| 1. Suppose that the equation |x|=ax+1 has one negative root but no positive root. Which of the followings is the range of a ? | |
| a) | a>-1 |
| b) | a=1 |
| c) | a 1 |
| d) | a<1 |
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| 1. Suppose that the equation |x|=ax+1 has one negative root but no positive root. Which of the followings is the range of a ? | |
| a) | a>-1 |
| b) | a=1 |
| c) | a1 |
| d) | a<1 |
2. Which of the followings is the solution of the
inequality  ? |
|
| a) | -1 |
| b) | -1  x 1 |
| c) | -1 x < 1 |
| d) | -1 < x 1 |
 4. The graph of the quadratic function y=ax2+bx+c
is shown in the figure. Among the six expressions ab, ac, a+b+c, a-b+c, 2a+b and 2a-b, how many of them are positive ? |
|
| a) | 2 |
| b) | 3 |
| c) | 4 |
| d) | None |
5. Let x
be a real number. Which of the following expressions is equal to  ? |
|
| a) | x |
| b) | |x| |
| c) | -x |
| d) | -|x| |
| 6. Suppose that |-a| > -a . Which of the following statements is true ? | |
| a) | a > 0 |
| b) | a <0 |
| c) | a <-1 |
| d) | -1 |
| 7. Which of the followings is the graph of the function y=1-|x-x2| ? | |
 |
|
| a) | The solid curve in figure 1. |
| b) | The solid curve in figure 2. |
| c) | The solid curve in figure 3. |
| d) | The solid curve in figure 4. |
| 8. Without using a calculator, determine which of the following numbers is the largest ? | |
| a) | tan48o + cot48o |
| b) | sin48o + cos48o |
| c) | tan48o + cos48o |
| d) | cot48o + sin48o |
| 9. The equation (x-a)(x-8)-1=0 has two integer roots. Which of the following statements about a is true ? | |
| a) | a <0 |
| b) | a is an integer. |
| c) | a = 0 |
| d) | a > 8 |
| 10. When the polynomial x12-x6+1 is divided by x2-1, which of the followings is the remainder ? | |
| a) | 1 |
| b) | -1 |
| c) | x-1 |
| d) | x+1 |
13. Which of the following sets is the domain of
the function ? |
|
| a) | The set of all real numbers. |
| b) | The set of all real numbers except 0. |
| c) | The set of all real numbers except -1. |
| d) | The set of all real numbers except 0 and -1. |
| 14. Suppose f is a function such that f(x)=-f(-x) for all x in R. Which of the following statements about f is not true ? | |
| a) | f(0)=0. |
| b) | The graph of f is symmetric about the origin. |
| c) | f(x) > 0 for all x in R. |
| d) | f(x)f(-x) 0 for
all x in R. |
15. Denote the empty set by  . Which of the following sets is not
a subset of the set {0,{0},}? |
|
| a) | |
| b) | {} |
| c) | {{0}} |
| d) | {{}} |
| 17. Let f(x) = ax5+bx3+cx-5. Suppose that f(-3)=7. Which of the followings is the value of f(3) ? | |
| a) | -17 |
| b) | -3 |
| c) | -7 |
| d) | 0 |
18. Let a > 1
and b a positive rational number. Suppose that ab+ a-b = 2 . Which of the followings is the
value of ab- a-b ? |
|
| a) | 0 |
| b) | 2 or -2 |
| c) | 2 |
| d) | -2 |
| 19. Suppose a <0 and -1 . Which of the followings is true about a, ab and ab2 ? | |
| a) | a > ab > ab2 |
| b) | ab2 > ab > a |
| c) | ab > a > ab2 |
| d) | ab > ab2 > a |
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. Which of the following expressions is equal to f(f(x)) ?
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