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1. |
The equation, 4x2 - 6x + 10 = 0, has |
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(a) | two real solutions |
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(b) | one real solution |
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(c) | three real solutions |
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(d) | four real solutions |
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(e) | no real solutions |
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2. |
The remainder of dividing the polynomial
x3 + x2
by x2 +1 is |
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(a) | 0 |
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(b) | 1 |
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(c) | -x -1 |
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(d) | x +1 |
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(e) | x |
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3. |
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(a) | 12 |
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(b) |
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(c) |
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(d) |
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| ( |
x+1
x - 3
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| ( |
x2 - 2x - 3
x+1
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(e) | |
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4. |
Find the midpoint of the line segment between (-2,1) and (4,5). |
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(a) | (-1,1) |
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(b) | (3,-1) |
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(c) | (3,3) |
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(d) | (3,1) |
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(e) | (1,3) |
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5. |
The set of points (x,y) such that
x2 -2x + y2 -6y = 6
is a circle of radius |
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(a) | 5 |
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(b) | 4 |
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(c) | 6 |
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(d) | 51/2 |
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(e) | 61/2 |
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6. |
The line containing the points (1,1) and (1,-1) is perpendicular
to the line
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(a) | x = 5 |
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(b) | y = -x -1 |
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(c) | y -1 = x -1 |
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(d) | y = 5 |
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(e) | y = 2x +1 |
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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) | -2/3 |
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(c) | -3/2 |
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(d) | -4/3 |
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(e) | 0 |
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8. |
If x = 3, find the smallest value of y which satisfies
y2x + 3yx2 + 54 = 0. |
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(a) | There is no smallest value. |
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(b) | -6 |
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(c) | -3 |
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(d) | 0 |
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(e) | 3 |
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9. |
How many real solutions for x are there to the equation
x2 + 3x + 8 = 0? |
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(a) | 0 |
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(b) | 2 |
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(c) | 3 |
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(d) | It cannot be determined. |
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(e) | 1 |
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10. |
163/2 is |
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(a) | 32 |
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(b) | 8 |
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(c) | 83 |
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(d) | 128 |
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(e) | 64 |
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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 any real number |
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(c) | x is not equal to 0 |
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(d) | x > 0 |
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(e) | 1 > x > -1 |
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12. |
Which of the following values of x satisfies
log2(3x) + log2(2x) = 3? |
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(a) | x = (3/2)1/2 |
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(b) | x = 4 |
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(c) | x = 5 |
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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) | 10 |
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(c) | 26 |
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(d) | 9 |
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(e) | 11 |
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14. |
If h(x) = x3, g(x) = x2+1 and f(x) = x +1, then h(g(f(0))) + f(g(h(0))) is: |
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(a) | 9 |
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(b) | 0 |
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(c) | 4 |
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(d) | 16 |
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(e) | 10 |
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15. |
If f(x) = 3x2 + 4
and g(y) = 2y1/2 + 5,
what is g(f(2))? |
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(a) | 20 |
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(b) | 9 |
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(c) | 13 |
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(d) | 10 |
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(e) | All of the other answers are incorrect. |
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16. |
The inequality x2 - 2x > -1 reduces to |
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(a) | x < -1 |
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(b) | x > -1 |
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(c) | x > 1 |
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(d) | x is not equal to 1 |
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(e) | x < 1 |
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17. |
The inequality x3 < 2x2 -x reduces to |
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(a) | x < 0 |
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(b) | x > 0 |
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(c) | x < 0 or x is not equal to 1 |
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(d) | x > 1 |
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(e) | x < 1 |
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18. |
| Under which of the following conditions does x
satisfy |
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(a) | All of the other answers are incorrect. |
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(b) | x - 1 > 0 and x + 2 > 0 |
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(c) | There are no values of x which satisfy this expression. |
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(d) | x + 2 > 0 |
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(e) | x is not equal to 1 and x + 2 > 0 |
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19. |
If 3x + 4y = 7 and 5x-4y = 1, find x and y. |
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(a) | x = 1 and y = -1 |
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(b) | x = -1 and y = 1 |
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(c) | x = 2 and y = 1 |
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(d) | x = 2 and y = 2 |
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(e) | x = 1 and y = 1 |
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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) | Cannot be determined
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(b) | y = 2 |
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(c) | y = 0 |
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(d) | y = 1 |
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(e) | y = 9/4 |
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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 = 30 |
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(e) | y = 0 |
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22. |
The radian measure of an angle of 45 degrees is |
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(a) | pi |
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(b) | 2pi/3 |
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(c) | pi/3 |
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(d) | pi/4 |
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(e) | pi/2 |
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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) | 2/(31/2) |
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(b) | 31/2/2 |
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(c) | 2/3 |
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(d) | 3/2 |
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(e) | 1/2 |
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24. |
Two lines each contain the point (0,0). One line
has slope 3 and the other line has slope 5. The
tangent of the angle interior to the lines is |
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(a) | 8 |
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(b) | 1/8 |
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(c) | 0 |
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(d) | 2 |
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(e) | 1 |
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