SPRING-BREAK PACKET 7 th grade mathematics

Transcription

1 M.S. 181 PABLO CASALS CHRISTOPHER WARNOCK, PRINCIPAL 800 BAYCHESTER AVENUE, BRONX, NY PHONE: Conceive, it, Believe it, Achieve it SPRING-BREAK PACKET 7 th grade mathematics (New York State Mathematics Test Preparation Reviewer) Student: Class: Due Date: 04/19/17 Prepared by: Mr T. Lindley & Mrs. J. Mataquel

2 Percent & Proportional Relationship 1. Dan works as a sales representative and he was asked to choose from the two salary options shown. $3,000 per month plus 7.6% commission on the representative s total sales $ 2,000 per week with no commission (1 month = 4 weeks) The average monthly total sales amount for each representative last year was $52,000. Based on this average, which of the two salary options would Dan choose to earn more? Show complete work. 2. Jodi, Jem, and Sally went shopping. Jem spent 15% less than Sally. Jodi spent 45% more than Jem and Sally spent $100. How much did they spend altogether? Show complete work. 3. Alex is in a buy and sell business. Last month he bought a car for $32,000. At the dealership, the car was displayed for sale for 24% more than it s buying price. If Alex will earn a 5%commission of the dealership price, how much commission will he get if the car is sold? Show complete work. 4. The table shows the prices of different numbers of envelopes on a website. For each order, the website applies a 3.5% sales tax to the price of the envelopes, plus a one-time shipping fee of $ Based on the information in the table, what will be the total cost for an order for 675 envelopes? Show complete work. ENVELOPE PRICE ($) 25 $3 50 $6 75 $9 100 $12 5. Daniel was given a 25% off of a game system that was originally priced at $384. He then sold the game system for 25% more than its discounted price. What was the price of the game system after this increase? Show complete work. 6. MS th grade enrolment is expected to increase by.4% next year. If m represents the current 7 th grade enrolment, what expression represents the expected 7 th grade enrolment next year? Show complete work. 7. Peter randomly selected 20% of the total number of customers in their restaurant and asked them about their tip amount. Of the customers surveyed, 28 chose a tip greater than $10. Based on the data, what is the most reasonable prediction of the number of customers in their restaurant who give a tip that is greater than $10? Show complete work.

3 8. Alana has a 20% off coupon that she can use in her favorite music store. If Alana plans to buy CD s that cost A, what expression represents Alana s total cost? Show complete work. 9. MS 181 accepted th grade students last year. This year the school accepted 486 students. What is the percent increase in the number of 6tth grade students accepted from last year to this year? Show complete work. 10. Henry deposited $ His money is expected to earn a simple interest of 7% per year on the initial amount deposited. If no money was added or removed from the account, what was the amount of interest Henry received at the end of six years? Show complete work. 11. Daniel bought a pack of markers for $17.00 and sold it to a classmate 35% more than the purchase price. Then he also charge his classmate a 5% tax. What was the total cost for the pack of markers? Show complete work. 12. Grace has a online store. The selling price of her books includes a 45% markup. Use an expression to find the selling price of a book that Grace bought for $132. Show complete work. 13. Mr. Davis earns $12.60 per hour for the first 20 hours he works in a week. He earns 3 1 /4 times that amount per hour for each hour beyond 20 hours in a week. Last week Mr. Davis worked 26 hours. How much money did he earn? Due to the nature of work Mr. Davis does, a health insurance payment of $14.55 was deducted from Mr. Davis earnings for the week. After the insurance deduction, payroll taxes equal to 28% of the balance were deducted. What was the amount that Mr. Davis received? Show complete work. 14. Mr. Reyes worked for a real estate agency. He sold a house for $520,000. The agency s fee for the sale was 6% of the sale price. Mr. Reyes received $4265 of the agency s fee as his commission. What percent of the agency s fee did Mr. Reyes receive? Show complete work. Expressions & Equations 15. The three steps shown were used to find an expression equivalent to 10x + 15x 30y. Step 1:? Step 2: -12y + 16x Step 3: 4(4x 3y) Which expression could be used as step 1? A. 25x 30y + 10x C. 6x 30y + 10x B. 10x 12y + 6x D. 15(x 2y) + 10x 16. Which expression represents a factorization of 48m + 72mp? A. 8(9m + 6p) C. 8p(6 + 9m) B. 8(6 + 9)mp D. 8m(9p + 6) 17. Tom earns $12 per hour and $15 for each delivery he makes. He wants to earn more than $150 in an 8-hour workday. What is the least number of deliveries he must make to reach goal? A. 3 B. 3.6 C. 4 D. None of the above

4 18. Which expression is equivalent to 5c c 4? A. 7c + 12 B. -7c - 4 C. 4 7c D. 7c Tom bought 42 yards of ribbons. The ribbon cost $2.25 per yard, including sales tax. If Tom paid with a $100 bill, how much change should he have received? A. $94.50 B. $6.50 C. -$5.50 D. $ Tammie has $22.00 to spend at the grocery store. She is going to buy bags of potatoes that cost $6.75 each and a gallon juice that cost $5.25. Write and solve an inequality that models this situation and could be used to determine the maximum number of bags of potatoes, p, Tammie can buy. Show complete work. 21. Members of a baseball team raised $ to go to a tournament. They rented a bus for $ and budgeted $32.75 per player for meals. They will spend all the money they raised. Write and solve an equation that models this situation and could be used to determine the number of players, p, he team could bring to the tournament. Show complete work. 22. A scientist uses a submarine to study ocean life. Ø She begins at sea level, which is at an elevation of 0 feet. Ø She travels straight down for 90 seconds at a speed of 3.5 feet per second. Ø She then travels directly up for 30 seconds at a speed of 2.2 feet per second. After this 120-second period, how much time, in seconds, will it take for the scientist to travel back to sea level at the submarine s maximum speed of 4.8 feet per second? Round your answer to the nearest tenth of a second. Show complete work. 23. Craig went bowling with $25 to spend. He rented shoes for $5.25 and paid $4.00 for each game. What was the greatest number of games Craig could have played? A. 4 B. 5 C. 6 D Which expression is equivalent to (7x 5) (3x 2)? A. 10x 7 B. 10x 3 C. 4x 7 D. 4x The population of a city is expected to increase by 7.5% next year. If p represents the current population, which expression represents the expected population next year? A. 1.75p B p C. p D Solve for x. 0.5x = 287 A. x = B. x = C. x = D. x = Which expression is equivalent to w 1.4w + 2.4? A. 0.4(6 + 2w) B. 0.8(9 + w) C. 1.6(3 + 2w) D. 3.6(2 + w)

5 28. For her cell plone plan, Heather pays $30 per month plus $0.05 per text. She wants to keep her bill under $60 per month. Which inequality represents the number of texts, t, Heather can send each month while staying within her budget? A. t < 600 B. t > 600 C. t < 1,800 D. t > 1, Katie boought 4 sweaters that each cost the same amount and 1 skirt that cost $20. The items she bought cost a otal of $160 before tax was added. What was the cost of each sweater? A. $20 B. $35 C. $40 D. $ Doug earns $10.50 per hour working at a restaurant. On Friday he spent 1 hours cleaning, 2 hours doing paperwork, and 1 " hours serving customers. What were Doug s earnings? A. $46.97 B. $47.25 C. $53.00 D. $ Sammy drew a rectangle that was w inches wide. The expression 2(2w) + 2(w) represents the perimeter of the rectangle that Sammy drew. Which statement relates the perimeter to the width of the rectangle? A. The perimeter is 6 inches more than the width. B. The perimeter is 6 times the width. C. The perimeter is 2 inches more than the width. D. The perimeter is 2 times the width. 32. The expression below was simplified using two properties of operations. 5(11z z) Step 1: 5(11z + 6z + 29) Step 2: 5(17z + 29) Step 3: 85z Which properties were applied in Steps 1 and 3, respectively? A. commutative property, then distributive property B. commutative property, then identity property C. associative property, then distributive property D. associative property, then commutative property 33. Mr. Gonzales has only $42.50 to spend at a clothing store. He wants to buy a shirt that costs $29, including tax, and some bracelets that cost $4.50 each, including tax. Write an equation to determine x, the maximum number of braclets Mr. Gonxzales could buy. Equation: Solve the equation to determine the number of bracelets Mr. Gonzales could buy. Show complete work.

6 Number System 34. The table below shows prices for shoe rental, games and snacks at the bowling alley. Gina rented shoes, bowled 3 games, and bought 1 order of nachos. She used a coupon for ½ off the price of her bowling games. What was Gina s total cost before tax was added? BOWLING ALLEY PRICES ITEM PRICE A. $5.75 Shoe Rental $2.75 One Game of Bowling $2.50 Small Soda $0.95 Large Soda $1.50 Nachos $1.75 B. $6.00 C. $8.25 D. $ Scientists determined that Antarctica s average winter temperature was C. The difference between this temperature and Antarctica s highest recorded temperature was What was Antarctica s highest recorded temperature? A C B C C C D C 36. Graham monthly bank statement showed the following deposits and withdrawals: - $25.20, $52.75, -$22.04, -$8.50, $94.11 If Graham s balance in the account was $47.86 at the beginning of the month, what was the account balance at the end of the month? Show complete work. 37. Convert to a decimal equivalent using long division. Show complete work. 38. Yesterday, the temperature at noon was F. By midnight, the temperature had decreased by 15.7 degrees. What was the temperature at midnight? A F B F C F D F 39. Evaluate ( 0.125) " A B C. 4.4 D What is the product of ( ) x ( )? A. " B. " C. " D. " 41. What is the decimal equivalent of? A B C D

7 42. What is the value of ( ) ( )? A. 1 " B. C. D. 1 " 43. Travis, Jessica and Robin are collecting donations for the school band. Travis wants to collect 20% more than Jessica, and Robin wants to collect 35% more than Travis. If the students meet their goals and Travis collects $43, how much money did they collect in all? A. $ B. $ C. $ D. $ Amber determined that the expression " is equivalent to ". Which statement " " describes the process Amber could have used? A. She divided by -15 and then divided the result by 41. B. She multiplied by -15 and then divided the result by 41. C. She divided by -15 and then multiplied the result by 41. D. She multiplied by -15 and then multiplied the result by A pile of newspapers in Ms. McGrath s art class was 17 inches high. Each consecutive week, for the next 5 weeks, the height of the pile of newspapers increased by 8 inches. " What was the height, in inches, of the pile after 3 weeks? A. 25 B. 26 C. 42 D Last week Rachel power walked 2 miles per day on each of the 7 days. During the same week, she also jogged 5 miles per day on 4 days. What was the total number of miles Rachel power walked and jogged last week? Show complete work Geometry 47. The scale of a model train is 1 inch to 13.5 feet. One of the cars of the model train is 5 inches long. What is the length, in feet, of the actual train car? A B C D (2014) The circumference of a circle is 11π inches. What is the area, in square inches, of the circle? Express your answer in terms of π. Show complete work. 49. What is the radius, in centimeters, of a circle that has a circumference of 16 π centimeters. A. 8 B. 16 C. 32 D. 64

8 50. The mean radius of earth is 6,371.0 kilometers and the mean radius of Earth s Moon is 1,737.5 kilometers. What is the approximate difference in the mean circumferences, in kilometers, of Earth and Earth s Moon? Round your answer to the nearest tenth of a kilometer. A. 40,030.2 B. 29,113.1 C. 14,556.6 D. 10,917.0 SHOW COMPLETE WORK: Practice 1: A circular window has a diameter of 14 in. What is area in terms of π? Practice 2: Find the radius of a circular garden with a circumference of 18π feet? Practice 3: Find the area of a circular walkway with a circumference of 12π meters? Express your answer in terms of π. Practice 4: Find the circumference of circle with an area of π144 cm? Express your answer in terms of π.