Question 1Easier
In the standard coordinate plane, a circle has center and radius 5. Which of the following is an equation of the circle?
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Answer: D —
A circle with center and radius has equation . With , , and , this is .
Study on the flyACTMathematicsCircles — arcs, sectors, angles, equations
Mathematics
Circles — arcs, sectors, angles, equations — ACT practice questions
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What this topic is
A sector is a slice of a circle, and its area is the fraction of a full turn that its central angle covers, multiplied by pi times the radius squared.
Arc length works the same way with the circumference. Circles — arcs, sectors, angles, equations also covers inscribed angles, which measure half the arc they cut off, and the standard equation of a circle, where center (h, k) and radius r give (x − h) squared plus (y − k) squared equals r squared.
Sign errors in that equation are frequent: a center with a negative x-coordinate produces a plus sign. ACT choices usually leave answers in terms of pi.
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Question 2Easier
A sector of a circle with radius 6 has central angle . What is the area of the sector?
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Answer: B —
Sector area .
Question 3Easier
A circle has a circumference of units. What is the area of the circle, in square units?
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Answer: D —
From , the radius is 5. Therefore, the area is square units.
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More ACT topics
Mathematics
- Real number system and number properties
- Integer and rational exponents
- Radicals and roots
- Complex numbers
- Vectors and matrices
- Fractions, decimals, and operations
- Percents and percent change
- Ratios, rates, and proportional relationships
- Linear equations and expressions in one variable
- Inequalities (linear and compound)
- Systems of equations
- Polynomial expressions and factoring
- Quadratic equations
- Radical and rational equations
- Exponential relationships
- Function notation and evaluating functions
- Linear functions and graphs
- Quadratic and polynomial functions
- Radical and rational functions
- Piecewise functions
- Exponential and logarithmic functions
- Key features and transformations of graphs
- Lines, angles, and polygons
- Triangles — congruence, similarity, Pythagorean theorem
- Surface area and volume of solids
- Coordinate geometry — distance, midpoint, slope, line equations
- Conic sections
- Right-triangle trigonometry and trig functions
- Measures of center and spread
- Data collection methods and study design
- Bivariate data and relationships (scatterplots, correlation)
- Probability and sample spaces
- Counting, combinations, and permutations
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