Hasan Abbas - Grade 7 Midterm Extra Practice Questions PDF

GRADE 7 MIDTERM EXTRA QUESTIONS A proportional relationship exists if the ratio of one quantity to the other is constant. MODULE 1 1. A car travels 240 miles in 4 hours. What is the unit rate in miles per hour? 2. A recipe calls for 3 cups of flour for 12 cookies. What is the unit rate i...

GRADE 7 MIDTERM EXTRA QUESTIONS A proportional relationship exists if the ratio of one quantity to the other is constant. MODULE 1 1. A car travels 240 miles in 4 hours. What is the unit rate in miles per hour? 2. A recipe calls for 3 cups of flour for 12 cookies. What is the unit rate in cups of flour per cookie? 3. A store sells 10 apples for $5. What is the unit rate in dollars per apple. What will be the cost of 14 apples? 4. A worker earns $360 for 30 hours of work. How much will he earn if he works for 24 hours? 5. What is the unit rate from the graph? Does the table represent proportional relationship? If yes find the constant of proportionality 1) 2) 3) Example 1. A recipe calls for 2/3 cup of sugar for every 1/4 cup of butter. What is the unit rate of sugar to butter? 2. A painter can paint 1/3 of a room in 1/2 hour. At this rate, how many rooms can he paint in one hour? 3. A runner can complete a 1/4 mile race in 3 minutes. At this rate, how many minutes would it take him to run a full mile? 1. Which graph is proportional and which is not? Give a reason for your answer. Calculate the constant of proportionality for the proportional graphs. Practice questions: The table shows the proportional relationship between pairs of sneakers Jake makes to sell at a craft fair and the revenue from selling them. A. Do the data in the table show a proportional relationship? How do you know? B. Draw the graph of this relationship. C. What is the constant of proportionality? D. write the equation of proportionality. Practice questions: The graph shows the number of cubic feet of water used over time at a water park that is open during the hours in the table. At this rate, how many cubic feet of water would be used at the water park on a Sunday? A. What is the unit rate in cubic feet per minute? B. What is the unit rate in cubic feet per hour? C. Write an equation for the number of cubic feet of water y used in x hours, and use it to solve the problem. D. How many cubic feet of water would be used at the water park on a Tuesday? Practice questions: 1. 2. A map of a national park uses a scale of 1 inch : 2 miles. If a trail in the park is actually 10 miles long, how long is the trail on the map? 3. A map of a city uses a scale of 1 centimeter : 500 meters. If a park is 2 centimeters long on the map, what is the actual length of the park in meters? MODULE 2 : Percent Change 1. The price of a shirt increased from $20 to $25. What is the percent increase in price? 2. A population of deer decreased from 100 to 80. What is the percent decrease in population? 3. The price of a laptop decreased from $1200 to $960. What is the percent decrease in price? 4. If a salary increased from $50,000 to $55,000, what is the percent increase? Markup and Discounts : 1. A store buys shirts for $15 each. The store then sells the shirts for $25 each. What is the percent markup on the shirts? 2. A bookstore buys books for $10 each. The bookstore then sells the books for $18 each. What is the percent markup on the books? 3. A shirt originally costs $40. It is now on sale for $32. What is the percent markdown? 4. A pair of shoes is marked down by 30%. If the original price was $120, what is the sale price? 5. A laptop originally costs $800. If the laptop is on sale for 25% off, what is the sale price? 6. A store buys shirts for $15 each. The store then sells the shirts for $25 each. What is the markup amount per shirt? Markup and Discounts (Writing equations) 1. A grocery store buys apples for $1.50 per pound and sells them with a markup of 50%. Write an equation representing the retail price y of a pound of apples in terms of the original cost x. 2. A restaurant buys chicken for $3 per pound and sells chicken dishes with a markup of 80%. Write an equation representing the retail price y of a chicken dish in terms of the original cost x of the chicken used to make it. 3.. A store is selling all toaster ovens at 15% off. Write an equation in the form y = kx to represent the sale price y in dollars of a toaster with an original retail price of x dollars. Then find the amount Jill paid for a toaster with an original retail price of $40. Tax and Gratuities 1. How much tax would you pay on a new TV that is $899 at Best Buy, if the tax rate is 6.5%? 2. Mrs. Lindenberger is buying some groceries. They total to $35.50. Sales tax is 4.5%. When she goes to pay, how much will she pay? 3. A mobile phone at Best Buy is $990 but they have to charge 6% sales tax. What is the amount of tax you would pay for the mobile phone? Commissions and Fees 1. Sharon makes money by commission rates. She gets 17% of everything she sells. If Sharon sold $37,000 worth of items this month, what is her commission for the month? 2. Linda sells furniture for a base monthly salary of $1,670 plus a commission of 4.5% of her total sales. Linda sold $607,500 of furniture in the last year. How much did Linda earn, including commission, last year? Simple Interest 1. Find the simple interest earned for principal of $2,000 at and 8% rate for 5 years. 2. Rachel invested $2,700 in a savings account earning 7% simple interest. If she invests for 2 years, how much money will she have in TOTAL? (Interest + principal) 3. Violeta Orpilla invested $4000 in an account that earns 5% interest yearly (simple interest). She forgets about it for 12 years. How much will be in the account after all that time?  MODULE 3 : Add and subtract Positive Integers John has an account balance of $20. He receives his weekly paycheck for work at his part-time job in the amount of $110. He can’t find a bike he wants, so he buys some comic books for $40. Then John finds his dream bike priced at $80, as shown. If he buys the bike now, what will his account balance be? 1. $20 2. $20+$110 =_______ 3. $130 - $40 =_______ 4. $____ - $80 = _______ Use the thermometer as a number line to answer the following questions. A. On Monday morning, it was 35 °F outside. Plot this on the thermometer. 35 °F B. By afternoon, the temperature rose 20 degrees. Is the movement up or down on the thermometer? ________________ The temperature on Monday afternoon was_______°F.  Tuesday’s high temperature was 25 °F. The temperature dropped 30 °F overnight. Model a 30 °F drop in temperature from 25 °F on the thermometer. What was the temperature overnight? The temperature overnight was ______°F. Jane wants to buy a new tablet that costs $100. She keeps a record of the money she earns and spends as shown. Will Jane have enough money to buy the tablet on Sunday? Plot all the points on the number line. 1. $ 60 2. $60 + $_____ = 3. $____ + $20 = 4. $____ - $ 10 = Does Jane have enough money to buy the tablet? __________  Add and Subtract Negative Integers 1.Latrell spins a wheel to find out 2.Mayumi spins the wheel next. 3.Scott started with the lowest how many points he adds to his The wheel stops on “–11 points.” score, he plays a penalty round. score. The wheel stops on “–5 In the penalty round, the wheel points. determines the number of points that are subtracted. The wheel stops on “- 7 points” Calculate all players current scores. 1. 8 + (-5) 2. 6 + (-11) 3. 3 - (-7) = 8 ___ = 6 ____ = 3 _____ = = =  The scores of three contestants on a game show are shown. The final question is worth 50 points. A correct answer adds 50 points to a contestant’s score. An incorrect answer deducts 50 points. PLAYER CORRECT ANSWER (+ 50) INCORRECT ANSWER (-50) MORGAN CARLOS KAYLEE 1. Natalie spins a wheel to 2.Gina has the combined lowest 3.Tyler has the combined lowest find out how many points she score of -6 and goes into a score of -6 and goes into a adds to her score. The wheel penalty round which indicates penalty round which indicates what will be subtracted. The what will be subtracted. The stops on “–6 points”. wheel stops on “-9 points” wheel stops on “- 2 points” Calculate all players current scores. 1. -2 + ( -6 ) 2. -6 - (-9) 3. -6 - ( -2 ) = -2 = -6 = -6 = = = MODULE 4 :Compute Sums of Integers A submarine descends to 800 feet below sea level. Then it descends another 200 feet. What is the submarine's final elevation? First, use a number line to find out. Then use absolute value to solve the same problem without a number line. A. Determine the final elevation of the submarine. Model the problem using the number line. B. Determine the submarine's final elevation. –800 + (–200) = The submarine's final elevation is ______feet. Recall that the absolute value of a number is the number’s distance from 0 on the number line. For example, the absolute value of –4 is 4 because –4 is 4 units from 0. A) Add the absolute values of the numbers. Choose which equation best represents the problem. |–800| + |–200| = ______ + ______ = ________ B) Find –100 + (–300) by first adding the absolute values. Find the answers in the order given in the original expression. |–100| + |–300| = ______ + _______ = ________ On another day, the temperature was 30 °F but a severe ice storm caused a temperature drop of 35 °F. How would you model this problem? Because the first number moves you right on the number line and the second number moves you left, subtract the lesser absolute value from the greater absolute value. |–35| – |30| = ___ – 30 = The football team lost 10 yards on one play and gained 7 yards on the next play. What integer represents the overall change in position? 1. Write an expression that represents the overall change in position. _______ + _______ 2. Subtract the lesser absolute value from the greater absolute value. |–10| – |7| = _____ - 7 = Later, the team lost 5 yards and then lost another 3 yards. Write an addition expression represents the overall change in position. _______ + ________ Compute Differences of Integers 1. The temperature in the afternoon was 20 °F, and it went down 30 °F by the evening. A. How would you model this problem? Use the number line to determine what the temperature was by evening. B. What subtraction equation can be used to determine the temperature that evening ? ______ - ______ = _____℉ Perry has $10. Perry also borrows $3 from Lily, and Lily tells him not to pay her back. 1. Write an expression to represent Perry’s net amount in dollars? 10 - ( ) = 2. How would you model this problem? Use the number line to determine Perry’s net amount of money in dollars. Perry’s net amount of money is _________$ 10 – (–3) = 10 +____ =. Jenny borrows $20 from Bill. Jenny is now in debt to Bill. Her debt can be represented as –20 dollars. Bill tells Jenny to ignore $12 of that loan. 1. How would you model this problem? Use the number line to determine the amount in dollars Jenny still owes Bill. 2. –20 – (–12) = –20 +_____ Jenny still owes Bill $______ Compute Sum and Difference of Rational Numbers 1. The scientist reduces the 2. On Wednesday, the temperature temperature by 3.5 °C on is increased by 20.7 °C. Show the Tuesday.Show the new temperature new temperature in °C. in °C. –____ + 20.7 = –9 – 3.5 = –12.5 – (_____) = 8.2 –9 + (____) = 3. On Thursday, the scientist 4. On the final day of the study, the increases the temperature by an temperature is decreased by 5 ½. additional 15.4 °C. Show the new Show the new temperature in °C temperature in °C. 23.6 − ____ = _____ ____ + 15.4 = _____ 23.6 + ( ____ ) = ______ 8.2 – (_____) = 23.6 1. A scuba diver jumps in the water and continues to descend until reaching −10.75 feet. How far did the diver descend? 4.5 - ( ______ ) = 4.5 + ______ = ________ ft 2. Use the number line to find the distance the diver traveled. 3. What is the difference between the diver’s ending point and starting point? -10.75 + ( - ____) = -10.75 - ______ = _______ ft Apply Properties To Multiple Step Addition and Subtraction Problems 1. Andy usually skates for about 6 hours per week. On Monday, he spent 1 ⅕ hours skating ; on Wednesday, he spent 2 ⅗ hours skating; and on Thursday, he spent 1 ⅚ hours skating. Andy wrote the following expression to find the number of hours he spent skating. Andy’s equation in order : 1 ⅕ + (2 ⅗ + 1 ⅚ ) A. How can the expression be rewritten to make it C. Proceed to solve the expression. simpler to add? (Look for common denominator) ______ + 1 ⅚ ______________________________________ 1. Convert mixed numbers to improper fractions B. Start solving the equation (PEMDAS) _______ + _______ ( 1 ⅕ + 2 ⅗ ) - Add the whole numbers first _____ +_____ = ______ = = _____ + _____ = ______ =______ Solve the following expressions : 1. 7 ⅓ - 3 ¾ 2. 2 ⅓+(4 ⅚+5 ⅓) 3. A runner trains for a marathon by running 3 ½ miles on Monday, 4 ⅕ miles on Wednesday, and 5 ⅗ miles on Friday. What is the total distance run during these three days? ( Write and expression) Terry is hiking in a valley at its lowest elevation. Abe is hiking on a different trail at an elevation of 23.5 meters above sea level. How much higher in elevation is Abe than Terry? (Convert the fraction into decimal form) 1. 23.5 - ( _____ ) = 23.5 + ______ = 23.5 + ______ = Abe is ________ meters higher in elevation than Terry. MODULE 5: Multiply Rational Numbers 1. Multiplying positive 2. Multiplying Negative numbers. numbers. What is the product of 3. Multiplying with Decimals a) Solve the following expressions : b)Find the product: DIVISION OF FRACTIONS 5 min Multiply and divide Rational NUmbers in context. A hot air balloon is flying at an altitude of 570 meters. Air is released from the balloon in order to change the altitude by –2.5 meters every second for 4 seconds. Calculate the new altitude. Step 1: Find the change in altitude. A hot tub holds 310 gallons of water. It is leaking, and the amount of water in the hot tub changes by −1.5 gallons every hour for 5 hours. What is the first step to working out this problem? How much water remains in the hot tub after 5 hours? 1. A mountain climber is at an altitude of 1,200 meters. Due to a sudden weather change, the climber descends at a rate of 3 meters every second for 8 seconds. What is the new altitude of the climber? 2. A kite is flying at an altitude of 150 meters. The wind causes the kite to descend at a rate of 3/2 meters every second for 5 seconds. What is the new altitude of the kite? MODULE 6 : Apply Properties and Strategies to Operate with Rational Numbers A family has a budget of $150 for groceries. They spend 1\4 of the budget on fruits and 1\3 on meat and poultry. Write and evaluate an expression to find how much money do they have left for other items. ? They family have $______ left. 1. A construction crew needs to build a fence that is 240 feet long. They complete 3\8 of the fence on the first day, and 1\4 on the second day. How many feet of fence do they use. Write and evaluate how many feet of fence so they use. 2. A gardener has a plot of land that is 120 square feet. They use 1\4 of the land for flowers and 1\3 for vegetables. How much land is left for other plants. Write and evaluate how much land is left? Estimate to check reasonableness - Rounding Solve Multi-step problems with Rational Numbers in Context Luis sees the sign shown and decides to hike to Wandering Twin Lake. He hike at an average rate of 1/3 mile in 6 min. 1. How many hours will it take Luis to reach Wandering Twin Lake? MODULE 7 : Write Linear Expressions in Different Forms for Situations Add, Subtract, and Factor Linear Expressions with rational Coefficients. The length of the entire path can be represented by the expression 20x + 8 a) Find an expression that represents the length of each side of the square. Complete the expressions on the diagram. b) Complete the equivalent expression for the length of the path, 20x + 8. 20x + 8 = 4(____)  Write two step equations for situations Scenario 1: Kendra is 3 times her daughter’s age plus 7 years. Kendra is 49 years old. a) Write an equation to find her daughter’s age? The cook at Sam’s Diner made 19 quiches today. This is 1 more and than 3 times the number of quiches he made yesterday. a) Write an equation to model how many quiches he made yesterday?  Simplify the following expressions: 1. 5x - 6 = 24 2. 3y + 7 = 40 3. 10a - 9 = 101