Sample Applied Skills Problems Grade 10 Math Directions: Students are allowed to use a calculator and the ISTEP+ reference sheet on each problem. 1. Data Analysis A1.DS.2 2. Quadratic A1.QE.5 3. Pythagorean Thm 8.GM.9 4. Linear Function A1.L.5 ----------------------------------------------------------------- 5. Linear Function A1.L.5 6. Linear Inequality A1.L.2 7. System of Equations A1.SEI.3 8. Exponential Function A1.QE.1 Page 1
Fitness Test 2 Score 1. A physical therapist randomly selected ten patients to complete two physical fitness tests. The patients scores on each test are shown in the scatterplot. 120 Test Scores 100 80 60 40 20 0 20 40 60 80 Fitness Test 1 Score 100 Do the data best represent a linear or a nonlinear association? Use words, numbers, and/or symbols to explain your answer. Answer association Page 2
Is there a positive or a negative association represented between the two variables in the scatterplot? Use words, numbers, and/or symbols to explain your answer. Answer association Page 3
2. A rectangle with an area of 104 square inches has a width that is 5 inches less than its length. Write an equation representing the area of the rectangle. Use x to represent the length of the rectangle. Solve your equation for all values of x. Show All Work Use your solution to the equation to identify the width and length of the rectangle. Explain how you determined which value(s) of x to use. Show All Work Page 4
3. The coordinate grid shows the location of a school and a park. Point K represents the location of Kim s home, and point T represents the location of Tim s home. y 6 4 2 T Park -6-4 -2 School 0 2 4 6 x K -2-4 -6 What is the shortest distance between the school and the park on the grid? Round your answer to the nearest tenth of a unit. Use words, numbers, and/or symbols to explain how you found your answer. Distance units Page 5
Tim claims that the distance from the school to the park is the same as the distance from Kim s home to Tim s home. Use words, numbers, and/or symbols to explain whether he is correct. Page 6
4. The table shows the price, P, for renting a car for d days from a car rental company. Number of Days d Price P 1 $115 2 $150 3 $185 4 $220 Construct a linear function that models the relationship between the price, P, and the number of days, d, for which the car is rented. Show the steps that are required in order to construct the model. Linear Function: Page 7
What is the slope of the line in? What does it represent in the context of the problem? Show All Work Slope Part C What is the value of this function when d = 0? What does this value represent in the context of the problem? Show All Work Page 8
Cost (dollars) 5. A maid service charges a $20 travel fee plus an hourly rate to customers. The maid service costs $50 for 3 hours of work and $70 for 5 hours of work. These charges include the travel fee and hourly rate. Write a linear function to show how the cost (c) is related the number of hours worked (h). Show All Work Linear Function 120 Graph the linear function on the coordinate plane. 100 c Maid Service Costs 80 60 40 20 0 2 4 6 8 10 12 Page 9 Time (hours) h
Part C Explain how to determine the cost for 8 hours of work by the maid service. Use words, numbers, and/or symbols to explain whether he is correct. Page 10
6. Jason is going to the Chicago Cubs baseball game tonight. He has $75 at most to spend which includes the price of the game ticket plus a certain number of hot dogs. Hot dogs at the stadium cost $6.50 each. The price of the ticket to get into the game is $45. What are the most hot dogs Jason can buy at the Chicago Cubs game? Define a variable Write an inequality Solve the inequality. Show all steps. Show All Work Number of hotdogs Page 11
7. You are running a concession stand at a fundraiser event. You are selling hot dogs and sodas. Each hot dog costs $1.50 and each soda costs $0.50. At the end of the night you made a total amount of $78.50. You sold 87 hotdogs and sodas combined. You must report the number of hot dogs sold and the number of sodas sold to your teacher. How many hot dogs were sold and how many sodas were sold? Define the variables Use the variables in to write a system of equations. First Equation: Second Equation: Page 12
Part C How many hot dogs were sold and how many sodas were sold? Solve the system of equations from. Show All Work Number of Hot Dogs Sold Number of Sodas Sold Page 13
8. The number of Flu virus bacteria in a science culture was initially counted to be 400 bacteria. The Flu virus was counted at different times as shown in the table. Flu Virus Count Time(Hours) Bacteria Count 0 400.5 700 1 1200 1.5 2100 2 3600 2.5 6200 3 10,800 Graph the table of values in on the provided coordinate plane. Connect the points with a smooth curve. Bacteria Count (thousands) y 11 10 9 8 7 6 5 4 3 2 1 Flu Virus 0 1 2 3 t Page 14 Time (hours)
Which of the three models best describes this data? Circle your model choice below. Model A y = 3t + 400 Model B y = 400(3) t Model C y = 3t 2 + t + 400 Explain your choice. Use words, numbers, and/or symbols. Part C A person gets violently sick when the Flu virus count reaches 32,000 bacteria within the body. About how long does this take to happen according to the data? Answer hours Explain your answer. Use words, numbers, and/or symbols. Page 15