Warm-up for Integrated Geometry and Algebra II

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1 Summer Assignment Warm-up for Integrated Geometry and Algebra II Who should complete this packet? Students who will be taking Integrated Geometry and Algebra II in the fall of 018. Due Date: The first day of school How many of the problems should I do? ALL OF THEM How should I organize my work? You should show all work in a separate sheets of graph paper. Keep your materials in a report cover or 3-prong folder How will my teacher know that I ve done the work? Your teacher will collect your work on the first day of school. Your teacher may choose to QUIZ or TEST you on this material if he or she feels it is necessary BE PREPARED! How well should I know this material when I return? You should recognize that you ve seen this material before, and you should also be able to answer questions like the ones in this packet. Note from your teachers: We feel that this summer work will truly help you succeed next year. We understand that summer is a time for relaxation and fun, but it is imperative that you spend some time before you return reviewing your materials. This assignment is mandatory, and you must treat it as you would any other extremely important homework assignment. You will be held accountable for this material. We also highly suggest that you do a bit of it at a time in the weeks leading up to school don t leave it for the last day!!!

2 Warm-up for Integrated Geometry and Algebra II Instructions: Complete the problems on graph paper in pencil. If a problem requires you to draw a diagram, please use a ruler and make an accurate sketch. At the top of each page of your work, your name and the page number of your work. Complete all the problems carefully. Show enough work to indicate your method of solution. Make sure your work justifies your answer. Keep the packet and your work in a folder. Place your completed work in a report cover or 3-prong folder. Remember, your teacher will collect your work on the first day of school! Late work will penalized and may NOT be accepted. What if I get stuck? - You should check out other additional study materials. Consult a standard algebra textbook. Find a study buddy or a classmate to help you remember the material. Consult the following websites for hints and examples:

3 Warm up for Integrated Geometry and Algebra II Page 1 1. Correctly apply order of operations to simplify each expression a. ( ) + + c. 15 ( 4 3 ) b Simplify each radical expression: a b c. ( 8 6) d A right triangle has a hypotenuse of 11 and a leg of 8. Find the length of the other leg. Include a sketch as part of your work. 4. Find the area and perimeter of the rectangle shown: 48 m 108 m 5. Simplify each expression: a. 3 b c. 74 g d Melaina s bedroom floor is 1 10 ft by ft. She buys 160 ft of carpet. Does she have enough to cover the floor? Make a sketch as part of your work.

4 Warm up for Integrated Geometry and Algebra II Page 7. Solve each equation. a. 18y = 3 b p d. 3( x ) = x e. 5r 6 4r r 5 9 = 10 9 = c. ( w) 4y 5y+ 6 = 7y+ 3 + = + f. ( ) 9. In ABC, the length of side AB = x 1, the length of side BC = x + 7, and the length of side 3 3x AC =. The perimeter of the triangle is 6. 4 a. Make a sketch of the triangle and label the sides. b. Find the length of each side of the triangle by writing and solving an equation involving perimeter. c. Is the triangle scalene, isosceles, or equilateral? Explain your answer. 10. In TRI, TR TI and mr T = 38. Find the measures of R and I. 11. Quadrilateral ABCD is a square. Find the value of x. A B 6x+5 C 8x-3 D 1. Point M=(1,-1) is the midpoint of AB where A=(-1,3). Find the coordinates of B. 13. Find the value of each variable. 1x 6x

5 Warm up for Integrated Geometry and Algebra II Page 3 You may work problems #14 & #15 directly on this sheet. Be sure to justify your answers. 14. For quadrilateral R=(-1,-6), A=(-,-3), Y=(8,1) and J=(9,-). a. What do you know about the diagonals of a parallelogram? b. What extra properties do you know about the diagonals of a rectangle? c. Use the properties of diagonals to diagnose quadrilateral RAYJ.

6 Warm up for Integrated Geometry and Algebra II Page The graph of PIG where P= ( 1,0); I = (3, ); G = ( 1,8) is shown at right. a. Show that PIG is a right triangle. b. Find the area of PIG using PG as the base. c. Find the area of PIG using PI as the base. d. Use trigonometry to determine the measure of angle R GPI.

7 Warm up for Integrated Geometry and Algebra II Page From the given information, graph the line described. Give the coordinates of two additional points on the graph, then write the equation of the line. 3 a. has slope and y-intercept ( 0, ) 4 b. passes through points P = (,5) and Q = ( 1,1) 17. Is each point on the graph of the line 3x y = 1? Use the equation, not a graph, to decide. Write yes or no. Show the computations that support your conclusion. a. ( 0, 4 ) b. ( 6,3 ) c. ( 4,0 ) 18. Graph ABC with A=(-5,5), B=(5,0), C=(-3,-4). a. Find the slope of suur BC. b. What is the slope of any line that is perpendicular to suur BC? c. Using your information from part b, draw the altitude from vertex A. d. At what point does your line in part c intersect side suur BC? Label that point as D. e. Extend line suur AD until it intersects the y-axis. What is the y-intercept? f. Use the slope and the y-intercept to write the equation of the altitude suur AD 19. Graph the lines x+ y = 1, x y = 16, and y = 3x+ 8. Algebraically, find the coordinates of the vertices of the triangle. 0. In the diagram, lines t j and k t are parallel. Find the values of x and y.

8 Warm up for Integrated Geometry and Algebra II Page 6 1. Solve for x, then find the measure of C. Solve each equation. Given an exact answer. If the answer is a radical, simplify it. a. x = 7 b. x 3 = 0 c. x 9= 7 3. The angle of elevation from point A to the top of a cliff is 38. If point A is 80 feet from the base of the cliff, how high is the cliff? 4. Plot T = (, 4), R= (5,3) A= (6, ) Find P so that TRAP is a trapezoid. Give evidence to show your shape is a trapezoid. 5. Plot AA = (3,); BB = (3,4) and CC = (6,7). Connect to form ABC. a. Plot TT = (,5); II = ( 4,5). Give coordinates for P so that TTTTTT AAAAAA. b. Using the T and I from part b, give coordinates for S so that IIIIII AAAAAA. c. Graph the reflection of ABC across the y-axis. d. Graph the reflection of ABC across the line xx = 6.

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