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Aaron S.

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Trigonometry

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Question:

sinx = 1/2. Write 3 possible values of x.

Aaron S.

Answer:

Using a calculator, arcsin 1/2 = 30, so x= 30 Using the symmetry of sine curve, there is another value between 0 and 180. 180 - 30 = 150, so x=150. Finally, as the sine curve has a period of 360, this means we can add 360 to any of our previous solutions for another one. 30 + 360 = 390. so x=390

Geometry

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Question:

The angles of a quadrilateral taken in order are x, 5x, 2x and 4x. Which of the following is the quadrilateral: a) kite b) parallelogram c) rhombus d) arrowhead e) trapezium

Aaron S.

Answer:

We can deduce from the question that all the angles are different in this quadrilateral. So we can rule a) b) and c) then. A Kite has 1 pair of equal angles, and a rhombus and parallelogram have 2 pairs of equal angles. As the sum of the interior angles of quadrilateral are 360 degrees, we can set up the equation: x + 5x + 2x + 4x = 360 12x = 360 x = 30 If x = 30, then the largest angle 5x is 150. As an arrowhead must have an angle greater than 180 degrees, the answer but be e) trapezium

Algebra

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Question:

The ratio of John's age to Bill's age is 1:2. In 12 years, the ratio of their ages will be 3:5. Calculate their ages.

Aaron S.

Answer:

J:B in 12 years: x:2x x+12:2x+12 = 3:5 (x+12)/3 = (2x+12)/5 5(x+12) = 3(2x+12) 5x+60 = 6x+36 x = 24 John is 24, Bill is 48

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