# 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:

- Calculate a number raised to an integer power
- Calculate a
^{0} - Calculate a number raised to a rational number power
- Apply standard order of operations
- Calculate factorial of a whole number
- Calculate |a| of a number
- Understand summation notation
- Understand scientific notation on a calculator
- Understand f(x) notation
- Understand g(f(x)) notation
- Understand case-defined function

## Algebra:

- Different ways of writing multiplication
- Different ways of writing division
- Apply distributive property
- Apply associate property
- Solve a linear equation (numerical answer)
- Solve a linear equation (answer is expression)
- Combine terms in an expression (add or multiply)
- Simplify an expression involving division
- Apply a/(b/c) = (ac)/b
- Apply a/sqrt(b) = (a)sqrt(b)/b
- Express a simple word problem as a linear equation
- Express a word problem involving rates as a linear equation
- Solve two simultaneous linear equations (numerical answer)
- Multiply two polynomial expressions
- Solve two simultaneous nonlinear equations
- Interpret inequality expression
- Solve a linear inequality with only positive coefficients
- Solve a linear inequality with negative coefficients
- Apply commutative property
- Recognize if there is no solution to two simultaneous linear equations

## Plotting:

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

## Exponents:

- Solve for n in x
^{n}= b, where n is an integer - Calculate x in x
^{n}= b, where n is an integer - Apply log(a
^{x}) = x log a - Apply log(ab) = log(a) + log(b)
- Apply log(a/b) = log(a) - log(b)
- Apply (a
^{x})(a^{y}) = a^{(x+y)} - Apply (a
^{x})/(a^{y}) = a^{(x-y)} - Apply x
^{(-a)}= 1/(x^{a}) - Know that e is a number between 2 and 3
- Express a word problem as an exponential equation
- Calculate common log of a number that is a power of 10
- Apply log base b of a = log a / log b

## Calculus:

- Recognize a derivative as the slope of a tangent line to a curve
- Identify regions of a function where derivative is negative, positive, or zero
- Recognize different notations for the derivative
- Calculate the value of a derivative at a specific value
- Identify regions of a function where its second derivative is negative, positive, and zero
- Define inflection point
- Define convex and concave
- Calculate a partial derivative
- Recognize different notations for the partial derivative
- Apply the product rule
- Apply the quotient rule
- Calculate the derivative of ln(x)
- Calculate the derivative of e to the x power
- Apply the chain rule
- Solve a rate problem
- Solve a min/max problem