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Mat 161 Test 1 Review Problems

1. a. Solve 2x3 – x2 – 3x = 0

b. Solve x4 – 13x2 + 36 = 0

c. Solve 3x2 – 6x – 5 = 0

d. Approximate the solutions to the equation in part c.

2. Solve the equation. [pic].

Be careful to check for any extraneous roots.

3. Solve each equation. Be careful to check for any extraneous roots.

a. [pic] = -2

b. [pic]

c. 2 - [pic] = 6

d. [pic]

4. Solve each of the following and write the solutions to the problems in parts c, d, and e in interval notation.

a. [pic] = 5

b. [pic] = x – 1

c. 8 – 4x > 2

d. [pic] [pic] 6

e. -3 [pic] 1 - x < 5

5. Given w = 6 + 4i and z = 2 – 3i.

a. Find [pic].

b. Find z – w.

c. Find u = [pic] and find Re(u) and Im(u).

d. Find i377.

6. Solve for the indicated variable.

a. S = 2[pic]r2 + 2[pic]rh (for h)

This is the formula for the Surface Area of a right Circular Cylinder.

b. [pic] = [pic] + [pic] (for [pic])

This is the formula that will find the total resistance in a circuit when resistors are in parallel.

7. Uniform Motion Problem (Distance-Rate-Time Problem)

Two trains are 495 miles apart from each other. At noon the two trains start traveling towards each other with the faster train traveling 15 mph faster than the other train. How fast is each train traveling if they meet each other at 3 pm sharp?

8. Mixture Problem

How much pure Hydrosulfuric Acid (H2SO4) should be mixed with 12 liters of a 20% Hydrosulfuric Acid solution to obtain a 40% Hydrosulfuric Acid solution.

9. Sales/Discount/Mark-up Problem

During a sale a hardware store discounts its leaf blowers by 15%. If leaf blower is on sale for $127.50, then what was the original price of the leaf blower?