Name; Class: Date; ID: A. Multiple Choice Identify the choke that best completes the statement or answers the question.

Transcription

1 Name; Class: Date; ID: A June Exam Review Trig Multiple Choice Identify the choke that best completes the statement or answers the question. _ 1. Determine tan Q and tan R. P 4 Q R a. tan Q = 0.3; tan R = 0.5 c. tan 0 = 2; tan R =0.6 b. tan Q = 2; tan R = 0.5 d. tan Q - 0.5; tan R = 2 2. Determine the angle of inclination of the Line to the nearest tenth of a degree. < 9.8 > a b c d This cabin's roof is built within 1 of the recommended angle for solar panels. Determine the approximate latitude of the cabin, to the nearest degree. solar panel a. 49 b. 29 c. 41 d The height of the Telus Plaza South in Edmonton is about 134 m. Stacy is lying on the ground near the building. The angle between the ground and her line of sight to the top of the building is 71. About how far is Stacy from the base of the building, to the nearest metre? a. 142 m b. 389 m c. 127 m d. 46 m 1

2 Name; ID: A 5. A helicopter is hovering 350 m above a road. A car stopped on the side of the road is 450 m from the helicopter. What is the angle of elevation of the helicopter measured from the car, to the nearest degree? a. 52 b. 39 c. 51 d Calculate the length of this rectangle to the nearest tenth of a metre. A B 7.3 D r C a. 8.1m. b. 3.2 m c. 6.6 m d, 3.6 m 7. A tree broke 10 ft. above the ground. The top of the tree now touches the level pound and the trunk is still partially attached to the stump. I'he angle of inclination of the tree is 39. To the nearest foot, determine the height of the tree before it broke. a. 26 ft. b. 23 ft. c. 22 ft. d. 16ft. 8. A balloon is flying at the end of a 200-m length of string, which is anchored to the ground. The angle of inclination of the string is 55. Calculate the height of the balloon to the nearest metre. a. 164 m b. 140 m c. 115 m d. 244 m 9. A water taxi leaves its dock, and travels 6 km due north to pick up medical supplies. It then travels 14 km due east to drop off the supplies at a hospital. To the nearest degree, what is the measure of the angle between the path i t took due east and the path it will take to return directly to its dock? a. 23 b. 65 c. 25 d The front of a tent has the shape of an isosceles triangle with equal sides 170 cm long. The measure of the angle at the peak of the tent is 109. Calculate the maximum headroom in the tent to the nearest centimetre. a. 138 cm b. 121 cm c. 99 cm d. 240 cm 2

3 111: A.. Determine the length of QR to the nearest metre. Q,/44' 10 m a. 79 m b. 159 m c. 118 m 12. Calculate the measure of ZGHJ to the nearest tenth of a degree. d. 110 m H 3 cm c C d Short Answer 13. fan B ~ 1.3; determine the measure of ZB to the nearest tenth of a degree. 14. The base of a ladder is 0.8 m from a wall of a house. The top of the ladder rests against the house 2.5 m above the ground. Determine the angle the ladder makes with the house, to the nearest degree. 15. A communications tower is 300 m high. Rebecca is driving toward the tower. The angle between the ground and Rebecca's line of sight to the top of the tower is 9. About how far is Rebecca from a point on the ground vertically below the top of the tower, to the nearest hundred metres? 16. A rectangle has length 14.0 cm. The angle between one shorter side of the rectangle and a diagonal is 68 Calculate the width of the rectangle, to the nearest tenth of a centimetre. 17. A ladder is 7 m long. It leans against a house. The base of the ladder is 1.8 m from the house. What is the angle of inclination of the ladder to the nearest tenth of a degree? 18. A road rises 1 m for every 9.3 m measured along the road. What is the angle of inclination of the road to the nearest tenth of a degree? 19. A 2.8-m cable is attached to a sign. The cable is anchored to the ground 1,9 m from the base of the sign. What is the angle of inclination of the cable to the nearest tenth of a degree? 20. A diagonal in a rectangle has length 15 in. The angle between a diagonal and the longer side of the rectangle is 22. Calculate the width of the rectangle to the nearest inch. 21. The angle of mclination of a road is 9. Determine the rise of the road, to the nearest metre, for every 100 m travelled along the road. 3

4 ID: A 22. Solve this right triangle. Give the measures to the nearest tenth. L M 23. Determine the length of WX to the nearest tenth of a centimetre, w Y 24, Francis wants to know the distance between the points where two guy wires are attached to a pole. The guy wires are anchored to the ground at the same point. 9.0 m from the base of the pole. The angle of inclination of the longer wire is 58 and the angle of inclination of the shorter wire is 41, To the nearest tenth of a metre, how far apart are die points where the guy wires are attached to the pole? 25. From the roof of Yee's building, the angle of elevation of the top of a taller building is 35. The angle of depression of the base of the building is 22. The buildings are 21 m apart. Determine the height of the taller building to the nearest metre. Problem A rectangle measures 7.1 cm by 5.6 cm. Determine the measure, to the nearest degree, of the acute angles formed by the intersection of the diagonals. * Calculate the area, to the nearest tenth of a square centimetre, of the circle inscribed in the equilateral triangle below. v 10.6cm C 4

5 ID: A 28. A boat was docked 25.0 m from the base of a cliff. A sailor used a clinometer to sight the top of the cliff. The angle between the horizontal and the line of siglit was 80. The sailor held the clinometer 1.3 m above the surface of the water. Determine the height of the cliff to the nearest tenth, of a metre. 29. Solve AI,MN. Give the measures to the nearest tenth. Explain your strategy. M r-, - ~ ^ I 4.7 cm 6.1 cm 30. This regular octagon has side length 17.0 cm. Determine the distance from one vertex to the opposite vertex, measured through the centre of the octagon. Give your answer to the nearest tenth of a centimetre Determine the length of the diagonals in this kite to the nearest tenth of a centimetre. B cm 63,9* 26. r 5

6 Class: Date: ID: A June Review Ch3 Factors and Products Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Determine the greatest common factor of 84, 210, and 336, a. 14 b c. 21 d Determine the least common multiple of 18, 30, and 66. a. 990 b. 495 c d One neighbour cuts his lawn every 4 days. Another 'neighbour cuts her lawn every 6 days. Suppose both neighbours cut their lawns today, flow many days will pass before both neighbours cut their lawns on the same day again? a. 24 days b. 18 days c. 2 days d. 12 days 4. What is the side length of the largest square that could be used to tile a rectangle that measures 9-ft. by 30 ft.? Assume the squares cannot be cut. a. 9 ft. b. 3 ft. c. 90 ft. d. 6 ft. 5. A cube has volume cm 3. What is the surface area of the cube? a cm 2 b cm 2 c. 22 cm 2 d cm 2 6. Determine the perfect cube whole number closest to a b c d Which of the following numbers is not both a perfect square and a perfect cube? a b c d Factor the binomial 12r; - 21a". a. a{\2 + 21a) c. 3«(4 + 9«) b. 3(4a + 9a 2 ) d. 6a(2 + 9a) 9. Factor the trinomial 56t 5 / - 32x 4 / - 72x 3 y''.. a. 8x\'(-7.r> --4 9y : ) c. -4x 3 y 5 (14x 2 y + 8x +18/) b. &cv(7x 2 v -4x + 9y 2 ) d. -&c 3 (7x 2 y 6 + 4xy 5 + 9y 7 ) 10. Factor the binomial -6m 2-24m 4. a. -6rn\l+4m 2 ) c. 6(m 2 +Am 4 ) b. -6m 2 (4m 2 ) d. -3m? (2 i- 8m 2 ) 11. Simplify the expression y 2 + \2y / - 36y - 38, then factor. a. -12<v 2-2v-4) c. -6(2/ + 4y + 8) b. -12(y 2 +2y + 4). d. -6(2/ +4y+1) 1

7 IB: A 12. Which of the following trinomials can be represented by a rectangle? a. y 1 t- 4y + 12 c. v" + 13y + 42 b. y'~r9y + 6 d. y y Complete.^ - )( -5) - * +105 a. (k-2l)(k~-~l6) = k 2 ~5k + m5 b. (k-2\)(k-5)~k 2 261: Factor: 72w 2-2\6w- 126 a. 6(6w i 3)(2w 7) b. 6(6w + 7)(2w-3) c, (k - 2l)(k -26) = k 2-5k +105 d. - 21)<^ ^ 5) = i: 2-16^ c, 6(6w - 7)(2w + 3) d. 6(6w 3)(2w \ 7) 15. Expand and simplify; (f + 7g)(2f 4g + 7) a. 2/+10/g + 7f+28g 2 +4% b. 2/ /g + 7/28g-f 49,e c. 2f fg + 7/-28g 2 +49g d. 2f - mfg + If 2Sg g 16. Which polynomial, written in simplijfied form, represents the area of this rectangle? 8x - Ay x + 3y a. 8x 2-20x>>-12>> 2 c. l(k 2 +40xy-24y 2 b. 8x 2 f \4xy - 12y 2 d. 8r t 20xy - I2y 2 2, c.. /r\te Expand and simplify: (IT ' - 5.r - 6)(5.x - 2x + 3) a. 1 Ox x 3-34r + 27x - 18 c. lox 4 + 2Lr - 24/ + 27x + 18 b. 1 Ox 4-21x 3-34x 2-3x + 18 d. 10x 4-29x 3-34x x Find an integer to replace f! so that this trinomial is a perfect square. 81v 2 -Dvw+10(hv 2 a. 180 c. 90 b. 900 d Factor: 49c 2 56c I 16 a. (7c ~4) 2 c. (14c -8) 2 b. (7c-4)(7c+4) d. (14c-8)(14c + 8) 2

8 ED: A 20. I^termine the area of the shaded region in factored form. a. 4(x +10) b. (3x + 8)(*+l0) 2X+9 c. (3*+10)(x + 8) d. (3*-8)(*-10) Short Answer 21. Bill and Betty do chores at home. Bill mows the lawn every 9 days, and Betty bathes the dog every 6 days. Suppose Bill and Betty do their chores today. How many days will pass before they both do their chores on the same day again? 22. Determine the square root of Write an expression for the width of this rectangle. 6a Area = 6a 2 + A2ab 24. Simplify 25a 3 b 2 - %a 2 b b' - 13a 3 b a 2 b 3 ~27b\ then factor. 25. Identify the greatest common factor of the terms in this set. %x 2 y,24y 2 A%xy 26. Expand and simplify: (11 + q)(5-q) 27. Factor: s 2-34s Find and correct the errors in this factorization. w 2-5w-5Q= (w-5)(w + X0) 3

9 ID; A 29. Find an integer to replace so that this trinomial can be factored. y 2 t y \ 30. Factor: I0z 2-35z! Copy and complete this statement. (24o - 6)(a - 135) = Expand and simplify: (9z 2-4z + 4)(Sz + 6) 33. Find and correct the errors in this solution. = 9a 2-65ah + 40a - 4ab ~~ 13d 2 + U = 9a - 69ab - 13b 2-40a + 2b 34. Factor: 9.v 2-4r 35. Factor fully: 35pV- 170pqr-25q 2 r 36. Find an integer to replace so that the trinomial is a perfect square. 25x 2 ~60xy+Dy 2 Problem 37. Chris completes one lap of a go-cart track every 50 s. D'Arcy completes one lap of the same track every 60 s. Suppose Chris and D'Arcy cross the starting line at the same time. How many seconds will pass before they cross the starting line at the same time again? How many laps will Chris have completed in that time? How many laps will D'Arcy have completed in that time? 38. a) Here are a student's solutions for factoring polynomials. Identify the errors in each solution. Write a correct solution. i) Factor: -22h - 32h 2 + Wt 3 Solution: -22h - 32h A 3 = -2h(l 1 +16// + $h 2 ) b) What should the student have done to check her work? 4

10 ID: A 3 9. Find the area of the rectangle l? A picture and its frame have dimensions as shown. a) Find an expression for the area of the frame, in factored form. b) Determine the area of the frame when 5=12 cm. 5

11 Class: Date: ID: A June Exam Review Ch4 Roofs and Powers Multiple Choke Identify the choice that best completes the statement or answers the question. 1. Identify the index of a. 2 7 b Identify the radicand of \l 4. a. 4 b. 4* 3. Evaluate a. 4 b. impossible 4. Which of these roots lies between 3 and 4? K/28? il-\72, *fl7, Kl-U% a. Zf-m h. J~VJ c. 7 c. 6 c c. d. 2 d. 8 d. 4 d. V Evaluate V a. 0.1 b. 1.3 c Estimate the value of *f4q to one decimal place. a b. 3.4 c Which of these numbers is irrational? d. 2.1 d. 5.7 v 16 a. -68 c, Write \/80 in simplest form. a. loifl b. 2k[lQ 9. Write 16^/3 as an entire radical. a. kfl6& b. ^12288 c. 8^/l0 c. V2304 d. 4lfs d. V Write \9 as a power. '2' v 4, C.,3 _1 d. '3V9 11. A cube has volume 1200 cubic inches. Write the edge length of the cube as a power. V1200 i m. b in. c in. d. 1200" 3 in 12. Evaluate (-216)~^ without using a calculator. 36 J_ 36 d - i 1

12 ID: A 13, Evaluate 81 without using a calculator a. b c Which power with a negative exponent is equivalent to -p^' a. b Given that 6 :0 = , what is 6~ 10? a How many times as great as 7 2 is 7 6? a. 7 1 b. r % c. 3-5 C d. (-5) d. 7* Simplify 36xV 4x*y 1.-> 2 2 a. 3.v y b. c Evaluate " 5 ( r 4 f 8 1 T V ) ( 1 10 \ 2, 3 <3 0 \ ) b A d Evaluate a If for a = 4 and A = -27. a ' 9 b. 72 c. -72 Short Answer 20. Evaluate ^ Evaluate Which of these numbers are rational numbers, but not integers? 3.12,-4, ^5, ^, 2.4, $JH, 0, 5~, if\6 23. Determine the side length of a square with area 72 cnf Write your answer to the nearest tenth of a centimetre. 2

13 II): A 24. Determine the edge length of a cube with volume 55 cm 3. Write your answer to the nearest tenth of a centimetre. 25. Write 8v 19 as an entire radical. 26. A cube has a volume of 1280 cubic feet. Determine the edge length of the cube as a radical in simplest form. 27. Evaluate * Write K 4 J as a radical. 29. Evaluate (-64) Arrange these numbers in order from least to greatest. 31. Evaluate without using a calculator. 32. Evaluate 81 without using a calculator. 3a 3 b~ 7 c~~ 33. Simplify (t _ 3 \ 3. Write using powers with positive exponents. 34. Simplify -> m n p Evaluate (0.4) 2. (0.4) 3 (0.4) «Problem 36. A square has an area of 1134 m 2. Determine the perimeter of the square. Write the answer as a radical in simplest form. 37. In isosceles AABC what is the lengtli of BC? Write your answer as a mixed radical. A ' 3

14 ID: A 38. Harish simplified Kl 1024 as shown; = 2-5-kfl = io-kfl Identify the error Harish made, then write a correct solution ? 39. Another formula for the approxunate surface area, SA square metres, of a person's body is SA ~ 0.025/i m, where h is the person's height in centimetres, and m is the person's mass in kilograms. a) Calculate the surface area of a newborn with height 48 cm and mass 7,3 kg. Write the answer as a decimal to the nearest hundredth of a square centimetre. 40. Here is Tanisha's solution for evaluating a power: = ( )' Identify the errors Tanisha made. Write a correct solution. 41. For a spherical space station, this formula is used to estimate the number of rotations per minute, N, required so that the force inside the station simulates the gravity' on Earth: _ r 42's/s ~'~2.,.. A = r, where r is the radius of the space station, m metres Suppose the radius of the space station is 12.7 m. Calculate the number of rotations per minute required to simulate the gravity on Earth. Write the answer to the nearest hundredth. 42. A cone with equal height and radius has volume 492 cm 3. What is the height of the cone to the nearest tenth of a centimetre? 4

15 Class: Date: ID: A Ch5 June Exam Review Ch5 Relations and Functions Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Identity the domain of this relation. {(8,'l0),(5,7),(9,-ll).(6.-8)} a. {8,7,9,10} c. {5,6,8,9} b. {-11,-8,7/10} d. {5,6,9,10} 2. For the function f(x) = 3..v - 8, determine x when f(x) = -10. a. 38 b. -22 c For the function g(x) - 2x - 9, determine g(3.4). a b. 2.2 c Write g(x) - -7x as an equation in two variables. d a. x--lx-2j5 b. g = -lx Which of these graphs represents a function? 0 ii) ' c. g~-lg-2j5 d. x = -lg~2.15 I 1 \y I i > i? T - 1 X... A \ iii) iv) a. ii b. i c. Ill d. iv 1

16 ID: A 6. Determine the domain and range of the graph of this function. a. 2 < x < 4; y < 3 b. x < 4; y < 3 7. Determine the range of the graph. c. x < 3; y < 4 d. x<4: -) r y<3 a. -3<y<5 c. 3 <.r < 3 b. 4<>? <5 d. -1 <y <3 8. For a service call, an electrician charges a $70 flat fee, plus $50 for every 30 min worked. Determine the rate of change of this linear relation. a. S50/h b. $120/h c, $70/h d. SlOO/h

17 ED: A 9, Each graph below shows distance, d metres, as a fimction of time, t hours. Which graph has a rate of change of 0.25 m/h and a horizontal intercept of 3 m? 3

18 ID: A 10. This graph shows the fuel consumption of a jeep with a full tank of gas at the beginning of a journey. When the jeep has travelled 350 km, about how much fuel is left in the tank? Distance (100s of km) a. about 32 L c. about 49 L b. about 36 I, d. about 28 I. Short Answer 11. Consider the relation represented by this arrow diagram. Represent the relation as a set of ordered pairs, contains this number of passengers

19 ID: A 12. This graph shows the speed of a hot air balloon, ±\ as a fimction of time, t, s Speed of a Hot Air Balloon f Time (s) Identify the independent and dependent variables. 13. Which equations represent linear relations? Create tables of values if necessary. a) 4x-v = 11 b) x 2 \y 2-12 c) x = 5~2y d) y = x x + Ix -: 3 e) y = x +11 f) j,_4 = This table represents the approximate relation between a distance in miles and the same distance in kilometres. Determine the rate of change of the relation.. Miles (mi.) Kilometres (km) Determine the rate of change and the vertical intercept of this graph. 'y 5

20 ID; A Problem 16. A gas station attracts customers by offering coupons worth $0.02 for every $1.00 spent on gasoline. Value of Gas Value of Purchase, v Coupons, ($) c ($) , 0.80 a) Use fimction notation to express c as a function of v. b) Copy and complete the table. c) What is the value of the coupons a customer will receive if she spends $60 on gasoline? d) How much does a customer have to spend on gasoline to receive $5.00 in coupons? 17. a) This is the graph of the function g{x) = 1 2v. Determine the range value when the domain value is A skydiver jumps from an altitude of 3600 m. For the first 12 s, her height in metres above the ground is described by this set of ordered pairs: j(0, 3600), (4,3514 j, (8, 3346),(12, 3151)}. Between 18 s and 36 s, her height above the ground is described by this set of ordered pairs: {(18,2821),(24,2491),(30,2161),(36,1831)}. Determine whetlier either set of ordered pairs represents a linear relation. Explain. 6

21 Class: Date: ID: A June Exam Review Ch6 Linear Functions Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A straight section of an Olympic downhill ski course is 34 m long. It drops 16 m in height. Determine the slope of this part of the course. 15 _8_ a b. d Which of these line segments are parallel? a. CD and EF b. EF and GH c. AB and CD d. AB and EF 3. Determine the slope of the line that is perpendicular to this line segment.! 4 t-- p -pe- \ -I c / /-,,.-> _i_! t - 4 x 5 a C " 5, 3 d. -- 1

22 Name;.11): A 4. A line passes through D( 5, 1) and N(12, 8). Determine the coordinates of two points on a line parallel to DN. a. (2, -10) and (24, -16) - c. (-10,2) and (24,-16) b. (-10, 24) and (2, -16) d. (-10, 2) and (-16, 24) 5, The slope of this line is What is the equation of the line? 1> a. y = -x +1 b. y = x - 1. c. y- d. ' y x+l 1 6. For a service call, a plumber charges a $95 initial fee, plus $30 for each hour he works. Write an equation to represent the total cost, C dollars, for / hours of work. a. / = c. C = 30r + 95 b. C = 95l + 30 d. C - 3 Or - 95 i 2

23 ID: A 1. Which graph has slope 3 and /-intercept. 0? a. c. _ 8, Jon has x egg cartons that hold 12 eggs and y egg cartons that hold 18 eggs. He uses these cartons to store 72 eggs. Which equation represents the relation? a. 12* + 18j>-72 = 0 c. 12*-~ 18y b. 12x-18y + 72~0 d. 12* + 18y + 72 = 0 * Short Answer 9. A treadmill is set with a rise of 9 in. and a run of 90 in. What is the slope of the treadmill? 10. A 10-if. ladder leans against a wall. The base of the ladder is on level ground 4 ft. from the wail. What is the slope of the ladder? 11. Describe the graph of the linear function whose equation is y = llr, 3

24 IB: A 12. For each equation, identify 'the slope and y-intercept of its graph. i) y = 4x ii) y = -T x m) y = -4x + ~ Write this equation in general form: v - ~ x Write "this equation in general form: y - 3 = (x + 4) i 5. Determine the slope of the line of this equation: 3x 4-5y Desmond works as a babysitter for two families. Family A pays $6.5 per hour. Family B pays $8 per hour. Last weekend, Desmond earned $75. Write an equation in general form for the relation. 17. Determine the slope of the line with this equation: 32x 8y Write this equation in general form: y (x - 5) 19. Write an equation for the graph of a linear fimction that has slope -5 and y-intercept 6, 20. Determine the.^-intercept and the y-intercept for the graph of this equation: llx - 3y + 24 = Write an equation for the graph of a linear function that has slope ~~ and y-intercept A line has x-jntercept 6 and y-intercept-i. Determine the slope of a line perpendicular to this line. 23. Determine the slope of a line that is parallel to the line through L(-10, 5) and K(6, -13). 24. Predict what will be common about the graphs of these equations. i) y = 3x-6 iii) y ^ - 4x - 6 ii) y - -3x - 6 iv) y - 4x Predict what will be common about the graphs of these equations. i) y = xt + 6 iii) y = 3x - 6 ii) y = 3x - 3 iv) y = 3x + 3 4

25 Name; ED: A Problem 26. Four students determined the slope of'the line through S( 9, -8) and T( 11, 12). The'ir answers were: 1, ~1, L and -1, Which answer is correct? How do you know? 27. Constraction workers are paving a road. The road must drop 2 cm for every 550 cm measured horizontally. a) What is the slope of the road? b) Suppose a section of the road drops 15.5 cm. How long is this section of the road measured horizontally? 28. A line passes through R(6, 9) and K(-6, 15). a) What is the slope of line RK? b) Line VB is parallel to RX. What is the slope of VB? Explain your answer. c) Line WX is perpendicular to RK. What is the slope of WX? Explain your answer. 29. Line segment OT has endpoints 0(4, -6) and T(-10, 6). Line segment VL has endpoints V(6, 8) and Lf-6, -6). a) Are these two line segments parallel, perpendicular, or neither? Justify your answer. b) Sketch the line segments to verify your answer to part a. 30. Write an equation to describe this function. Verify the equation An equation of a line is y = mx + 5. Determine the value of m when the line passes through the point J(--6, 3). 32. Francine runs a T-shirt company. For each order she receives, Francine charges a flat fee of $40, plus $10.95 per T-shirt. a) Write an equation for the total cost, C dollars, for ordering n T-shirts. b) Marnell ordered 67 T-shirts. What was the total cost? c) Jakub paid a total cost of $ How many T-shirts did he order? 5