Standard Level Review
NO CALCULATORS ON THIS SECTION
1) Consider f(x) = -4(x-3)2 + 2.
a) State the coordinate of the vertex.
b) Find the axes intercepts.
c) The graph of function g(x) is obtained by translating the graph of f(x) vertically through b units. For what value of b will the graph of g(x):
i) have exactly one x-intercept
ii) have no x-intercepts
iii) havetwo x-intercepts.
2) a) Consider the geometric sequence: 4, -12, 36, -108, …
i) Write down the common ratio.
ii) Find the 10th term.
b) Consider the geometric sequence x, x – 2, 2x – 7, …
i) Find x
ii) Does the sum of the corresponding geometric series converge? Explain your answer.
c) Suppose the sequence x, x-2, 2x – 7, … is arithmetic. Find:
i) itscommon difference, d
ii) x.
3) Solve for x:
a) log3X = 4b) e5-2x = 8c) ln(x2 – 3) – ln(2x) = 0d) = x
4) A and B are mutually exclusive events where P(A) = x and P(⌐B) = 0.43.
a) Write P(A UB) in terms of x.b) Find x given that P(A U B) = 0.73c) Find P(A ∩ B)
5) Bag C contains 4 blue and 1 yellow tickets. Bag D contains 2 blue and 3 yellow tickets. An ordinary 6 sided die is used to select one of the two bags. If a 1 or 2 is rolled, bag C is chosen. Otherwise, bag D is chosen. A ticket is drawn at random from that bag. B
a) Copy and complete the tree diagram, showing all probabilities. C
b) Find the probability that a yellow ticket is drawn from bag D. Y
c) Find the probability of drawing a yellow ticket from either bag. B
d) If a blue ticket is chosen, find the probability that that it came from bag D. D
e) In a gambling game, a player wins $6 for getting a blue ticket and $9 for getting a yellow Y
ticket. Find the players expected return.
6) A square has sides of length 16 cm. The midpoints of the opposite sides are connected to form four smaller squares inside the original square, as shown, with the lower left square being colored black. The upper right square has the midpoints of its sides found and the opposites sides are connected in the same way. The four squares that are formed have the lower left square colored black, as before. The process is repeated again with the upper right square.
Let xn represent the length of the side of the new square.
Let An represent the area of each new square that is colored black.xn
16
a) The following table gives the value of xn and An, for 1 n 3. Copy and complete the chart:
n / 1 / 2 / 3xn / 8 cm / 2 cm
An / 64 cm2 / 16 cm2
b) The process described above is repeated. Find A8.
c) Determine the total area of all the first 8 colored squares that can be drawn.
CALCULATORS ARE ALLOWED NOW
7) The line L1 passes through the points A(2,1,-3) and B(3,3,0).
a) Show .
b) Hence, write down
i) a direction vector for L1.
ii) a vector equation for L1.
Another line L2 has equation . Determine whether the lines L1 and L2 intersect at some point P.
c) Find the coordinates of P, if it exists.
d) i) Write down the direction vector for L2.
ii) Hence, find the angle between L1 and L2.
8) Find the constant term of the expansion of .
9) Dora notices that the number of cups of coffee she drinks in a day varies depending on how much sleep she gets the previous night. She records the following data:
Time sleeping (hours) / 6 / 8 / 6.5 / 5 / 9 / 5.5 / 7.5 / 6 / 8 / 8.5 / 7Number of cups of coffee / 3 / 1 / 2 / 4 / 0 / 4 / 2 / 4 / 0 / 1 / 2
a) Draw a scatter diagram of this data.
b) Calculate Pearson’s correlation coefficient.
c) Determine and write the line of best fit.
d) Calculate .
e) Graph the mean point.
f) Find a second point using the line of best fit to graph the line of best fit.
g) Describe the correlation of the points as
i) none, weak, moderate, or strong;
ii) positive or negative.
E C
10) Consider the figure shown.
= 30oD
a) Find the length of and .
b) Calculate the measure of and . AB
c) Find the area of BCD.
11) The following diagram shows two perpendicular vectorsand .
a) Let . Represent on the graph.
b) Given that and , where n Z, find n.
Answers(?):
1) a) v(3, 2)2) a) i) r = -33) a) x = 81
b) y-int (0, -34) ii) 78732 b) x =
x-int ( , 0) b) i) x = 4, -1 c) x = 3
c) i) b = -2 ii) If x = 4 sum converges since r = ½ d) x = -1/2
ii) b < -2 c) i) d = -2
iii) b > -2 ii) x = 3
4/5
n / 1 / 2 / 3xn / 8 / 4 / 2
An / 64 / 16 / 4
4) a) x + .575) a) 1/36) a)
b) x = .16 1/5
c) 0
2/3 2/5 b) A8 = 1/(44)or 1/256
c) S8 = 454225/5323
3/5
b) 2/5
c) 7/15
d) 2/3
e) $7.40
7) a) 8) 849) a)
b) i) b) -.937
ii) , where t = time c) (7, 2.09)
= , where s = time d) y -1.09x + 9.71
c) P( 13/4, 7/2, 3/4) e)
d) i) f) (9, -0.0856) points varied
ii) g) i) strong (between 80 and 100%)
ii) negative
10) a) DB 4.09 m, CB 9.86 m11) a) b) n = 14/3
b) 68.2o and 57.5o -
c) 17.0 cm2
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