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Digital SAT Math : Circles – Practice Questions

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SAT MAth Practice questions – all topics

  • Geometry and Trigonometry Weightage: 15% Questions: 5-7
    • Area and volume
    • Lines, angles, and triangles
    • Right triangles and trigonometry
    • Circles

SAT MAth and English  – full syllabus practice tests

 Question  Foundation

In the xy-plane, a circle with radius 2 has center \((0,0)\). Which of the following is a equation of the circle?
A) \(x^2+y^2=2\)
B) \(x^2+y^2=4\)
C) \(x^2-y^2=2\)
D) \(x^2-y^2=4\)

▶️Answer/Explanation

Ans:B

The general equation of a circle with center \((h, k)\) and radius \(r\) is:
\[
(x – h)^2 + (y – k)^2 = r^2
\]

Center \((0,0)\)
Radius \(2\)

Substitute these values into the equation:
\[
(x – 0)^2 + (y – 0)^2 = 2^2
\]

Simplify:
\[
x^2 + y^2 = 4
\]

▶️Formula Booklet

Question

\(x\)2-6\(x\)+\(y\)2-8\(y\)=0

The graph of the given equation in the \(xy\)-plane is a circle. What is the radius of the circle? 

  1. 2
  2. 3
  3. 4
  4. 5
Answer/Explanation

Ans: D

Question

In the \(xy\)-plane, a circle with radius 2 has center (0,0). Which of the following is a equation of the circle?

  1. \(x\)2+\(y\)2=2
  2. \(x\)2+\(y\)2=4
  3. \(x\)2-\(y\)2=2
  4. \(x\)2-\(y\)2=4
Answer/Explanation

Ans: B

Question

In the \(xy\)-plane, the points (-3, 10) and (3, 10) are endpoints of the diameter of a circle. Which equation represents this circle? 

  1. \(x\)2+(\(y\)-10)2=9
  2. (\(x\)+3)2+\(y\)2=36
  3. (\(x\)+3)2+(\(y\)-10)2=9
  4. (\(x\)+3)2+(\(y\)-10)2=36
Answer/Explanation

Ans: A

Question

\((x + 3)^{2} + (y – 7)^{2} = 100\)
In the \(xy\)-plane, the graph of the given equation is a circle. Which point \((x, y)\) lies on the circle? 

  1. (3, -4)
  2. (3, -1)
  3. (3, 1)
  4. (3, 4)
Answer/Explanation

Ans: B

More SAT Math Practice Questions.............

Question Easy

The circle above with center O has a circumference of 36. What is the length of minor \( \overline{AC}\)?
A. 9
B. 12
C. 18
D. 36

Answer/Explanation

Ans: A
Rationale
Choice A is correct. A circle has 360 degrees of arc. In the circle shown, O is the center of the circle and \(\angle AOC\) is a central angle of the circle. From the gure, the two diameters that meet to form are perpendicular, so the measure of \(\angle AOC\) is  \(90\circ \). Therefore, the length of minor arc \( \overline{AC}\) is \(\frac{90}{360}\) of the circumference of the circle. Since the circumference of the circle is 36, the length of minor arc \( \overline{AC}\) is \(\frac{90}{360} \times 36=9\) Choices B, C, and D are incorrect. The perpendicular diameters divide the circumference of the circle into four equal arcs; therefore, minor arc \( \overline{AC}\) is \(\frac{1}{4}\) of the circumference. However, the lengths in choices B and C are, respectively, \(\frac{1}{3}\) and \(\frac{1}{2}\) the circumference of the circle, and the length in choice D is the length of the entire circumference. None of these lengths is \(\frac{1}{4}\) the circumference.

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