1. [latex]{ x }^{ 2 }y>0[latex]
[latex]x{ y }^{ 2 }<0[latex]
| Quantity A | Quantity B |
| [latex]x[latex] | [latex]y[latex] |
2. On the number line shown above, the tick marks are equally spaced. Which of the following statements about the numbers [latex]x, y[latex], and [latex]z[latex] must be true?
Indicate all such statements.
(A) [latex]xyz<0[latex]
(B) [latex]x+z=y[latex]
(C) [latex]z(y-x)>0[latex]
3. Which of the following could be the graph of all values of [latex]x[latex] that satisfy the following inequality
4. [latex]X[latex] is the set of all integers [latex]n[latex] that satisfy the inequality
| Quantity A | Quantity B |
| The absolute value of the greatest integer in [latex]X[latex] | The absolute value of the least integer in [latex]X[latex] |
5. If [latex]0<a<1<b[latex] which of the following is true about the reciprocals of , [latex]a[latex] and [latex]b[latex] ?
A [latex]1<\frac{ 1 }{ a }<\frac{ 1 }{ b }[latex]
B [latex]\frac{ 1 }{ a }<1<\frac{ 1 }{ b }[latex]
C [latex]\frac{ 1 }{ a }<\frac{ 1 }{ b }<1[latex]
D [latex]\frac{ 1 }{ b }<1<\frac{ 1 }{ a }[latex]
E [latex]\frac{ 1 }{ b }<\frac{ 1 }{ a }<1[latex]
6. If which of the following could be the value of [latex]t[latex] ? ⎪[latex]t+3[latex]⎪>[latex]5[latex],
Indicate all such values.
(A) [latex]-9[latex]
(B) [latex]-6[latex]
(C) [latex]-2[latex]
(D) [latex]0[latex]
(E) [latex]2[latex]
(F) [latex]3[latex]
7. [latex]a+\frac { b }{ 10 }>0[latex]
[latex]b+\frac { a }{ 10 }>0[latex]
| Quantity A | Quantity B |
| [latex]a[latex] | [latex]b[latex] |
8. If [latex]x<y<0[latex] which of the following inequalities must be true?
(A) [latex]y+1<x[latex]
(B) [latex]y-1<x[latex]
(C) [latex]x{ y }^{ 2 }<x[latex]
(D) [latex]xy<{ y }^{ 2 }[latex]
(E) [latex]xy<{ x }^{ 2 }[latex]
9. |[latex]x[latex]| [latex]+[latex] |[latex]y[latex]| = [latex]2[latex] and [latex]x + y = 0[latex]
| Quantity A | Quantity B |
| [latex]x[latex] | [latex]y[latex] |
10. [latex]2x + 1 > 3x + 2[latex] and [latex]5x + 2 > 4x[latex]
| Quantity A | Quantity B |
| [latex]x[latex] | [latex]1[latex] |
11. If [latex](x + 1)2-2x > 2(x + 1) + 2[latex], then x cannot equal which one of the following?
(A) [latex]-5[latex]
(B) [latex]-3[latex]
(C) [latex]0[latex]
(D) [latex]3[latex]
(E) [latex]5[latex]
12. If [latex]x > 2[latex] and [latex]x < 3[latex], then which of the following is positive?
(I) [latex](x-2)(x-3)[latex]
(II) [latex](2-x)(x-3)[latex]
(III) [latex](2-x)(3-x)[latex]
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only
13. If [latex]6< 2x -4<12[latex], which of the following could be a value of [latex]x[latex]?
(a) [latex]4[latex]
(b) [latex]5[latex]
(c) [latex]7[latex]
(d) [latex]8[latex]
(e) [latex]9[latex]
14. A bicycle wheel has spokes that go from a center point in the hub to equally spaced points on the rim of the wheel. If there are fewer than six spokes, what is the smallest possible angle between any two spokes?
(A) [latex]18[latex] degrees
(B) [latex]30[latex] degrees
(C) [latex]40[latex] degrees
(D) [latex]60[latex] degrees
(E) [latex]72[latex] degrees
15. If [latex]x + y + z = 0[latex] and [latex]z = 8[latex], which of the following must be true?
(A) [latex]x < 0[latex]
(B) [latex]y < 0[latex]
(C) [latex]x-y < 0[latex]
(D) [latex]z-y > 0[latex]
(E) [latex]x + y < 0[latex]
Answer:
1 B
2 Choice A: [latex]xyz<0[latex] AND Choice B: [latex]x+z=y[latex] AND Choice C: [latex]z(y-x)>0[latex]
3 C
4 C
5 D
6 A, F
7 A
8 E
9 D
10 B
11 C
12 B
13 C
14 E
15 E
