Math Guided Self Placement

You should choose a placement of MATH 0005 if most of the following statements describe you:

• I rely on a calculator to add, subtract, multiply, and divide whole numbers and decimals.
• I forgot (or never really learned) how to add, subtract, multiply, and divide fractions.
• I’m not sure how to solve problems involving proportions and percents.
• I have difficulty understanding what I need to do to solve a word problem.
• I have never really liked math.
• Math has always a been a struggle for me and I think I will need a lot of extra support.
• I am motivated and able to spend 10 or more hours each week on this math class outside of class time.

This class is designed to prepare you for Math 0070, 75 and 1001. The emphasis is on order of operations, integers, polynomials, and solving equations.

You should choose a placement of MATH 0006 if most of the following statements describe you:

1. I know how to add, subtract, multiply, and divide whole numbers and decimals without a calculator. Sample problems:
   • $439.1 + 56.89 + 17 + 2.768$
   • $53.2 – 17.908$
   • $14.325 \times 0.12$
   • $25.172 \div 0.14$
2. I know how to add, subtract, multiply, and divide fractions and mixed numbers. Sample problems:
   • $3\frac{4}{5} + 8\frac{2}{3}$
   • $13\frac{4}{9} - 7\frac{5}{6}$
   • $2\frac{2}{3} \times 4\frac{1}{5}$
   • $6\frac{4}{7} \div \frac{8}{21}$
3. I feel comfortable solving problems involving proportions and percents without a calculator. Sample problems:

    

   • $\frac{8}{14} = \frac{?}{35}$
   • What is 43% of 900?
   • 105 is 84% of what number?
   • What percent of \$80 is \$65?
4. I am motivated and able to spend 10 or more hours each week on this math class outside of class time.

If you agree with or can answer 8 of the following questions without the use of a calculator, then this should be an appropriate placement.

1. I took 3 or more years of math classes in high school
2. I am willing and able to spend 12 or more hours each week on this math class outside of class time
3. I have taken an algebra OR geometry OR trigonometry class and got a B- or better
4. Reduce $\frac{30}{54}$ to simplest form
5. Write 0.025 as a fraction in simplest form.
6. Rewrite $4\frac{5}{8}$ as an improper fraction.
7.  Rewrite 0.34 as a percent.
8. Multiply the following fractions.  Write answer in simplest form.
   
   $\frac{3}{8} X \frac{4}{15}$
9. Subtract the following fractions:
   
   $\frac{5}{7} - \frac{3}{5}$
    
10. Add the following mixed numbers:
     
    $4\frac{1}{5} + 3\frac{1}{6}$
     
11. Solve for x in the equation $2x + 6 = 7$
     
12. Evaluate the expression $-4x - y$ for $x =3$ and $y = -8$

Math 0070 Learning Outcomes (Prerequisite course to Math 0080)

1. Simplify arithmetic, polynomial and radical expressions
2. Factor polynomial expressions
3. Solve and apply linear equations in one variable
4. Solve linear inequalities in one variable
5. Solve and apply quadratic equations in one variable
6. Graph and apply linear and quadratic functions in 2 variables

If you are familiar with and able to answer at least 7 of the following questions, then this should be an appropriate placement.

1. Simplify
   
   $9\sqrt{45}$
    
2. Simplify
   
   $\frac{(3x-6)}{3}$
    
3. Factor Completely
   
   $2x^2 - 6x - 20$
    
4. Solve
   
   $4(2x - 5) = 2$
    
5. Solve
   
   $\frac{1}{2}(8x - 4) = 6x + 3$
    
6. Solve
   
   $x^2 - 3x - 10 = 0$
    
7. Solve for r
   
   $A=2(r + p)$
    
8. Solve and graph the solution on a number line
   
   $-3x + 5 > 26$
    
9. Given that the function $y = 2(x - 1)^2$ represents the area of sand in a double sandbox, were x = length and a side of the one box including the border of the box. Find the total Area of the sand if $x = 6 ft$
    
10. Graph the linear equation $y = -\frac{1}{2}x + 5$

Math 0080 Learning Outcomes (Prerequisite course to Math 1110)

1. Work with interval, inequality, graphical and functional notation.
2. Solve compound, absolute value, polynomial inequalities; and linear, radical, rational, literal, exponential and logarithmic equation
3. Simplify and perform operations on polynomials, rational expressions and simplify expressions with rational exponents
4. Perform operations with complex numbers
5. Solve systems of linear equations
6. Manipulate and graph linear, polynomial, exponential and logarithmic functions

If you are familiar with and able to answer at least 7 of the following questions, then this should be an appropriate placement.

1. Simplify
   
   $9\sqrt{45} + 4\sqrt{5} - 7\sqrt{20}$
    
2. Simplify
   
   $\frac{(3x - 6)}{3}$
    
3. Factor completely
   
   $2x^3 - 6x^2 - 20x$ 
    
4. Solve
   
   $\frac{4(2x - 5)}{-3} = 2$
    
5. Solve
   
   $\frac{3}{4}(8x - 4) = 6x + 3$
    
6. Solve
   
   $-3x^2 - 15x + 18 = 0$
    
7. Solve the system equations
   
   $\left\{\begin{array}{c}x -3y = 3\\3x + 5y = -19\end{array}\right.$
    
8. Solve for r
   
   $A = 2r + p$
    
9. Solve and graph the solution on a number line
   
   $3x + 5 > 5x + 25$
    
10. Given that the function $y = -\frac{1}{2}x + 10$ represents thousands of people recovered from a mild burn, where x = days since the burn occurred, a) graph it and b) interpret its slope and y-intercept.

Math 1119 Learning Outcomes (prerequisite to Math 1120)

1. Demonstrate mastery of polynomial functions
2. Demonstrate mastery of rational functions
3. Demonstrate mastery of exponential and logarithmic functions
4. Demonstrate mastery of solving systems using matrices.

If you are familiar with and able to answer at least 7 of the following questions, then this should be an appropriate placement.

1. Find the domain of the function
   
   $\pmb{f}(x) = \frac{\sqrt{x}}{x^2 - 4}$
    
2. Find all real zeros of the following function. Then use the zeros to factor
   
   $\pmb{f}$ over the real numbers. $\pmb{f}(x) = x^3 - 2x^2 - 5x + 6$
    
3. Determine whether the function is even, odd or neither:
   
   $\pmb{f}(x) = 2x - \sqrt{x^2}$, where $\pmb{x}$ is any real number.
4. Solve the exponential equation:
   
   $2^{2x -1} = 4$
    
5. Solve the logarithmic equation:
   
   $\pmb{log}_3(3x - 1) = 2$
    
6. Graph the quadratic function:
   
   $\pmb{f}(x) = (x + 2)^2 - 2$
7. Graph the polynomial function and label intercepts:
   
   $\pmb{f}(x) = (x - 1)^2(x + 4)$
    
8. Graph the piecewise function:
   
   $\pmb{f}x = \left\{\begin{array}{c} -2x + 3  \,\,\pmb{if} \,\,x < 1\\3x - 2 \,\,\pmb{if}\,x\ge 1\end{array}\right\}$
    
9. For $\pmb{f}(x) = 3x^2 - 2x + 4$, find the difference quotient $\frac{\pmb{f}(x + h) -\pmb{f}(x)}{h}$ in simplified form.
    
10. Solve the following system of equations using matrices:
    
    $\left\{\begin{array}{c}2x + y = -4\\4z- 2y = 0\\3x - 2z + -11\end{array}\right\}$

Learning Outcomes for both Math 1119 and Math 1120 should be mastered for placement of Math 1180. 

MATH 1119 Learning Outcomes (prerequisite to MATH 1120)

1. Demonstrate mastery of polynomial functions
2. Demonstrate mastery of rational functions
3. Demonstrate mastery of exponential and logarithmic functions
4. Demonstrate mastery of solving systems using matrices

Math 1120 Learning Outcomes (prerequisite to Math 1180)

1. Summarize the limit concept
2. Summarize the definition and common applications of the derivative
3. Find derivatives of all basic function types
4. Solve applications involving derivatives
5. Summarize the definition and common applications of the integral
6. Evaluate basic integrals 

If you are familiar with and able to answer at least seven of the following questions, then MATH1180 should be an appropriate placement.

1. State the domain and range of the following functions:
   1. $\pmb{f}(x) =x^2 + 1$
   2. $\pmb{f}(x) =\pmb{cos}(x)$
   3. $\pmb{f}(x) =\frac{1}{x^2}$
   4. $\pmb{f}(x) =\pmb{tan}^{-1}x$
   5. $\pmb{f}(x) =\pmb{e}^{-x}$
   6. $\pmb{f}(x) =\pmb{In}(x + 1)$
2. Determine whether the functions below are even, odd or neither:
   1. $\pmb{f}(x) =x^2 + 1$
   2. $\pmb{f}(x) =\pmb{cos}(x)$
   3. $\pmb{f}(x) =\frac{1}{x^2}$
   4. $\pmb{f}(x) =\pmb{tan}^{-1}x$
   5. $\pmb{f}(x) =\pmb{e}^{-x}$
   6. $\pmb{f}(x) =\pmb{In}(x + 1)$
3. Solve:
   1. $12x^3 - 12x^2 - 24x = 0$
   2. $2xe^{-3x} - 3x^{2} e^{-3x} = 0$
   3. $\frac{1}{3}x^{-\frac{2}{3}} -\frac{2}{3}x^{-\frac{4}{3}} = 0$
4. Solve for z: $3x^2 + 3y^2z =6xz + 6y$
5. Write as sums and/or differences of multiples of logs so that no log contains exponents or radicals:
   
   $\pmb{In}\biggl(\frac{5x^2\sqrt[3]{1 - x}}{4(x + 1)^2}\biggr)$
    
6. Graph
   
   $\pmb{f}(x) = \left\{\begin{array}{c}x \quad-5\le x < 0\\ 3\quad x = 0\\ \frac{1}{2}x\quad > 0\end{array}\right.$
    
7. Graph the region bounded by the given curves
   1. $y = sin(x), y = cos(x), x = 0, x =\frac{\pi}{2}$
   2. $y = 2x - x^2, y = x^2$
   3. $y = e^{-x}, x = 1, x = 2$
       
8. A rectangular garden is to be fenced off and divided in two by another fence parallel to one side of the garden.  Four hundred feet of fencing is used.  Find the dimension of the garden that will maximize the total enclosed area. What is the maximum area?
    
9. Find the exact value without a calculator of
   1. $\pmb{cos}\Bigl(\frac{-\pi}{6}\Bigr)$
   2. $\pmb{tan}\Bigl(\frac{-2\pi}{3}\Bigr)$
   3. $\pmb{sin}\Bigl(\frac{7\pi}{4}\Bigr)$
       
10. Solve: $1 + 2\pmb{cos}(x) < 0; \quad 0 \le x < 2\pi$