# Available Skills for Quantitative Foundations

Institutions can select the skills to be included in the students’ assessment.  Students are only tested on selected skills.  Quantiative  Foundations consists of one or more questions to assess each skill and instructional web pages to teach and review each skill.

## Calculation:

1. Calculate a number raised to an integer power
2. Calculate a0
3. Calculate a number raised to a rational number power
4. Apply standard order of operations
5. Calculate factorial of a whole number
6. Calculate |a| of a number
7. Understand summation notation
8. Understand scientific notation on a calculator
9. Understand f(x) notation
10. Understand g(f(x)) notation
11. Understand case-defined function

## Algebra:

1. Different ways of writing multiplication
2. Different ways of writing division
3. Apply distributive property
4. Apply associate property
5. Solve a linear equation (numerical answer)
6. Solve a linear equation (answer is expression)
7. Combine terms in an expression (add or multiply)
8. Simplify an expression involving division
9. Apply a/(b/c) = (ac)/b
10. Apply a/sqrt(b) = (a)sqrt(b)/b
11. Express a simple word problem as a linear equation
12. Express a word problem involving rates as a linear equation
13. Solve two simultaneous linear equations (numerical answer)
14. Multiply two polynomial expressions
15. Solve two simultaneous nonlinear equations
16. Interpret inequality expression
17. Solve a linear inequality with only positive coefficients
18. Solve a linear inequality with negative coefficients
19. Apply commutative property
20. Recognize if there is no solution to two simultaneous linear equations

## Plotting:

1. Recognize whether a function is linear
2. Determine the sign of a linear function's slope
3. Determine the linear function through 2 points
4. Identify a plot of a polynomial equation
5. Identify a plot of a exponential equation
6. Distinguish between positive and negative exponents in a plot of an exponential equation
7. Plot a point on a graph (Cartesian coordinates)

## Exponents:

1. Solve for n in xn = b, where n is an integer
2. Calculate x in xn = b, where n is an integer
3. Apply log(ax) = x log a
4. Apply log(ab) = log(a) + log(b)
5. Apply log(a/b) = log(a) - log(b)
6. Apply (ax)(ay) = a(x+y)
7. Apply (ax)/(ay) = a(x-y)
8. Apply x(-a) = 1/(xa)
9. Know that e is a number between 2 and 3
10. Express a word problem as an exponential equation
11. Calculate common log of a number that is a power of 10
12. Apply log base b of a = log a / log b

## Calculus:

1. Recognize a derivative as the slope of a tangent line to a curve
2. Identify regions of a function where derivative is negative, positive, or zero
3. Recognize different notations for the derivative
4. Calculate the value of a derivative at a specific value
5. Identify regions of a function where its second derivative is negative, positive, and zero
6. Define inflection point
7. Define convex and concave
8. Calculate a partial derivative
9. Recognize different notations for the partial derivative
10. Apply the product rule
11. Apply the quotient rule
12. Calculate the derivative of ln(x)
13. Calculate the derivative of e to the x power
14. Apply the chain rule
15. Solve a rate problem
16. Solve a min/max problem