SAT Question of the Day – Find the Area of the Square

September 15, 2014

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In the figure below Triangle ABC is a right triangle with angle B = 900. Each of the sides AB = BC = 6 units. Find the area of the red square   Hint: Use the concept of similar triangles to solve the problem Click for solution to Question of Day – Sep 15th solution

SAT Question of the Day – Find the Area of the Shaded Region

September 12, 2014

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In the figure below, ABCD is a square with sides 20 units. The four shaded leaves are formed by circles whose diameter is 20 units. Find the area of the 4 shaded leaves? Click for solution to SAT Question of Day

Binomial Theorem – Additional Practice Examples

September 8, 2014

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Problem 1: The second, third and fourth terms in the expansion (x+a)n are 240, 720 and 1080 respectively. Find the values of x, a and n Problem 2: The sum of coefficients of the first three terms in the expansion below is 559.  Also x  ≠ 0 and m is a natural number. Find the term containing […]

Binomial Theorem – Practice Examples

September 4, 2014

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1. Expand (1-2x)5 using the binomial theorem 2. Find the coefficient of x5 in the expansion (x+3)8 Things to Remember:  Binomial Theorem: (r+1)th Term in the Expansion: Combination Formula:    Click for solution to Problem 1 and 2

Prove Cos π/7 – Cos 2π/7 + Cos 3π/7 = 1/2

August 28, 2014

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Prove the following Trigonometric identity:   Cos π/7 – Cos 2π/7 + Cos 3π/7 = 1/2 Hint: Use the various trigonometric identities including the product to sum formulas Trigonometric Identities – Problem 1

Trigonometric Equations – Double and Half Angles

August 25, 2014

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Solve the following Trigonometric equations using double and half angle formulas 1. Find the principle solutions for cos 2x + 2 sin x = 0 2. Find the principle solutions for sin2x = cos2(x/2) Things to Remember: Sum and Difference Forumlas: 1. Sin(X+Y) = SinX CosY + CosX Sin Y 2. Sin(X-Y) = SinX CosY – […]

Permutation and Combination Problems

August 16, 2014

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Solve the following problems: Problem 1: Given a deck of standard cards with 52 cards, find the following: How many ways can you draw 3 cards out of the 52 cards How many ways will the three cards be all aces? How many ways will the three cards be anything but aces? How many ways […]

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