MATHEMATICS 2201 MidTerm Review 2015

Transcription

1 MATHEMATICS 2201 MidTerm Review 2015 Formula: Unit 1 Acute Triangle Trigonometry (law of Sines and Cosines) Chapter 3 in Text 1. Which is a proper application of the cosine law for? 2. Which triangle can you use the law of sines to find?

2 3. What is the measure of? 4. What is the length of? Which is expressed as an entire radical? Unit II (Chapter III Text) 6. Which expression is equivalent to? 7. Simplify: ( )

3 8. Simplify: 9. What are the restrictions on for the radical equation:? 10. Simplify: 11. Simplify: 12. A study of income in a large city states the mean family income is $ The study states the results are accurate 9 times out of 10. What is the confidence level in this situation? (Unit III Chapter IV Text) 90% 95% 99% 100%

4 13. How many scores are greater than or equal to 50? Which graph represents data which approximates the normal distribution?

5 16. The number of goals by all hockey players in the NHL is normally distributed. The mean number of goals is 18 with a standard deviation of 4 goals. In what goal range would 6 of the players score? 17. A random survey of 100 teens reported that 28% of those surveyed exercise at least three times per week. The results are considered accurate within percent, 19 times out of 20. If the sample size is increased, which statement is most accurate? The margin of error will decrease The margin of error will increase The mean will decrease The mean will increase 18. What is the -intercept of? Unit IV Chapter 6 Text A parabola passes through the points (4, 9) and ( 8, 9). What is the equation of the axis of symmetry? 20. What is the vertex of the graph? ( ) ( ) ( ) ( )

6 21. What is the range of ( )? { } { } { } { } E) 22. What is the vertex of? ( ) ( 3, 68) ( 10) ( 4) 23. What is ( )( ) in form? What are the x-intercepts? 24. For the graph, what are the x-intercepts and vertex of the quadratic function? More Multiple Choice Practice

7 25. What is the measure of? C 6.8 cm A cm B ( ( ( ( 26. Which equals the measure of? 5 A 7 C B 9 ( ( ( )( ) ) ( ( ( )( ) ) ( ( ( )( ) ) ( ( ( )( ) ) 9. Simplify completely: ( ( ( ( 10. Simplify completely: ( ( ( (

8 11. Write as an entire radical. ( ( ( ( 12. A student was asked to simplify Which step contains her first error? but did not complete a correct solution. Solution: Step 1: Step 2: Step 3: Step 4: ( 1 ( 2 ( 3 ( Simplify completely: ( ( ( ( 14. What are the restrictions on the variable for? ( ( ( (

9 F r e q u e n c y 15. Which represents data with the largest standard deviation? ( ( ( ( The histogram shown represents the heights of hockey players on a professional hockey team. How many players have a height between 1.8 m and 2.0 m? Heights of Hockey Players Heights (m) ( 10 ( 18 ( 24 ( 28

10 17. A set of data is normally distributed. What percent of the data is within two standard deviations of the mean? ( 47.5 ( 68 ( 95 ( The function has axis of symmetry. Which represents the function? ( y (-2, -1) x ( y (-2, -1) x ( y (-2, 23) x ( y (-2, 23) x 19. What is the domain and range for ( ) ( )? ( and ( ) ( and ( ) ( and ( ) ( and ( )

11 20. A parabola has x-intercepts of ( ) and ( ). What is the axis of symmetry? ( ( ( ( 21. What is the vertex of? ( ( ) ( ( ) ( ( ) ( ( ) 22. The graph of a quadratic function has vertex ( ) and opens upward. How many x- intercepts does it have? ( 0 ( 1 ( 2 ( What is the equation of the function graphed below? y -1 3 x ( ( )( ) ( ( )( ) ( ( )( ) ( ( )( )

12 Long Answer All workings must be shown to warrant full marks! Unit 1 Acute Triangle Trig 1 Using the law of sines find the missing sides indicated. 2 Using the law of sines find the missing angles indicated. The Law of Cosines 3. Determine the missing measurements using the law of cosines. a) b)

13 4. Determine the length of the tunnel. 5. a) What information do you need to know about an acute triangle to use the sine law? b) What information do you need to know about an acute triangle to use the cosine law? 6. State an appropriate cosine law for the following triangles for angle x, angle y, angle z. Trig ratios only! 7. a) Determine the height of the flagpole b) Determine the angle of elevation. 8. Identify the law used to solve each triangle. Explain why. Solve triangle A and D ONLY!. a) b) c) d)

14 Applications of Sines and Cosines, and trig ratios A ladder 20 feet long leans against the side of a house. Find the height, h, from the top of the ladder to the ground if the angle of elevation of the ladder is 670. (Draw a diagram.) 11. In the diagram below, what is the length of BC to the nearest tenth of a centimetre? Find the value of x below by using the law of sine and/or cosines. Find the value of x. Unit II Radicals (Chapter 4 in Text) Short Answer Stuff. Write as an entire radical: 2. Which choice lists these numbers in decreasing order? a) 1. b) c)

15 3. Which is the simplest form of: 4. Which expression is the simplest form of : 5. Which expression is the rationalized simplest form of: Part II: 6.? Simplify the following: )( ) Determine the perimeter and area of the following rectangle, in simplest form. Perimeter Area Simplify: 9. Multiply: 10. Rationalize the denominator and simplify.? Show all workings. Answers without complete workings will not merit full marks. ( 7.? E) F) Solve: state any extraneous roots. 12. State the restrictions on x, solve the equation, and then check for extraneous roots x y z a 8 20 x 7 y x8 y18 4 5x y d 7 g10 n3 H) 64x5-8x + 6x y 6 d) 1 x3 e) 20 x f) 5 20 x5 27c c 3 27x3 I) Multiply: 4 x ( 3x 7) x E) 4 2 x 8 2 Simplify: 8 G) 2 x 8 10 ( ) 5 x 4) C ) ( )

16 15. State the restrictions on: 1 1 y x 4 y x 4 y 2x 10 E) x and F) x G) x x 4 x Joss has been contracted to water lawns for he summer using circular sprayers. The radius of sprayed water, r, in metres, is modeled by: r 0.25A, where A is the area of grass watered in square metres. Determine the area covered for a circle with a radius of 24 m. 17. The speed of a tsunami can be modeled by: S 356 d, where S is the speed in kilometres per hour and d is the average depth of the water in kilometers. Determine the average depth of the waves of a tsunami traveling at 40 km/h to the nearest hundredth of a kilometer. 18. The formula for the motion of a pendulum is: T 2 L is the length of the pendulum in metres. A pendulum took 18 s to swing once. Determine the length of the pendulum. End Unit II Radicals L 4.9 Unit III Statistics Part II ONLY! 1. The following are public exam marks for English 3201 this past June , where T is the time in seconds and back and forth a) Determine the range, mean, and standard deviation, correct to two decimal places using technology if you wish. (Or you may do it manually as well but you have no extra time!) Range:= Mean= b) Create a frequency table, histogram and frequency polygon using a bin width of 10. Class(Bin) Tally Frequency 3. A survey determined all the students at Menihek High School have a mean height of 170cm and a standard deviation of 8.5cm. a) Sketch a normal curve to show the distribution of Menihek High School student heights. Mark the values that are 1, 2, and 3 standard deviations from the mean as well as all percentages that lie within the intervals.

17 b) If there are 550 students at Menihek, determine the number of students who have a height between 161.5cm and 187cm? 4. Bell Aliant offers a deal on the new iphone 5. The iphone 5 has a mean life of 2.7 years with a standard x deviation of 0.7. Please Note z a) What is the probability that a new iphone 5 will last longer than 3 years? (In other words, what percent of phones last longer than 3 years?) DRAW A DIAGRAM to accompany any part of your solution! b) If Apple offers a 1 year warranty, what percentage of phones will they have to replace? 5. A cell phone has a 1 year warranty. The mean lifespan of the phone is approximately 2.5 years with standard deviation of 0.80 years. The SOURCE sold 4000 of this particular brand last year. Using a standard normal distribution, determine how many of these phones will fail before the warranty expires? If the extended warranty is bought for an extra year (1.5 years), what is the likelihood (probability) that someone will make a claim on the warranty as a percentage? 5. Felicity wants to know if Peter Penashue will be re-elected as the MP for Labrador. In a recent survey, 400 Labradorians were asked if they would be voting for Penashue, 42% said yes. This survey is considered accurate within 4.7 percent points, 19 times out of 20. a) Determine the confidence level and the confidence interval. b) If there are eligible voters in Labrador, state the range of the number of people who are considering voting for Peter Penashue. End Unit III Unit IV Quadratic Functions (Parabolas) Chapter 6 in Text 6-1 to For each quadratic function below determine the following: i) direction of opening and the y-intercept ii) if the parabola is wider or more narrow than the base graph of y = x 2 iii) iv) the equation of the axis of symmetry using x= -b/2a the coordinates of the vertex algebraically and/or with technology v) a table of values with 5 points on the parabola with the vertex in the middle vi) vii) a sketch of the graph on graph paper withy the five points including vertex and AOS state the domain and range of the quadratic function (the parabola) 1 A y x x B y x x C y x x D y x x ) 4 ) ) ) 1 2 Given the equation in factored form below find: x-intercepts (change signs on factors) y-intercept (sub in x = 0) equation of the AOS (average the x-intercepts) coordinates of the vertex (Aos, sub in ans in c to get y value or read off from table on calc)

18 i) y = -(x+6)(x-10) ii) y = -6x(x-4) iii) y =.5(x+4)(x-8) 3 Find the equation of the parabolas below in FACTORED FORM. x-intercepts are x = 6, x = -3, and y-intercept = 4 x-intercepts are x = 6, x = -3, and y-intercept = 4 4 A soccer ball is kicked from ground level and lands on the ground 3 seconds later. (Xintercepts) It reaches a maximum height of 6 m.(y coordinate of vertex). Find the equation of the path of the ball in FACTORED FORM. Use it to determine the height of the ball after 2.5 seconds. 5 A golf ball is kicked from ground level and lands on the ground 5 seconds later. (Xintercepts) It reaches a maximum height of 40 m.(y coordinate of vertex). Find the equation of the path of the ball in FACTORED FORM. Use it to determine the height of the ball after 2 seconds. 6 An osprey (a member of the eagle family) is pitched on the top of a telephone pole 20 m high. It dives down and attacks a squirrel that is at ground level 10 m from the pole. Its dive follows the path of a parabolic function. Find an equation to describe the path taken in factored form and use it to determine the height of the bird 6 m from the pole. 7 End!

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