Mathematics 563-106 Competency 2 Secondary 1 MATHEMATICS 106 USES MATHEMATICAL REASONING PRACTICE MIDYEAR EXAM
PART A: MULTIPLE CHOICE EACH QUESTION IS WORTH 4 MARKS 1. Which of the following expressions represents 392 written as a product of prime factors? A) 2 3 2 7 C) 3 2 2 7 B) 2 3 7 2 D) 2 3 + 7 2 2. Which of the following statements is TRUE? A) 20 + ( 60) = 40 C) 100 ( 2) 2 = 104 B) 10 + 95 = 105 D) 200 50 = 250 3. Four students in a math class are arguing about who received the best mark on a quiz: Rick received 31/40 Vanessa received 19/25 John received 12/15 Pietro received 74% Which student received the best mark in the class? A) Rick C) John B) Vanessa D) Pietro
4. Anne and her friends Jack, Max and Kebira have lots of DVDs. Anne has 12 DVDs Jack has 8 DVDs less than double the amount Anne has Max has triple the amount of DVDs as Anne Kebira has double the amount of DVDs as Jack How many DVDs do they have together? A) 40 C) 72 B) 64 D) 96 5. Tommy, Marian, Michael and Tanya notice that it is the 10 th time they have gone snowboarding together. While going up the chairlift, they thought it would be fun to each find a different way to express the number 10. Who is correct? A) Tommy says: 15 6 3 + 12 3 = 10 B) Marian says: 15 + 6 + 3 12 3 = 10 C) Michael says: 15 6 3 4 + 3 = 10 D) Tanya says: 15 + 6 3 4 3 = 10 6. One day Jenna sends an email to three friends. The next day, each of these friends then sends an email to three of their friends and this pattern continues for seven days. Which of the following series of operations represents the total number of emails that have been sent after seven days? A) 3 7 C) 3 + 6 + 9 + 12 + 15 + 18 + 21 B) 3 6 9 12 15 18 21 D) 3 + 3 2 + 3 3 + 3 4 + 3 5 + 3 6 + 3 7
PART B: SHORT ANSWER EACH QUESTION IS WORTH 4 MARKS 7. At the end of December, Harry had $625 in his bank account. Starting in January, he withdrew $50 four times, and he deposited $135 five times. In February, he withdrew $65 seven times, and he deposited $200 twice. During March break, he took $600 from his bank account. How much money did Tom have in his bank account at the end of March break? ANSWER: Harry had $ in his bank account at the end of March break. /4 8. In the Cartesian plane below, what are the coordinates of points E, F, G and H? y E G H 1 1 F x The coordinates of the points are : /4
9. Solve each problem using the correct order of operations. Show all work. a) 26 + 6 (2 + 4) 3 6 7 = (2 marks) b) 2 + (3 0 6) [(12 4) 3 2 + 10 5 + 2] = (2 marks) 10. James is preparing a fruit juice cocktail. He mixes 4 different fruit juices (apple, orange, mango and peach) together in a large container. Patrick mixes together the following amounts of each juice: Apple juice Orange juice Mango juice Peach juice 1 2 3 1 2 L 4 L 5 L 2 L 2 3 4 2 What is the total volume of fruit juice cocktail that Patrick makes?
PART C: APPLICATION EACH QUESTION IS WORTH 10 MARKS 11. Michel Therrien, the coach of the Montreal Canadiens, decided to hold a practice at an outdoor rink. Outdoor ice will only be good to skate on if the temperature is -10 C or lower. The temperature progresses day-by-day as follows: It starts at -14 C, then drops by 7 C, followed by a rise of 20 C, it then falls 19 C, and goes up by 5 C on the day of the practice. Can the Habs practice outside? The temperature on the day of the practice is. Yes, the Habs can practice outside. It is cold enough. No, the Habs can t practice outside. It is too warm.
12. The first one thousand (1000) fans to walk into an arena at the charity hockey game will have a chance to win prizes. The prizes will be handed out based on the order in which people enter the arena. Every 15th person will receive a special edition puck. Every 25th person will receive a thermos. Every 60th person will receive a T-shirt. Therefore, it is possible for some fans to win more than one prize. How many of the first 1000 fans will win all three prizes? Ans: people will win all three prizes.
13. Dean, Linda and Margaret are buying two tickets to Hawaii as a gift for their parents 25 th Wedding Anniversary. The trip costs $3100 per parent. Here is how they will split up the total cost: Margaret will pay 33% of the total cost. Linda will pay 8 5 of the amount left over after Margaret s contribution. Dean will pay the remaining amount. How much money will each of the children pay?
14. Jonathan is a track and field athlete. To improve his athletic performance, his trainer sets up a one-year cross-training program divided into three activities. Every 2 days, he must practice track and field. Every 5 days, he must work out at the gym. Every 7 days, he must go running. His trainer offers to take him out to a restaurant for dinner when he accomplishes all three activities on the same day. Dinner for two costs $29.75 and the trainer will leave a 15% tip after each meal. How much money will the trainer pay for the dinners for one full year (365 days)? ANSWER The trainer will pay $ for the dinners for one year.
15. A group of friends recorded the heights of five different trees for a science project: a fir, a maple, an oak, a pine and a birch. The fir tree is 22.0 m tall and the maple tree is 24.5 m tall. They lost the measurements of the three other trees! They do remember the following information: The oak tree is 5% taller than the fir tree. The pine tree is 5 8 times the height of the maple tree. The height of the birch is equal to the sum of the heights of the fir, the maple and the oak trees divided by three. What is the sum of the heights of the five trees?
16. Amy is having a party and plans to give each guest a box of cookies. She wants to prepare as many boxes of cookies as possible containing an identical combination of cookies. Each box of cookies will contain the same number of chocolate cookies, the same number of lemon cookies and the same number of almond cookies. Amy made 72 chocolate cookies, 60 lemon cookies and 48 almond cookies. What is the greatest number of boxes Amy can prepare and how many of each type of cookie must be in each box in order for all of the cookies to be used?