EXAM REVIEW 1

​EXAM REVIEW

By J-Lorenzo Fabe

Multiple Choice

During a parade, a rotating spotlight mounted at the center of a circular plaza turns through an angle of 45°. Which explanation best describes the portion of the plaza it lights up?

• The light covers 1/8 of the circle since 45° is one-eighth of 360°.

• The light covers half the circle since 45° is close to 90°.

• The light covers the entire circle since it keeps rotating.

• The light covers an arc based on how far the beam reaches, not its angle.

Multiple Choice

A merry-go-round has horses equally spaced around the edge. The central angle between two consecutive horses is 30°. Which statement best describes the arc between them?

• The arc also measures 30° because the intercepted arc equals the central angle.

• The arc measures 60° because it’s double the central angle.

• The arc measures 15° because it’s half the central angle.

• The arc depends only on the radius, not the angle.

Multiple Choice

An artist draws a circular window and places a straight bar from the center to the rim for support. Which statement best describes this bar?

• It is a radius because it connects the center to a point on the circle.

• It is a chord since it lies completely inside the circle.

• It is a diameter because it passes through two points.

• It is a tangent because it touches the circle at only one point.

Multiple Choice

A giant pizza is cut straight through its center so that two equal halves are made. Which geometric term best describes the line of the cut?

• Chord

• Radius

• Diameter

• Tangent

Multiple Choice

A car drives along a curved road that just touches a circular park at one point but doesn’t enter it. Which explanation best describes this road?

• It is a secant because it cuts through the circle twice.

• It is a chord because it lies within the circle.

• It is a tangent because it touches the circle at exactly one point.

• It is a radius because it connects to the center.

Multiple Choice

A drone flies in a perfect circle around a tall tower. If it travels along an arc that forms a 90° central angle, what part of its flight path has it covered?

• One-fourth of the circle

• One-half of the circle

• One-third of the circle

• The entire circle

Multiple Choice

A tree is planted at the center of a circular park. A bench is placed directly on the park’s edge. Which best describes the distance from the tree to the bench?

• It represents the radius of the park.

• It represents the diameter of the park.

• It represents a tangent to the park.

• It represents the chord of the park.

Multiple Choice

A city engineer connects two points on the circular edge of a water tank to measure across it but doesn’t pass through the center. What kind of line segment did the engineer draw?

• Radius

• Chord

• Diameter

• Tangent

Multiple Choice

Two points, A(1, 2) and B(7, 5), mark opposite ends of a footbridge on a coordinate map. Which reasoning correctly finds the bridge’s length?

• Use the distance formula: subtract x’s and y’s, square, add, then take the square root.

• Add the x’s and y’s together and divide by 2.

• Multiply the differences of x and y.

• Subtract the smaller coordinates from the larger and divide by 2.

Multiple Choice

A surveyor wants to find the midpoint of a line between houses at (4, 6) and (10, 2). Which explanation correctly describes how to locate it?

• Find the average of the x-coordinates and the average of the y-coordinates.

• Subtract the smaller coordinates from the larger and divide by 2.

• Add all coordinates and divide by 4.

• Multiply both coordinates by ½ to get the midpoint.

Consider the problem below.

PROBLEM 1: The Arc of Lights at Sinulog Festival

During the Sinulog Festival, organizers are decorating a circular stage with colorful lights placed along its edge. They want every performer standing on the edge of the stage to see an inscribed angle of 45° formed by two lights placed along the rim of the circle.

If the center of the stage represents the center of the circle, how should the two lights be positioned around the edge so that the arc between them matches the angle seen by the performers?

Explain your reasoning.

PROBLEM 1: The Arc of Lights at Sinulog Festival

During the Sinulog Festival, organizers are decorating a circular stage with colorful lights placed along its edge. They want every performer standing on the edge of the stage to see an inscribed angle of 45° formed by two lights placed along the rim of the circle.

If the center of the stage represents the center of the circle, how should the two lights be positioned around the edge so that the arc between them matches the angle seen by the performers?

Explain your reasoning.

How will you solve the problem? Write your complete solution as the “Evidence” using such mathematical concept/s in your activity notebook.

Open Ended

PROBLEM 1: The Arc of Lights at Sinulog Festival

During the Sinulog Festival, organizers are decorating a circular stage with colorful lights placed along its edge. They want every performer standing on the edge of the stage to see an inscribed angle of 45° formed by two lights placed along the rim of the circle.

If the center of the stage represents the center of the circle, how should the two lights be positioned around the edge so that the arc between them matches the angle seen by the performers?

Explain your reasoning.

Why did you use such a way/method to solve each problem? Explain how your claim and evidence are connected. Write your answer as the “Reasoning” .

Open Ended

PROBLEM 1: The Arc of Lights at Sinulog Festival

During the Sinulog Festival, organizers are decorating a circular stage with colorful lights placed along its edge. They want every performer standing on the edge of the stage to see an inscribed angle of 45° formed by two lights placed along the rim of the circle.

If the center of the stage represents the center of the circle, how should the two lights be positioned around the edge so that the arc between them matches the angle seen by the performers?

Explain your reasoning.

What is your final answer to the question in the problem? Write your answer as the “Claim”.

​END OF SLIDE