22M:001 Basic Algebra I - Final Exam
1. Find an equation for the line passing through the point (1, 2) and perpendicular to the line with equation:
2x + 3y = 1
2. Solve for B: A = 
(B + b)h.
3. Solve the system: x + y = 3 and -3x + y = 1
4. Subtract and leave in lowest terms: 
.
5. Solve the equation 2x2 + 6x = 10.
6. The longer leg of a right triangle is two meters longer than twice the short leg. The hypotenuse is two meters less than three times the short leg. Find the lengths of all three sides of the triangle.
7. Factor as completely as possible: 8x2y – 14xy3 + 6y5.
8. Simplify by writing as a rational expression and canceling common factors: 
.
9. Express as a single power of m the expression 
.
10. Solve the equation (if possible) = 
.
11. Multiply and combine like terms: (x3 + 1)(x6 – x3 + 1).
12. Solve 2x2 + 6x < -4 and graph the solution set.
13. For what values of k does the equation 2x2 + 3x + k = 0 have no real solution?
14. A 60% solution of salt is to be mixed with an 80% solution of salt to get 40 liters of a 65% solution of salt. How many liters of each solution should be used?
15. Graph y – 1 = 2x2 – 4x.