1. (Test2/Q $24 /$ Calculator)
| $$x^{2}+y^{2}+4 x-2 y=-1$$
The equation of a circle in the $x y$-plane is shown above. What is the radius of the circle?
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2. (Test $4 / \mathrm{Q} 24 /$ Calculator)
In the circle above, segment $A B$ is a diameter. If the length of arc $\widehat{A D B}$ is $8 \pi$, what is the length of the radius of the circle?
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3. (Test $4 / Q 36 /$ Calculator)
| Note: Figure not drawn to scale. In the figure above, the circle has center $O$ and has radius 10 . If the length of arc $\overparen{A B}$ (shown in bold) is between 5 and 6 , what is one possible integer value of $x$ ? |
4. (Test5/Q 2/No Calculator)
The circle above with center $O$ has a circumference of 36. What is the length of minor arc $\widehat{A C}$ ?
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5. (Test5/Q 29/Calculator)
| $$x^{2}+20 x+y^{2}+16 y=-20$$
The equation above defines a circle in the $x y$-plane. What are the coordinates of the center of the circle?
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6. (Test5/Q 36/Calculator)
| Point $P$ is the center of the circle in the figure above. What is the value of $x$ ? |
7. (Test6/Q 20/No Calculator)
| Points $A$ and $B$ lie on a circle with radius 1 , and $\operatorname{arc} \overparen{A B}$ has length $\frac{\pi}{3}$. What fraction of the circumference of the circle is the length of arc $\overline{A B}$ ? |
8. (Test6/Q 27/Calculator)
In the $x y$ "plane, the graph of $2 x^{2}-6 x+2 y^{2}+2 y=45$ is a circle. What is the radius of the circle?
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9. (Test $7 / \mathrm{Q} 29 /$ Calculator)
A circle in the $x y$-plane has equation $(x+3)^{2}+(y-1)^{2}=25$. Which of the following points does NOT lie in the interior of the circle?
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10. (Test $7 / \mathrm{Q} 34 /$ Calculator)
| Point $C$ is the center of the circle above. What fraction of the area of the circle is the area of the shaded region? |
11. (Test8/Q 9/No Calculator)
| $$(x-6)^{2}+(y+5)^{2}=16$$
In the $x y$-plane, the graph of the equation above is a circle. Point $P$ is on the circle and has coordinates $(10,-5)$. If $\overline{P Q}$ is a diameter of the circle, what are the coordinates of point $Q$ ?
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12. (Test8/Q 20/No Calculator)
| Note: Figure not drawn to scale. In the circle above, point $A$ is the center and the length of arc $\overparen{B C}$ is $\frac{2}{5}$ of the circumference of the circle. What is the value of $x$ ? |
13. (Test $1 / \mathrm{Q} 2 /$ No Calculator)
For $i=\sqrt{-1}$, what is the sum $(7+3 i)+(-8+9 i)$ ?
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14. (Test2/Q 11/No Calculator)
Which of the following complex numbers is equivalent to $\frac{3-5 i}{8+2 i}$ ? (Note: $i=\sqrt{-1}$ )
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15. (Test $4 / \mathrm{Q} 14 / \mathrm{No}$ Calculator)
| $$\frac{8-i}{3-2 i}$$
If the expression above is rewritten in the form $a+b i$, where $a$ and $b$ are real numbers, what is the value of $a$ ? (Note: $i=\sqrt{-1}$ )
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16. (Test6/Q 3/No Calculator)
What is the sum of the complex numbers $2+3 i$ and $4+8 i$, where $i=\sqrt{-1}$ ?
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17. (Test $7 / Q 4 /$ No Calculator)
Which of the following complex numbers is equal to $(5+12 i)-\left(9 i^{2}-6 i\right)$, for $i=\sqrt{-1} ?$
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18. (Test $1 / \mathrm{Q} 3 /$ Calculator)
In the figure above, lines $\ell$ and $m$ are parallel and lines $s$ and $t$ are parallel. If the measure of $\angle 1$ is $35^{\circ}$, what is the measure of $\angle 2$ ?
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19. (Test2/Q 36/Calculator)
| In the figure above, point $O$ is the center of the circle, line segments $L M$ and $M N$ are tangent to the circle at points $L$ and $N$, respectively, and the segments intersect at point $M$ as shown. If the circumference of the circle is 96, what is the length of minor arc $\overline{L N}$ ? |
20. (Test $3 / Q 11 /$ No Calculator)
| Note: Figure not drawn to scale.
In the figure above, lines $k_{3} \ell$, and $m$ intersect at a point. If $x+y=u+w$, which of the following must be true? I. $x=z$ II. $y=w$ III. $z=t$
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21. (Test $3 / Q 18 /$ No Calculator)
| Note: Figure not drawn to scale. Two isosceles triangles are shown above. If $180-z=2 y$ and $y=75$, what is the value of $x$ ? |
22. (Test3/Q 23/Calculator)
The angles shown above are acute and $\sin \left(a^{\circ}\right)=\cos \left(b^{\circ}\right)$. If $a=4 k-22$ and $b=6 k-13$, what is the value of $k$ ?
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23. (Test5/Q 20/No Calculator)
| Intersecting lines $r, s$, and $t$ are shown above, What is the value of $x$ ? |
24. (Test5/Q $19 /$ Calculator)
In $\triangle A B C$ above, what is the length of $\overline{A D}$ ?
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25. (Test7/Q $17 /$ No Calculator)
| In the figure above, $\overline{M Q}$ and $\overline{N R}$ intersect at point $P, N P=Q P$, and $M P=P R$. What is the measure, in degrees, of $\angle Q M R$ ? (Disregard the degree symbol when gridding your answer.) |
26. (Test7/Q 14/Calculator)
In the figure above, what is the value of $x$ ?
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27. (Test8/Q 4/No Calculator)
In the figure above, $R T=T U$. What is the value of $x$ ?
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28. (Test $8 / \mathrm{Q} 5 /$ Calculator)
| Note: Figure not drawn to scale.
In the figure above, lines $\ell$ and $m$ are parallel, $y=20$, and $z=60$. What is the value of $x$ ?
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Answer
| 1 A | $\quad$ Explanation |
| 2 C | $\quad$ Explanation |
| 3 29,...34 | $\quad$ Explanation |
| 4 A | $\quad$ Explanation |
| 5 B | $\quad$ Explanation |
| 6 80 | $\quad$ Explanation |
| 7 0.166666667 | $\quad$ Explanation |
| 8 A | $\quad$ Explanation |
| 9 D | $\quad$ Explanation |
| 10 0.277777778 | $\quad$ Explanation |
| 11 A | $\quad$ Explanation |
| 12 144 | $\quad$ Explanation |
| 13 A | $\quad$ Explanation |
| 14 C | $\quad$ Explanation |
| 15 A | $\quad$ Explanation |
| 16 C | $\quad$ Explanation |
| 17 D | $\quad$ Explanation |
| 18 D | $\quad$ Explanation |
| 19 32 | $\quad$ Explanation |
| 20 B | $\quad$ Explanation |
| 21 105 | $\quad$ Explanation |
| 22 C | $\quad$ Explanation |
| 23 97 | $\quad$ Explanation |
| 24 B | $\quad$ Explanation |
| 25 30 | $\quad$ Explanation |
| 26 D | $\quad$ Explanation |
| 27 C | $\quad$ Explanation |
| 28 B | $\quad$ Explanation |
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