**Question 1. **What is the graph of 3x^{2} + y^{2} = 18? What are its lines of symmetry? What are the domain and range?

**Question 2.** Prove that for all integers n > 10,

n - 2 < n^{2} - n/12

**Question 3.** Solve the equation sin (Π/4 - x) - sin (x + Π/4) = 1 for 0 ≤ x ≤ 2Π. Explain each step and substantiate your conclusions.

**Question 4.** The office needs cabinets. The price for the first type of cabinet is $10, it needs 6 ft^{2} of floor space, and it has a storage volume of 8 ft^{3}. The price for the second type of cabinet is $20, it needs 8 ft^{2} of floor space, and it has a storage volume of 12 ft^{3}. The company wants to spend no more than $140 and the office can hold up to 72 ft^{2} of cabinets. How can the storage volume be maximized?

**Question 5. **Prove that 5 +8+ 11 + ..... + (3n + 2) = n(3n + 7)/2 is valid for every positive integer n. Explain each step.

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