Nichols School Mathematics Department. Summer Work Assignment. Warm-up for Advanced Algebra II

Transcription

1 Summer Work Assignment Warm-up for Advanced Algebra II Who should complete this packet? Students who will be taking Advanced Algebra 2 in the fall of 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 folder with 3-prongs or report cover. How will my teacher know that I ve done the work? Your teacher will collect your notebook 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. If the material is revisited in your next class, it will only be for a brief amount of time your teacher will assume that all you need is a quick refresher. Note from your teachers: We feel that this summer work will truly help you succeed this 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 packet 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 Advanced Algebra II Instructions: Complete the problems on graph paper in pencil. If a problem requires a diagram, please use a ruler and draw the diagram carefully. At the top of each page of your work, write your name and the page number. 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 page order in a report cover or folder with 3 prongs. Remember, your teacher will collect your work on the first day of school! Late work will be penalized and may NOT be accepted. What if I get stuck? - You should check out other additional study materials. Consult a standard algebra or geometry textbook. Find a study buddy or a classmate to help you remember the material. Consult the following websites for hints and examples:

3 Warmup for Advanced Algebra II page 1 1. Simplify each expression. 2 a. 42 ( + 35 ) 3 b c. ( ) ( ) 4 2b b 2. Write an equation of the line that passes through the points 5 2 1, &, Write the equation of a line in standard form that passes through the point P = ( 2,5) and is perpendicular to the vector 3,8. 4. Given P = ( 3,1) and Q = ( 2,3), find coordinates for R and S that make PQRS a rectangle that is twice as long as it is wide. Hint: Use a vector! uuur uuur 5. If A= (4, 3), B= (6,1), and C = ( 2, t), find the value of t if AB BC. 6. A penguin begins at the point P = ( 1, 5). It marches with constant speed and direction, reaching the point (1,0) one minute later. a. Write parametric equations the penguin s path. b. When the does the penguin cross the y-axis? c. A speedier penguin marches along the same path at twice the speed. Write parametric equations for this faster penguin s motion. 7. Plot points A = ( 5, 3) & B = (8, 4). a. If P = (x, y), write an equation that states P is equidistant from A and B. b. Simplify your equation in part a, showing all the steps. 8. In ABC, the length of side AB = 2x 1, the length of side 3x 2 AC =. The perimeter of the triangle is a. Find the length of each side of the triangle. b. Is the triangle scalene, isosceles, or equilateral? 2 BC = x + 7, and the length of side 3

4 Warmup for Advanced Algebra II page 2 9. Miera begins bicycling in the coordinate plane according to the parametric equations x= 1 2 t; y = 12 5t. Hanna is pedaling along the path described by the parametric equations x= 11 4 t; y = 1 t. a. Is there a point where their paths will cross? If so, what point? b. Will they collide? 10. What type of quadrilateral is RAYJ where R=(-1,-6), A=(1,-3), Y=(11,1) and J=(9,-2)? Justify your answer using slopes. 11. What type of quadrilateral is TAUL with vertices T=(4,6), A=(6,-4) U=(-4,-2) and L=(-2,4). Justify your answer using properties of the diagonals. 12. RST has vertices R = ( 2, 4), S = (5,3), and T = ( 3,1) drawn to side ST.. Find the equation of the median 13. Graph ABC with A=(-7,4), B=(5,0), C=(-3,-4). a. Find the equation of suur BC. b. Find the equation of the line parallel to suur BC that goes through vertex A and graph it. c. Find the equation of the altitude from vertex A and graph it. 14. In ABC medians BM, AD, and CN intersect at P. If CN = 48, find CP and PN. 15. Let A = (5, 2). Find A, the image of A, when A is reflected across the line y = 2x. 16. If RS = 6, find the length of the image of RS under a dilation with scale factor Consider the transformation Txy (, ) ( 2 x, 2y) =. a. Plot the triangle OPQ where O= (0, 0), P= (2, 1), and OPQ under the transformation. b. how would you describe this transformation? c. What is the pre-image of ( 3, 4 )? 3 Q =,1 2, then find the image

5 Warmup for Advanced Algebra II page Algebraically find the coordinates of the vertices of the triangle enclosed by the lines 2x+ y = 12, x 2y = 16, and y = 3x A room s length is 3 feet less than twice its width. The area of the room is 135 square feet. What are the room s dimensions? (Make sure to draw a diagram!) Find the points of intersection of the parabola y = x 4 and the line x+ y = 2. Find the solution algebraically, then use the graph to confirm the validity of your solution. 21. Write the equation of the circle with center ( 1, 1) that passes through the point 1, Write the equation of the line tangent to the circle with equation the point (4,3). 2 2 x y x y = 125 at 23. Circle O has of diameter 14 cm. Chord AB is 1 cm from the center. Find the length of AB. 24. An airplane is approaching an airport at an altitude of 6400 m. The pilot has orders to descend at a constant angle of 6 when coming in for a landing. How far from the runway should the pilot begin his descent? (Round your answer to the nearest km.). 25. The ratio of interior to exterior angles in a regular polygon is 3:2. a. Find the measure of an exterior angle. b. Name the polygon. 26. A regular hexagon ABCDEF of radius 1 is positioned on the coordinate plane with its center at (0,0) and vertex A at (1,0). Find the coordinates of the vertex B assuming B is in the first quadrant. (exact values, not decimal approximations)

6 Warmup for Advanced Algebra II page In ABC, uuur AD bisects R CAB. Find the value of x. 28. Given TRY : NOW, the area of TRY is 630, the area of NOW is 25.2, and OW = Find RY. 29. Find the ratio of areas for each pair of triangles. a. ABC to ADE b. ADE to ADF 30. If P = (6, 1, 4) and Q = (2,1, 1), give coordinates for a point R on the z-axis so that R PQR is a right angle