Silver Spring International Middle School Algebra Summer Packet

Transcription

1 Name: Silver Spring International Middle School Algebra Summer Packet It is NOT mandatory to complete but, STRONGLY encouraged.

2 MONTGOMERY COUNTY PUBLIC SCHOOLS SILVER SPRING INTERNATIONAL MIDDLE SCHOOL An IB World School 313 Wayne Avenue, Silver Spring, MD Phone: Fax: June 15 th, 2017 Dear Parents and Students, The Silver Spring International Math Department asks that students review math concepts over the summer. This helps students retain mathematics knowledge and prepares them for success upon their return to school in the fall. It is recommended that your child spend some time over the summer break to maintain his/her math skills. Students will have access to a site that is designed to help all MCPS middle grades students maintain their math skills during the summer months. These online resources will provide students with multiple opportunities to review concepts from this past school year. As students access the website they will select the page that matches the mathematics course they will be enrolling in for the upcoming school year ( ). The course page will then provide links to several different units of study. Each unit will contain multiple online resources, such as video tutorials, games, and many more challenging tasks. Please make sure that your child is signed onto their google account prior to logging into the website otherwise students may not be able to easily access some of the resources. The online tools can be found on the following website: Please feel free to choose an alternative summer math program if you feel one better fits your family s needs. We suggest the program to be aligned with the Common Core to best prepare the student for the year ahead. If you will be without consistent internet access to use an online service or if you want supplemental materials, there are additional practice packets on SSI s website. The alternative packets can be found on our website at: If you do not have internet access at home, below is one location where you can have the free use of computers and the internet in Silver Spring. Silver Spring Library 900 Wayne Ave. Silver Spring, MD Hours Monday through Thursday 9am - 9pm Friday/Saturday 10am - 6pm Sunday 1-5pm Thank you for your support and have a wonderful summer! We look forward to seeing you in September! Sincerely, The SSI Math Department

3 Solving Equations Examples: Undo the number (coefficient) without a letter (variable) by adding or subtracting that number on both sides of the equals. Undo the number (coefficient) next to the letter (variable) by multiplying or dividing that number on both sides of the equals. 1. Solve the equation. 3x + 4 = Solve the equation. -5x 9 = 16 Subtraction property of equality Addition property of equality x = 9-5x = 25 Division Property of equality 3 3 Division Property of equality -5-5 Simplify x = 3 Simplify x = - 5 Check: 3x + 4 = 13 Check: -5x 9 = 16 for x = 3 3(3) + 4 = 13 for x = -5-5(5) 9 = = = = = 16 Exercises: Solve the two-step equations. Show all work. Check your answers. 1. 5x + 6 = x + 6 = x 6 = x 3 = x + 2 = x + 4 = x + 7 = x 24 = z 18 = -132 Page 1

4 Solving Equations Distributive Property : Multiply the number in front of the parenthesis with each term inside the parenthesis. Combine like terms, if needed. Undo the number (coefficient) without a letter (variable) by adding or subtracting that number on both sides of the equals. Undo the number (coefficient) next to the letter (variable) by multiplying or dividing that number on both sides of the equals. Example: -3(x -2) = -15 Distributive Property - 3(x) (-3)(2) = -15-3x + 6 = -15 Subtraction property of equality - 6 = -6-3x = -21 Division property of equality -3-3 Simplify x = 7 Check: -3(x 2) = -15 for x = 7-3(7 2) = -15-3(5) = = -15 Exercises: Solve the equations. Show all your work. Check your answers. 1) 3(2y 3) = 27 2) 4(2y 3) = 28 3) 2(3 + 4m) 9 = 45 4) 3(5 + 3m) 8 = 88 5) 5r (2r + 8) = 16 6) 6b (3b + 8) = 16 Page 2

5 7) 6 2(3x 1) = 2 8) 10 3(2x 1) = 1 9) 2x 1 = 4 + x 10) 5x 2 = 6 + x 11) 5 2x = 3x 7x ) 10 3x = 2x 8x ) 4 + 3x 6 = 3x + 2 x 14) 5 + 4x 7 = 4x 2- x Page 3

6 15) 5(d + 4) = 7(d -2) 16) 3(t 2) = 9(t + 2) 17) 8(2t + 1) = 4(7t + 7) 18) 7(5x 2) = 6(6x -1) 19) 3(r 6) + 2 = 4(r + 2) 21 20) 5(t + 3) + 9 = 3(t 2) + 6 Page 4

7 Area and Perimeter Directions: Determine the area and perimeter. Be sure to show all your work for each problem. 1. Rectangle with length = 2.4 cm and width = 3.6 cm. Area Perimeter 2. Square with side length = 5 mm. Area Perimeter 3. Circle with a radius of 20 centimeters. Area Circumference 4. Parallelogram with lengths of 11 yards, height of 7 yards and sides of 5 yards. Area Perimeter Page 5

8 Measuring Angles Directions: Find the measures of the missing angles. Be sure to show all your work in the space below. 1. Line m is parallel to line n. Find the measure of each numbered angle. m<1 = m<2 = m<3 = m<4 = m<5 = m<6 = m n 2. Solve for x and find the measure of each of the four angles. x = m<1 = m<2 = m<3 = m<4 = (x+25) x (x+15) (x+20) 4 Page 6

9 Measuring Angles Directions: Find the measures of the missing angles. Be sure to show all your work in the space below. a) m<aod = b) m<aob = c) m<sqr = d) m<p= e) m<xzy = f) m< ZYX = g) m<x = h) m<jnm = i) m<nlm = j) m< NLK = k) m<fog = l) m<goh = m) m<eof = n) m<uvw = o) m<vwu = p) m<uwt = Page 7

10 Surface Area and Volume Directions: Use the following information to determine the SURFACE AREA and VOLUME. Be sure to show all your work in the space below. See pages 1& 2 for any needed formulas mm 2x 8x x 3 mm 2 mm 3. 3 mm 4. 8 mm 6 mm 0.5 mm Page 8

11 Laws of Exponents Directions: Simplify using the Rules for Exponents. Rules for Exponents a 1 = a a 0 = 1 when a 0 Negative Exponents: a -n = 1 when a 0 a n Product Rule: a m a n = a m + n Quotient Rule: a m = a m n a n Power Rule: (a m ) n = a mn Product to Power: (ab) n = a n b n x 6 x 2 x 3. a 3 a x3 x 8 6. x5 x 5 7. (x 3 ) 2 8. (y 2 ) 3 9. (a 3 b) (x 2 ) 3 (x 5 ) (x 2 ) 3 (x 5 ) (x) 2 (x 2 ) Express using a positive exponent: 14. Express using a negative exponent: y 5 Page 9

12 Finding Slope Directions: Find the slope of each line (rise/run) Find the slope of the line that passes through each pair of points. m y x rise run 7. A(1, -5), B(6, -7) 8. C(7, -3), D(8, 1) 9. E(7, 2), F(12, 6) 10. G(8, -3), H(11, -2) 11. J(5, -9), K(0, -12) 12. L(-4, 6), M(5, 3) Page 10

13 Equation of a line Directions: Graph the equation of the line in slope-intercept form. y = mx + b Graph an Equation in Slope-Intercept Form 1. Graph y = 3 2 x Graph y = 3x Graph y = x 2 4. Graph y = -4x Graph y = 2 1 x 6. Graph y = x 3 Page 11

14 Equation of a line Directions: Graph the equation of the line in slope-intercept form. y = mx + b Page 12

15 Mixed Review 1. On the grid provided, draw a right triangle with whole number side lengths and a hypotenuse of 10 units. The length of each square is one unit. 2. A square, with side length s, has an area of 324 square centimeters. This equation shows the area of the square. What is the side length of the square in centimeters? s 2 = Six friends are going to buy pizza. Their choices are to buy 2 medium 10- inch diameter pizzas for $7.00 each, or 1 large 14-inch diameter pizza for $ Both include tax and tip. The friends agree that their best choice is the one that gives them the most pizza for their money. Which is the best choice? Explain your answer. Resource: Smarter Balanced Assessment Consortium Practice test Grade 8, 2013

16 4. Rachel says the sum of a positive number and a negative number always equals a negative number or zero. a. Create an example that that supports Rachel s claim. b. Create an example that that shows Rachel s claim is false. Resource: Smarter Balanced Assessment Consortium Practice test Grade 8, 2013

17 5. Draw the image of the figure after the following translations. a. A reflection over the x-axis. b. A horizontal translation 7 units to the left. Resource: Smarter Balanced Assessment Consortium Practice test Grade 8, 2013

18 6. Justin s car can travel Kim s car can travel 1 77 miles with miles with 1 3 gallons of gas gallons of gas. At these rates, how far can each car travel with one gallon of gas? Graph the number of miles for each car on the number line. 7. The school is 100 meters from Jason s house. The following describes his most recent trip: He walked 50 meters toward school in 2 minutes. He realized that he left a book at home. He turned around and walked home at the same speed. He spent 1 minute looking for his book. He walked all the way to school at twice his original speed. Finish the graph so that is accurately represents Jason s trip. Resource: Smarter Balanced Assessment Consortium Practice test Grade 8, 2013

19 8. Graph each value appropriately in the correct position on the number line Two sides of a right triangle have lengths of 10 and 6 units. There are two possible lengths for the third side. a. What is the shortest possible side length, in units? b. What is the longest possible side length, in units? 10. Kayla asked 10 students in her class whether they owned a dog or a cat or both. Write any number 0-9 to complete the table, given this information: 40% of the students own a dog. 30% of the students own a cat. 10% of the students own both a cat and dog. Resource: Smarter Balanced Assessment Consortium Practice test Grade 8, 2013

20 11. Segment FG begins at point F(-2, 4) and ends at point G(-2, -3). The segment is translated by <x 3, y + 2> and then reflected across the y-axis to form segment F G. How long is segment F G. 12. Coffee costs $2.00 per pound at a coffee shop. Graph a line that shows the proportional relationship between the number of pounds of coffee purchased and the total cost. 13. A sphere and a cone have the same volume. Each figure has a radius of 3 inches. What is the height of the cone? 3 in 3 in Resource: Smarter Balanced Assessment Consortium Practice test Grade 8, 2013

21 14. Joe solved this linear system correctly. 6x + 3y = 6 y = -2x + 2 These are the last two steps of his work. 6x 6x + 6 = 6 6 = 6 Which statement about this linear system must be true? a. x must equal 6 b. y must equal 6 c. There is no solution to this system. d. There are infinitely many solutions to this system. 15. Using digits 0-9, write numbers in each of the boxes to complete each equation given the number of solutions. Resource: Smarter Balanced Assessment Consortium Practice test Grade 8, 2013

22 16. Kyle was given a problem to solve. The problem and his work are shown. a. What part of Kyle s work contains the mistake? b. What part of the problem should Kyle read again to fix his mistake? Resource: Smarter Balanced Assessment Consortium Practice test Grade 8, 2013

23 17. A game that uses a spinner and two number cubes is played at a game night. To win the game, a player must have two results: The spinner s arrow stops in a red section. The number cubes both land with an even number facing up. The person in charge of the night wants 10% of the players to win. Label the spinner with the colors red, green, and blue to design one that reaches the goal. 18. Look at these numbers. 2, 3, 5, 7 Classify the numbers by ALL that apply. a. Integer b. Irrational c. Rational d. Real Resource: Smarter Balanced Assessment Consortium Practice test Grade 8, 2013

24 More Review Answers 1. A right triangle with leg lengths of 6 units and 8 units and a hypotenuse of 10 units. 2. s = medium pizzas Sample explanation: the area/amount of the two choices of pizza is about the same, but the large pizza costs more than 2 medium ones. 4. A. sample: = 0 B. sample: = 1 5. a. b. the figure reflected across the x-axis the figure translated 7 units to the left 6. Justin s car at the 25-mile mark and Kim s car at the 31-mile mark 7. Resource: Smarter Balanced Assessment Consortium Practice test Grade 8, 2013

25 More Review Answers a. 2 b inches 14. D 15. A. 8x 3x + 2 x = 4x + 3 B. 8x 3x + 2 x = 3x + 3 C. 8x 3x + 2 = 4x the bats are on sale for 10% off and 90% 0.9 = $ red sections, 2 blue sections, and one green section 18. B and D Resource: Smarter Balanced Assessment Consortium Practice test Grade 8, 2013