# SAT CollegeBoard Practice Test (1-8) Circle and Geometry

###### 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?
 A) 2 B) 3 C) 4 D) 9

###### 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?
 A) 2 B) 4 C) 8 D) 16

###### 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 $\widehat{A C}$ ?
 A) 9 B) 12 C) 18 D) 36

###### 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) $(20,16)$

###### 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?
 A) 5 B) $6.5$ C) $\sqrt{40}$ D) $\sqrt{50}$

###### 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) $(3,2)$

###### 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 $Q$ ?
 A) $(2,-5)$ B) $(6,-1)$ C) $(6,-5)$ D) $(6,-9)$

###### 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 $(7+3 i)+(-8+9 i)$ ?
 A) $-1+12 i$ B) $-1-6 i$ C) $15+12 i$ D) $15-6 i$

###### 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) $\frac{7}{34}+\frac{23 i}{34}$

###### 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) $\frac{11}{3}$

###### 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) $8+24 i$

###### 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) $14+18 i$

###### 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) $145^{\circ}$

###### 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. $z=t$
 A) I and II only B) I and III only C) II and III only D) I, II, and III

###### 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 $k$ ?
 A) $4.5$ B) $5.5$ C) $12.5$ D) $21.5$

###### 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 $\overline{A D}$ ?
 A) 4 B) 6 C) $6 \sqrt{2}$ D) $6 \sqrt{3}$

###### 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 $x$ ?
 A) 45 B) 90 C) 100 D) 105

###### 27. (Test8/Q 4/No Calculator)

In the figure above, $R T=T U$. What is the value of $x$ ?
 A) 72 B) 66 C) 64 D) 58

###### 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

 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