MATH 12A TERM 2 CUMULATIVE REVIEW
DIRECTIONS: PLEASE DO NOT WRITE ON THIS SECTION. PLACE YOUR ANSWERS IN THE SPACE PROVIDED.
1. Solve for x: (log3x)2 – log3x2 – 15 = 0
a) 3
b) 5
c) 125
d) 243
2. Solve for x: 5x + 2 = 27?
a) -1.51
b) -.041
c) 0.05
d) 2.05
3. What is the inverse of the function y = 4x ?
a) y = log4 x
b) y = logx 4
c) x = log4 y
d) x = logy 4
4. Which represents 3 log A + 3 log B – log C written as a single logarithm?
a)
b)
5. What is the value of x in the equation (log3 x) + 1 = -2 ?
a) - c) 8
b) d) 27
6. Which pair of graphs illustrates a function and its inverse?
7. What is the converse of:
“If a triangle is inscribed in a semi-circle, then the triangle is a right triangle.” ?
a) If a triangle is inscribed in a semi-circle, then the triangle is not a right triangle.
b) If a triangle is not inscribed in a semi-circle, then the triangle is not a right triangle.
c) If a triangle is a right triangle, then it is inscribed in a semi-circle.
d) If a triangle is a right triangle, then it cannot be inscribed in a semi-circle.
8. If the graph of is stretched vertically by a factor of 2 and horizontally by a factor of 5, what is the new equation?
a)
b)
9. A circle has a center and one end point of a diameter at
(5, -2). What are the coordinates of the other end point?
a) (-13, 2)
b)
10. What is the transformational form of x2 + y2 + 4x – 9 =0 ?
a)
b)
11. Which is the equation of an ellipse with center (-5, 6), major axis of 4 units and a minor axis of 2 units?
a)
b)
12. If CD = 10 and C is at (8,-3) and D is at (2,y), what are all the possible values for y?
a) -11 and 11 c) –8 and 8
b) –11 and 5 d) –5 and 5
13. Which mapping rule describes the transformation of x2 + y2 = 1 needed to produce
(x + 2)2 + (y + 1)2 =
a) (x, y) ®
b) (x, y) ®
14. If ‘O’ is the center of the circle, what is the perimeter of the shaded region in centimetres?
a) 2
b) 6 + 2
c) 6 + 6
d) 8
15. If ‘O’ is the center of the circle shown, what is the value of x?
a) 4
b) 8
c) 16
d) 64
16. If ‘O’ is the center of the circle shown having AB, AE, CB and CD as tangents, what is the measure of Ð DOE in degrees?
a) 75
b) 100
c) 110
d) 150
17. PT is tangent to the circle at P and ÐQRP is inscribed in the circle. What is the measure of ÐQPT in degrees?
a) 12
b) 20
c) 24
d) 40
18. On the circle shown having center “O”, what is the measure of x in degrees?
a) 32
b) 64
c) 128
d) 296
19. The circle shown has center ‘O’ and has MN tangent to the circle at point M. If MN = 15 and OM = 8, what is the measure of NP?
a) 9
b) 15
c) 17
d) 25
20. In the diagram, AB and AC are tangents to circle center “O”. If ÐBOC = 160°, what is the measure of x in degrees?
a) 10
b) 20
c) 80
d) 90
21. Which is a permutation?
a) Number of ways to award 5 prizes of $100.00
b) Number of ways to award 5 prizes valued at $500.00, $100.00, $75.00, $50.00, and $25.00
c) Number of ways to form a committee from 5 students from a class
d) Number of ways to select three students to put chairs in the gym
22. What is the simplest form of ?
a) 1
b)
c) r
d)
23. Eight friends are seated around a circular table. What is the total number of different arrangements for seating?
a) 5040
b) 40320
c) 45360
d) 362880
24. What is the value of n in ?
a) -9
b) 8
c) 71
d) 72
25. A bag contains 5 green marbles, 4 red marbles and 3 yellow marbles. If 2 marbles are taken from the bag at random, without replacement, what is the probability of selecting one red marble and one green one.?
a)
b)
26. 85 people were surveyed and asked if they owned a DVD player or a VHS player. The results are shown in the diagram. Based on the diagram, what is the probability that a person owns a DVD or a VHS player?
a)
b)
27. Which is an example of a combination?
a) The number of ways to arrange five different pictures on a wall
b) The number of ways to arrange five flute players in the front row of an orchestra
c) The number of ways to select 6 people to do an oral report from 20 students
d) The number of ways to arrange Volumes 1 to 8 of an encyclopedia set on a shelf.
28. On Survivor Island, a license plate consists of three characters. The first digit from 0 to 9, the second is an A or an E, and the third is a different digit from 0 to 9. How many different license plates are possible if no characters can be repeated?
a) 144
b) 162
c) 180
d) 200
29. Three students are selected from a Math Club of twenty students to be the president, the vice president, and the treasurer. How many ways can this group be selected?
a)
b)
30. At a chain of fast food restaurants, 6 of the 10 different available desserts each have more than 20g of fat. If three different desserts are selected at random, approximately what is the probability that the first three selected will each have more than 20g of fat?
a) 0.180
b) 0.167
c) 0.216
d) 0.300