High School Math (Minnesota Academic Standards)

Strand 2: Algebra

• 9.2.1.1 Understand functions and evaluate them in function notation within their domains.
• 9.2.1.2 Tell functions from other relations given by equations, graphs or tables.
• 9.2.1.3 Find the domain of a function from a formula, graph or context.
• 9.2.1.4 Draw conclusions from graphs of functions and relations.
• 9.2.1.5 Find the vertex, axis of symmetry and intercepts of quadratic graphs in different forms.
• 9.2.1.6 Read intercepts, zeros, maxima, minima and increasing/decreasing intervals from graphs.
• 9.2.1.7 Understand and find asymptotes of exponential and reciprocal linear functions.
• 9.2.1.8 Describe a function's rate of change from its graph or table.
• 9.2.1.9 Show how translations change a function's formula and graph, using graphing technology.
• 9.2.2.1 Solve problems with linear and quadratic functions in context.
• 9.2.2.2 Model growth and decay such as investments, depreciation and population with exponential functions.
• 9.2.2.3 Sketch linear, quadratic and exponential functions and move between graphs, tables and equations.
• 9.2.2.4 Describe geometric sequences recursively and explicitly and write partial sums recursively.
• 9.2.2.5 Solve problems with finite geometric sequences and series, such as loans and interest, with spreadsheets.
• 9.2.2.6 Graph common nonlinear functions and their translations with technology.
• 9.2.3.1 Evaluate polynomial, rational, radical and absolute value expressions where defined.
• 9.2.3.2 Add, subtract and multiply polynomials and divide by polynomials of equal or lower degree.
• 9.2.3.3 Factor common monomials, quadratics and differences of squares.
• 9.2.3.4 Add, subtract, multiply, divide and simplify algebraic fractions.
• 9.2.3.5 Check complex-number solutions of quadratics by substitution.
• 9.2.3.6 Use rules of rational exponents, including nth roots, to write equivalent expressions.
• 9.2.3.7 Justify steps in proving expressions equivalent; know that checking values cannot prove equivalence.
• 9.2.4.1 Solve quadratic equations and inequalities in context by factoring, completing the square, graphing or formula.
• 9.2.4.2 Model situations with exponential equations and solve them graphically or numerically with technology.
• 9.2.4.3 Understand how number systems extend to complex numbers to solve some quadratics.
• 9.2.4.4 Model situations with systems of linear inequalities and graph them with solid or dashed boundaries.
• 9.2.4.5 Solve linear programming problems in two variables graphically.
• 9.2.4.6 Represent situations with two-variable absolute value inequalities and solve them graphically.
• 9.2.4.7 Solve radical equations, knowing that algebra can produce extraneous solutions.
• 9.2.4.8 Judge whether solutions make sense in context and compare with graphical or numerical estimates.

Strand 3: Geometry & Measurement

• 9.3.1.1 Find surface area and volume of pyramids, cones and spheres with tools or formulas.
• 9.3.1.2 Decompose figures to find perimeter, area, surface area and volume.
• 9.3.1.3 Use units correctly in measurement calculations and convert between systems.
• 9.3.1.4 Understand that scaling by k multiplies lengths by k, areas by k² and volumes by k³.
• 9.3.1.5 Judge the accuracy of values from measurement calculations and make reasonable estimates.
• 9.3.2.1 Understand the roles of axioms, definitions, undefined terms and theorems in arguments.
• 9.3.2.2 Interpret logical statements and relate a conditional to its inverse, converse and contrapositive.
• 9.3.2.3 Judge whether arguments are valid and use counterexamples to disprove claims.
• 9.3.2.4 Write geometric proofs, including by contradiction, in two-column, paragraph or flowchart form.
• 9.3.2.5 Use technology tools to test conjectures and build multi-step arguments.
• 9.3.3.1 Use properties of parallel and perpendicular lines and transversal angles to solve problems and justify.
• 9.3.3.2 Use angle relationships (corresponding, vertical, complementary, supplementary and others) to solve and justify.
• 9.3.3.3 Use properties of equilateral, isosceles and scalene triangles to solve problems and justify.
• 9.3.3.4 Use the Pythagorean Theorem and its converse to solve problems and justify.
• 9.3.3.5 Use properties of 45-45-90 and 30-60-90 triangles to solve problems and justify.
• 9.3.3.6 Use congruence and similarity to solve problems and justify.
• 9.3.3.7 Classify polygons, including quadrilaterals and regular polygons, and use their properties.
• 9.3.3.8 Use properties of circles to solve problems and justify.
• 9.3.4.1 Understand how similar right triangles define sine, cosine and tangent and find them for acute angles.
• 9.3.4.2 Use sine, cosine and tangent to find lengths and areas in right-triangle figures.
• 9.3.4.3 Use calculators or tables to find angles in right triangles from trig ratios.
• 9.3.4.4 Use coordinate geometry to find lengths, midpoints and slopes of segments and polygons.
• 9.3.4.5 Derive the equation of a circle with center (h, k) and radius r using the Pythagorean Theorem.
• 9.3.4.6 Apply reflections, translations, dilations and 90° rotations about the origin to figures on a grid.
• 9.3.4.7 Use algebra to solve geometry problems, such as lengths in similar triangles.

Strand 4: Data Analysis & Probability

• 9.4.1.1 Describe data with box plots and statistics such as quartiles and standard deviation.
• 9.4.1.2 Analyze how changes in a data set affect its summary statistics.
• 9.4.1.3 Use scatterplots, regression lines and correlation coefficients to predict and judge reliability.
• 9.4.1.4 Fit a normal curve using mean and standard deviation, estimate percentages and spot data it does not fit.
• 9.4.2.1 Evaluate data reports in the media by looking at sources, design, analysis and misleading graphs.
• 9.4.2.2 Identify misleading uses of data and claims that confuse correlation with causation.
• 9.4.2.3 Design simple experiments and explain how sampling, bias and question wording affect data.
• 9.4.3.1 Use multiplication and addition principles and tree diagrams to count outcomes and find probabilities.
• 9.4.3.2 Estimate probabilities from experiments or simulations using relative frequency.
• 9.4.3.3 Understand the Law of Large Numbers as it links model and experimental probabilities.
• 9.4.3.4 Use random numbers from technology or tables to simulate chance events and support fair decisions.
• 9.4.3.5 Find probabilities of intersections, unions and complements, conditional probability and independence.
• 9.4.3.6 Use Venn diagrams to show intersections, unions and complements and relate them to and, or, not.
• 9.4.3.7 Use formulas for the probability of intersections, unions and complements of events.
• 9.4.3.8 Use probability to make real-world decisions.
• 9.4.3.9 Relate conditional probabilities to relative frequencies in contingency tables.