Monthly Archives: September 2015

Product of Tangents

What is the value of the following product? Source: NCTM Mathematics Teacher, November 2006 SOLUTION Similarly, The product of tangents equals . Answer: Alternative solution Apply the formula to our product The product of tangents equals . Advertisements

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Absolute Value

How many different real-valued pairs satisfy this system of two equations? Source: NCTM Mathematics Teacher, November 2006 SOLUTION Suppose Substitute the value of into Eq. or We have two pairs and . Suppose Substitute the value of into Eq. or … Continue reading

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Altitude

In triangle , and . If is a point on such that is perpendicular to , what is ? Source: NCTM Mathematics Teacher, November 2006 SOLUTION Area of triangle by Heron’s formula Area of triangle Area of triangle using base … Continue reading

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Parallelogram

is a parallelogram with , and . If the area of the parallelogram is , what is the value of ? Source: NCTM Mathematics Teacher, November 2006 SOLUTION Draw a perpendicular to . If the x-coordinate of equals , its … Continue reading

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Sine and Cosine

Suppose the roots of the quadratic equation are and . What is the value of ? Source: NCTM Mathematics Teacher, November 2006 SOLUTION If and are roots of the quadratic equation, Develop the product Compare the terms of the above … Continue reading

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Square Root Function

How many positive real numbers are solutions to ? Source: NCTM Mathematics Teacher, November 2006 SOLUTION The graphs of the two functions and show two intersection points There are two solutions to . Answer:

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Log Base 2

What is the value of Source: NCTM Mathematics Teacher, November 2006 SOLUTION We change all the different bases to base Answer:

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Passing Tests

A group of boys and girls took a test. Exactly of the boys and exactly of the girls passed the test. If an equal number of boys and girls passed the test, what fraction of the entire group passed? Source: … Continue reading

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Ratio of Sectors

In the figure, and are sectors of two concentric circles centered at . The length of is one-third the length of . What is the ratio of the area of the region to the area of the sector ? Source: … Continue reading

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