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 $x$ ?
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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?
A) $(-20,-16)$
B) $(-10,-8)$
C) $(10,8)$
D) $(20,16)$
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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 $x$ ?
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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 $\overline{A B}$ ?
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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?
A) 5
B) $6.5$
C) $\sqrt{40}$
D) $\sqrt{50}$
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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?
A) $(-7,3)$
B) $(-3,1)$
C) $(0,0)$
D) $(3,2)$
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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?
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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 $Q$ ?
A) $(2,-5)$
B) $(6,-1)$
C) $(6,-5)$
D) $(6,-9)$
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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 $x$ ?
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13. (Test $1 / \mathrm{Q} 2 /$ No Calculator)
For $i=\sqrt{-1}$, what is the sum $(7+3 i)+(-8+9 i)$ ?
A) $-1+12 i$
B) $-1-6 i$
C) $15+12 i$
D) $15-6 i$
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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: $i=\sqrt{-1}$ )
A) $\frac{3}{8}-\frac{5 i}{2}$
B) $\frac{3}{8}+\frac{5 i}{2}$
C) $\frac{7}{34}-\frac{23 i}{34}$
D) $\frac{7}{34}+\frac{23 i}{34}$
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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: $i=\sqrt{-1}$ )
A) 2
B) $\frac{8}{3}$
C) 3
D) $\frac{11}{3}$
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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 $i=\sqrt{-1}$ ?
A) 17
B) $17 i$
C) $6+11 i$
D) $8+24 i$
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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 $i=\sqrt{-1} ?$
A) $-14-18 i$
B) $-4-6 i$
C) $4+6 i$
D) $14+18 i$
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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 $\angle 2$ ?
A) $35^{\circ}$
B) $55^{\circ}$
C) $70^{\circ}$
D) $145^{\circ}$
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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 $\overline{L N}$ ?
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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. $z=t$
A) I and II only
B) I and III only
C) II and III only
D) I, II, and III
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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 $x$ ?
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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 $k$ ?
A) $4.5$
B) $5.5$
C) $12.5$
D) $21.5$
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23. (Test5/Q 20/No Calculator)
| Intersecting lines $r, s$, and $t$ are shown above, What is the value of $x$ ?
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24. (Test5/Q $19 /$ Calculator)
In $\triangle A B C$ above, what is the length of $\overline{A D}$ ?
A) 4
B) 6
C) $6 \sqrt{2}$
D) $6 \sqrt{3}$
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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.)
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26. (Test7/Q 14/Calculator)
In the figure above, what is the value of $x$ ?
A) 45
B) 90
C) 100
D) 105
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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 $x$ ?
A) 120
B) 100
C) 90
D) 80
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Answer
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