A set of multiple choice maths questions are presented. The answers are provided and are located at the lower part of the page. The questions have been designed to test for deep understanding of maths concepts. Detailed explanations and solutions to these questions are also provided.

## Questions 1

If Logx (1 / 8) = - 3 / 2, then x is equal to
A. - 4
B. 4
C. 1 / 4
D. 10

## Questions 2

20 % of 2 is equal to
A. 20
B. 4
C. 0.4
D. 0.04

## Questions 3

If Log 4 (x) = 12, then log 2 (x / 4) is equal to
A. 11
B. 48
C. -12
D. 22

## Questions 4

The population of a country increased by an average of 2% per year from 2000 to 2003. If the population of this country was 2 000 000 on December 31, 2003, then the population of this country on January 1, 2000, to the nearest thousand would have been
A. 1 846 000
B. 1 852 000
C. 1 000 000
D. 1 500 000

## Questions 5

f is a quadratic function whose graph is a parabola opening upward and has a vertex on the x-axis. The graph of the new function g defined by g(x) = 2 - f(x - 5) has a range defined by the interval
A. [ -5 , + infinity)
B. [ 2 , + infinity)
C. ( - infinity , 2]
D. ( - infinity , 0]

## Questions 6

f is a function such that f(x) < 0. The graph of the new function g defined by g(x) = | f(x) | is a reflection of the graph of f
A. on the y axis
B. on the x axis
C. on the line y = x
D. on the line y = - x

## Questions 7

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

## 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.

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