## Varsity Ciphering 2007

**Round 1**

1. Find the distance from R(6, -4) to the line with the equation y = 12.

2. Solve 2cos^{2}x+cosx=1 for 0 ≤ x < 2π.

3. Shown in the figure is a right triangle ABC with line segments with the
indicated measures. Find the value of x . Express the answer as a reduced
fraction.

4. If 100×19.98×1.998×1000=x^{2} find x for x > 0.

5. The length of one side of an equilateral triangle is 4 centimeters. Find the
length of an altitude of the triangle.

6. Simplify the following : (x^{-1}+y^{-1)}/(x^{-1}−y^{-1)}. Leave no negative exponents nor
complex fractions.

7. State the period of y=1/2 tan 8x.

8. If @ is defined for all positive numbers a and b by
a@b = 5−2ab−b^{2} find 5 @ 2.

**Round 2**

1. Find the value of “k” so that the slope of the line through the points (5, k)
and (9, 4) is 3/2.

2. Solve 2sinx+1=0 on the interval [0,2π).

3.Shown in the figure are similar trapezoids ABCD and EBFG with line segment
measures as indicated. Find the measure of AD.

4. An island has no currency, instead it has the following
exchange rate:

50 bananas = 20 coconuts

30 coconuts = 12 fish

100 fish = 1 hammock

How many bananas equal 1 hammock?

5. In the triangle shown with the indicated measures find the value of z .

6. Solve the following : .

7. Starting from the origin and for x ≥ 0 in radians what are the coordinates of
first occurrence of the maximum point of the graph of ? y=−2cos2x

8. The spinner shown is a circle subdivided into sectors with central angles as
shown. Find the probability that the spinner will land on “lose a turn”.

**Varsity Ciphering 2007 Answers**

Round 1

Round 2