112 Geometry & Applications Exam Review Name: ______
QUIZ 1
1. Match the following terms with their correct definitions ______1. Diameter A. A line segment joining the circle’s center and a point on its curve ______2. Radius B. A line segment with endpoints on the circle ______3. Midpoint C. A chord that passes through the circle’s center ______4. Complementary Angles D. Figures that are identical in size and shape ______5. Central Angle E. A line that intersects the midpoint of a line segment at right angles ______6. Subtends F. Divides a line segment in half ______7. Chord G. A triangle with two congruent sides. ______8. Perpendicular Bisector H. A line that intersects two or more lines ______9. Isosceles Triangle I. Two angles whose measures sum to 180 degrees ______10. Minor Arc J. Two angles whose measures sum to 90 degrees K. A triangle with all three angles measuring 60 degrees L. Is opposite to M. The arc that is less than half a circle’s circumference N. Has its vertex at the circle’s centre
2. In each of the diagrams below, determine which properties are required and use them to find the missing lengths indicated. a) OE = 9 b) OD = 10 CD = 8 OC = 7
QuickTime™ and a QuickTime™ and a OA = _____ TIFF (Uncompressed) decompressor TIFF (Uncompressed) decompressor are needed to see this picture. AB =_____ are needed to see this picture. AB = _____
3. In a circle, a chord is 16 cm in length and is 10 cm from the center of the circle. Determine the length of the circle’s diameter. Include a diagram and show your work. 4. AB and CD are two parallel chords on opposite sides of a circle's center. If the length of AB is 16 cm, the length of CD is 12 cm, and the circle's diameter is 18 cm, what is the perpendicular distance between the two chords? Include a diagram and show your work. 5. In the diagram to the right, OB is 12 cm, CD is 5 cm. What is the length of AB? Show your work. 6. Write the converse of the statements below. If the converse statement is true, re-write the statement QuickTime™ and a using "iff". If the converse statement is false, explain why. TIFF (Uncompressed) decompressor are needed to see this picture. a) If a shape is a square, then it has four sides. b) If two chords of a circle are equal in length, then they are equidistant from the center of the circle. QUIZ 2
7. Make a sketch of a line with endpoints C(-2,-9) D(3,-5). Find the slope, distance and midpoint of the line. Show all of your work and include formulas. 8. Prove that a triangle with vertices D(4,1) E(7,3) F(6,-2) is right angled. Sketch the triangle, show your formulas, work, and include a statement. 9. The circle shown has chords AB and CD as indicated, where A(-6,2), B(- 1,7), C(-1,-3), and D(4,2). Use the diagram to answer the questions that follow: a) Calculate the distance of AB and CD. b) What do you notice? c) What can you deduce about the lengths of the center to each chord? d) Which chord property is demonstrated here? 10. Write a formal congruency proof (statement/reason table) for the situations below. a) Given: RS ⊥ SU, VU ⊥ SU, T is the midpoint of SU and RS = VU Prove: ∆ RST is congruent to ∆ TVU b) Given: ABⅡDE, AC = CE Prove: AB = DE
QUIZ 3
1. Answer the following questions using the diagram below.
QuickTime™ and a a. What type of angle is AOC ? ______TIFF (Uncompressed) decompressor ∠ are needed to see this picture. b. What type of angle is ∠ABC ? ______c. If angle ∠AOC = 80˚, what is the measure of ∠ADC ? ______d. If ∠AOC = 80˚, what is the measure of arc ∠ABC ? ______
2. Find the missing measures in each diagram. a. b.
w = ______x = ______x = ______
QuickTime™ and a y = ______QuickTime™ and a TIFF (Uncompressed) decompressor TIFF (Uncompressed) decompressor y = ______are needed to see this picture. are needed to see this picture.
z = ______
c. d.
x = ______x = ______y = ______y = ______
QuickTime™ and a TIFF (Uncompressed) decompressor are needed to see this picture. QuickTime™ and a z = ______TIFF (Uncompressed) decompressor are needed to see this picture.
DE is a tangent
e. f. w = ______a = ______b = ______x = ______c = ______QuickTime™ and a TIFF (Uncompressed) decompressor QuickTime™ and a are needed to see this picture. TIFF (Uncompressed) decompressor d = ______are needed to see this picture. y = ______e = ______z = ______f = ______g = ______g. SP and SR are tangents. a = ______
b = ______
QuickTime™ and a TIFF (Uncompressed) decompressor c = ______are needed to see this picture. OS= ______
QUIZ 4
1. Define the unit circle in terms of its equation, radius and center coordinates. 2. The equation of a circle is (x+4)2 + (y-2)2 = 100. Determine algebraically whether each point lies inside, outside, or on the circle. a. (3,-2) b. (2,10) c. (-8,-3) 3. Identify the center and radius and mapping rule (as a transformation of the unit circle x2 + y2 = 1) of each circle. a. x2 + y2 = 81 b. (x-3)2 + (y-6)2 = 252 center: ______center: ______radius: ______radius: ______maping rule: ______maping rule: ______
c. (x-5)2 + (y+7)2 = 25 d. (x-2)2 + y2 = 16 center: ______center: ______radius: ______radius: ______maping rule: ______maping rule: ______
4. Use the center point and radius to create the equation of the following circles. a. Center: (0,-4) radius = 4 b. Center: (-6,-2) radius = 10 c. Center: (-4,4) radius = 6 d. Center: (7,3) radius = 5
5. Determine the center and the radius of each circle under each mapping rule. a. (x,y) (x+2, y-1) c. (x,y) (10x-5, 10y+6) center: ______center: ______radius: ______radius: ______
b. (x,y) (2x-5, 2y+1) d. (x,y) (4x+1, 4y) center: ______center: ______radius: ______radius: ______
6. Find the equation of a circle that has a diameter with the endpoints given by the points A(3,-5) and B(9,-5). Sketch the circle. 7. Write the equation and mapping rule (as a transformation of the unit circle x2 + y2 = 1) for each new circle. a. The circle (x+3)2 + (y+1)2 = 25 is translated 2 units left and its radius is stretched by a factor of 3. b. The circle (x-2)2 + (y-4)2 = 36 is translated 3 units right and 4 units up.
QUIZ 5
1. A circle with center point (2,-1) has a radius of 4. a. Sketch the circle. b. Write the equation of the circle in Standard Form (SF) c. Write the equation of the circle in Transformational Form (TF) d. Write the equation of the circle in General Form (GF) 2. Convert the following from SF to GF. (x+1)2 + (y-6)2 = 25
3. Convert the following from TF to GF. [ x ]2 + [ (y-3) ]2 = 1 4. Convert the following from GF to TF. x2 + y2 + 4 x - 6y - 3 = 0 5. On the graph below you are going to create a circle. The circle must have a radius greater than 1 and its center point can be anywhere except the origin. (write your center and radius in the space below) Center: ______Radius: ______6. Write the equation of the circle you sketched in each of the following forms: a. Standard Form b. Transformational Form c. General Form
QUIZ 6
1. Answer the following questions for each of the equations below:
a. [ (x-1) ]2 + [ (y+2) ]2 = 1 b. [ (x-1) ]2 + [ (y+2) ]2 = 1
a. Sketch each of the equations on the graphs below. a. b. b. Write a mapping rule to express each equation as a transformation of the unit circle x2 + y2 = 1. a. b. c. If the equation is a circle, state the length of the radius, if the equation is an ellipse, state the lengths of the major and minor axes. a. b. d. Convert the equation of the ellipse into standard form. e. Convert the equation of the ellipse into general form.
2. During a game of Equation Battleship, a student had her destroyer on the points (-6,5), (-5,5) and (-4,5). If the following bombs were thrown during the game, would her ship sink? If yes, which bomb(s) would sink her destroyer? Show her ship and the bombs on the graph below and include a complete sentence for your final answer. bomb a. [ x ]2 + [ y ]2 = 1 bomb b. [ (x-3) ]2 + [ (y-2) ]2 = 1 bomb c. [ (x+4) ]2 + [ (y-4) ]2 = 1 bomb d. 4(x)2 + 16(y-5)2 = 64
QUIZ 7
1. Use the diagram to the right to answer the following questions: a. Label the diagram with the following labels: initial arm terminal arm angle of rotation reference angle quadrants (1,2,3,4) quandrant angles (0°,90°,180°,270°,360°)
b. If the angle of rotation in the diagram above is 305°, what is the reference angle?
c. Find one positive and one negative coterminal angle for 305°. Sketch the coterminal angles on the coordinate planes below. d. If the circle above was a unit circle, what would be the coordinates of point P? Round your answer to 3 decimals. e. If the circle above had a radius of 5, what would be the coordinates of point P? Round your answer to 2 decimals.
2. In which quadrant do the following angles fall? a. 32° b. 105° c. 234° d. 335° 3. State the reference angles for each of the angles in question 2. a. b. c. d. 4. P(θ) = (-0.5, -0.866) is a point on the unit circle. a. Make a sketch on the coordinate plane to the right. b. What is the reference angle (to the nearest degree)? c. What is the angle of rotation (to the nearest degree)? 5. A circle with center (0,0) has a radius of 7. If the point (-5.362, 4.499) is on the circle, find the angle of rotation (to the nearest degree). Include a sketch. 6. Use the CAST rule to determine whether each of the following trig ratios would be positive or negative. a. cos290° b. tan35° c. cos150° d. sin240° 7. Recreate the triangles that have special angles of 30°, 60° and 45°. 8. State the exact value (no decimals) of the following trig ratios (don’t forget the CAST rule for positives and negatives) a. tan60° b. cos30° c. sin45° d. sin315° e. tan210° f. cos120°
9. Determine the exact values for coordinates (x,y) of the terminal point for a 150° angle of rotation on a unit circle.
QUIZ 8
1. What are the symbols for the following terms? a. Sample mean: ______b. Population mean: ______c. Sample standard deviation: ______d. Population standard deviation: ______2. Mrs. Parlee wants to compare exam scores of her two grade 11 math classes. She randomly Morning Afternoon selected 10 exams from each class and recorded the marks (%) in the table to the right. Class (%) Class (%) a. Does the data in the table represent a sample or a population? Explain. 50 42 56 56 b. Determine the measures of central tendency (mean, median and mode) for each set of 56 58 exam marks. 65 65 Morning Class: Afternoon Class: 68 65 71 73 74 75 Mean: ______Mean: ______78 80 Median: ______Median: ______85 85 Mode: ______Mode: ______87 91
c. In your own words, describe the difference between sample and population standard deviation. d. Determine the standard deviation of each set of exam marks. Show your work and include the formula. Formulas:
Morning Class: Afternoon Class:
e. In your opinion, did one of the classes do better on the exam? Explain your answer using your descriptive data (mean, median, mode or standard deviation).
3. Other than using statistics for analyzing marks, name 2 real life examples in which we use statistics. Explain how statistics are used in each situation. 4. The data below represent maximum daily temperatures ( oC) for May 2010. Using a bin width of 3oC, create a histogram to display this data (show your bin/frequency table). 9.5 11.5 15.3 16.7 17.3 20 10.1 12.1 15.5 16.9 17.5 20.8 10.3 14.3 15.9 16.9 17.9 21.1 10.6 14.4 16.1 16.9 18.5 21.5 10.9 14.9 16.7 17.2 18.6 23 23.8 5. The mean temperature for the summer of 2000 (June, July & August - 98 days) was 23.5oC with a standard deviation of 3.5 oC. Use this information to answer the following: a. Indicate the values on a normal distribution curve. b. 68% of the temperatures were between ______and ______. c. 95% of the temperatures were between ______and ______. d. 99.7% of the temperatures were between ______and ______. e. What percentage of the temperatures were between 13 oC and 20 oC ? ______f. What percentage of the temperatures were less than 23.5 oC ? ______g. What percentage of the temperatures were greater than 27 oC %? ______h. How many days were likely above 34 oC ? ______i. How many days were likely below 27 oC ? ______j. The following temperatures were recorded in previous summers. Determine if they are significantly different from the mean temperature of the summer of 2000. i. 15 oC ii. 25 oC iii. 26 oC iv. 32 oC v. 17 oC vi. 34 oC 6. What is the difference between descriptive and inferential statistics? Provide examples. 7. Mr. McKiel wants to conduct a survey to find out the number of students who are physically active at SRHS. He only has a short time to collect his data so he will ask a sample of 100 students. a. Give an example of how he could collect his data using a biased sample. What makes this method biased? b. Give an example of how he could collect his data using an unbiased sample. What makes this method unbiased? 8. Answer the following questions using the word bank of sampling methods below. A. Cluster Sample B. Convenience Sample C. Simple Random Sample D. Stratified Random Sample E. Systematic Sample F. Voluntary Response Sample
a. Which of the sampling methods above are biased? b. Jessica wants to get student reaction to the new theatre project in the high school. To conduct her survey, she sets up a booth in the lobby at lunch and asks students to complete her questionnaire. What type of sampling is this? Explain. c. Jack wishes to survey students about their favourite food in the cafeteria. He decides to line the students up single file and survey every fifth student. What type of sample method has Jack chosen? Explain.