If the graph of y = f(x) is transformed into the graph of 2y - 6 = - 4 f(x - 3), point (a , b) on the graph of y = f(x) becomes point (A , B) on the graph of 2y - 6 = - 4 f(x - 3) where A and B are given by
A. A = a - 3, B = b
B. A = a - 3, B = b
C. A = a + 3, B = -2 b
D. A = a + 3, B = -2 b +3
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Questions 8
When a parabola represented by the equation y - 2x 2 = 8 x + 5 is translated 3 units to the left and 2 units up, the new parabola has its vertex at
A. (-5 , -1)
B. (-5 , -5)
C. (-1 , -3)
D. (-2 , -3)
Questions 9
The graphs of the two linear equations a x + b y = c and b x - a y = c, where none of the coefficients a, b, c is equal to zero,
A. are parallel
B. intersect at the point (0,0)
C. intersect at two points
D. perpendicular
Questions 10
The graphs of the two equations y = a x 2 + b x + c and y = A x 2 + B x + C, such that a and A have different signs and that the quantities b 2 - 4 a c and B 2 - 4 A C are both negative,
A. intersect at two points
B. intersect at one point
C. do not intersect
D. none of the above
Questions 11
For x greater than or equal to zero and less than or equal to 2 π, sin x and cos x are both decreasing on the intervals
A. (0 , π/2)
B. (π/2 , π)
C. (π , 3 π / 2)
D. (3 π / 2 , 2 π)
Questions 12
The three solutions of the equation f(x) = 0 are -2, 0, and 3. Therefore, the three solutions of the equation f(x - 2) = 0 are
A. - 4, -2, and 1
B. -2, 0 and 3
C. 4, 2, and 5
D. 0, 2 and 5
Questions 13
The three solutions of the equation f(x) = 0 are - 4, 8, and 11. Therefore, the three solutions of the equation f(2 x) = 0 are
A. - 2, 4, and 11/2
B. - 8, 16 and 22
C. - 4, 8, and 11
D. 2, 19 / 2 and 7 / 2
Questions 14
A school committee consists of 2 teachers and 4 students. The number of different committees that can be formed from 5 teachers and 10 students is
A. 10
B. 15
C. 2100
D. 8
Questions 15
Five different books (A, B, C, D and E) are to be arranged on a shelf. Books C and D are to be arranged first and second starting from the right of the shelf. The number of different orders in which books A, B and E may be arranged is
A. 5!
B. 3!
C. 2!
D. 3! * 2!
Questions 16
The mean of a data set is equal to 10 and its standard deviation is equal to 1. If we add 5 to each data value, then the mean and standard deviation become
A. mean = 15 , standard deviation = 6
B. mean = 10 , standard deviation = 6
C. mean = 15 , standard deviation = 1
D. mean = 10 , standard deviation = 1
Questions 17
The exam scores of all 500 students were recorded and it was determined that these scores were normally distributed. If Jane's score is 0.8 standard deviation above the mean, then how many, to the nearest unit, students scored above Jane?
A. 394
B. 250
C. 400
D. 106
Questions 18
If f(x) is an odd function, then | f(x) | is
A. an odd function
B. an even function
C. neither odd nor even
D. even and odd
Questions 19
The period of | sin (3x) | is
A. 2 π
B. 2 π / 3
C. π / 3
D. 3 π
Questions 20
When a metallic ball bearing is placed inside a cylindrical container, of radius 2 cm, the height of the water, inside the container, increases by 0.6 cm. The radius, to the nearest tenth of a centimeter, of the ball bearing is
A. 1 cm
B. 1.2 cm
C. 2 cm
D. 0.6 cm
Questions 21
The period of 2 sin x cos x is
A. 4 π 2
B. 2 π
C. 4 π
D. π
Questions 22
The probability that an electronic device produced by a company does not function properly is equal to 0.1. If 10 devices are bought, then the probability, to the nearest thousandth, that 7 devices function properly is
A. 0.057
B. 0.478
C. 0.001
D. 0
Answers to the above questions
1b, 2c, 3d, 4a, 5c, 6b, 7d, 8a, 9d, 10c
11b, 12d, 13a, 14c, 15b, 16c, 17d, 18b, 19c, 20b
21d, 22a.
