinds Aluminum Blinds Wood Blinds 36 inches to 47 inches 48 inches to 59 inches Price per Item Price per Item when 2 or more of the same item are purchased $39.95 $44.95 $49.95 $59.95 $64.95 $69.95 $79.95 $84.95 $89.95 $49.95 $54.95 $59.95 $69.95 $74.95 $79.95 $89.95 $94.95 $99.95 How much would you pay (before taxes) for three 30 inch wood blinds and one 48 inch vinyl blind? $__________ 28A Tylena owns a bakery where she has one full-time employee and two part-time employees. Her weekly payroll is shown in the table below. Employment Status Full-time Part-time Part-time Employee Kiana Colin Kadeer Hours per Week Hourly Wage 40 24 16 $14.35 $12.15 $11.75 If she increases the full-time employee’s hourly wage by 40 cents and each of the part-time employee’s hourly wage by 25 cents, how much will her weekly payroll increase? $__________ 29A 3 2 Order 2.5 10 , 1.09 10 , 458, 9 10 , 6752, 3.456 10 from smallest to largest. 4 2 _____________, _____________, _____________, _____________, _____________, _____________ 30A The numbers in the following sequence are increasing by the same amount each time. Determine the next number in the sequence. Express the number on scientific notation. 9.2 10 , 9.4 10 , 9.6 10 , 9.8 10 ,… 2 2 2 2 ____________________ NSSAL ©2015 10 Draft C. D. Pilmer Proportional Reasoning 1A By mass, for every one part of an iceberg exposed above the water line, there are seven parts of the iceberg hidden below the water line. If you attempting to find the mass of the exposed portion of an iceberg that totaled 46 tonnes, which one of these expressions would you use? (a) (c) 2A 1 x 7 46 1 46 7 x 1 x 8 46 7 46 (d) 8 x (b) The local fitness store had a sale on running shoes. They advertised the following. Running Shoe Sale! Buy one pair – get the second (of equal or lesser value) for half price. If you wish to buy two pairs of shoes regularly priced at $49.95 and $34.95, how much in total will you pay during the sale (before taxes)? $__________ 3A A local hospital examined the types of injuries or accidents that appeared in their emergency room. They created the circle graph shown on the right based on their findings. (a) What is the ratio of work injuries to respiratory problems in lowest terms? (i) 7:4 (ii) 4:7 (iii) 33:100 (iv) 100:33 (b) If 2400 emergency room visits were examined to create the circle graph, how many more visits were there for automobile accidents compared to home injuries? __________ visits NSSAL ©2015 11 Draft C. D. Pilmer 4A A public library looked at the 7200 books in their collection and classified the books into five categories. The results of this classification process are reported in the circle graph shown on the right. If the library purchased an additional 800 fiction books, what percentage of the library’s total collection would now be fiction books? __________ 5A A basketball player had the following statistics during a five game tournament. Game 1 2 3 4 5 Free Throw Attempts 8 11 14 7 10 Free Throws Made 5 8 10 6 7 Over the five game tournament, what percentage of this player’s free throw attempts were not made? __________ 6A John works five 8-hour days each week. For part of his job, he repairs gasoline powered lawnmowers. Over one workweek, he records how much time he spends each day on such repairs. The information is recorded in the chart below. Monday 1 hr 45 min Tuesday 2 hr 30 min Wednesday 2 hr 15 min Thursday 3 hr Friday 1 hr 30 min What fraction of this workweek was spent on gasoline powered lawnmower repairs? 1 11 (a) (b) 4 40 9.2 3 (c) (d) 40 10 7A Colin is going on a four day road trip. On the first day of the trip, Colin travelled 650 kilometres. On the second day, he travelled 780 kilometres. If the distance travelled over these two days represented 40% of the total distance covered on the road trip, what was the total distance he travelled over the four days? ___________ kilometres NSSAL ©2015 12 Draft C. D. Pilmer 8A Richard originally bought a rectangular lot measuring 0.7 km by 0.5 km. Over the next few years he bought up the surrounding lots until he had one large rectangular lot measuring 2.1 km by 1.5 km. From the original small lot to the large lot, what is the percentage increase in the area? __________% 9A Order the numbers (a) (c) 4 3 1 8 10A , , 2 5 2 5 , , 1 8 4 , , 3 7 , 2 , 10 5 7 11 , 10 12 7 11 , 10 12 Order the numbers 75%, 4 3 , 11 , and 12 1 from smallest to largest. 8 (b) Order the numbers 90%, , 7 , 2 , 4 , 11 8 10 5 3 12 1 2 7 11 4 (d) , , , , 8 5 10 12 3 9 , 40%, 11 , 1.1, and 0.05 from smallest to largest. 16 12 9 11 (a) 40%, 0.05, 75%, , , 1.1 16 12 9 11 (c) 0.05, , 40%, , 75%, 1.1 16 12 11A 1 3 5 , -1.2, 1 10 9 (b) 0.05, 40%, (d) 0.05, 9 16 , 7 , 16 11 , 75%, 11 , 1.1 12 , 1.1, 40%, 75% 12 , and 8% from smallest to largest. 8 ________, ________, ________, ________, ________, ________ 12A Sonja’s first geography test score was 85%. On her second test, her mark dropped by 15%. If there were 80 questions on the second test that were all of the same value, how many of those did she get correct? (a) 60 (b) 49 (c) 56 (d) 52 13A A hotel is built on a rectangular lot measuring 80 metres by 60 metres. Half of the lot is used for the hotel structure, which includes the gym and indoor pool facilities. If the pool facilities represents 15% of the structure, what is area of the pool facilities? __________ m2 NSSAL ©2015 13 Draft C. D. Pilmer 14A The gross and take home pays of three employees are provided below. Brian Maurita Kimi Gross Pay $1280 $1440 $1120 Take Home Pay $921.60 $1022.40 $828.80 The deductions are what percentage of Kimi’s gross pay? __________% 15A Hinto and his boss Sarah are house painters. For every $2 that Hinto makes, Sarah makes $3. If they make $3560 for painting a house, how much does Sarah make on this job? $__________ 16A A liquidation store has 20 designer winter jackets. They normally sell each winter jacket for $150. To get rid of this stock before spring arrives, they take 10% off the current price each week until all are sold. If 25% of the stock sells in week one of the sale and 75% sells in week two, how much money in total did the store bring in on the sale of these winter jackets? $__________ 17A A new hardware store is opening and they need to hire staff for the 40 different job openings. They classified the job openings into 5 categories and looked at the number of openings in each category and the number of applications they received for those openings. All of this information is captured in the graph to the right. (a) Which category of job had a ratio of 7 applicants for every 3 openings? _____________________________ (b) Which category of job had 3.5 times more applications than applications for the accounting positions? _____________________________ NSSAL ©2015 14 Draft C. D. Pilmer 18A 7 of a company’s employees take advantage of the optional life insurance policy. What 20 percentage of the employees do not participate in this option? Each year, about __________% 19A A particular store marks up all its products by 30% after they are purchased from a supplier. If the store is selling a product $58.95, how much did the store pay for the product from the supplier? $__________ 20A A store buys T-shirts from its suppliers for $7.80 each. The store sells those same shirts for $10.95 to its customers. What percentage of the selling price is profit? __________% 21A Margo paid $8.24 in sales tax on a purchase. If she paid 15% sales tax, what was the selling of the item (i.e. price before taxes)? $__________ 22A A company, that sells electrical supplies, looked at the items purchased by a particular electrical contractor, L. Theriault Electric, during the month of May. The information is found in the table below. Item # 34152 34078 28345 32583 Purchases by L. Theriault Electric in May Description Switch, DPDT 240v 100a Switch, DPDT 240v 50a Circuit Breaker, SP 120v 30a Switch, SPDT 240v 100a 28361 Circuit Breaker, DP 120v, 15a Quantity 30 24 48 60 72 The combined sales of items 34078 and 28361 to L. Theriault Electric equal what percentage of the total items sold to this contractor? __________% 23A NSSAL ©2015 What fraction, decimal and percent are represented by the shaded portion of the trapezoid? 1 2 (a) , 0.5, 50% (b) , 0.4, 40% 2 5 1 1 1 (c) , 0.3 , 33 % (d) , 0.2, 20% 3 2 3 15 Draft C. D. Pilmer 24A Of all the items produced at the factory on Wednesday, 9 of them passed inspection. If 2070 passed 10 inspection, how many were produced that day? __________ items 25A A box, which is a rectangular-based prism, has a length of 30 cm. It has a width that is two-thirds of the length. The height of box is five-sixths of the length. What is the volume of the box? __________ cm3 26A A positive number less than or equal to 1 is represented by x. Four expressions involving x are provided 2 below. 1 x 1 5 2 x 2 x x Which one of the following series lists the expressions from smallest to largest? 5 1 2 (a) , , x 1, x 2 x x 1 5 2 (b) , , x 1, x x x2 5 1 2 (c) x 1 , x , , 2 x x 1 5 2 (d) x , x 1 , , x x2 27A If half the class are girls, and 20% of the girls speak French, what fraction of the class are French-speaking girls? ____________ 28A If x 2 9 , then determine x3 and express it as a mixed number. 4 __________ 29A Lise works 6 hours per day on Monday, Tuesday, and Thursday and 7.5 hours per day on Wednesday and Friday. She does not work on Saturday and Sunday. If she earns $387.75 per week, what is her average earning rate in dollars per hour? $__________ per hour NSSAL ©2015 16 Draft C. D. Pilmer 30A A hole with a diameter of 5 inches is being drilled into the center of a rectangular steel 8 plate that measures 2 3 inches by 1 3 inches. What is the closest distance between the 8 4 edge of the hole and the edge of the steel plate? __________ inches 31A Determine the missing measure. _________ inches ? 32A Four squares having side lengths of 1 3 inches are cut from the corners of a 8 rectangular sheet of metal measuring 9 inches by 7 inches. After the four squares are removed, the sheet metal can be folded to create a box that is open on the top. What are the dimensions of the box? __________ inches by _________ inches by _________ inches NSSAL ©2015 17 Draft C. D. Pilmer Statistics and Probability 1A Jacob ran the 100 metre dash in different competitions in 2013 and 2014. His times for each race are shown in the chart below. All times are measured in seconds. 2013 2014 11.85 12.04 12.32 11.78 11.97 11.45 12.06 12.01 What is the difference in his mean times between 2013 and 2014? __________ seconds 2A For one week in January, Praveen recorded the daytime temperature lows. However, he forgot to record Wednesday’s daytime low. Sun -4 oC Mon -8 oC Tues -3 oC Wed ? Thurs 1 oC Fri -4 oC Sat -11 oC If he is knows that the average daytime temperature low for that week is -5oC, then what was the temperature low for the day he missed? __________oC 3A You are told that a golfer’s scores for six rounds of golf have been listed from lowest to highest. However, the lowest and highest scores are not provided. ? 76 82 88 93 ? Which one of these statements is correct? (a) The mean of the golfer’s score for six rounds of golf can be determined with the information that was provided above. (b) The mode of the golfer’s score for six rounds of golf can be determined with the information that was provided above. (c) The median of the golfer’s score for six rounds of golf can be determined with the information that was provided above. (d) The mean, median, and mode of the golfer’s score for six rounds of golf cannot be determined with the information that was provided above. 4A Sapphire started a new job in the sales division of a company. The company tracked her daily sales over the first four weeks and recorded the information in the table below. Workweek 1 Workweek 2 Workweek 3 Workweek 4 Mon $263 $486 $649 $869 Tues $386 $515 $809 $1167 Wed $345 $624 $1025 $1384 Thurs $437 $745 $1181 $1538 Fri $529 $890 $1096 $1342 What is the difference in her mean sales on workweek one compared to her mean sales on workweek four? $___________ NSSAL ©2015 18 Draft C. D. Pilmer 5A How many different three-digit numbers can you make if the hundreds digit is a 1 or 2, and the ones digit is odd? (a) 100 (b) 90 (c) 60 (d) 10 6A A bag contains 5 red marbles, 3 blue marbles, and 4 green marbles. What is the probability of randomly pulling a green marble followed by a red marble from the bag if you do not return the first marble to the bag after the first pull? 31 28 (a) (b) 36 33 5 5 (c) (d) 36 33 7A Three adults exercised each day over the last 10 days. The number of minutes that each exercised each day can be found in the table below. Nasrin 40 50 55 30 25 25 35 60 70 65 Michael 30 20 20 40 60 70 75 55 45 90 Rana 30 40 50 40 45 60 90 90 75 65 What is median number of minutes that Rana exercised over this 10 day period? ___________ minutes 8A The bar graph shows the snowfall for five Nova Scotian communities over three days. (a) What is the mean snowfall for these five communities on Friday? __________ centimetres (b) What is the snowfall range for these five communities on Wednesday? __________ centimetres NSSAL ©2015 19 Draft C. D. Pilmer 9A Six adults are asked to read the same article in a magazine. The mean reading time for the article is 182 seconds. If four of the adults have reading times of 146, 168, 185, and 213 seconds, which one of these statements describes the reading times of the other two adults? (a) The two adults each have a reading time of 190 seconds. (b) One of the adults has a reading time of 178 seconds and the other has a reading time of 202 seconds. (c) The combined reading time of the two adults is 380 seconds. (d) None of the above statements is correct. 10A A telecommunications company conducted a survey in the area that they serve. They asked people of different ages if they use a computer and/or use a smartphone outside of the work or school environment. The graph below describes the results the company obtained. (a) Which one of these conclusions can be made based on the information found in this graph? (i) In the near future, there is a strong likelihood that smartphone use will be greater than computer use? (ii) During the time of the survey, the percentage of computer usage is higher than the percentage of smartphone usage within each of the five age ranges captured in the survey. (iii) People older than 65 years of age use smartphones the least. (iv) Computer usage is higher than smartphone usage because computers are generally an easier type of technology to master. (b) If 300 people between the ages of 45 and 54 were interviewed for the survey, how many responded that they use a smartphone outside of the work or school environment? __________ people (c) If the 2000 people were interviewed for the survey, how many more 25 to 34 year olds than 35 to 44 year olds use a computer outside of the work or school environment? (i) 4 people (ii) 80 people (iii) 180 people (iv) Cannot be determined; not enough information is provided. NSSAL ©2015 20 Draft C. D. Pilmer 11A The graph below shows the low and high temperatures for five Nova Scotian communities on March 25, 2015. What was the greatest range in temperatures experienced by one of these five communities on this date? __________oC 12A Final numerical and letter grades for a math class are supplied in the card below. Student Marcus A. Tiva C. Jun F. Catherine G. Rana J. Scott M. Sapphire R. Charu T. Final Numerical Grade 84% 98% 75% 71% 88% 67% 91% 78% Final Letter Grade AA+ B BA C+ A+ B+ What is the difference between Catherine G’s numerical grade and the median numerical grade for this class? __________% NSSAL ©2015 21 Draft C. D. Pilmer 13A In a phone survey, 35 participants were asked to indicate how many cats and dogs they presently own. The results are shown in the table below. Number of Cats Tally Number of Dogs 0 0 1 1 2 2 3 3 4 or more 4 or more Tally What is the mode of the data set concerned with dog ownership? __________ 14A A bag contains 20 marbles. They come in three different colors: blue, red and yellow. The probability of drawing a blue marble on a single draw is 0.30. The probability of drawing a red marble on a single draw is 0.45. How many of each marble are there? __________ blue marbles 15A __________ red marbles __________ yellow marbles A survey asked 300 people which of the three primary colors, red, yellow or blue, was their favorite. Blue 2 5 was selected by of the people, red was selected by of the people, and the remainder selected yellow. 5 12 How many of the 300 selected yellow? __________ people 16A If x is chosen at random from the set {2, 3, 4} and y is chosen at random from the set {6, 7, 8}, what is the probability, rounded to the nearest hundredth, that x y is divisible by 3? (a) 0.60 (b) 0.67 (c) 0.56 (d) 0.44 17A A number is randomly chosen from first 5 positive integers. What is the probability that the number is less than the mean? __________ 18A The mean of 100 observations was calculated as 36 but it turned out that one of the observations was misread as 83 but in reality it was 53. What will be the correct mean? __________ NSSAL ©2015 22 Draft C. D. Pilmer 19A The number of part-time and full-time staff at a particular company changed significantly between 2007 and 2012. (a) Which one of these statement best describes these changes? (i) During this time, both the part-time and full-time staff numbers increased resulting in an increase in the total number of employees from year to year. (ii) During this time, the number of full-time employees initially increased then decreased, but the steady increase in the number of part-time employees resulted in an increase in the total number of employees from year to year. (iii) During this time, the number of part-time employees initially increased then decreased. There was a steady increase in the number of full-time employees, yet the total number of employees decreased from year to year. (iv) During this time, both the number of full-time and part-time employees initially increased then decreased. This resulted in a gradual increase in the total number of employees from year to year. (b) What is the ratio of part-time staff to full-time staff in 2008? (i) 1 : 2 (ii) 2 : 1 (iii) 1 : 3 (iv) 3 : 1 (c) What is the approximate percentage increase in the number of full-time staff between 2009 and 2010? (i) 30% (ii) 52% (iii) 8% (iv) 17% 20A NSSAL ©2015 A bag contains 30 ping pong balls numbered 1 through 30. If a ball is chosen at random from the bag, what is the probability of not drawing an odd numbered ping pong ball that is greater than or equal to 21? 21 13 (a) (b) 30 15 5 1 (c) (d) 6 6 23 Draft C. D. Pilmer 21A Two towns conducted two surveys regarding methods of transportation their citizens use to get to work. Town A surveyed 1200 people and generated the first circle graph. Town B surveyed 800 people and generated the second circle graph. Town A: 1200 people surveyed Town B: 800 people surveyed (a) What is the ratio of the number of people in Town A who drive to work to the number of people in Town B who drive to work? (i) 211 148 (ii) 40 (iii) 37 60 (iv) 37 3 2 (b) Two circle graphs were used to display the findings of these two surveys. Which of the following graphical representations cannot be used to display these same findings? (i) Two separate bar graphs (ii) A double bar graph (iii) A line graph (iv) Both (i) and (ii) (c) A third town, Town C, has very similar statistics as Town B except 2% fewer people drive their own vehicle to work and 2% more walk to work. If 900 people were interviewed for Town C’s survey, how many stated that they drive their own vehicle to work? __________ people NSSAL ©2015 24 Draft C. D. Pilmer Measurement 1A A wheel with a radius of 15 centimetres is rolled along the ground so that it completes 6 revolutions. How far does the wheel travel? (a) 90 cm (b) 5 cm (c) 180 cm (d) 1350 cm 2A As shown on the right, three identical circles are surrounded snuggly by a rectangle. Which expression describes the area of the resulting shaded area? (a) 16r 6 r (b) 16r 9 r 2 (c) 3r 3 r 2 3A 2 2 (d) 12r 3 r 2 r 2 A grain silo, which is comprised of half a sphere and a cylinder, is shown on the right. If a can of paint covers 10 m2, how many cans of paint are needed to cover the outside of the silo? 4m __________ cans 18 m 4A A square-based pyramid has a volume of 720 cm3. If the height of the pyramid is 15 cm, what is the length of each side of the base? __________ cm 5A Harold is wrapping a rectangular box with wrapping paper. The box measures 50 cm by 40 cm by 30 cm. How much wrapping paper will he need if he also needs 20% more for folding and taping purposes? (a) 9400 cm2 (b) 60 000 cm2 2 (c) 72 000 cm (d) 11 280 cm2 NSSAL ©2015 25 Draft C. D. Pilmer 6A Three identical circles fit snuggly into a larger circle in the manner shown on the right. The dotted line passes through the center of all four circles. What is the ratio of the shaded region to non-shaded region? 2 (a) 1 3 (b) 1 7 (c) 2 5 (d) 2 7A The two figures on the right have the same area. The first figure is a rectangle and the second figure is a right triangle. Find the missing sides of the triangle. x y 40 cm x = __________ cm y = __________ cm 32 cm 12 cm 8A The distances around the outside of these two figures, the circle and rectangle, are the same. If so, find the missing dimension of the rectangle. 10.5 cm 4.3 cm x x = __________ cm 9A You are going to use the small cylinder to transfer water to the large cylinder. If you can fill the small cylinder to 90% of its capacity, how many times will transfer water from the small cylinder to the large cylinder to completely fill the large cylinder? 30 cm 12 cm 34 cm 20 cm __________ times NSSAL ©2015 26 Draft C. D. Pilmer 10A Four identical balls fit snuggly in a cylindrical can. The diameter of each ball is 7 cm. What is the volume of the cylindrical can? __________ cm3 7 cm 11A A spherical balloon is being blown up. At one point, its diameter is 30 cm. A few seconds later, its diameter is 42 cm. What is the percent increase in the volume of the spherical balloon during this time span? __________% 12A The dome being designed for the top of a new building is half a sphere. The dome was originally designed to have a radius of 25 metres, but the architect later decided to increase that radius by 20%. What is the ratio of the surface area of the new dome to the surface area of the original dome? (a) (c) 6 5 (b) 32 (d) 25 13A 25 4 5 A sector is a pie-shaped portion of a circle. Determine the area of the sector (the shaded region) on the right. 3.7 cm __________cm2 14A 36 120o Jim leaves the house at 10:45 a.m. and drives at an average speed of 80 km/h. How far has he travelled by 2:30 p.m? ___________kilometres NSSAL ©2015 27 Draft C. D. Pilmer 15A Three friends participated in a two day bicycle race where they travelled 70 kilometres on the first day and made the return trip of 70 kilometres on the second day. Their times for each day are provided in the chart below. First Day 2 hr 27 min 2 hr 22 min 2 hr 31 min Sarah Marc Nashi Second Day 2 hr 23 min 2 hr 18 min 2 hr 29 min What was Marc’s average speed over the two day bicycle race in kilometres per hour? __________km/h 16A The heights of three different saplings are recorded over a five month period in the chart below. May 8 cm 10 cm 9 cm Cherry Oak Maple June 11 cm 15 cm 13 cm Heights of Saplings July 15 cm 22 cm 20 cm August 20 cm 31 cm 28 cm September 23 cm 37 cm 32 cm What is the difference in the oak sapling’s height in June and its height in September in metres? __________ metres 17A The smaller circle’s area is 3 that of the larger circle. If the 5 radius of the larger circle is 5.2 cm, what is the radius of the smaller circle? 5.2 cm __________ cm 18A A square and isosceles triangle share a side. This shared side is 20 cm long. The area of the triangle is 65% of that of the square. Find the height, h, of the isosceles triangle. h __________ cm NSSAL ©2015 28 Draft C. D. Pilmer 19A The radius of a cone is changed from 2 metres to 3 metres, but the height remains the same at 6 metres. What is the percentage increase in the volume of the cone? __________% 20A Potash is mined and used mostly in the making of fertilizers. The eight counties with the largest reserves of potash are listed in the table below. Country Canada Reserves Russia 3.3 10 tonnes Belarus 7.5 10 tonnes Brazil 3.0 10 tonnes China 2.1 10 tonnes Germany 1.5 10 tonnes United States 1.3 10 tonnes Chile 7.0 10 tonnes 4.4 10 tonnes 9 9 8 8 8 8 8 7 The combined potash reserves for Canada and Russia are how much larger than the combined reserves for the United States and Chile? Express the answer without using scientific notation. ____________________ tonnes 21A The masses of the planets and sun are shown in the first table below. The other table shows the average distance between the planets and the sun Planet or Sun Mass Planet Distance from Sun Sun 1.99 10 30 kg Mercury 5.79 10 km Jupiter 1.90 10 27 kg Venus 1.08 10 km Saturn 5.68 10 26 kg Earth 1.50 10 km Neptune 1.02 10 26 kg Mars 2.28 10 km Uranus 8.68 10 25 kg Jupiter 7.79 10 km Earth 5.97 10 24 kg Saturn 1.43 10 km Venus 4.87 10 24 kg Uranus 2.87 10 km Mars 6.42 10 23 kg Neptune 4.50 10 km Mercury 3.30 10 23 kg 7 8 8 8 8 9 9 9 About how many times greater is the mass of the Sun than the mass of Venus? (a) 4 000 000 (b) 400 000 (c) 40 000 (d) 4 000 NSSAL ©2015 29 Draft C. D. Pilmer 22A What is the volume of the object on the right? (a) 1920 cm3 (b) 305 cm3 (c) 322 cm3 (d) Not enough information is supplied. 5 cm 5 cm 8 cm 12 cm 23A The scale on a map is 1 : 200 000. Two towns are 12 cm apart on the map. How far apart are the two towns in kilometres? __________ km 24A The rectangular slab for a building measures 48 metres by 24 metres. On the plans for that same building, the slab measures 60 centimetres by 30 centrimetres. What is the scale of the plans? (a) 1 : 800 (b) 1 : 125 (c) 1 : 60 (d) 1 : 80 25A Bob is 80 kilometres ahead moving at 90 kilometres per hour, and Chantelle is traveling at 110 kilometres per hour. How long for Chantelle to catch Bob? __________ hours 26A How many square tiles, each measuring 400 cm2, will be needed to cover a floor of dimension 3.8 m by 2.6 m? __________ tiles 27A What is the largest area that can be totally surrounded by 80 metres of fencing? (a) 509 m2 (b) 12.7 m2 (c) 400 m2 (d) 536 m2 28A A circle is inscribed in a square of area 9 cm2. What will be the area of the circle? __________ cm2 NSSAL ©2015 30 Draft C. D. Pilmer Graphs and Functions 1A If the point (2, -3) is reflected in the x-axis, what are the coordinates of the image point? (a) (2, 3) (b) (-3, 2) (c) (-2, -3) (d) (-2, 3) 2A There are numerous quadratic functions that have the x-intercepts -2 and 3. Which one of these equations would describe all of those possible quadratic functions? Please note that the variable a represents any real number other than zero. y a x (a) y a x x 6 (c) 3A 2 2 6 y a x 2 2 5x 6 (b) y a x x 6 (d) The quadratic functions y x 6 x a and y x 2 x b have been graphed on the same coordinate system. The values for the constants a and b have deliberately not been supplied. 2 2 y x2 6 x a y x2 2 x b Use this information to solve the quadratic equation 1 x 6 x a . There may be one solution, two solutions, or no solution to this question. 2 ____________________________ NSSAL ©2015 31 Draft C. D. Pilmer 4A Three linear functions have been plotted on the same coordinate system. Two of the three functions have the equations x y a and 2x y b , where the values for the constants a and b have deliberately not been supplied. Use this information to solve the following system of equations. x y a and 2x y b (a) (-1, -1) (b) (-4, 2) (c) (2, 5) (d) (0, 1) 5A In the beginning, a tower comprised of six blocks was constructed. Every minute, a new row of blocks was added in the manner shown below. t = 0 minutes t = 1 minute t = 2 minutes t = 3 minutes The total number of bricks in the tower is a function of time. Determine the two numbers that should be entered into the equation below which describes the number of blocks, b, in terms of the time, t, in minutes. b = _______t + _______ NSSAL ©2015 32 Draft C. D. Pilmer 6A A large container, which can hold 20 litres of water when filled to the brim, is being drained at a constant rate. The diagrams show those changes in one minute intervals. 10 L time = 0 minutes 10 L 10 L time = 1 minute 10 L time = 2 minutes time = 3 minutes The number of litres of water in the container is a function of time. Determine the two numbers that should be entered into the equation below where the amount of water, w, measured in litres is expressed in terms of time, t, measured in minutes. w = _______t + _______ 7A A ball is thrown vertically into the air. The ball’s height above the ground is on the vertical axis. Time is on the horizontal axis. (a) (b) (c) (d) 8A Tyrus has been removing water from a cylindrical steel drum using a water pump. The pump has three modes; off, slow and fast. The graph shows the relationship between the depth of the water in the drum and time. __________ centimetres (b) On average, what is the rate of change in the depth of the water with respect to time during this 20 minute interval? 100 Depth of Water in Centimetres (a) By how much does the depth of the water decrease in the 10 to 15 minute interval? 120 80 60 40 20 0 0 __________centimetres per minute NSSAL ©2015 5 10 15 20 Time in Minutes 33 Draft C. D. Pilmer 9A Which one of these tables of values corresponds to a linear function (i.e. a function that can be written in the form y mx b , where m and b are constants.)? (a) (b) x -4 -1 0 2 6 11 10A y 5 7 9 11 13 15 (c) x -1.5 -1 -0.5 0 0.5 1 (d) x -1 0 1 2 3 4 y 2 3 5 8 12 17 x -4 -2 0 2 4 6 y 9 5 1 -3 -7 -11 Which equation is equivalent to the equation y 2 x 6 ? (a) x 2 y 6 (c) x 11A y 1 2 4 8 16 32 1 y3 2 (b) x 1 y 3 2 (d) x 2 y 6 The graph of the linear function, f, is shown on the right. (a) Determine f(-3). __________ (b) Which one of the following equations represents the straight line shown on the right? (i) (ii) 4 x 3 y 6 4x 3 y 6 (iii) 3x 4 y 8 (iv) 3x 4 y 8 12A If f x 3x 4 , for what value of x does f x 14 ? (a) -38 (b) 6 (c) 46 (d) 3 1 3 13A If f x x 4 x 5 , find f 3 . 2 __________ 14A If f x x 3x 2 , for what values of x does f x 2 ? 2 x = __________ or x = __________ NSSAL ©2015 34 Draft C. D. Pilmer 15A If the point (-3, 6) is horizontally translated 5 units and vertically translated 2 units, what would be the new coordinates? ( _______, _______ ) 16A Three points representing three of the four corners of a four-sided figure have been provided. The four-sided figure is a parallelogram, but not a rectangle. If you are restricted to the region shown on the coordinate system to the right, determine the coordinates of the fourth corner. ( _______, _______ ) 17A A triangle is provided on the right. Its vertices are at (-3, 4), (4, 4), and (-1,-3). If each grid on the coordinate system represents 1 cm by 1 cm, determine the perimeter of the triangle to the nearest tenth of a centimetre (i.e. to one decimal point). __________ cm NSSAL ©2015 35 Draft C. D. Pilmer 18A A right angle triangle has been drawn on a coordinate system where each grid represents 1 cm by 1 cm. Its vertices are at (1, 6), (5, 6), and (5, 1). (a) What is the perimeter of the triangle? __________ cm (b) If this triangle is enlarged such that its area increases by 50%, what would be the area of this enlarged triangle? __________ cm2 Which one of these points lies on the linear function y (a) (-4, 12) (c) (-6, 0) 20A 2 Janice needs some gravel for her driveway. She can purchase it from two different companies. The two companies charge different trucking fees and different rates for each tonne of gravel. The following graphs show the relationship between the cost, c, in dollars and the number, n, of tonnes of gravel ordered for the two companies. (a) Determine the equation that describes the cost of the gravel for Company A in terms of the number of tonnes of gravel ordered. 110 105 Company A 100 95 90 85 80 75 Company B 70 65 60 55 50 45 40 35 30 25 c = _______n + _______ (b) When is it more economical to order from Company A? (i) n > 3 (ii) n > 55 (iii) 10 < n < 55 (iv) 0 < n < 3 NSSAL ©2015 x 4? 3 (b) (9, -2) (d) (-15, 0) Cost in Dollars 19A 36 20 15 10 5 0 0 1 2 3 4 5 6 7 8 9 Tonnes of Gravel Draft C. D. Pilmer A bacteria population is growing in a Petri dish. The concentration of bacteria per square centimeter is on the vertical axis. The time, in hours, is on the horizontal axis. (a) How long does it take for the population of bacteria to double in size? __________ hours (b) What is the concentration of bacteria after four hours? __________ bacteria per square centimetre 240 Concentration in Bacteria per Square Centimetre 21A 220 200 180 160 140 120 100 80 60 40 20 0 0 1 2 3 4 5 6 Time in Hours 22A What are the coordinates of the point shared by the linear functions y 2 x 11 and y 3 x3? 2 ( _______, _______ ) 23A If f x 5 x 7 and g x 3x 5 , for what value of x does f x g x ? __________ NSSAL ©2015 37 Draft C. D. Pilmer Algebra 1A The dimensions of the rectangle are 3n 5 cm and 2n 3 cm. If the perimeter of the rectangle is 96 cm, what is the value of n? __________ cm 2A Asra is packing smaller boxes of identical size into a larger box. The smaller boxes are cubes with a side length of 2n. The larger box has the dimensions 14n by 10n by 6n. Which expression describes the numbers of smaller boxes that will fit into the larger box? (a) 420n2 (b) 15 (c) 30n (d) 105 3A If you are given the volume of a sphere and asked to find the radius of the sphere, which one of these formulas would allow you to do so? (a) r 4V (c) r 4A (b) r 3 3 3 3 V 4 3V (d) r 4 3 4V 3 The formula d st describes the relationship amongst distance (d), speed (s), and time (t). If you have to travel 385 kilometres, how much time, in hours, would you save travelling at 110 kilometres per hour compared to 100 kilometres per hour? __________hours 5A A child’s admission to an amusement park is $1 less than half of an adult’s admission. If a child and adult admission total $41.75, which one of these equations could be used to calculate the cost, c, of an adult admission? (a) 2c 1 c 41.75 (b) 2 c1 c 41.75 (c) 1 2 6A NSSAL ©2015 c1 c 41.75 (d) 1 c 1 c 41.75 2 Yisha is purchasing gravel for her driveway. The gravel company charges $48 per tonne plus a flat delivery fee of $62. If she has $470 to spend on gravel and delivery, which equation will allow her to determine the number of tonnes, t, she can purchase? (a) 62 48t 470 (b) 48 62t 470 (c) 470 48t 62 (d) 470 62t 48 38 Draft C. D. Pilmer 7A Hamid works in a home appliance store. He can either earn $280 per week plus a 10% commission on his sales, or $360 per week plus 5% commission on his sales. What do Hamid’s sales have to be in order for the two earning options to pay the same amount? $__________ 8A Candice is 2 years less than triple her daughter’s age. If their ages total 46 years, how old is Candice? ___________ years 9A If 7 2 56 , determine the value of k. k __________ 10A If 2 x 10 y 6 , then what does 2 (a) 2 (c) 6 x 5 y equal? (b) 4 (d) 8 11A If x 3x 18 , what are the possible values for x? (a) -9 or -2 (b) -6 or 3 (c) 9 or 2 (d) 6 or -3 12A The sides of a rectangle are represented by the expressions x 3 and x 1 . If the area of the rectangle is 96 cm2, what is the value of x? 2 96 cm2 __________ cm 13A The variable x in the expression 4 x 3 2 x 9 is represented on the number line below by: A -8 -7 -6 -5 -4 (a) point B and all points less than B (c) point A and all points greater than A 14A C B -3 -2 -1 0 1 2 3 (b) all points less than point B (d) all points less than point C The area of the rectangle is represented by the expression x 2 x 24 . If the length of the rectangle is represented by the expression x 4 , what expression would represent the width of the rectangle? 2 _______________ 15A NSSAL ©2015 If a b 16 , b c 11 and a c 15 , then what will be the average of a, b and c? (a) 10 (b) 8 (c) 7 (d) 9 39 Draft C. D. Pilmer 16A What will be the value of k in the equation 2 x kx 6 0 if ‘2’ is the root of this equation? 2 __________ 17A The average of five consecutive numbers is 24. What will be largest number of these? __________ 18A If the sum of two numbers is -3 and the difference of the same two numbers is 11, what will be the product of these two numbers? __________ 19 A The dimensions of the figure are shown. (a) Which one of these expressions represents the perimeter of the figure? (i) 10x + 7y (ii) 24xy (iii) 17xy (iv) 14x + 10y 7x 2y 5y (b) Which one of these expressions represents the area of the figure? (i) 24xy (ii) 29xy (iii) 23xy (iv) 17xy 3x 20A When 15 is added to the sum of two consecutive numbers, the answer is 62. What are the two consecutive numbers? __________ and __________ 21A With the expression 2 3 (a) (b) (c) (d) x 4 , if x is decreased by 12, then the expression: increases by 8 decreases by 9 increases by 4 decreases by 6 22A With the expression 2 3 , if x is increased by 2, then the expression increases by a factor of: (a) 26 (b) 9 (c) 6 (d) 18 23A If a 2 x , b x 3 , and c x (a) 3x 14 x 9 (b) 5 x 8 x 9 (c) 3x 8 x 9 (d) 5 x 14 x 9 2 2 NSSAL ©2015 4 2 2 x , then express a b 10c in terms of x. 5 2 2 40 Draft C. D. Pilmer 24A Solve the equation x 3x 4 5 . (a) x = -1.854 or x = 4.854 (c) x = 4 or x = -1 2 (b) x = 1.854 or x = -4.854 (d) x = -4 or x = 1 25A Where does the quadratic function y x 3x 10 intersect the x-axis? (a) (5, 0) and (-2, 0) (b) (0, -10) (c) (-10, 0) (d) (-5, 0) and (2, 0) 26A Where is the linear function y 3x 6 above the x-axis? (a) x > -6 (b) x > 2 (c) x < -6 (d) x < 2 27A An angle, in degrees, is represented by x. If its supplementary angle, in degrees, is represented by the expression 3x + 20, what is the value of x? 2 __________ o NSSAL ©2015 41 Draft C. D. Pilmer Geometry and Trigonometry 1A Two planes leave the same airport at the same time. One travels north at 240 km/h and the second flies west at 180 km/h. How far apart will the planes be in 90 minutes? __________ km 2A A right triangular lot is shown below. If you travelled 220 metres around the outside of the lot, what percentage of the perimeter have you travelled? 130 m 80 m ___________% 3A Two brothers are dividing the rectangular family property into two equal parts in the manner shown on the diagram. If they wish the put a fence along that dividing line, how long will the fence be (to the nearest metre)? 65 m __________ metres 65 m A diagram of Angela’s property is shown on the right. She has all but one dimension for her property. If she needs to put fencing around the property, how much will she need? 40 m fence 20 m 4A 20 m 19 m ___________ metres 20 m 10 m 5A Determine the length of x to the nearest centimetre. 10 cm 18 cm NSSAL ©2015 17 cm 27 cm __________ cm 42 x Draft C. D. Pilmer 6A An angle is equal to one third of its supplement. What would be the measure of that angle in degrees? __________o 7A If the difference between the two acute angles of a right triangle is 10ᵒ, what is the ratio of the smaller acute angle to the larger acute triangle in simplest terms? __________ 8A Marcus wants to know the width of a river but he has no means to take that measurement directly. He decides to make some measurements along the shoreline to accomplish this task. The distance from A to B is 68 m. The distance from B to C is 49 m. The distance from B to D is 55 m. Determine the width of the river. (a) 38.6 m (c) 60.6 m 9A River A B C D (b) 76.3 m (d) 34.7 m In a certain right-angle triangle, one acute angle is two-thirds of the right-angle. What is the measure of the other acute triangle in degrees? __________o 10A In the diagram, CD is 30% larger than EB. If EB measures 40 centimetres and AE measures 35 centimetres, determine the length of AD. A __________ centimetres B E D 11A NSSAL ©2015 The circle is made up of six sectors: three shaded sectors and three non-shaded sectors. If the central angle of each shaded sector is 70 o, what fraction of the circle is not shaded? 7 5 (a) (b) 12 12 11 17 (c) (d) 36 36 43 C 70o 70o 70o Draft C. D. Pilmer 12A What is the measure of EFG ? F __________o G 120 o 100o C 13A E D What is the measure of DFG ? E __________o D 30o 35o F G 14A What is the measure of IMJ ? M L N 80o __________o 140o H 15A K J I If NP = 6.7 cm and OP = 5.5 cm, what is the length of NO? P 35o __________ cm Q 125o N O 16A Two trees stand side by side on level ground. The smaller tree is 3 metres tall and casts a shadow 4.2 metres long. At the same time, the larger tree casts a shadow 5.6 metres long. How tall is the larger tree? __________ metres NSSAL ©2015 44 Draft C. D. Pilmer Answers We have identified the difficulty level of each question (1 – easiest, 3 – challenging). We have also indicated whether the question is representative of the 2002 test series or the 2014 test series. We are working under the assumption that anything indicative of the 2002 test series will still likely appear in the 2014 test series. Word Problems: Whole Numbers and Money (pages 1 to 10) 1A Level 2 2002 Test Series (b) Lana has one-fourth the number of keys as compared to Ajay. 2A Level 1 2002 Test Series (a) 10 3A Level 2 2002 Test Series (d) Dan is younger than Genevieve by 4 years. If he is 52 years old, then Genevieve is 48 years old. 4A Level 1 2002 Test Series (a) 40, 30, 70 5A Level 1 2002 Test Series (c) Rajani ran 6 kilometres per day over 7 days. In that period of time she ran 42 kilometres. 6A Level 2 2002 Test Series (b) between 8 and 9 7A Level 2 2002 Test Series (d) 21 8A Level 1 2002 Test Series 300 9A Level 1 2002 Test Series 1350 10A Level 1 2002 Test Series 180 11A Level 1 2002 Test Series (c) $400 12A Level 1 2002 Test Series (a) $295 13A Level 2 2002 Test Series 945 130 45 (c) 4 14A Level 2 2002 Test Series (a) 10 5 12.70 1.91 NSSAL ©2015 45 Draft C. D. Pilmer 15A Level 3 2002 Test Series (d) 12 90 2 480 16A Level 3 2002 Test Series (d) output 3 input 4 17A Level 2 2002 Test Series $153 18A Level 2 2002 Test Series $77 19A Level 2 2002 Test Series $80 20A Level 3 2002 Test Series $344 21A Level 2 2002 Test Series 48 mm 22A Level 3 2002 Test Series (a) 5oC (b) 19 oC 23A Level 3 2002 Test Series (a) Candice Spencer 24A Level 2 2002 Test Series $99.75 25A Level 3 2002 Test Series $1296 26A Level 3 2002 Test Series 42 bikes 27A Level 3 2002 Test Series $239.80 28A Level 2 2002 Test Series $26 29A Level 3 2002 Test Series 2 3 3.456 10 , 458, 9 10 , 2.5 10 , 6752, 1.09 10 2 30A Level 3 2002 Test Series 1 10 NSSAL ©2015 4 3 46 Draft C. D. Pilmer Proportional Reasoning (pages 11 to 17) 1A Level 2 2002 Test Series (b) 1 x 8 46 2A Level 1 2002 Test Series $67.43 3A Level 2 2002 Test Series (a) (i) 7:4 (b) 264 visits 4A Level 3 2002 Test Series 44.2% or 44% 5A Level 2 2002 Test Series 28% 6A Level 2 2002 Test Series 11 (b) 40 7A Level 2 2002 Test Series 3575 kilometres 8A Level 3 2002 Test Series 800% 9A Level 2 2002 Test Series 1 2 7 11 4 (d) , , , , 8 5 10 12 3 10A Level 2 2002 Test Series 9 11 (b) 0.05, 40%, , 75%, , 1.1 16 12 11A Level 3 2002 Test Series 7 1 3 -1.2, , , 8%, , 90% 8 10 5 12A Level 2 2002 Test Series (c) 56 13A Level 3 2002 Test Series 360 m2 14A Level 2 2002 Test Series 26% 15A Level 2 2002 Test Series $2136 NSSAL ©2015 47 Draft C. D. Pilmer 16A Level 3 2002 Test Series $2497.50 17A Level 2 2002 Test Series (a) Checkout (b) Floor Staff 18A Level 1 2002 Test Series 65% 19A Level 2 2002 Test Series $45.35 20A Level 1 2002 Test Series 29% 21A Level 2 2002 Test Series $55 22A Level 2 2002 Test Series 41% 23A Level 1 2002 Test Series 2 (b) , 0.4, 40% 5 24A Level 2 2002 Test Series 2300 items 25A Level 3 2002 Test Series 15 000 cm3 26A Level 3 2014 Test Series 1 5 2 (d) x , x 1 , , x x2 27A Level 2 2002 Test Series 1 10 28A Level 2 2002 Test Series 3 3 8 29A Level 2 2002 Test Series $11.75 per hour 30A Level 3 2002 Test Series 9 inches 16 NSSAL ©2015 48 Draft C. D. Pilmer 31A Level 2 2002 Test Series 7 inches 4 16 32A Level 3 2002 Test Series 3 1 1 6 inches by 4 inches by 1 inches 8 4 4 Statistics and Probability (pages 18 to 24) 1A Level 1 2002 Test Series 0.23 seconds 2A Level 3 2002 Test Series -6oC 3A Level 3 2002 Test Series (c) The median of the golfer’s score for six rounds of golf can be determined with the information that was provided above. 4A Level 2 2002 Test Series $868 5A Level 2 2002 Test Series (a) 100 6A Level 1 2002 Test Series 5 (d) 33 7A Level 1 2002 Test Series 55 minutes 8A Level 2 2002 TestSeries (a) 11 centimetres (b) 25 centimetres 9A Level 3 2002 Test Series (c) The combined reading time of the two adults is 380 seconds. 10. Level 2 2002 Test Series (a) (ii) During the time of the survey, the percentage of computer usage is higher than the percentage of smartphone usage within each of the five age ranges captured in the survey. (b) 204 people (c) (iv) Cannot be determined; not enough information is provided. 11A Level 1 2002 Test Series 21oC 12A Level 1 2002 Test Series 10% NSSAL ©2015 49 Draft C. D. Pilmer 13A Level 1 2002 Test Series 2 14A Level 2 2002 Test Series 6 blue marbles 9 red marbles 15A Level 2 2002 Test Series 55 people 16A Level 3 2014 Test Series (c) 0.56 Level 2 2002 Test Series 0.4 17A 5 yellow marbles 18A Level 3 2002 Test Series 35.7 19A Level 2 2002 Test Series (a) (ii) During this time, the number of full-time employees initially increased then decreased, but the steady increase in the number of part-time employees resulted in an increase in the total number of employees from year to year. (b) (i) 1 : 2 (c) (iv) 17% 20A Level 2 2002 Test Series 5 (c) 6 21A Level 2 2002 Test Series 60 (a) (iii) 37 (b) (iii) A line graph (c) 315 people Measurement (pages 25 to 30) 1A Level 1 2002 Test Series (c) 180 cm 2A Level 3 2002 Test Series (d) 12r 3 r 2 2 3A Level 3 2014 Test Series 56 cans 4A Level 3 2002 Test Series 12 cm 5A Level 1 2002 Test Series (d) 11 280 cm2 NSSAL ©2015 50 Draft C. D. Pilmer 6A Level 3 2002 Test Series 2 (a) 1 7A Level 3 2002 Test Series x = 44 cm, 43.9 cm, or 43.86 cm y = 30 cm 8A Level 2 2002 Test Series x = 3 cm 9A Level 3 2002 Test Series 12 times 10A Level 2 2002 Test Series 1077 cm3 11A Level 3 2002 Test Series 174% 12A Level 3 2014 Test Series 36 (b) 25 13A Level 1 2002 Test Series 14.3 cm2 14A Level 1 2002 Test Series 300 kilometres 15A Level 2 2002 Test Series 30 km/h 16A Level 1 2002 Test Series 0.22 metres 17A Level 3 2002 Test Series 4 cm 18A Level 3 2002 Test Series 26 cm 19A Level 3 2002 Test Series 225% 20A Level 2 2002 Test Series 7 500 000 000 tonnes 21A Level 3 2002 Test Series (b) 400 000 22A Level 1 2002 Test Series (d) Not enough information is supplied. NSSAL ©2015 51 Draft C. D. Pilmer 23A Level 1 2002 Test Series 24 km 24A Level 2 2002 Test Series (d) 1 : 80 25A Level 1 2002 Test Series 4 hours 26A Level 1 2002 Test Series 247 tiles 27A Level 3 2002 Test Series (a) 509 m2 28A Level 2 2002 Test Series 7.1 cm2 Graphs and Functions (pages 31 to 37) 1A Level 1 2002 Test Series (a) (2, 3) 2A Level 2 2002 Test Series (a) y a x x 6 2 3A Level 1 2014 Test Series -3 4A Level 3 2002 Test Series (a) (-1, -1) 5A Level 1 2002 Test Series b = 3t + 6 6A Level 1 2002 Test Series w = -4t + 20 7A Level 1 2002 Test Series (a) 8A Level 2 2002 Test Series (a) 50 centimetres (b) -5 centimetres per minute NSSAL ©2015 52 Draft C. D. Pilmer 9A Level 1 2014 Test Series (d) x y -4 9 -2 5 0 1 2 -3 4 -7 6 -11 10A Level 3 2002 Test Series (c) x 1 y3 2 11A Level 2 2014 Test Series (a) 4 (b) (iv) 3x 4 y 8 12A Level 1 2014 Test Series (b) 6 13A Level 1 2014 Test Series -8 14A Level 2 2014 Test Series x = -4 or x = 1 15A Level 1 2002 Test Series (2, 8) 16A Level 1 2002 Test Series (-3, -2) 17A Level 3 2002 Test Series 22.88 cm 18A Level 2 2002 Test Series (a) 15.4 cm (b) 15 cm2 19A Level 1 2002 Test Series (b) (9, -2) 20A Level 2 2002 Test Series (a) c = 15n + 10 (b) (iv) 0 < n < 3 21A Level 1 2002 Test Series (a) 2 hours (b) 120 bacteria per square centimetre 22A Level 2 2002 Test Series (4, -3) NSSAL ©2015 53 Draft C. D. Pilmer 23A Level 1 2014 Test Series 6 Algebra (pages 38 to 41) 1A Level 2 2002 Test Series 8 cm 2A Level 3 2002 Test Series (d) 105 3A Level 3 2014 Test Series (c) r 3 3V 4 4A Level 2 2002 Test Series 0.35 hours 5A Level 2 2002 Test Series 1 c 1 c 41.75 (d) 2 6A Level 1 2002 Test Series (c) 470 48t 62 7A Level 3 2002 Test Series $1600 8A Level 2 2002 Test Series 34 years 9A Level 2 2002 Test Series 3 10A Level 3 2014 Test Series (d) 8 11A Level 1 2002 Test Series (b) -6 or 3 12A Level 2 2002 Test Series 9 cm 13A Level 2 2002 Test Series (b) all points less than point B 14A Level 2 2002 Test Series x-6 15A Level 3 2002 Test Series (c) 7 NSSAL ©2015 54 Draft C. D. Pilmer 16A Level 3 2014 Test Series 7 17A Level 2 2002 Test Series 26 18A Level 3 2002 Test Series -28 19A Level 2 2002 Test Series (a) (iv) 14x + 10y (b) (iii) 23xy 20A Level 2 2002 Test Series 23 and 24 21A Level 1 2002 Test Series (a) increases by 8 Level 2 2002 Test Series (b) 9 22A 23A Level 2 2002 Test Series (d) 5 x 14 x 9 2 24A Level 1 2014 Test Series (b) x = 1.854 or x = -4.854 25A Level 2 2014 Test Series (a) (5, 0) and (-2, 0) 26A Level 3 2014 Test Series (b) x > 2 27A Level 1 2002 Test Series 40o Geometry and Trigonometry (pages 42 to 44) 1A Level 2 2002 Test Series 450 km 2A Level 3 2002 Test Series 70.4% 3A Level 1 2002 Test Series 60 metres 4A Level 2 2002 Test Series 66.9 metres 5A Level 3 2002 Test Series 8 cm NSSAL ©2015 55 Draft C. D. Pilmer 6A Level 3 2002 Test Series 45o 7A Level 2 2002 Test Series 4:5 8A Level 3 2002 Test Series (d) 34.7 m 9A Level 1 2002 Test Series 30o 10A Level 1 2002 Test Series 45.5 centimetres 11A Level 1 2002 Test Series 5 (b) 12 12A Level 2 2002 Test Series 70o 13A Level 2 2002 Test Series 65o 14A Level 2 2002 Test Series 60o 15A Level 3 2002 Test Series 3.8 cm 16A Level 1 2002 Test Series 4 metres NSSAL ©2015 56 Draft C. D. Pilmer