MCR3U - Practice Mastery Test #9 & #10

Transcription

1 Name: Class: Date: MCRU - Practice Mastery Test #9 & #0 Multiple Choice Identify the choice that best completes the statement or answers the question.. Factor completely: 4x 0x + 5 a. (x + 5)(x 5) b. (4x 5)(x 5) c. (4x 5)(x ) d. (x 5). A relation is defined by y = 4x(x 6) + 4. Its axis of symmetry has equation... a. x = -6 b. x=- c. x = d. x = 6. Which line is the line of best fit for the data shown below? a. line b. line c. line d. line 4 4. The graphs of functions are... # # a. neither b. # only c. # only d. both 5. What is the next number in the sequence,8,8,,... a. 48 b. 4 c. 46 d If y = x - x - 4 then its zero(s) are at a. 4 and b. 4 and c. 4 and d. 4 and 7. The equation of the image of y = x after a reflection in the x-axis is a. y = x + b. y = x + c. y = x d. y = ( x) +

2 Name: a. 7 b. 5 c. 6 d. 9. Simplify (x )(x + ) (x + )(x ) (x )(x + ) x(x + ) a. - x b. - c. 6x + x x d. x x 0. Simplify x 4x x a. x + 4 b. x c. -x d. -4. If t n = 5 (n )then t 7 =? a. b. 5 c. 4 d.. What is the next number in the sequence,,48, 9,...? a. 768 b. 4 c. 44 d. 5. What is the next number in the sequence,,48,9,...? a. 768 b. 6 c. 40 d What is the next number in the sequence,,0.5,0.5,...? a. 0.5 b. 0 c d The sequence 8, -4,, -,... is a. arithmetic b. geometric c. neither a or b 6. The sequence 8, 4, 0, -4,... is a. arithmetic b. geometric c. neither a or b 7. Evaluate 7 a. 9 b. 9 c. 6 d Simplify Ê x y ˆ Ê x y 4 ˆ. Assume x,y 0 a. y b. x 6 y c. x 9 y d. x 6 y 7 9. Simplify Ê a ˆ. Assume a 0 a. a 7 6 b. a c. a d. a 5

3 Name: 0. Ê P 4, ˆ 5 5 is a point on the unit circle and is on the terminal arm of angle θ. Which of the following is true? a. cos θ = 5 and tan θ = 4 c. cos θ = 4 5 and tan θ = 4 b. sin θ = 4 and tan θ = d. sin θ = and tan θ = Ê. P, 4 ˆ 5 5 is a point on the unit circle and is on the terminal arm of angle θ. Which of the following is true? a. sin θ = and tan θ = 4 c. sin θ = 4 and tan θ = b. cos θ = 4 5 and tan θ = 4 d. cos θ = 5 and tan θ = 4. The input/output diagram illustrates a number of transformations to y=sin(x).. The correct sequence of vertical transformations applied to y=sin(x) is... a. a vertical translation of units down, followed by a vert. stretch of factor 5 b. a vertical stretch of factor followed by a vert. translation of units down 5 c. a vertical translation of units up, followed by a vert. stretch of factor 5 d. a vertical stretch of factor 5 followed by a vert. translation of units up, In the diagram, A is closest to a. 67 b. 70 c. 5 d If θ is an angle in a triangle, and cos θ = - 0.6, then θ is approximately a. 4.6 b. 8.4 c. 5.6 d Which trigonometric ratio of angle S is easiest to determine x in the following diagram? a. sin S b. cos S c. tan S

4 Name: 6. Which equation would be used to determine x in the following diagram? a. a = b + c bc cosa c. c = a + b ab cos C b. b = a + c ac cosb d. a sina = b sinb = c sinc 7. If sinθ = where 0 θ 60, then a. θ = -60 or θ = -0 c. θ = 0 or θ = 40 b. θ = 40 or θ = 00 d. θ = 50 or θ = 0 8. How many terms are there in the following series? a. 7 b. 0 c. 4 d Which expression represents the sum of the first 0 terms of the series ? a. 0 È 0 È () + (0 )4 ÎÍ c. () + (0)4 ÎÍ b. 0 È 0 È (4) + (0 ) ÎÍ d. (4) + (0) ÎÍ 0. Which expression represents the sum of the first terms of the series ? a. 0 È È () + (0 )4 ÎÍ c. () + (0)4 ÎÍ b. 0 È È (4) + (0 ) ÎÍ d. (4) + (0) ÎÍ 4

5 MCRU - Practice Mastery Test #9 & #0 Answer Section MULTIPLE CHOICE. ANS: D Arrange the tiles into a rectangle: So 4x 0x + 5 = (x 5) PTS:. ANS: C Two points are at (0,4) and (6,4), so the axis of symmetry is a vertical line halfway between these two points, so x = PTS:. ANS: D If you imagine each of the points being little magnets and the line of best fit being a needle, hopefully you can imagine it moving into the spot that line 4 occupies. It is 'closer' to more points than any other line and shows the general trend of the data. PTS: 4. ANS: A Neither graph passes the vertical line test (one value of x has more than one value of y). PTS:

6 5. ANS: D + 6 = = = It appears that the differences between the terms is increasing by 4, so the next term should be 8 more than or 50. PTS: 6. ANS: A The easiest way to do this problem is probably to just sub in x=4,or x= 4 and then x= or x= to find out which ones work. OR On the TI-8, type in the equation into the y= screen, and the look at the graph or table to see what its zeros are. x or factor the expression... x x x 4 4x 4 so... y = (x - 4) (x + ), and its zeros are at 4 and. or... complete the square or use the quadratic formula. PTS: 7. ANS: A The original equation defines a parabola with vertex at (0,-) that opens up. When it is reflected in the x-axis, it will have vertex at (0,), and will open down, so its equation will be y = x +. We could also do this problem with an input/output diagram, but this is a parabola, so it should be easy for you to picture. PTS: 8. ANS: B 4 + = + 8 = 5 To add fractions, get a common denominator () by multiplying the numerator and denominator of the first fraction by and then the numerator and denominator of the second fraction by 4. Now that we have a common denominator, add the numerators and keep the same base. PTS:

7 9. ANS: D (x )(x + ) (x )(x + ) (x + )(x ) x(x + ) = ()() (x )() if x? 4, ()() x() = x x Divide out identical factors PTS: 0. ANS: C Factor the numerator. Note that factoring out -x, makes the other factor the same as the denominator. x 4x x x( x + ) = Divide out identical factors x = -x if x? PTS:. ANS: A t n = 5 (n ) t 7 = 5 (7 ) = 5 (6) = 5 + ( 6) = Just plug in 7 for n in the formula and follow order of operations. (Subtract first, then multiply by and then add 5) Or just enter the formula on the calculator as u(n) = 5 (n ) in the Y= menu (after switching the mode from func(tion) to seq(uence) ), and then go to the home screen and enter... u(7) and press return. PTS:. ANS: A Each term is 4 times the previous term (check by dividing consecutive terms), so if we take 9 and multiply it by 4, we get 768. PTS:. ANS: A Each term is 4 times the previous term (check by dividing consecutive terms), so if we take 9 and multiply it by 4, we get 768. PTS:

8 4. ANS: A Each term is 0.5 times the previous term (check by dividing consecutive terms), so if we take 0.5 and multiply it by 0.5, we get 0.5. PTS: 5. ANS: B Each term is the previous term multiplied by -0.5, so the sequence is geometric. (It has a common ratio) PTS: 6. ANS: A The differences between successive terms is always -4, so the sequence is arithmetic (common difference). PTS: 7. ANS: A 7 Ê = 7 = ( ) ˆ We are using the fact that Ê x a b ˆ = x ab to split up the power. An exponent of means that you take the rd root of the base. I.e., = 7 so 7 =. = = 9 PTS: 8. ANS: Ê A x y ˆ Ê x y 4 ˆ = x + ( ) y + 4 = x 0 y = y To multiply powers with the same base, add the exponents Note that x 0 is equal to (as long as x is not 0) PTS: 4

9 9. ANS: C Ê a = a ˆ Ê ˆÊ ˆ To take the power of a power, multiply the exponents. Reduce. = a PTS: 0. ANS: C The x coordinate of the point is cos θ, so cos θ = 4 5. The y coordinate of the point is sin θ, so sin θ = 5 and tan θ = sinθ cos θ = = 4 PTS:. ANS: D The x coordinate of the point is cos θ, so cos θ = 5. The y coordinate of the point is sin θ, so sin θ = 4 5 and tan θ = sinθ cos θ = = 4 PTS: 5

10 . ANS: A The input/output diagram for the function is shown below. Horizontally, we have to work backwards from the base function, so the first operation that we have to undo is add, so the first horizontal transformation is a translation of units left. The second operation we have to undo, working away from the base function, is multiply by 4, so the second horizontal transformation is a horizontal stretch of factor 4 Vertically, we work forward from the base function, and the first operation is subtract, so the first vertical transformation is translation of units down. The second operation is divide by 5, so the nd vertical transformation is a stretch of factor 5 PTS:. ANS: A Sin A = opp (any trig ratio could be used) hyp = Ê sin ˆ 67û Since A is acute, it is approximately 67 PTS: 4. ANS: B Make sure the calculator is set to degrees (see MODE), and get cos - (-0.6). PTS: 5. ANS: A x is the opposite side and 7 is the hypotenuse, so we have to use sin S = opp hyp PTS: 6. ANS: D We know all angles and one side, so use the sine law as follows: x 0 = sin60 û sin70 û PTS: to find x 6

11 7. ANS: B The unit circle shows us the coordinates of all points with principal angles 0, 45 and 60. It shows that sinθ = at points L and N. These points are 60 away from the x axis, so the angles are 40 and 00 PTS: 8. ANS: A This is a geometric series with a =, r =, and t n = 458 Using the formula we get... t n = ar n PTS: 458 = () n 458 = ()n 79 = n 6 = n 6 = n 7 = n OR... the last number is 79 times as big as the first number. 79 = 6, so the first number has been multiplied by six times to get to 458. Therefore, there are 7 numbers in all (one more than the number of times its been multiplied by ) 7

12 9. ANS: B This is an arithmetic series with a = 4, d = and n = 0. Using the formula we get... S n = n È a + (n )d ÎÍ = 0 È ÎÍ (4) + (0 ) PTS: 0. ANS: D This is an arithmetic series with a =, d = and n =. Using the formula we get... S n = n È a + (n )d ÎÍ = = PTS: È ÎÍ () + ( ) È ÎÍ 4 + (0) 8