# Summer Review Packet for All Students Enrolling in Algebra 1 Next Year

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2 Calculators in Math Class Used wisely, calculators can be a powerful instructional tool. Students are expected to bring an appropriate calculator to class on a daily basis. Please note that cell phone calculator applications cannot be used on any test or quiz. To meet Common Core Expectations, a Graphing Calculator is recommended for all math classes. Students will need to become comfortable and knowledgeable with graphing calculator technology and features in preparation for the new state test which will be administered to all students in Grade 11. A suitable Graphing Calculator can be purchased for approximately \$ One example of an appropriate graphing calculator would be the TI-83 Plus. A slightly more expensive graphing calculator would be the TI-84 Plus. In preparation for the new school year, graphing calculators are usually on sale during the month of August. For some applications, a Scientific Calculator may also be used in class. A suitable Scientific Calculator can be purchased for less than \$ An example of an appropriate calculator would be the Texas Instruments TI-30XIIS Scientific Calculator. Course Calculator Type Algebra 1 Geometry Algebra 2 Precalculus Calculus Statistics & Probability Graphing Calculator preferred Graphing Calculator preferred Graphing Calculator Graphing Calculator Graphing Calculator Graphing Calculator If a student cannot afford the purchase of a graphing calculator, the school has a limited supply that can be loaned to students for the school year. To borrow a calculator for the school year, a loan form must be signed by the parent or guardian indicating that the student will replace the calculator with an equivalent one in an unopened package if the calculator is damaged or lost.

3 1. Analyze the numerical expressions below. Which of these expressions are equivalent to ? (Circle the expressions that are equivalent.) 8.EE.1 A. 4 8 B C. 4 1 D. 1 2 E. 2 6 F Use the correct mathematical notation to represent all the possible square roots and cube roots in the table below. Then simplify. The first one is done for you as an example. 8.EE.2 A. What is the square root of 4? 4 = 2 or -2 D. What is the cube root of 8? B. What is the square root of 81? E. What is the cube root of 1? C. What is the square root of 25? F. What is the cube root of 64? 3. In the table above, you were asked to evaluate square roots of perfect squares and cube roots of perfect cubes. The square root of 2 however is not a perfect square. The 2 is said to be irrational. In your own words, what does that mean? 8.NS.1

4 4. Can you approximate the value of 7 without a calculator? 7 8.NS.1 Explain how you determined this approximation without using a calculator. Use the table below for Questions 5-7: A 2 x B 1 x 10 8 C 3 x 10 2 D 5 x 10 5 E 4 x 10 5 F 5 x Rank the numbers in the table below from smallest to largest. 8.EE.3 (smallest) < < < < < < (largest) 6. Compare the smallest number above with the largest number. About how many times larger is the largest number compared to the smallest number? The largest number is about times larger than the smallest number. In your own words, explain how you determined this. 8.EE.3 7. If you multiplied the number in cell A (above) by the number in cell B, what answer would you obtain? Express your answer in Scientific Notation. 8.EE.4

5 8. The data table below shows the bonus an employee receives based on the number of IPads she sells during a one week period. Construct a scatter plot for this data. Number of ipads Bonus Pay (\$) SP1 and 8.F.1 Does your scatter plot represent a function? Why or why not? 9. Solve each of the equations in the table below. Show your work in the table. 8.EE.7 A. x + 8 = 10 B. 2x + 3 = 5x C. 3(x + 2) = 24 D. 2(4 x) = 8 E. x + 3 = 5 + x F. 2x + 5x + 3 = 3 + 7x

6 10. Solve the following systems of equations. Show your work below. 8.EE.8 A 4x + 6y = 32 3x 6y = 3 B y = 2x + 3 x + 2y = In your own words, explain the difference between solving a linear equation and solving a system of linear equations.

7 The Function Machine x y 12. Complete the following statement: 8.F.1 In order to be a function, for every x-value that goes into the function machine, there must be only y-value that comes out of the function machine. 13. Given the dimensions described below for the Function Machine, complete the table. Show your work and the formulas used for your computations. 8. G.7 and 8. G.9 (The Function Machine is not drawn to scale!) Rectangular prism: Right circular cylinder: Equilateral triangle: Right triangle: length = 4 cm height = 4 cm side = 1 cm height = 4 cm width = 4 cm radius = 2 cm height = 3 cm base = 8 cm 2 height = 6 cm A. Volume of rectangular prism: B. Volume of cylinder: C. Area of the equilateral triangle: D. Perimeter of the equilateral triangle: E. Hypotenuse of the right triangle: F. Area of the right circular side of the cylinder:

8 14. Complete the tables below for each given function. 8.F.1 and 8.F.3 x y y = x + 3 A = s 2 s A Are both of these functions linear functions? Why or why not? 15. Which function has the greater rate of change? Explain your reasoning below. 8.F.2 First Function x y Second Function y = 5x + 2 The function has the greater rate of change. I know this because. 16. Analyze the graph to the right. What is the equation of this line? Thank you for your time and effort to complete this review packet. We look forward to meeting you and working with you at the High School!

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