Given the rule:
Problem 2Here is an input-output rule: Complete the table for the input-output rule:
Problem 3 (from Unit 4, Lesson 15)Andre’s school orders some new supplies for the chemistry lab. The online store shows a pack of 10 test tubes costs \$4 less than a set of nested beakers. In order to fully equip the lab, the school orders 12 sets of beakers and 8 packs of test tubes.
Problem 4 (from Unit 4, Lesson 14)Solve: \(\begin{cases} y=x-4 \\ y=6x-10\\ \end{cases}\) Problem 5 (from Unit 4, Lesson 9)For what value of $x$ do the expressions $2x+3$ and $3x-6$ have the same value? Lesson 2Problem 1Here are several function rules. Calculate the output for each rule when you use -6 as the input. Problem 2A group of students is timed while sprinting 100 meters. Each student’s speed can be found by dividing 100 m by their time. Is each statement true or false? Explain your reasoning.
Problem 3 (from Unit 4, Lesson 15)Diego’s history teacher writes a test for the class with 26 questions. The test is worth 123 points and has two types of questions: multiple choice worth 3 points each, and essays worth 8 points each. How many essay questions are on the test? Explain or show your reasoning. Problem 4These tables correspond to inputs and outputs. Which of these input and output tables could represent a function rule, and which ones could not? Explain or show your reasoning. Table A:
Table B:
Table C:
Table D:
Lesson 3Problem 1Here is an equation that represents a function: $72x+12y=60$. Select all the different equations that describe the same function:
Problem 2 (from Unit 4, Lesson 13)
Problem 3Brown rice costs \$2 per pound, and beans cost \$1.60 per pound. Lin has \$10 to spend on these items to make a large meal of beans and rice for a potluck dinner. Let $b$ be the number of pounds of beans Lin buys and $r$ be the number of pounds of rice she buys when she spends all her money on this meal.
Problem 4 (from Unit 4, Lesson 6)Solve each equation and check your answer.
Lesson 4Problem 1The graph and the table show the high temperatures in a city over a 10-day period.
Problem 2The amount Lin’s sister earns at her part-time job is proportional to the number of hours she works. She earns \$9.60 per hour.
Problem 3Use the equation $2m+4s=16$ to complete the table, then graph the line using $s$ as the dependent variable.
Problem 4 (from Unit 4, Lesson 13)Solve the system of equations: \(\begin{cases} y=7x+10 \\ y=\text-4x-23 \\ \end{cases}\) Lesson 5Problem 1Match each diagram to the function described, then label the axes appropriately
Problem 2 (from Unit 4, Lesson 13)The solution to a system of equations is $(6,\text-3)$. Choose two equations that might make up the system.
Problem 3 (from Unit 5, Lesson 3)A car is traveling on a small highway and is either going 55 miles per hour or 35 miles per hour, depending on the speed limits, until it reaches its destination 200 miles away. Letting $x$ represent the amount of time in hours that the car is going 55 miles per hour, and $y$ being the time in hours that the car is going 35 miles per hour, an equation describing the relationship is: $$55x + 35y = 200$$
Problem 4The graph represents an object that is shot upwards from a tower and then falls to the ground. The independent variable is time in seconds and the dependent variable is the object’s height above the ground in meters.
Lesson 6Problem 1Match the graph to the following situations (you can use a graph multiple times). For each match, name possible independent and dependent variables and how you would label the axes.
Problem 2
Jada fills her aquarium with water. The graph shows the height of the water, in cm, in the aquarium as a function of time in minutes. Invent a story of how Jada fills the aquarium that fits the graph. Problem 3 (from Unit 5, Lesson 4)Recall the formula for area of a circle.
Problem 4 (from Unit 3, Lesson 11)The points with coordinates $(4,8)$, $(2,10)$, and $(5,7)$ all lie on the line $2x+2y=24$.
Lesson 7Problem 1The equation and the tables represent two different functions. Use the equation $b=4a-5$ and the table to answer the questions. This table represents $c$ as a function of $a$.
Problem 2 (from Unit 5, Lesson 2)Match each function rule with the value that could not be a possible input for that function.
Problem 3Elena and Lin are training for a race. Elena runs her mile a constant speed of 7.5 miles per hour. Lin’s times are recorded every minute:
Problem 4 (from Unit 4, Lesson 4)Find a value of $x$ that makes the equation true: $$\text-(\text-2x+1)= 9-14x$$ Explain your reasoning, and check that your answer is correct. Lesson 8Problem 1Two cars drive on the same highway in the same direction. The graphs show the distance, $d$, of each one as a function of time, $t$. Which car drives faster? Explain how you know. Problem 2Two car services offer to pick you up and take you to your destination. Service A charges 40 cents to pick you up and 30 cents for each mile of your trip. Service B charges \$1.10 to pick you up and charges $c$ cents for each mile of your trip.
Problem 3Kiran and Clare like to race each other home from school. They run at the same speed, but Kiran's house is slightly closer to school than Clare's house. On a graph, their distance from their homes in meters is a function of the time from when they begin the race in seconds.
Problem 4 (from Unit 3, Lesson 11)Write an equation for each line. Lesson 9Problem 1On the first day after the new moon, 2% of the moon's surface is illuminated. On the second day, 6% is illuminated.
Problem 2In science class, Jada uses a graduated cylinder with water in it to measure the volume of some marbles. After dropping in 4 marbles so they are all under water, the water in the cylinder is at a height of 10 milliliters. After dropping in 6 marbles so they are all under water, the water in the cylinder is at a height of 11 milliliters.
Problem 3 (from Unit 4, Lesson 5)Solve each of these equations. Explain or show your reasoning. Problem 4For a certain city, the high temperatures (in degrees Celsius) are plotted against the number of days after the new year. Based on this information, is the high temperature in this city a linear function of the number of days after the new year?Problem 5 (from Unit 4, Lesson 15)The school designed their vegetable garden to have a perimeter of 32 feet with the length measuring two feet more than twice the width.
Lesson 10Problem 1The graph shows the distance of a car from home as a function of time. Describe what a person watching the car may be seeing. Problem 2 (from Unit 5, Lesson 7)The equation and the graph represent two functions. Use the equation $y=4$ and the graph to answer the questions.
Problem 3This graph shows a trip on a bike trail. The trail has markers every 0.5 km showing the distance from the beginning of the trail.
Problem 4 (from Unit 4, Lesson 9)The expression $\text-25t+1250$ represents the volume of liquid of a container after $t$ seconds. The expression $50t+250$ represents the volume of liquid of another container after $t$ seconds. What does the equation $\text-25t+1250=50t+250$ mean in this situation? Lesson 11Problem 1Cylinder A, B, and C have the same radius but different heights. Put the cylinders in order of their volume from least to greatest.
Problem 2Two cylinders, $a$ and $b$, each started with different amounts of water. The graph shows how the height of the water changed as the volume of water increased in each cylinder. Match the graphs of $a$ and $b$ to Cylinders P and Q. Explain your reasoning. Problem 3Which of the following graphs could represent the volume of water in a cylinder as a function of its height? Explain your reasoning.
Problem 4 (from Unit 5, Lesson 3)Together, the areas of the rectangles sum to 30 square centimeters.
Lesson 12Problem 1
Problem 2Several glass aquariums of various sizes are for sale at a pet shop. They are all shaped like rectangular prisms. A 15-gallon tank is 24 inches long, 12 inches wide, and 12 inches tall. Match the dimensions of the other tanks with the volume of water they can each hold.
Problem 3Two paper drink cups are shaped like cones. The small cone can hold 6 oz of water. The large cone is $\frac43$ the height and $\frac43$ the diameter of the small cone. Which of these could be the amount of water the large cone holds?
Problem 4 (from Unit 5, Lesson 7)The graph represents the volume of a cylinder with a height equal to its radius.
Problem 5 (from Unit 3, Lesson 10)Select all the points that are on a line with slope 2 that also contains the point $(2, \text-1)$.
Problem 6 (from Unit 4, Lesson 14)Solve: \(\begin{cases} y=\text-2x-20 \\ y=x+4 \\ \end{cases}\) Lesson 13Problem 1Match each set of information about a circle with the area of that circle.
Problem 2
Problem 3At a farm, animals are fed bales of hay and buckets of grain. Each bale of hay is in the shape a rectangular prism. The base has side lengths 2 feet and 3 feet, and the height is 5 feet. Each bucket of grain is a cylinder with a diameter of 3 feet. The height of the bucket is 5 feet, the same as the height of the bale.
Problem 4Three cylinders have a height of 8 cm. Cylinder 1 has a radius of 1 cm. Cylinder 2 has a radius of 2 cm. Cylinder 3 has a radius of 3 cm. Find the volume of each cylinder. Problem 5 (from Unit 5, Lesson 12)A one-quart container of tomato soup is shaped like a rectangular prism. A soup bowl shaped like a hemisphere can hold 8 oz of liquid. How many bowls will the soup container fill? Recall that 1 quart is equivalent to 32 fluid ounces (oz). Problem 6 (from Unit 5, Lesson 8)Two students join a puzzle solving club and get faster at finishing the puzzles as they get more practice. Student A improves their times faster than Student B.
Lesson 14Problem 1Complete the table with all of the missing information about three different cylinders.
Problem 2A cylinder has volume $45\pi$ and radius 3. What is its height? Problem 3Three cylinders have a volume of 2826 cm3. Cylinder A has a height of 900 cm. Cylinder B has a height of 225 cm. Cylinder C has a height of 100 cm. Find the radius of each cylinder. Use 3.14 as an approximation for $\pi$. Problem 4 (from Unit 5, Lesson 13)A gas company’s delivery truck has a cylindrical tank that is 14 feet in diameter and 40 feet long.
Problem 5 (from Unit 5, Lesson 5)Here is a graph that shows the water height of the ocean between September 22 and September 24, 2016 in Bodega Bay, CA.
Lesson 15Problem 1A cylinder and cone have the same height and radius. The height of each is 5 cm, and the radius is 2 cm. Calculate the volume of the cylinder and the cone. Problem 2The volume of this cone is $36\pi$ cubic units. What is the volume of a cylinder that has the same base area and the same height? Problem 3 (from Unit 5, Lesson 14)A cylinder has a diameter of 6 cm and a volume of $36\pi$ cm3.
Problem 4 (from Unit 5, Lesson 10)Lin wants to get some custom T-shirts printed for her basketball team. Shirts cost \$10 each if you order 10 or fewer shirts and \$9 each if you order 11 or more shirts.
Problem 5 (from Unit 5, Lesson 6)In the following graphs, the horizontal axis represents time and the vertical axis represents distance from school. Write a possible story for each graph. Lesson 16Problem 1 (from Unit 5, Lesson 15)The volume of this cylinder is $175\pi$ cubic units. What is the volume of a cone that has the same base area and the same height? Problem 2A cone has volume $12\pi$ cubic inches. Its height is 4 inches. What is its radius? Problem 3A cone has volume $3 \pi$.
Problem 4 (from Unit 5, Lesson 6)Three people are playing near the water. Person A stands on the dock. Person B starts at the top of a pole and ziplines into the water. Person C climbs out of the water and up the zipline pole. Match the people to the graphs where the horizontal axis represents time in seconds and the vertical axis represents height above the water level in feet. Problem 5 (from Unit 5, Lesson 3)A room is 15 feet tall. An architect wants to include a window that is 6 feet tall. The distance between the floor and the bottom of the window is $b$ feet. The distance between the ceiling and the top of the window is $a$ feet. This relationship can be described by the equation $$a = 15 - (b + 6)$$
Lesson 17Problem 1A cylinder has a volume of $48 \pi$ cm3 and height $h$. Complete this table for volume of cylinders with the same radius but different heights.
Problem 2A cylinder has a radius of 3 cm and a height of 5 cm.
Problem 3A graduated cylinder that is 24 cm tall can hold 1 L of water. What is the radius of the cylinder? What is the height of the 500 ml mark? The 250 ml mark? Recall that 1 liter (L) is equal to 1000 milliliters (ml). Problem 4 (from Unit 5, Lesson 16)An ice cream shop offers two ice cream cones. The waffle cone holds 12 ounces and is 5 inches tall. The sugar cone also holds 12 ounces and is 8 inches tall. Which cone has a larger radius? Problem 5 (from Unit 5, Lesson 15)A 6 oz paper cup is shaped like a cone with a diameter of 4 inches. How many ounces of water will a plastic cylindrical cup with a diameter of 4 inches hold if it is the same height as the paper cup? Problem 6 (from Unit 5, Lesson 9)Lin’s smart phone was fully charged when she started school at 8:00 a.m. At 9:20 a.m., it was 90% charged, and at noon, it was 72% charged.
Lesson 18Problem 1There are many cylinders with a height of 18 meters. Let $r$ represent the radius in meters and $V$ represent the volume in cubic meters.
Problem 2 (from Unit 5, Lesson 3)As part of a competition, Diego must spin around in a circle 6 times and then run to a tree. The time he spends on each spin is represented by $s$ and the time he spends running is $r$. He gets to the tree 21 seconds after he starts spinning.
Problem 3 (from Unit 5, Lesson 7)The table and graph represent two functions. Use the table and graph to answer the questions.
Problem 4A cone has a radius of 3 units and a height of 4 units.
Lesson 19Problem 1A baseball fits snugly inside a transparent display cube. The length of an edge of the cube is 2.9 inches. Is the baseball’s volume greater than, less than, or equal to $2.9^3$ cubic inches? Explain how you know. Problem 2 (from Unit 5, Lesson 18)There are many possible cones with a height of 18 meters. Let $r$ represent the radius in meters and $V$ represent the volume in cubic meters.
Problem 3A hemisphere fits snugly inside a cylinder with a radius of 6 cm. A cone fits snugly inside the same hemisphere.
Problem 4
Problem 5 (from Unit 5, Lesson 9)After almost running out of space on her phone, Elena checks with a couple of friends who have the same phone to see how many pictures they have on their phones and how much memory they take up. The results are shown in the table.
Lesson 20Problem 1Match the description of each sphere to its correct volume.
Problem 2
Problem 3Sphere A has radius 2 cm. Sphere B has radius 4 cm.
Problem 4 (from Unit 5, Lesson 16)Three cones have a volume of $192\pi$ cm3. Cone A has a radius of 2 cm. Cone B has a radius of 3 cm. Cone C has a radius of 4 cm. Find the height of each cone. Problem 5 (from Unit 5, Lesson 5)The graph represents the average price of regular gasoline in the United States in dollars as a function of the number of months after January 2014.
Problem 6 (from Unit 4, Lesson 15)While conducting an inventory in their bicycle shop, the owner noticed the number of bicycles is 2 fewer than 10 times the number of tricycles. They also know there are 410 wheels on all the bicycles and tricycles in the store. Write and solve a system of equations to find the number of bicycles in the store. Lesson 21Problem 1A scoop of ice cream has a 3 inch radius. How tall should the ice cream cone of the same radius be in order to contain all of the ice cream inside the cone? Problem 2Calculate the volume of the following shapes with the given information. For the first three questions, give each answer both in terms of $\pi$ and by using $3.14$ to approximate $\pi$. Make sure to include units.
Problem 3A coin-operated bouncy ball dispenser has a large glass sphere that holds many spherical balls. The large glass sphere has a radius of 9 inches. Each bouncy ball has radius of 1 inch and sits inside the dispenser. If there are 243 bouncy balls in the large glass sphere, what proportion of the large glass sphere’s volume is taken up by bouncy balls? Explain how you know. Problem 4 (from Unit 5, Lesson 13)A farmer has a water tank for cows in the shape of a cylinder with radius of 7 ft and a height of 3 ft. The tank comes equipped with a sensor to alert the farmer to fill it up when the water falls to 20% capacity. What is the volume of the tank be when the sensor turns on? Lesson 22No practice problems for this lesson. |