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Practice Questions

EOC Challenge Set: Geometry Connections

Use this stronger set to blend radians, sectors, similarity, trig, and measurement modeling in questions that feel closer to upper-level EOC review.

Practice Set 5

10 Geometry Challenge Questions

This challenge set focuses on multi-step circle work, scale reasoning, trig relationships, coordinate distance, and surface-area modeling.

10 questionsEOC challenge

Question 1

A sector has arc length 10π and central angle 5π/6 radians. What is the radius?

Radian

Desmos Move: Use s = rθ and solve for r by dividing the arc length by the radian measure.

Question 2

A smaller similar polygon has perimeter 18, and the scale factor to the larger polygon is 1.5. What is the larger perimeter?

Similarity

Desmos Move: Perimeter changes by the same linear scale factor as side lengths.

Question 3

A sector has radius 12 and central angle π/3 radians. What is its area to the nearest tenth?

Sector Area

Desmos Move: Use A = 1/2 r²θ when the angle is given in radians.

Question 4

Which geometric place contains all points that are the same distance from the endpoints of a segment?

Locus

Desmos Move: Think about where a point would have equal distance to both endpoints in a coordinate sketch.

Question 5

If sin θ = 5/13 and the hypotenuse is 26, what is the length of the side opposite θ?

Trig

Desmos Move: Since sin θ = opposite / hypotenuse, multiply the ratio by the given hypotenuse.

Question 6

Find the distance between (-3, -4) and (5, 2).

Distance

Desmos Move: The changes are 8 and 6, which makes another 6-8-10 triangle.

Question 7

Which expression gives the total surface area of a closed cylinder?

Surface Area

Desmos Move: A closed cylinder includes two circular bases and the curved side.

Question 8

If the linear scale factor from a figure to its image is 1/3, what is the area scale factor?

Scaling

Desmos Move: Area changes by the square of the linear scale factor.

Question 9

A wheel with radius 14 inches turns through π/2 radians. How far does a point on the rim travel?

Arc Length

Arc length measures the distance traveled along the rim.

Desmos Move: Arc length in radians is s = rθ.

Question 10

A 12-foot ramp makes a 30° angle with the ground. About how high does it rise?

Modeling

Desmos Move: Use sin(30°) = height / 12, or remember that sin(30°) = 1/2.