SampleTest

# SampleTest - 14) Find all values of x such that cos 2 x-cos...

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Sample Readiness Test 1) Find all the real roots of the equation: 4 x 4 + 15 x 2 - 4 = 0. 2) Solve: | 2 x + 1 | = x + 3. 3) Simplify: x 3 - 3 x 2 + 2 x x 4 - 8 x . 4) Find the equation of the form y = mx + b of the line through the points (2 , 3) and the midpoint of the line segment joining ( - 1 , 4) and (3 , 2). 5) Calculate the coordinates of the point(s) where the line through the point ( - 1 , 2) with slope 1 / 2 intersects the circle with centre the origin and radius 5. 6) Find all values of k so that 4 kx 2 + 3 x + k = 0 has two distinct real roots. 7) Solve: 4 7 x = 32 3 x - 1 . 8) Solve: log 4 ( x + 4) - 2 log 4 ( x + 1) = 1 2 for x > 0. 9) Solve: e 3 x - 2 = 4. 10) Express x in terms of the other variables in the diagram below: ± t - Y x j H H H H H H H H H H H H H H H h r 11) Given triangle ABC with B = 120 and AB = 5 and BC = 12, ﬁnd the length of AC . 1

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12) Find the perimeter of the region bounded by the lines y = ± 3 x and the circle ( x - 5) 2 + y 2 = 25 shown by the solid line below: 6 - s s ± ± ± ± ± ± ± J J J J J J J . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........ ........ ........ ........ ........ ........ ........ ........ ........ ... . .. . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. .. s s y x y = 3 x y = - 3 x ( x - 5) 2 + y 2 = 25 13) Sketch the curve y = 2 x 2 - 4 x + 3 and label the vertex and intercepts.
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Unformatted text preview: 14) Find all values of x such that cos 2 x-cos x = sin 2 x , where 0 ≤ x ≤ 2 π . 15) A wire 36 cm in length is cut into two parts, one of which has length x . The piece of length x is formed into a circle, and the other piece is formed into a square. Find a function that expresses the total area A ( x ) enclosed by the circle and the square. 2 ANSWERS 1) x = ± 1 2 2) x = 2 ,-4 3 3) x-1 x 2 + 2 x + 4 4) y = 3 5) (3 , 4) and (-5 , 0) 6)-3 4 < k < 3 4 ,k 6 = 0 7) x = 5 8) x = 1 2 9) x = 2 + ln 4 3 10) x = rt √ r 2-h 2 11) √ 229 12) 10 + 20 π 3 13) 6 y-x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . r (1,1) r 3 14) x = 0 , 2 π 3 , 4 π 3 , 2 π 15) A ( x ) = ± 9-x 4 ² 2 + x 2 4 π where 0 < x < 36 3...
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## This note was uploaded on 10/24/2009 for the course MATH 135 taught by Professor Andrewchilds during the Winter '08 term at Waterloo.

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SampleTest - 14) Find all values of x such that cos 2 x-cos...

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