Chapter practice examination

Original untimed practice examination. Not a secure or official placement test.

Original untimed practice examination. Not a secure or official placement test. Solutions are available as revealable feedback and in a separate complete answer key. No answer submissions or accounts are required.

Assessment · 24 questions

Questions

Show your thinking; use diagrams when they help. Do not open solutions during your first attempt.

A1
A student answers the following question with “scalene”. Explain whether the answer is correct, then solve the question and justify your answer. Original question: A triangle has side lengths 11, 11, and 13 units. Classify it by its side lengths. (3 points)
Reveal explanation
Answer: isosceles
The suggested answer is not correct. Isosceles means exactly two equal sides. These lengths satisfy the triangle inequality.
Scoring: 1 point for identifying the given answer as incorrect; 1 for explaining the error; 1 for giving the corrected solution and appropriate units.
A2
An angle measures 139°. Is it acute, right, or obtuse? (2 points)
Reveal explanation
Answer: obtuse
Compare 139° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
Angle of 139 degrees; angle size depends on rotation, not ray length.
A3
Using a compass set to 22 mm, draw a circle. What must be the distance from the center to every point on the circle? (3 points)
Reveal explanation
Answer: 22 mm
The fixed compass opening is the radius. Keep its needle fixed and rotate the pencil to keep every perimeter point 22 mm from the center.
Scoring: 1 point for the center, 1 for the accurate radius, 1 for a complete labeled circle.
The radius runs from center to edge. The diameter crosses the center from edge to edge.
A4
A circle has diameter 32 cm. What is its radius? (2 points)
Reveal explanation
Answer: 16 cm
The radius is half the diameter. 32 ÷ 2 = 16 cm.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
The radius runs from center to edge. The diameter crosses the center from edge to edge.
A5
A student answers the following question with “obtuse”. Explain whether the answer is correct, then solve the question and justify your answer. Original question: An angle measures 50°. Is it acute, right, or obtuse? (3 points)
Reveal explanation
Answer: acute
The suggested answer is not correct. Compare 50° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Scoring: 1 point for identifying the given answer as incorrect; 1 for explaining the error; 1 for giving the corrected solution and appropriate units.
Angle of 50 degrees; angle size depends on rotation, not ray length.
A6
A triangle has side lengths 5, 5, and 5 units. Classify it by its side lengths. (2 points)
Reveal explanation
Answer: equilateral
Equilateral means three equal sides. These lengths satisfy the triangle inequality.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
A7
A triangle has side lengths 3, 4, and 5 units. Classify it by its side lengths. (2 points)
Reveal explanation
Answer: scalene
Scalene means no equal sides. These lengths satisfy the triangle inequality.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
A8
A triangle has side lengths 14, 14, and 16 units. Classify it by its side lengths. (2 points)
Reveal explanation
Answer: isosceles
Isosceles means exactly two equal sides. These lengths satisfy the triangle inequality.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
A9
A student answers the following question with “scalene”. Explain whether the answer is correct, then solve the question and justify your answer. Original question: A triangle has side lengths 13, 13, and 13 units. Classify it by its side lengths. (3 points)
Reveal explanation
Answer: equilateral
The suggested answer is not correct. Equilateral means three equal sides. These lengths satisfy the triangle inequality.
Scoring: 1 point for identifying the given answer as incorrect; 1 for explaining the error; 1 for giving the corrected solution and appropriate units.
A10
A triangle has side lengths 10, 10, and 12 units. Classify it by its side lengths. (2 points)
Reveal explanation
Answer: isosceles
Isosceles means exactly two equal sides. These lengths satisfy the triangle inequality.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
A11
An angle measures 42°. Is it acute, right, or obtuse? (2 points)
Reveal explanation
Answer: acute
Compare 42° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
Angle of 42 degrees; angle size depends on rotation, not ray length.
A12
Using a compass set to 9 mm, draw a circle. What must be the distance from the center to every point on the circle? (3 points)
Reveal explanation
Answer: 9 mm
The fixed compass opening is the radius. Keep its needle fixed and rotate the pencil to keep every perimeter point 9 mm from the center.
Scoring: 1 point for the center, 1 for the accurate radius, 1 for a complete labeled circle.
The radius runs from center to edge. The diameter crosses the center from edge to edge.
A13
A student answers the following question with “acute”. Explain whether the answer is correct, then solve the question and justify your answer. Original question: An angle measures 101°. Is it acute, right, or obtuse? (3 points)
Reveal explanation
Answer: obtuse
The suggested answer is not correct. Compare 101° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Scoring: 1 point for identifying the given answer as incorrect; 1 for explaining the error; 1 for giving the corrected solution and appropriate units.
Angle of 101 degrees; angle size depends on rotation, not ray length.
A14
An angle measures 31°. Is it acute, right, or obtuse? (2 points)
Reveal explanation
Answer: acute
Compare 31° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
Angle of 31 degrees; angle size depends on rotation, not ray length.
A15
Identify the most specific shape: a quadrilateral has four right angles, adjacent side lengths 9 cm and 11 cm. (2 points)
Reveal explanation
Answer: rectangle
The shape is a rectangle. Check right angles, equal-length sides and parallel lines; the description distinguishes it from the other listed types.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
A16
Using a compass set to 21 mm, draw a circle. What must be the distance from the center to every point on the circle? (3 points)
Reveal explanation
Answer: 21 mm
The fixed compass opening is the radius. Keep its needle fixed and rotate the pencil to keep every perimeter point 21 mm from the center.
Scoring: 1 point for the center, 1 for the accurate radius, 1 for a complete labeled circle.
The radius runs from center to edge. The diameter crosses the center from edge to edge.
A17
A student answers the following question with “rhombus with no right angles”. Explain whether the answer is correct, then solve the question and justify your answer. Original question: Identify the most specific shape: a quadrilateral has four right angles and four equal sides of 5 cm. (3 points)
Reveal explanation
Answer: square
The suggested answer is not correct. The shape is a square. Check right angles, equal-length sides and parallel lines; the description distinguishes it from the other listed types.
Scoring: 1 point for identifying the given answer as incorrect; 1 for explaining the error; 1 for giving the corrected solution and appropriate units.
A18
A circle has diameter 44 cm. What is its radius? (2 points)
Reveal explanation
Answer: 22 cm
The radius is half the diameter. 44 ÷ 2 = 22 cm.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
The radius runs from center to edge. The diameter crosses the center from edge to edge.
A19
An angle measures 78°. Is it acute, right, or obtuse? (2 points)
Reveal explanation
Answer: acute
Compare 78° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
Angle of 78 degrees; angle size depends on rotation, not ray length.
A20
An angle measures 165°. Is it acute, right, or obtuse? (2 points)
Reveal explanation
Answer: obtuse
Compare 165° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
Angle of 165 degrees; angle size depends on rotation, not ray length.
A21
A student answers the following question with “10 cm”. Explain whether the answer is correct, then solve the question and justify your answer. Original question: A circle has diameter 18 cm. What is its radius? (3 points)
Reveal explanation
Answer: 9 cm
The suggested answer is not correct. The radius is half the diameter. 18 ÷ 2 = 9 cm.
Scoring: 1 point for identifying the given answer as incorrect; 1 for explaining the error; 1 for giving the corrected solution and appropriate units.
The radius runs from center to edge. The diameter crosses the center from edge to edge.
A22
A circle has radius 24 cm. What is its diameter? (2 points)
Reveal explanation
Answer: 48 cm
A diameter joins two radii end to end through the center: 24 + 24 = 48 cm.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
The radius runs from center to edge. The diameter crosses the center from edge to edge.
A23
An angle is 60°. A student calls it obtuse because the rays look long. Explain the error. (3 points)
Reveal explanation
Answer: Acute
60° is below 90°, so the angle is acute; ray length is irrelevant.
Scoring: 1 point for the correct claim; 1 for a mathematical justification; 1 for a clear diagram, example, or relevant calculation when applicable.
A24
Two circles have diameters 10 cm and 12 cm. Which has the larger radius and by how much? (3 points)
Reveal explanation
Answer: Second circle, by 1 cm
Their radii are 5 cm and 6 cm; changing diameter by 2 cm changes radius by 1 cm.
Scoring: 1 point for the correct claim; 1 for a mathematical justification; 1 for a clear diagram, example, or relevant calculation when applicable.

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