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1. |
The equation, 4x2 - 6x + 10 = 0, has |
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(a) | three real solutions |
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(b) | no real solutions |
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(c) | one real solution |
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(d) | four real solutions |
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(e) | two real solutions |
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2. |
The remainder of dividing the polynomial
x3 + x2
by x2 +1 is |
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(a) | -x -1 |
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(b) | 1 |
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(c) | 0 |
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(d) | x |
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(e) | x +1 |
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3. |
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(a) |
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(b) |
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(c) | |
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(d) | 12 |
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(e) |
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| ( |
x+1
x - 3
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| ( |
x2 - 2x - 3
x+1
| ) |
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4. |
The set of points (x,y) such that
x2 + y2 = 9
is |
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(a) | a circle of radius 9 centered at (0,0) |
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(b) | a circle of radius 3 centered at (0,0) |
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(c) | a parabola |
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(d) | a circle of radius 3 centered at (1,1) |
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(e) | an hyperbola |
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5. |
Which of the following points is closer to the point
(1,1) than the point (2,2) is to (1,1)? |
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(a) | (0,1) |
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(b) | (2,0) |
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(c) | (1, 5/2) |
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(d) | (0,2) |
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(e) | (0,0) |
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6. |
The distance from the point (x,y) to the point (2,3)
is twice the distance from the point (x,y) to the point (5,7).
What is the maximum possible distance from (x,y) to (2,3)? |
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(a) | 15 |
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(b) | 5 |
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(c) | 25 |
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(d) | 4 |
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(e) | 10 |
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7. |
Let f(x) = 3x + 2. For which
x is f(x) = -2? |
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(a) | -4/3 |
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(b) | 0 |
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(c) | 4/3 |
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(d) | -2/3 |
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(e) | -3/2 |
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8. |
If x = y and
x2y2 - 5xy + 6 = 0, then
which of the following is possible? |
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(a) | x = 3 |
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(b) | x = 6 |
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(c) | x = 2 |
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(d) | x2 = 6 |
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(e) | x2 = 3 |
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9. |
Find the largest solution of
x3 + 4x2 + 3x = 0. |
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(a) | x = 1 |
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(b) | x = -2 |
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(c) | x = 0 |
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(d) | x = -1 |
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(e) | x = -3 |
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10. |
Simplify (x/2x3)(y2/y). |
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(a) | (x y2)/(2x3y) |
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(b) | 2x-2y - 1 |
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(c) | (1/2)x-2 + y |
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(d) | (x/2)-2 y |
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(e) | (1/2)x - 2 y |
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11. |
Which of the following describes the domain of log(|x|)? |
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(a) | x < 0 |
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(b) | x is not equal to 0 |
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(c) | 1 > x > -1 |
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(d) | x > 0 |
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(e) | x is any real number |
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12. |
Which of the following values of x satisfies
log2(3x) + log2(2x) = 3? |
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(a) | x = 5 |
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(b) | x = (3/2)1/2 |
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(c) | x = 4 |
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(d) | x = 3/5 |
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(e) | x = (4/3)1/2 |
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13. |
If f(x) = x2 + 1
and g(x) = 2x - 1, then f(g(2)) = |
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(a) | 5 |
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(b) | 9 |
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(c) | 10 |
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(d) | 11 |
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(e) | 26 |
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14. |
If f(x) = 3x + 3 and g(y) = 2(y + 1) + 5, what is g(f(2))? |
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(a) | 25 |
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(b) | All of the other answers are incorrect. |
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(c) | 23 |
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(d) | 9 |
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(e) | 11 |
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15. |
If f(x) = 3x + 3 what is f(f(2))?
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(a) | All of the other answers are incorrect.
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(b) | 81 |
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(c) | 30 |
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(d) | 9 |
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(e) | Not defined. |
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16. |
The expression -18 < -6x < 12
is equivalent to which of the following? |
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(a) | -2 > x > -3 |
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(b) | 3 > x > -2 |
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(c) | 3 > x > 2 |
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(d) | All of the other answers are incorrect. |
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(e) | 2 > x > -3 |
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17. |
The inequality (x - 1)2 > 1 is equivalent to |
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(a) | 0 < x and x < 2 |
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(b) | x < 0 |
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(c) | x < -2 |
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(d) | x > 2 |
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(e) | x < 0 or x > 2 |
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18. |
| Under which of the following conditions does x
satisfy |
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(a) | x + 2 > 0 |
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(b) | x is not equal to 1 and x + 2 > 0 |
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(c) | x - 1 > 0 and x + 2 > 0 |
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(d) | All of the other answers are incorrect. |
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(e) | There are no values of x which satisfy this expression. |
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19. |
If 3x + 4y = 7 and 5x-4y = 1,
then xy is |
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(a) | Cannot be determined |
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(b) | 1 |
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(c) | 2 |
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(d) | 4 |
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(e) | 3 |
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20. |
If y + 4x - 18 = 0 and y2 = x, then there is a solution with y given by |
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(a) | y = 9/4 |
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(b) | y = 1 |
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(c) | y = 0 |
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(d) | y = 2 |
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(e) | Cannot be determined
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21. |
If y + 4x - 5 = 0 and y = x2,
then there is a solution with y given by
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(a) | y = 20 |
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(b) | Cannot be determined |
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(c) | y = 25 |
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(d) | y = 0 |
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(e) | y = 30 |
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22. |
The radian measure of an angle of 60 degrees is |
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(a) | pi |
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(b) | pi/3 |
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(c) | pi/2 |
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(d) | 2(pi/3) |
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(e) | pi/4 |
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23. |
If sin(a) = 1, cos(b) > 0, and sin(b) = 1/2,
then sin(a + b) is |
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(a) | 31/2/2 |
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(b) | 2/3 |
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(c) | 1/2 |
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(d) | 3/2 |
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(e) | 2/(31/2) |
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24. |
If sin(a + b) = 1 and
tan(a) = 0,
then tan(b) is |
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(a) | 0 |
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(b) | undefined |
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(c) | 1/4 |
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(d) | 1/2 |
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(e) | 1 |
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