Mayde Creek Junior High December 2015

Transcription

1 7 th Grade Pre-AP Math Midterm Review Guide Mayde Creek Junior High December 2015 Name Period Teacher

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3 Thursday, December 10, 2015 Rational Number Operations and Unit Rate Today s Objectives: Gators will be able to: extend previous knowledge of sets and subsets using a visual representation to describe relationships between sets of rational numbers add, subtract, multiply, and divide rational numbers fluently apply and extend previous understandings of operations to solve problems using addition, subtraction, multiplication, and division of rational numbers represent constant rates of change in mathematical and real-world problems given pictorial, tabular, verbal, numeric, graphical, and algebraic representations, including d = rt calculate unit rates from rates in mathematical and real-world problems determine the constant of proportionality (k = y/x) within mathematical and real-world problems solve problems involving ratios, rates, and percents, including multi-step problems involving percent increase and percent decrease, and financial literacy problems convert between measurement systems, including the use of proportions and the use of unit rates Things to Remember When Adding and Subtracting Fractions Multiplying Fraction Dividing Fractions Adding and Subtracting Decimals Multiplying Decimals Dividing Decimals

4 Sets and Subsets Review Name at least one number for each description. 1. A whole number but not a natural number. 2. An integer but not a whole number. 3. An integer and a natural number. 5. A rational number but not an integer.

5 Percent of Change A figure has an area of 10 square units. You increase its area to 15 square units. By what percent does the area of the figure change? 1. Let each square on your graph paper have an area of 1 square unit. Draw a figure that has an area of 10 square units. Shade all of the squares using one color. 2 Add squares to the figure so that its area becomes 15 square units. Shade the added squares with another color. 3 Find the ratio of the added area to the original area. Express the result as a percent. This percent is called the percent of change. Percent of Change Formula =

6 Financial Literacy Vocabulary 1. is the amount of money paid to the government, in addition to the actual cost of an item, based on a specific rate or percent. 2. Discount is the 3. is the amount of money paid to a server/waiter, in addition to the actual cost of an item, usually 15% or higher. 4. Commission is the

7 1. Maria measured 4 amounts of water for an experiment in science lab. The amounts were 0.35 liter, 1.27 liters, 1.25 liters, and 1.38 liters. After the experiment, she combines the water into one beaker. To help set up for the next lab, she then redistributes the total amount evenly into 5 smaller beakers. What is the amount of water in each beaker? 2. Juan is planning a birthday party for his brother. He has an allowance of $ for the party. He went shopping and spent $35.56 for decorations, $14.35 for snacks, $21.50 for a present, and $13.50 for drinks. How much of his allowance did Juan have remaining after the shopping trip? How can you model your thinking? Is your answer reasonable? How do you know? 3. The Smith family bought a new television set. The television cost $997.20, including tax. They plan to pay for the television in 12 equal monthly payments. How much will they pay each month? 4. Mary is finishing a research project for her history class. On Monday she worked for hours, Tuesday for 3 1 hours, and Wednesday 3 for 2 2 hours. What was the average amount of 3 time spent each day working on her research project? What number sentence can you create to help solve this problem? Bonus: What is the average time in hours and minutes?

8 5. Mrs. Davis had a fruit salad recipe that called for 3 cup of fresh peaches per serving. 4 She used 9 cups of peaches to prepare the recipe. How many servings of the salad did she prepare? 6. While the family went on vacation Lisa boarded her cat at a kennel that charged $9.25 per day. If Lisa boarded her cat for 1 week and 2 days. If her deposit was 1 of the 5 total cost, what was the amount of her deposit? How can you model your thinking? 7. The 4 members on Arnold s relay team ran in a race. Their individual times were 1.23 minutes, 1.31 minutes, 1.35 minutes, and 1.18 minutes. The winning team ran the race in 5.02 minutes. What was the difference between the winning team s time and Arnold s team s time? 8. Johnnie worked 14 1 hours last week at the 2 local newspaper office. He is paid $6.50 per hour. How much money did he earn last week? Is your answer reasonable? How do you know?

9 9. A machine can make 14,400 screws in 8 hours. A second machine can make twice as many screws per hour. What is the constant of proportionality between the number of screws and the number of minutes for the second machine? 10. A drill bit completes 390 rotations in 1 minute. Which is the best estimate of the number of rotations the drill completes in 19 minutes? Answer: screws per minute. 11. Linda can type about 76 words per minute. Which is the best estimate of the number of words she can type in 1 an hour? A packet of tomato seeds for the garden costs $2.10, including tax. There are 30 seeds in each packet. What is the cost of 40 seeds? How can you model your thinking?

10 13. What is the unit price of the box of cereal? 14. What is the cost, in dollars per inch, of the sandwich with the lowest unit cost? Sandwich Size Cost ($) 6-inch inch inch Marisa s car gets an average of 28 miles per gallon of gas. She plans to drive 200 miles today and 220 miles tomorrow. How many gallons of gas should she expect to use in all? 16. A duck flew at 18 miles per hour for 3 hours, then at 15 miles per hour for 2 hours. How far did the duck fly in all?

11 Friday, December 11, 2015 Today s Objectives: Gators will be able to: Similar Figures and Transformations generalize the critical attributes of similarity, including ratios within and between similar shapes solve mathematical and real-world problems involving similar shape and scale drawing generalize the properties of orientation and congruence of rotations, reflections, translations, and dilations of two-dimensional shapes on a coordinate plane differentiate between transformations that preserve congruence and those that do not explain the effect of translations, reflections over the x- or y-axis, and rotations limited to 90, 180, 270, and 360 as applied to two-dimensional shapes on a coordinate plane using an algebraic representation Transformations Similar Figures Review Comparing Within and Between s

12 1. Solve for x. Solve for x. 3. Solve for x. 4. Solve for x.

13 5. Joanie made a scale drawing of her jewelry box. The actual box measured 10 inches by 8 inches by 5 inches. If she used a scale of 1 centimeter represents 2.5 inches, what were the dimensions of the drawing? 6. Solve for x. Length: Width: Height: 7. A woman who is 5 feet 5 inches tall is standing near the Space Needle in Seattle, Washington. She casts a 13-inch shadow at the same time that the Space Needle casts a 121-foot shadow. How tall is the Space Needle? 8. Use the diagram to determine the distance across Catfish Lake. Assume the triangles are similar.

14 9. Pentagon JKLMN is similar to pentagon VWXYZ. What is the measurement of angle X? 10. A six-foot-tall person is standing next to a flagpole. The person is casting a shadow feet in length, while the flagpole is casting a shadow 5 feet in length. How tall is the flagpole? 11. HIJ is similar to STR. What is the perimeter of STR? 12. Triangle LMN is similar to triangle XYZ. What is the length of YX?

15 Let s Review the Coordinate Plane An is a pair of numbers such as (6,-3) used to locate a point in the coordinate plane. 2) The is the first number, and it corresponds to a location on the 3) The is the second number, and it corresponds to a location on the 4) The horizontal number line is called the 5) The vertical number line is called the 7) The ordered pair for the origin is: (, ) 6) The is the point at which the number lines intersect.

16 Task 1: Patterns of TRANSLATIONS Directions: Complete the graphs in Parts A and B. Use this information to discuss and answer the questions in Part C. PART A: 1) Graph, label, and connect the following points to create a quadrilateral. D ( -5, 5 ) E ( -2, 4 ) F ( -1, 2 ) G ( - 4, 1 ) 2) The quadrilateral is in Quadrant. This quadrilateral is the pre-image. 3) Color the quadrilateral blue. 4) Translate the blue quadrilateral 5 units left and 2 units down. Color this translation red. The red quadrilateral is the image. 5) Identify the coordinates of this translation in the table below. Blue Quadrilateral D ( -5, 5 ) E ( -2, 4 ) F ( -1, 2 ) G ( - 4, 1 ) Red Quadrilateral PART B: 1. Graph, label, and connect the following points to create a pentagon. H ( -3, -1 ) J ( -1, -3 ) K ( -2, -6 ) L ( - 4, -6 ) M ( -5, -3 ) 2. The pentagon is in Quadrant. This pentagon is the pre-image. 3. Color the pentagon orange. 4. Translate the blue pentagon 4 units right and 5 units up. Color this translation green. The green pentagon is the image. 5. Identify the coordinates of this translation in the table below. Blue Pentagon H ( -3, -1 ) J ( -1, -3 ) K ( -2, -6 ) L ( - 4, -6 ) M ( -5, -3 ) Red Pentagon

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18 Try out your rule: Translate the point 6 units to the left. image x-coordinate y-coordinate 5-2 preimage preimage image x-coordinate y-coordinate X y Translate the point 3 units down. image x-coordinate y-coordinate 5-2 preimage preimage image x-coordinate y-coordinate x y Translate the point 3 units up and 4 units to the left. image x-coordinate y-coordinate 5-2 preimage preimage image x-coordinate y-coordinate X y

19 Task 2: Patterns of REFLECTIONS Directions: Complete the graphs in Parts A and B. PART A: 1) Graph, label, and connect the following points to create a triangle. A ( 3, 5 ) B ( 4, 2 ) C ( 1, 1 ) 2) The triangle is in Quadrant. This triangle is the pre-image. 3) Color the triangle blue. 4) Reflect the blue triangle over the x-axis. Color this reflection red. The red triangle is the image. 5) Identify the coordinates of this reflection in the table below. Blue Triangle Red Triangle A ( 3, 5 ) B ( 4, 2 ) C ( 1, 1 ) PART B: 1) Graph, label, and connect the following points to create a quadrilateral. D ( -5, 5 ) E ( -2, 4 ) F ( -1, 2 ) G ( - 4, 1 ) 2) The quadrilateral is in Quadrant. This quadrilateral is the pre-image. 3) Color the quadrilateral blue. 4) Reflect the blue quadrilateral over the y-axis. Color this reflection red. The red quadrilateral is the image. 5) Identify the coordinates of this reflection in the table below. Blue Quadrilateral D ( -5, 5 ) E ( -2, 4 ) F ( -1, 2 ) G ( - 4, 1 ) Red Quadrilateral

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21 Try out your rule: Reflect the pre-image over the x-axis. 5-2 preimage preimage x y image image Reflect the pre-image over the y-axis. image x-coordinate y-coordinate 5-2 preimage preimage image x-coordinate y-coordinate x y

22 Task 3: Patterns of ROTATIONS Directions: In your small group, complete the graphs in Parts A, B, and C. Use this information to discuss and answer the questions in Part D. Part A: 1) Graph, label, and connect the following points to create a segment. B ( -5, 5 ) C ( -2, 4 ) 2) The segment is in Quadrant. This segment is the pre-image. 3) Rotate the segment 90º counterclockwise around the origin. 4) What are the coordinates of this rotation? Segment B ( -5, 5 ) C ( -2, 4 ) 90º counterclockwise 5) Color this rotation blue. The blue segment is the image. 6) Now rotate the original segment 90º clockwise around the origin. 7) What are the coordinates of this rotation? Segment B ( -5, 5 ) C ( -2, 4 ) 90º clockwise 8) Color this rotation red. The red segment is another image.

23 Part B: 1) Graph, label, and connect the following points to create a triangle. D ( - 4, -1 ) E ( -1, -2 ) F ( -5, -5 ) 2) The triangle is in Quadrant. This triangle is the pre-image. 3) Rotate the triangle 180º counterclockwise around the origin. 4) What are the coordinates of this rotation? Triangle D ( - 4, -1 ) E ( -1, -2 ) F ( -5, -5 ) 180º counterclockwise 5) Color this rotation blue. The blue triangle is the image. 6) Now rotate the original triangle 180º clockwise around the origin. 7) What are the coordinates of this rotation? Triangle D ( - 4, -1 ) E ( -1, -2 ) F ( -5, -5 ) 180º clockwise 8) Color this triangle red. The red triangle is another image.

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25 Try out your rule: Rotate the pre-image 90º clockwise. 5-2 preimage preimage x y image image Rotate the pre-image 180º counterclockwise. preimage preimage image 5-2 image x y Rotate the pre-image 270º clockwise. preimage preimage image 5-2 image x y

26 Monday, December 14, 2015 Today s Objectives: Gators will be able to: Equations and Inequalities model and solve one-variable, two-step equations and inequalities write one-variable, two-step equations and inequalities to represent constraints or conditions within problems represent solutions for one-variable, two-step equations and inequalities on number lines write a corresponding real-world problem given a one-variable, two-step equation or inequality determine if the given value(s) make(s) one-variable, two-step equations and inequalities true It takes two steps to solve an equation or inequality that has more than one operation: 1. Simplify using the inverse of addition or subtraction. 2. Simplify further by using the inverse of multiplication or division. Remember, when you multiply or divide an inequality by a negative number, you must reverse the inequality symbol Symbol Number Line Meaning = > <

27 Solve each two-step equation. 1. 8x + 3 = 29 Solve the inequality. Graph the solution. 4. 2(k 5) < x = (n 10) < (x + 4) = (8 + y) 7. In a basketball game, Trina scored 6 points less than twice the number of points Rachel scored. Trina scored 12 points. How many points did Rachel score? 8. It costs Guido $0.20 per minute to forward voic messages as texts to his cell phone. He already spent $4 in forwarding messages this month. If he can spend $10 this month on forwarding messages, write and solve an inequality to find how many more minutes he has left. Interpret the solution.

28 9. Stephanie makes $6.60 an hour plus tips working at a restaurant. On a particular day, she worked 8 hours and made $ Write and solve an equation to determine the amount she made in tips. Use a problem-solving model to solve. 10. Moesha is creating and recording a video for her English class. The video has to be at least 60 seconds in length, and she has recorded 43 seconds. Find an inequality and its solution that shows how many more seconds Moesha has to add to the video. 11. Solve 6x Solve 0.2(x + 14) = 22.

29 13. Solve the inequality. Graph the solution. a. 4b 1 < Three times Geoff s age plus 3 is Myrka s age. Myrka is 48. What is Geoff s age? b c 28 c. n + 11 > A woodworker builds a cabinet in 20 hours. The cabinet is sold at a store for $500. Write and solve an inequality that represents the hourly wage the store can pay the woodworker and still make a profit of at least $ A killer whale has eaten 75 pounds of fish today. It needs to eat at least 140 pounds of fish each day. a. A bucket holds 15 pounds of fi sh. Write and solve an inequality to represent how many more buckets of fish the whale needs to eat. b. Should the whale be given four or five more buckets of fish? Explain.

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