Skills available for West Virginia Precalculus standards
IXL's Precalculus skills will be aligned to the West Virginia Next Generation Content Standards and Objectives (Common Core) soon! Until then, you can view a complete list of Precalculus standards below.
Standards are in black and IXL math skills are in dark green. Hold your mouse over the name of a skill to view a sample question. Click on the name of a skill to practice that skill.
Represent complex numbers and their operations on the complex plane.
M.4HSTP.2 Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.
M.4HSTP.3 Represent addition, subtraction, multiplication and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. (e.g., (–1 + √3 i)³ = 8 because (–1 + √ 3 i) has modulus 2 and argument 120°.
M.4HSTP.5 Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||, v).
M.4HSTP.8.c Understand vector subtraction v – w as v + (–w), where –w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order and perform vector subtraction component-wise.
M.4HSTP.9.b Compute the magnitude of a scalar multiple cv using ||cv ||= |c|.||v||. Compute the direction of cv knowing that when |c|v ≠ 0, the direction of cv is either along v (for c > 0) or against v (for c < 0).
M.4HSTP.14 Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.
Analyze functions using different representations.
M.4HSTP.19 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.
TIF Trigonometric and Inverse Trigonometric Functions of Real Numbers
Extend the domain of trigonometric functions using the unit circle.
M.4HSTP.23 Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π–x, π+x, and 2π–x in terms of their values for x, where x is any real number.
Explain volume formulas and use them to solve problems.
M.4HSTP.31 Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures.
MP Modeling with Probability
Calculate expected values and use them to solve problems.
M.4HSTP.32 Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.
M.4HSTP.34 Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. (e.g., Find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiple-choice test where each question has four choices, and find the expected grade under various grading schemes.)
M.4HSTP.36.b Evaluate and compare strategies on the basis of expected values. (e.g., Compare a high-deductible versus a low-deductible automobile insurance policy using various, but reasonable, chances of having a minor or a major accident.)