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Department of Mathematics
MATH 100, PRECALCULUS MIDTERM 2
Wednesday March 15, 2006 11.30 – 12.
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INSTRUCTIONS
- Do NOT open this booklet until permission is given.
- Calculators are NOT permitted.
- Please formulate and motivate your answers. Well-phrased and complete explanations are more important than just an answer. It should be clear how you obtained your answer.
- If the space provided for the answer is insufficient, please use the back side of the PREVIOUS page. Clearly mark which question you are answering in that case.
- If a question is unclear or appears to contain an error, please ask for clarification.
- The maximum mark for this exam is 40. In front of each question, the maximal mark for that question is given.
- This exam consists of 9 PAGES (including this one), and contains one double-sided GREEN formula sheet.
- Any notes you make on the formula sheet are NOT considered to be part of your exam.
1. QUESTION
In this question we let f be the quadratic function
f (x) = x^2 + 6x − 10.
[4] (a) Compute the vertex of the graph of f.
ANSWER
[2] (b) What is the axis of symmetry of this parabola?
3. QUESTION
In this question we take f (x) =
x^2 − 4 x^2 + 2x
[3] (a) Factor the numerator and the denominator of f and simplify f.
ANSWER
[2] (b) Give the domain of f in set notation. Indicate why this is the domain.
ANSWER
[1] (c) Find the zero(es) of f.
[2] (d) Compute f (−3), f (−1), f (1) and f (3).
ANSWER
[2] (e) Write the solution set of the inequality (^) xx (^22) +2−^4 x ≥ 0 in interval notation.(Hint: you might want to use a number line.)
5. QUESTION
In this question all angles are in radians.
[2] (a) Compute the period of y = cos(2x).
ANSWER
[4] (b) What is the phase shift of y = cos(2x + π)?
[4] (c) Graph y = cos(2x + π) + 3 for 0 ≤ x ≤ 2 π, by successively graphing y = cos(x), y = cos(2x), y = cos(2x + π) and y = cos(2x + π) + 3 on the axes below. Do not forget to put scales on the axes. Make sure that the minima, maxima, and zeroes of cos(x), are clearly visible. Label your graphs clearly.
