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New Hampshire Math Standards - Advanced Mathematics
MathScore aligns to the New Hampshire Math Standards for Advanced Mathematics. The standards appear below along with the MathScore topics that match. If you click on a topic name, you will see sample problems at varying degrees of difficulty that MathScore generated. When students use our program, the difficulty of the problems will automatically adapt based on individual performance, resulting in not only true differentiated instruction, but a challenging game-like experience.
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View the New Hampshire Math Standards at other levels.
Number and Operations
M:N&O:AM:1 Demonstrates conceptual understanding of the real number system as an extension of the rational numbers by representing real numbers as infinite decimal expansions (that provide successive rational approximations to the number) and as points on a number line. Determines whether the decimal expansion of a rational number given in fractional form eventually repeats or terminates (without using a calculator). (Fractions to Decimals , Repeating Decimals )M:N&O:AM:2 No standard at this level
M:N&O:AM:3 No standard at this level
M:N&O:AM:4 Accurately solves problems.
• Solves problems involving scientific notation and assesses the precision of the answer in terms of significant digits. (Scientific Notation 2 , Scientific Notation )
• Solves problems involving complex numbers by adding, multiplying, dividing, and computing conjugates; interprets complex numbers geometrically; and understands complex numbers as an extension of the real numbers (e.g., arising in solutions of polynomial equations).
• Manipulates complex numbers using rectangular and polar coordinates.
• Finds the nth roots of a complex number using De Moivre's Theorem.
• Solves compound interest problems including continuously compounded interest. (Compound Interest , Continuous Compound Interest )
M:N&O:AM:5 No standard at this level
M:N&O:AM:6 No standard at this level
M:N&O:AM:7 No standard at this level
M:N&O:AM:8 Explores field properties with vectors and matrices; algebraically/geometrically interpret vectors, vector addition, and scalar multiplication in the plane; and solves problems using matrices (e.g., inverses, identity, determinants, and augmented matrices).
Geometry and Measurement
M:G&M:AM:1 No standard at this levelM:G&M:AM:2 Extends and deepens knowledge and usage of proofs and proof techniques; and uses geometric models to represent and distinguish between Euclidean and Non-Euclidean Systems.
M:G&M:AM:3 No standard at this level
M:G&M:AM:4 No standard at this level
M:G&M:AM:5 No standard at this level
M:G&M:AM:6 Derives and uses formulas for lengths of arcs and areas of sectors and areas of segments of circles.
M:G&M:AM:7 Uses radian measure appropriately when solving problems; converts between radian measure and degree measure; and understands why radian measure is useful.
M:G&M:AM:8 No standard at this level
M:G&M:AM:9 Solves problems using analytic geometry (including three-dimensions) and circular trigonometry (e.g., find the equation of a circle inscribed in a triangle; find the distance between opposite vertices in a rectangular solid); explores and interprets the characteristics of conic sections graphically and algebraically including understanding how different planar slices of a double cone yield different conic sections; knows the characterization of conic sections as loci of points in the plane satisfying certain distance requirements, and uses the distance formula to obtain equations for the conic sections.
M:G&M:AM:10 No standard at this level
Functions and Algebra
M:F&A:AM:1 Computes partial sums of infinite arithmetic and geometric sequences, determines when an infinite geometric series converges, and finds its sum. Connects arithmetic and geometric sequences to linear and exponential functions, respectively. Works between recursive and explicit representations.M:F&A:AM:2 Demonstrates conceptual understanding of linear and nonlinear functions and relations.
• Understands functions and relations from a set-theoretic perspective, and operations on functions including composition.
• Analyzes characteristics of classes of functions and inverse functions (exponential, logarithmic, trigonometric) to include domain, range, intercepts, increasing and decreasing intervals and rates of change, periodicity, end behavior, maximum and minimum values, continuity, and asymptotes; graphs classes of functions; and understands domain restrictions and their effects on functions.
• Analyzes properties of functions including onto (surjectivity), critical points and inflection points. Determine graphically and analytically whether a function is even, odd or neither.
• Analyzes informally the idea of continuity and limits.
M:F&A:AM:3 Demonstrates conceptual understanding of algebraic expressions.
• Simplifies complex fractions.
• Uses the Remainder Theorem, the Factor Theorem and Rational Root Theorem for polynomials.
• Knows the Fundamental Theorem of Algebra and that non-constant polynomials always factor into linear factors over the complex numbers.
• Understands the difference between factoring polynomials over integer, rational, real, and complex numbers.
M:F&A:AM:4 Demonstrates conceptual understanding of equality.
• Solves equations and verifies/proves identities involving trigonometric expressions.
• Solves equations involving exponential and logarithmic expressions; graphs and interprets the solutions.
• Uses matrices or determinants to solve systems of equations with or without technology.
• Knows and applies the Intermediate Value Theorem to find exact or approximate solutions of equations or zeros of continuous functions.
Data, Statistics, and Probability
M:DSP:AM:1 No standard at this levelM:DSP:AM:2 Analyzes and interprets measures of dispersion (standard deviation, variance, and percentiles) and central tendency for the normal distribution; and interprets the correlation coefficient and the coefficient of determination in the context of data.
M:DSP:AM:3 Uses technology to explore the method of least squares and median-median for linear regression.
M:DSP:AM:4 No standard at this level
M:DSP:AM:5 Solves probability problems (e.g., by applying concepts of counting, random variables, independence/dependence of events, and conditional probability). (Probability , Probability 2 , Object Picking Probability )
M:DSP:AM:6 No standard at this level \
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