MAT 1033 FINAL WORKSHOP REVIEW

SECTION 1.1: SETS OF NUMBERS AND INTERVAL NOTATION

1. Let and . Graph the set and the set
and express the answers for both in interval notation and set builder notation.

Graph for: Interval Notation: Set Builder Notation:

Graph for : Interval Notation: Set Builder Notation:

SECTION 2.1: LINEAR EQUATIONS IN TWO VARIABLES

2. Graph . State the x-intercept and the y-intercept.

x-intercept:

y-intercept:

CTION 2.2: SLOPE OF A LINE

3. Two points for each of two lines are given. Determine if the lines are parallel,
perpendicular, or neither.

L1: 4, -6 and 3, -2

L2: 3, -1 and 7,0

SECTION 2.3: EQUATIONS OF A LINE

4. Write the equation of the line that contains the point 0, -3 and is parallel to the line

Equation:

SECTION 4.2: INTRODUCTION TO FUNCTIONS

5. Let . Find h(2) .

SECTION 3.1: SOLVING SYSTEMS OF EQUATIONS BY THE GRAPHING METHOD

6. Solve the system of equations by using the graphing method.

Solution:

SECTION 3.2: SOLVING SYSTEMS OF EQUATIONS BY THE SUBSTITUTION METHOD

7. Solve the system of equations by using the substitution method.

Solution:

SECTION 3.3: SOLVING SYSTEMS OF EQUATIONS BY USING THE ADDITION METHOD

8. Solve the system of equations by using the addition method.

Solution:

SECTION 3.4: APPLICATIONS OF SYSTEMS OF EQUATIONS IN TWO VARIABLES

9. A school carnival sold tickets to ride on a Ferris Wheel. The charge was $1.50 per adult
and $1.00 per student. If 54 tickets were sold for a total of $70.50, how many of each
type of ticket were sold?

Number of adult tickets:

Number of student tickets:

SECTION 4.3: DIVISION OF POLYNOMIALS
10. Divide the polynomial using long division:

Answer:

SECTION 4.5: FACTORING TRINOMIALS

11. Factor:

Answer:

SECTION 4.6: FACTORING BINOMIALS

12. Factor:

Answer:

SECTION 4.8: SOLVING EQUATIONS BY USING THE ZERO PRODUCT RULE

13. Solve:

SECTION 5.1: RATIONAL EXPRESSIONS AND RATIONAL EQUATIONS

14. Simplify:

Answer:

SECTION 5.2: MULTIPLICATION AND DIVISION OF RATIONAL EXPRESSIONS

15. Multiply:

Answer:

SECTION 5.3: ADDITION AND SUBTRACTION OF RATIONAL EXPRESSIONS
16. Add or subtract as indicated:

Answer:

SECTION 5.4: COMPLEX FRACTIONS
17. Simplify:

Answer:

SECTION 5.5: SOLVING RATIONAL EQUATIONS

18. Solve:

SECTION 5.6: APPLICATIONS OF RATIONAL EQUATIONS AND PROPORTIONS

19. Solve:

SECTION 6.1: DEFINITION OF AN nTH ROOT

20. Simplify the following expression. Assume all variables are positive real numbers:

Answer:

SECTION 6.2: RATIONAL EXPONENTS

21. Simplify the expression by using the properties of rational exponents. Write the final
answer using positive exponents only. Assume all variables are positive real numbers:

Answer:

SECTION 6.3: SIMPLIFYING RADICAL EXPRESSIONS

22. Simplify. Assume all variables are positive real numbers:

Answer:

SECTION 6.4: ADDITION AND SUBTRACTION OF RADICALS

23. Simplify. Assume all variables are positive real numbers:

Answer:

SECTION 6.5: MULTIPLICATION OF RADICALS

24. Multiply and simplify. Assume all variables are positive real numbers:

Answer:

SECTION 6.6: DIVISION OF RADICALS AND RATIONALIZATION

25. Rationalize the denominator:

Answer:

SECTION 6.8: COMPLEX NUMBERS

26. Divide the complex numbers. Write the answer in the form

Answer:

SECTION 7.1: SQUARE ROOT PROPERTY
27. Solve the equation by using the square root property:

SECTION 8.1: COMPOUND INEQUALITIES

28. Solve the inequality and graph the solution. Write the answer in interval notation:
or

Graph:

Interval Notation:

SECTION 8.3: ABSOLUTE VALUE EQUATIONS

29. Solve:

SECTION 8.5: LINEAR INEQUALITIES IN TWO VARIABLES

30. Graph the solution set: and