Monthly Archives: October 2014

Measure of Angle

Let be a rectangle with , and let be an equilateral triangle. and intersecting (not the extension of ) at and , respectively. If is the midpoint of , how many degrees are in angle ? Source: NCTM Mathematics Teacher … Continue reading

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Series 1/5+1/25+2/125+3/625+…

Compute , where each numerator after the second is the sum of the two preceding numerators and each denominator is times the preceding one. Source: NCTM Mathematics Teacher 2006 SOLUTION Subtract from Solving for Answer:

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Miscopied Quadratic Equation

Two students attempted to solve a quadratic equation . Although both students did the work correctly, one miscopied the middle term and obtained the solution set , while the other miscopied the constant term and obtained a solution set . … Continue reading

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Sum of Odd Numbers

Suppose the odd numbers are grouped in the following way: What is the sum of the numbers in the tenth grouping? Source: NCTM Mathematics Teacher 2006 SOLUTION Brute force method It doesn’t take long to write out the consecutive odd numbers … Continue reading

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Cutting Pizza

What is the largest number of pieces into which a circular pizza can be cut with straight cuts? Source: NCTM Mathematics Teacher 2006 SOLUTION Please refer to post “Regions in the Plane” posted 1/5/2012. Answer:

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Volume of Octahedron

An octahedron is formed by connecting the centers of the faces of a cube. What is the ratio of the volume of the cube to that of the contained octahedron? Source: NCTM Mathematics Teacher 2006 SOLUTION Suppose the cube side … Continue reading

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Positive Base b

In what positive base does the equation for multiplication of base hold? Source: NCTM Mathematics Teacher 2006 SOLUTION In base the multiplication means In positive base the multiplication means Simplify or Positive base Verification Answer:

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Rearrange 3053354

What is the number of different 7-digit numbers that can be made by rearranging the digits of ? Source: NCTM Mathematics Teacher 2006 SOLUTION We try a smaller problem to gain understanding. How many different 3-digits numbers can we make … Continue reading

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Leg of Isosceles Triangle

The length of each leg of an isosceles triangle is , and the length of the base is . Determine all possible real values of . Source: NCTM Mathematics Teacher 2006 SOLUTION For  to be a triangle (Triangle Inequality Theorem) … Continue reading

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44 or 45 Diagonals

What is the number of sides of a regular polygon for which the number of diagonals is or ? Source: NCTM Mathematics Teacher 2006 SOLUTION The number of diagonals of a convex polygon of vertices (or sides) is given by … Continue reading

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