Math 20-1 Year End Review

Transcription

1 M0- Year End Review.docx Name: Math 0- Year End Review hapter Sequences & Series... Pages hapter Trigonometr... Pages hapters & Quadratic Functions & Equations... Pages hapter Radicals... Pages hapter Rational Expressions... Pages hapter 7 bsolute Value & Reciprocal Functions... Pages hapter Sstems... Pages hapter Inequalities... Pages 7 nswers... Pages hapter Sequences & Series. Which of the following numbers occurs in the sequence,,, 0,,...?. The common difference in the arithmetic sequence,,,,... is 7. The common difference in the arithmetic sequence,,,,,... is. In the formula for the general term of an arithmetic sequence t n = 7 + (n ) (.), the common difference is Which of the given formulas for the general term of the sequence,, 7,,,... is correct?. What is the th term of the sequence,., 0.,.,.,? The sum of the series ( ) + ( 7) + ( ) + + ( ) is 0. The sum of an arithmetic series where t =, t = 7, and n = is

2 M0- Year End Review.docx. The sum of an arithmetic series where,, and n = is For the arithmetic series (07) + (0) + () + + (), the values of, d, and n are, d =, n = = 07, d =, n = = 07, d =, n = = 07, d =, n =. On the first da of the month, Michael places in a jar. The next da, he places 7 in the jar. The third da, he places in the jar, and so on for das. What amount will be in the jar at the end of this period of time? $.7 $. $. $.. The common ratio for the geometric sequence,, 0., 0.0,... is. The population of a communit was 000 at the beginning of 000. ssuming a rate of growth of.% per ear since 000, what will the population be at the beginning of 0? In the formula for the general term of a geometric sequence, the common ratio is. The eighth term in the sequence, 70, 0,, is 7. The th term in the sequence,,,,... is

3 M0- Year End Review.docx 7. The first three terms of the sequence given b,,,,,,,, are. How man terms are in the sequence,,,,,, 07? 0. The sum of a geometric series where..7.., r =, and n = is approximatel 0. The sum of the geometric series is The sum of the geometric series is. The th term of the geometric series What is the value of S for the series + 7 +?. If ou researched our ancestors back generations, how man people would ou need to research? etermine the sum of the infinite geometric series is

4 M0- Year End Review.docx. What is the sum of the infinite geometric series ? etermine the sum of the infinite geometric series with t = and r =. 0. The sum of an infinite geometric series is and its common ratio is. What is the first term of the series? 0. Which of the following best describes the series 0 + ( ) + ( 7 ) + ( ) + 0? The series is convergent and has a sum of 00. The series is divergent and has a sum of 00. The series is divergent and has no sum. The series is convergent and has no sum. 0. The first three terms of the sequence defined b are 0., 0.,. 0., 0., 0. 0., 0., , 0.,. hapter Trigonometr. What is the reference angle for in standard position? 0. What is the reference angle for 00 in standard position? What are the three other angles in standard position that have a reference angle of? 0 0

5 M0- Year End Review.docx. What is the exact sine of? / / / /. What is the exact cosine of?. Which set of angles has the same terminal arm as 0? 0, 0, 0 00, 0, 0 0, 0, 0 00, 70, 0

6 M0- Year End Review.docx 7. The point (0, ) is on the terminal arm of angle?,,,,,,,,. Which is the set of exact primar trigonometric ratios for the. The coordinates of a point P on the terminal arm of an angle are shown. What are the exact trigonometric ratios for,, and? iagram not drawn to scale. (,) x. Marco is 0 m due east of the centre of the park. His friend Ra is 0 m due south of the centre of the park. Which is the correct expression for the exact distance between the two bos? m m m m

7 M0- Year End Review.docx 0. What is the exact value for?. n angle is in standard position such that. What are the possible values of, to the nearest degree, if? and 7 and and 7 and 7. Solve to the nearest tenth of a unit for the unknown side in the ratio..... etermine the length of x, to the nearest tenth of a centimetre. x 0º cm 70º iagram not drawn to scale etermine, to the nearest tenth of a centimetre, the two possible lengths of a. a cm 7.º cm iagram not drawn to scale. 7. cm and. cm. cm and. cm 7. cm and. cm. cm and. cm 7

8 M0- Year End Review.docx. etermine, to the nearest tenth of a degree, the two possible measures of. cm cm º iagram not drawn to scale. and. and 0.. and 7 and 7. Which of the following triangles cannot be solved using the sine law? iagrams not drawn to scale. º 7º º 0 º º

9 M0- Year End Review.docx 7. If, c = 0. cm, and b = 0. cm, and is acute, what is the measure of, to the nearest tenth of a degree? c b a iagram not drawn to scale Which strateg would be best to solve for x in the triangle shown? x º 0 cm 7º iagram not drawn to scale. cosine law primar trigonometric ratios sine law none of the above

10 M0- Year End Review.docx. Which strateg would be best to use to solve for x? x cm 0 cm º iagram not drawn to scale. primar trigonometric ratios sine law cosine law none of the above 0. etermine the measure of x, to the nearest tenth of a degree. 0 cm x cm cm iagram not drawn to scale

11 M0- Year End Review.docx. What is the length of x, to the nearest tenth of a metre? x m m º iagram not drawn to scale.. If 7.7 m. m. m 7. m, r = 0 cm, and p = cm, what is the length of q, to the nearest centimetre? P q R r p Q iagram not drawn to scale. cm 0 cm cm cm

12 M0- Year End Review.docx. Solve the following triangle, rounding side lengths to the nearest tenth of a unit and angle measures to the nearest degree. iagram not drawn to scale., b =, a =.,, c =.0,, c =.0,, c =.7,, c =.. While fling, a helicopter pilot spots a water tower that is 7. km to the north. t the same time, he sees a monument that is. km to the south. The tower and the monument are separated b a distance of. km along the flat ground. What is the angle made b the water tower, helicopter, and monument? 7. km. km. km iagram not drawn to scale. 0 hapter & Quadratic Functions and Equations. What are the x-intercepts of? and and and and. What is the axis of smmetr of? x = x = x = x =

13 M0- Year End Review.docx 7. What is the quadratic function in vertex form for the parabola shown below? x 7 0. What is the vertex of? (, ) (, ) (, ) (7, )

14 M0- Year End Review.docx. Which graph represents the quadratic function? x x x x 0 0. What are the domain and range of? omain: Range: omain: Range:. The vertex of a parabola is located at represents the parabola? omain: Range: omain: Range:. If the parabola has a -intercept of, which quadratic function

15 M0- Year End Review.docx. What information can be determined from the quadratic function? the vertex is at (, ) and the graph opens upward the vertex is at (, ) and the graph opens downward the vertex is at (, ) and the graph opens downward the vertex is at (, ) and the graph opens upward. Which function is not quadratic?. Identif the characteristics of this graph. vertex: (, ) axis of smmetr: -intercept: 0. x-intercepts: and 7 opens downward vertex: (, ) axis of smmetr: -intercept: 0. x-intercepts: and 7 opens upward vertex: (, ) axis of smmetr: -intercept: 0. x-intercepts: and 7 opens upward vertex: (, ) axis of smmetr: -intercept: 0. x-intercepts: and 7 opens downward x 0 0

16 M0- Year End Review.docx. What is written in standard form?. What are the coordinates of the vertex of the quadratic function? (, ) (, ) (, ) (, ) 7. What is the function. What is the function written in standard form? written in standard form?

17 M0- Year End Review.docx. Which graph represents the quadratic function with the following characteristics: x-intercepts at and 0 maximum of x x x x If the points and are on the graph of the quadratic function, what are the values of b and c? and and and and 7

18 M0- Year End Review.docx 7. The table shows the path of an extraterrestrial missile, where x is the horizontal distance, in metres, from the launch pad and h is the height, in metres, of the missile above the launch pad. Horizontal distance, x Height, h What quadratic equation can be used to model the data set? 7. What is the equation of the quadratic function in vertex form? 7. What is the equation of the quadratic function in vertex form? 7. Which quadratic function in standard form represents? 7. State whether the function of the vertex. maximum at maximum at 7. The vertex of the quadratic function has a maximum or minimum value and identif the coordinates minimum at minimum at is 77. What is the vertex form of? +

19 M0- Year End Review.docx 7. onvert to vertex form. Round coefficients to two decimal places, if necessar. 7. What is the axis of smmetr for the quadratic function? x = x = 7 x = x = 0. How man x-intercepts does the graph of the quadratic function have? 0 x 0 unknown 0

20 M0- Year End Review.docx. What are the x-intercepts of the quadratic function graphed here? 0 x 0 and. and.. What are the x-intercepts of the quadratic function graphed here? 0 x 0.. there are none.0 0

21 M0- Year End Review.docx. What is the x-intercept of the quadratic function graphed here? 0 x What are the roots of the quadratic function? 0. and and. What are the roots of the quadratic function? and 0 0. and. Factor completel. 7. Factor completel.. Solve. x = and x = x = and x = x = and x = x = and x =

22 M0- Year End Review.docx. etermine the roots of the quadratic equation. x = 0 and x = x = 0 and x = x = 0 and x = x = and x = 0. etermine the roots of the quadratic equation. x = and x = x = and x = x = and x = x = and x =. Solve. and and and and. rectangle has dimensions and, where x is in centimetres. If the area of the rectangle is 7 cm, what is the value of x, to the nearest tenth of a centimetre? x + 0 x. The value of k that makes the expression a perfect square trinomial is 0 7. The vertex form of is. Which is the vertex form of? Round coefficients to the nearest hundredth if necessar.

23 M0- Year End Review.docx. Solve. + and + and 7. The roots, to the nearest hundredth, of. and 0.. and 0.. and 0.. and 0. are. The roots, to the nearest hundredth, of are 7. and.. and 0.. and 0.. and 0.. rectangle with an area of is x centimetres wide and (x + ) centimetres long. To the nearest tenth of a centimetre, the width and length are 0.0 cm and 0.0 cm. cm and. cm. cm and. cm.0 cm and.0 cm 00. When lex rides his dirt bike off a ramp, his path can be modelled b, where d is the horizontal distance from the ramp and h is the height, both in metres. How far awa from the ramp does he land, to the nearest tenth of a metre?.0 m 0. m 7. m. m 0. The x-intercepts, to the nearest hundredth, of are 0.7 and and. 0. and and The number of real roots for the equation is 0 impossible to tell 0. For a science experiment, a projectile is launched. Its path is given b, where h is the height of the projectile above the ground and d is the horizontal distance of the projectile from the launch pad, both in metres. How far awa from the launch pad is the projectile when it begins to fall, to the nearest tenth of a metre?. m 7.7 m 0. m.7 m

24 M0- Year End Review.docx 0. The table shows the coordinates of the curve of a parabolic arch at the entrance to a park, where x is the horizontal distance from one side of the arch and h is the height of the arch above ground, both in metres. x h The quadratic equation that models the data is hapter Radicals 0. Find a simplified expression for the perimeter of this shape. Not to scale What does the expression simplif to? 07. State the side length of a square with an area of 7 cm in simplified radical form. cm 7. cm 7 cm cm 0. Express in simplified form. 0. etermine the value of the expression when and.

25 M0- Year End Review.docx 0. Simplif Simplif Simplif the expression ( ) + ( ) ( ) ( ) The volume, V, in cubic units, of a clinder is given b, where r is the radius and h is the height, both in the same units. Find the exact radius of a clinder with a height of cm and a volume of 7 cm. Express our answer in simplest form. cm cm cm cm. Express in simplest form.. Find a simplified expression for the area of this shape. Not to scale Express in simplest form. 7. Express in simplest form.

26 M0- Year End Review.docx. n equilateral triangle has an area of. cm. What is the side length of the triangle, to the nearest tenth of a centimetre? s =? rea =. cm. cm. cm. cm.0 cm. n equilateral triangle has an area of. cm. What is the height of the triangle, to the nearest tenth of a centimetre? h =? cm 0.0 cm. cm cm

27 M0- Year End Review.docx 0. radical expression is being simplified. In which step of the process was an error made? Step Step Step Step. etermine the range of the function. { R} {x R} { R, 0} {x R, x }. etermine the value of the function when.. Solve. x = x = 7 x = 7 x =. Solve x = x = x = x =. Solve. x = x = x = x =. Solve. x = x = x = x = 7

28 M0- Year End Review.docx 7. Solve. x = x = x = x =. Solve. x = x = or or. What are the restrictions on x if the solution to the equation involves real numbers? hapter Rational Expressions 0. Marco tested three values of x in two rational expressions and found that one value of x returned different values for in the two given expressions. Which of the following conclusions is correct? The two rational expressions are not equivalent. The two rational expressions are equivalent part of the time. More testing is needed to draw a conclusion. The two rational expressions are equivalent.. The non-permissible value(s) for the rational expressions x x x x x. The non-permissible value(s) for the expression is (are) is (are) x x and x 7 there are no restrictions. What is in simplest form? State an non-permissible values.,,,,,,,,

29 M0- Year End Review.docx. Simplif.. What is the simplified version of the rational expression?. When full simplified, ignoring non-permissible values, 7. When full simplified, ignoring non-permissible values, is equal to is equal to. Simplif the rational expression.. Simplif the rational expression. Express our answer with positive exponents onl.

30 M0- Year End Review.docx 0. Express the product in simplest form.. Express the quotient in simplest form.. When full simplified, x x is equal to x x. When full simplified, is equal to. When full simplified, ignoring restrictions on the variable, is equal to. Simplif the rational expression. 0

31 M0- Year End Review.docx. When full simplified, ignoring restrictions on the variable, is equal to 7. Simplif. State an non-permissible values.,,,,. In a biathlon race, Murra must ccle 0 km and then run 0 km. Using as his ccling speed and as his running speed, what is the correct simplified expression for the total time needed to complete the race?. ourtne and Kurtis are planning to travel 0 km in a car b travelling at x kilometres per hour for the first half of the distance, and then increasing their speed b km/h to finish the distance. Which is the correct simplified expression for the total time of the trip? 0. Solve the rational equation. Identif all non-permissible values., x = 0, x = 0, x =,. Solve the rational equation. x = 0 x = 0 x = and x = 0 and. Evan starts out on a snowmobile trail and travels at km/h. onnie leaves 0 min later, travelling at v kilometres per hour, and overtakes Evan after t hours. How fast would onnie have to travel to overtake Evan in 0 min? Express our answer to the nearest tenth.. km/h.0 km/h.7 km/h 0.0 km/h

32 M0- Year End Review.docx. What is the exact solution to the equation. Solve. x = and x = and x = x = and x = and x = x = and x = x = hapter 7 bsolute Value and Reciprocal Functions. Evaluate the expression Evaluate the expression etermine the value of the absolute value expression.. etermine the value of the absolute value expression Identif where on the number line is located x 0. Evaluate. 7

33 M0- Year End Review.docx. The graph of is x 0 0 x x 0 0 x

34 M0- Year End Review.docx. Given the graph of, which is the graph of? x x 0 0 x x 0 0 x

35 M0- Year End Review.docx. What are the domain and range of?. What are the domain and range of?

36 M0- Year End Review.docx. The graph of is 7 7 x x 7 7 x x

37 M0- Year End Review.docx. The graph of is 7 7 x x 7 7 x x 7

38 M0- Year End Review.docx 7. The graph of is x 0 0 x x 0 0 x

39 M0- Year End Review.docx. Given the graph of, which is the graph of? 7 x 7 7 x x 7 7 x x

40 M0- Year End Review.docx. Solve. or or 70. etermine the solution to. x = or x = no solution x = or x = x = 7. etermine the solution to 7 x = or x = 7 x = or x = no solution x = 7. What is the solution to? x = or x = x = or x = x = x = 0

41 M0- Year End Review.docx 7. Which graph represents the solution to? 0 0 x 0 x x 0 x 0 7. Solve. x = 0 x = 0, x = x = x = 0, x = 7. Solve. x = and x = and x = and x = and

42 M0- Year End Review.docx 7. Which graph represents the reciprocal of the linear function? x x x x

43 M0- Year End Review.docx 77. Which graph represents the reciprocal of? x x x x 0

44 M0- Year End Review.docx 7. Which graph represents the reciprocal of? x x x x 7. The equation of the vertical asmptote for the reciprocal of = x is x = x = x = x = 0. Omit. Omit

45 M0- Year End Review.docx

46 M0- Year End Review.docx hapter Sstems. The approximate solutions to the sstem of equations shown below are 7. Omit 7 7 x 7 and and and and. Omit. Omit. Omit

47 M0- Year End Review.docx 7.How man solutions are represented b the graph shown below? x 7 two solutions one solution three solutions no real solution 7

48 M0- Year End Review.docx. What sstem of equations is represented b the following graph? x 7

49 M0- Year End Review.docx. What sstem of equations is represented b the following graph? x 7

50 M0- Year End Review.docx 0. Which graph represents the sstem of equations shown below? x x x x 0 0

51 M0- Year End Review.docx. Which graph represents the sstem of equations shown below? x x x x. How man times does a line tangent to a parabola cross the parabola? twice once three times none of these. The line intersects the quadratic function at one point. What are the coordinates of the point of intersection?. Find the coordinates of the point(s) of intersection of the line = and the quadratic function. (, ) ( 0, ) and (, ) 7 (0, 0) (, ) and ( 0, )

52 M0- Year End Review.docx. Solve the following sstem: = 7 (, ) 7 ( 0, ) and (, ) (, ) and ( 0, ) (0, 0). etermine the -intercept of a line with a slope of that is tangent to the curve =. 7. The cross-section of a tunnel is in the shape of a parabola. The parabolic shape of the tunnel is given b the function. What is the width of the tunnel, to the nearest hundredth of a metre, at a height of m? iagram not to scale. x.00 m 7. m.00 m.0 m. The line intersects the quadratic function at two points. What are the coordinates of the two points of intersection? (0,0) and (0, 0) and and (, ) and. Solve the following sstem of equations: (0,0) and (, ) and and (0, 0) and 00. What are the coordinates of the point(s) of intersection of the line? and and, and and and the quadratic function

53 M0- Year End Review.docx 0. What are the solutions for the following sstem of equations? and and and and 0. What are the solutions for the following sstem of equations? and and and and 0. What are the coordinates of the point(s) of intersection of the quadratic functions? and and and and and 0. Solve the sstem and. Express our answers as exact values. (, ) and (, ) (, ) and (, ) (, ) and (, ) (, ) and (, ) Four corners are cut from a rectangular piece of cardboard that measures ft b ft. The cuts are x feet from the corners, as shown in the figure below. fter the cuts are made, the sides of the rectangle are folded to form an open box. The area of the bottom of the box is ft. x x x x feet x x feet x x iagram not drawn to scale 0. What two equations represent the area,, of the bottom of the box?

54 M0- Year End Review.docx 0. What are the approximate dimensions of the box? Give our answer to one decimal place. width =. ft width =. ft length =. ft length =. ft height =. ft height = 0. ft width =.0 ft length =.0 ft height = 0. ft width =. ft length =. ft height = 0. ft 07. What is the approximate volume of the box? Give our answer to one decimal place.. ft. ft.0 ft. ft hapter Inequalities 0. The graph of is x x x x

55 M0- Year End Review.docx 0. The graph of is x x x x

56 M0- Year End Review.docx 0. Which inequalit represents the graph shown below? x 7 > < x x > < x x

57 M0- Year End Review.docx. The graphical solution to < x is x x x x. Which inequalit represents the graph shown below? 7

58 M0- Year End Review.docx x 7 > > x x x x sports store makes a profit of $0 on ever pair of cross-countr skis sold and $ on ever set of snowshoes sold. The manager s goal is to have a profit of at least $700 a da from the sales of these two items.. If x represents the number of pairs of cross-countr skis sold and represents the number of pairs of snowshoes sold, what inequalit models the combinations of ski and snowshoe sales that will meet or exceed the dail profit goal?

59 M0- Year End Review.docx. Which graph represents the combinations of ski and snowshoe sales that will meet or exceed this dail sales goal? x 7 0 x x 7 0 x

60 M0- Year End Review.docx banquet room can seat up to 00 guests. Each rectangular table seats guests and each circular table seats guests.. If r represents the number of rectangular tables and c represents the number of circular tables, which graph represents the possible combinations of rectangular and circular tables? r r c c r r c c. If the banquet organizers want to have close to the same number of rectangular and circular tables, what combination of tables could the use and still seat the maximum number of people? rectangular and circular tables rectangular and circular tables 7 rectangular and 7 circular tables rectangular and circular tables 0

61 M0- Year End Review.docx 7. Which graph represents the solution to the inequalit? x x x x. Which number line represents the solution set to the inequalit? Which graph represents the solution to the inequalit?

62 M0- Year End Review.docx 0. The solution set to the inequalit is. The solution set to the inequalit is. rectangle is x centimetres wide and x centimetres long. If the area of the rectangle has to be between cm and 0 cm, what are the possible values of x? x 70 x 70 x 0 x people will attend a concert if tickets cost $0 each. ttendance will decrease b 0 people for each $ increase in the price. The concert promoters need to make a minimum of $ 00.. What quadratic inequalit represents this situation?. What is the range of ticket prices the concert promoters can charge and still make at least the minimum amount of mone desired?

63 M0- Year End Review.docx. Which graph represents the solution to the inequalit? x x x x

64 M0- Year End Review.docx. Which graph represents the solution to the inequalit? x x x x 7. Which graph represents the solution to the inequalit? x x

65 M0- Year End Review.docx x x. The solution to the inequalit is x x x x

66 M0- Year End Review.docx. Which quadratic inequalit is represented b the graph shown below? x 7

67 M0- Year End Review.docx 0. Which point does not satisf the inequalit? x 7 0 rock is thrown upward with an initial velocit of m/s. The motion of the rock can be modelled b the equation.. To the nearest hundredth of a second, for what period of time is the rock s altitude greater than m?. For how long is the rock s altitude greater than m? nswer to the nearest hundredth of a second.. s. s. s 0. s 7

68 M0- Year End Review.docx Math 0- Year End Review nswer Section MULTIPLE HOIE. NS:. NS:. NS:. NS:. NS:. NS: 7. NS:. NS:. NS: 0. NS:. NS:. NS:. NS:. NS:. NS:. NS: 7. NS:. NS:. NS: 0. NS:. NS:. NS:. NS:. NS:. NS:. NS: 7. NS:. NS:. NS: 0. NS:. NS:. NS:. NS:. NS:. NS:. NS: 7. NS:. NS:. NS: 0. NS:. NS:. NS:. NS:. NS:. NS:. NS: 7. NS:. NS:. NS: 0. NS:. NS:. NS:. NS:. NS:. NS:. NS: 7. NS:. NS:. NS: 0. NS:. NS:. NS:. NS:. NS:. NS:. NS: 7. NS:. NS:. NS: 70. NS: 7. NS: 7. NS: 7. NS: 7. NS: 7. NS: 7. NS: 77. NS: 7. NS: 7. NS: 0. NS:. NS:. NS:. NS:. NS:. NS:. NS: 7. NS:. NS:. NS: 0. NS:. NS:. NS:. NS:. NS:. NS:. NS: 7. NS:. NS:. NS: 00. NS: 0. NS: 0. NS: 0. NS: 0. NS: 0. NS: 0. NS: 07. NS: 0. NS: 0. NS: 0. NS:. NS:. NS:. NS:. NS:. NS:. NS: 7. NS:. NS:. NS: 0. NS:. NS:. NS:. NS:. NS:. NS:. NS: 7. NS:. NS:. NS: 0. NS:. NS:. NS:

69 M0- Year End Review.docx. NS:. NS:. NS:. NS: 7. NS:. NS:. NS: 0. NS:. NS:. NS:. NS:. NS:. NS:. NS: 7. NS:. NS:. NS: 0. NS:. NS:. NS:. NS:. NS:. NS:. NS: 7. NS:. NS:. NS: 0. NS:. NS:. NS:. NS:. NS:. NS:. NS: 7. NS:. NS:. NS: 70. NS: 7. NS: 7. NS: 7. NS: 7. NS: 7. NS: 7. NS: 77. NS: 7. NS: 7. NS: 0. NS:. NS:. NS:. NS:. NS:. NS:. NS: 7. NS:. NS:. NS: 0. NS:. NS:. NS:. NS:. NS:. NS:. NS: 7. NS:. NS:. NS: 00. NS: 0. NS: 0. NS: 0. NS: 0. NS: 0. NS: 0. NS: 07. NS: 0. NS: 0. NS: 0. NS:. NS:. NS:. NS:. NS:. NS:. NS: 7. NS:. NS:. NS: 0. NS:. NS:. NS:. NS:. NS:. NS:. NS: 7. NS:. NS:. NS: 0. NS:. NS:. NS: