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The midterm 1 exam for math 100-d200, taught by r. Pyke, at simon fraser university, held on october 3, 2007. The exam covers various topics in mathematics, including solving inequalities, finding points on circles, determining symmetry and intercepts of equations, finding limits, and graphing functions. Students are required to clearly explain their answers and only scientific calculators are allowed.
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Question Score Max 1 5 2 5 3 5 4 6 5 8 6 5 7 5 8 15 Total 54
(1) [Marks: 5] Solve the following inequality. Express your answer in interval notation. ∣∣∣ ∣^4 xx −+ 1 1
∣∣∣ ∣ >^2
(4) [Marks: 6] Determine whether the graphs of the following equations possess symmetry with respect to the x-axis, y-axis, or origin, and find any x and y intercepts.
(5) [Marks: 8] Find the following limits by simplifying the expression first.
(6) [Marks:5] Find the domain of the following function.
(c) Make a sketch of the graph.
(d) Find the points of intersection between this parabola and the line y = 3x − 3.
(e) From this, sketch the region in the xy-plane of the points (x, y) that satisfy the inequalities 3 x − 3 ≤ y ≤ − 3 x^2 + 24x − 36