Grade 12 Geometric Mean Worksheet

This worksheet focuses on understanding and calculating the geometric mean in various mathematical contexts, including right triangles and sequences, suitable for Grade 12 students.

Grade 12 Math GeometryGeometric Mean

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Includes

2 Short AnswerFill in the BlanksMultiple ChoiceCustomTrue / False

Standards

CCSS.MATH.CONTENT.HSG.SRT.B.5CCSS.MATH.CONTENT.HSG.SRT.C.7CCSS.MATH.CONTENT.HSA.SSE.A.1.B

Topics

Geometric MeanGeometryAlgebraGrade 12Mathematics

8 sections · Free to use · Printable

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Geometric Mean Exploration

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Read each question carefully and provide the best answer. Show all your work for full credit.

1. Define the geometric mean of two positive numbers, 'a' and 'b'. How does it differ from the arithmetic mean?

2. The geometric mean of 4 and 9 is .

3. If the geometric mean of two numbers is 10 and one of the numbers is 5, the other number is .

4. In a right triangle, the altitude drawn to the hypotenuse divides the hypotenuse into two segments. The length of the altitude is the geometric mean of the lengths of these two segments. If the segments are 3 cm and 12 cm, what is the length of the altitude?

4 cm

6 cm

7.5 cm

9 cm

5. Consider a right triangle ABC with the right angle at B. An altitude BD is drawn to the hypotenuse AC. If AD = 2 and DC = 8, find the length of BD. Sketch the triangle and label the given lengths.

6. The geometric mean of any set of positive numbers is always less than or equal to their arithmetic mean.

True

False

7. A stock's value increased by 10% in the first year and 20% in the second year. What is the average annual growth rate (geometric mean)?