MathsQ&A by dot point

Interpret the parts of an expression (terms, factors, coefficients) in context, and rewrite expressions using structure, including factoring and the properties of exponents, to reveal meaning such as a zero, a rate, or a percent change.

Create equations and inequalities in one variable and use them to solve problems; solve linear equations and inequalities including those with variables on both sides; rearrange literal equations (formulas) to isolate a chosen variable; and graph the solution set of an inequality on a number line.

Add, subtract, and multiply polynomials (closure), and factor quadratic and higher expressions using common factors, the difference of two squares, and trinomial factoring, including a leading coefficient other than 1.

Solve quadratic equations in one variable by factoring (zero-product property), completing the square, and the quadratic formula; recognize when a method is required by the problem; and interpret the solutions in a real-world context.

Solve systems of linear equations algebraically (substitution and elimination) and graphically; solve a linear-quadratic system; create and solve systems from contexts; and graph the solution region of a system of linear inequalities.

Understand the definition of a function and function notation; evaluate functions; identify domain and range; and interpret the key features of a graph (intercepts, intervals of increase and decrease, relative maxima and minima, and average rate of change) in context.

Distinguish linear from exponential growth (constant difference versus constant ratio), construct linear and exponential functions from descriptions, tables, or two points, and interpret their parameters (initial value, rate of change, growth factor) in context.

Represent and interpret one-variable data with dot plots, histograms, and box plots; compute and interpret measures of center (mean, median) and spread (range, interquartile range, standard deviation informally); identify outliers; and compare two distributions.

Graph quadratic functions and identify key features (vertex, axis of symmetry, zeros, y-intercept, maximum or minimum); relate the three forms; and describe the effect of transformations on the parent function.

Construct and interpret scatter plots; fit a linear (or exponential) model to bivariate data; interpret the slope and intercept in context; compute and interpret residuals; and distinguish the correlation coefficient from causation.

Understand the inverse relationship between exponential and logarithmic functions; convert between exponential and logarithmic form; apply the product, quotient, and power properties of logarithms; and use the natural base e and natural logarithm.

Identify the amplitude, period, midline, and phase shift of a sinusoidal function from its equation; graph sine and cosine functions; and build a sinusoidal model of a periodic real-world situation.

Convert between degrees and radians; use the unit circle to define the sine and cosine of any angle as coordinates of a point; evaluate the trig functions at special angles; and apply the Pythagorean identity.

Write explicit and recursive formulas for arithmetic and geometric sequences; find a specified term; use sigma notation; and apply the arithmetic and finite geometric series sum formulas.

Solve exponential equations (matching bases or taking logarithms) and logarithmic equations (condensing then rewriting in exponential form), check for extraneous solutions, and model exponential growth, decay, and compound interest.

Define the imaginary unit i and operate with complex numbers (add, subtract, multiply); use the discriminant to determine the nature of a quadratic's roots; and solve quadratics with complex roots using the quadratic formula or completing the square.

Divide polynomials using long division and synthetic division; apply the Remainder Theorem (the remainder when dividing by x minus a equals the value of the polynomial at a) and the Factor Theorem to test for factors and find zeros.

Find the zeros of a polynomial from its factored form; use multiplicity to decide whether the graph crosses or touches the x-axis; and use the degree and leading coefficient to determine end behavior, then sketch the graph.

Convert between radical and rational-exponent form; simplify radical and rational-exponent expressions using the exponent laws; and solve radical equations, checking for extraneous solutions introduced by squaring.

Simplify rational expressions by factoring and cancelling (noting domain restrictions); add, subtract, multiply, and divide them; and solve rational equations, checking for extraneous solutions introduced by the denominators.

Compute conditional probability from two-way tables; apply the addition rule for the probability of A or B; apply the multiplication rule for A and B; and test for independence of two events.

Recognize the properties of a normal distribution; use the empirical (68-95-99.7) rule; compute a z-score; and use z-scores (with a calculator or table) to find the proportion of data in an interval.

Fit linear, exponential, and other regression models to data; interpret the parameters and the correlation coefficient in context; use a residual plot to judge whether a model is appropriate; and use a model to make predictions.

Distinguish sample surveys, experiments, and observational studies; recognize random sampling and sources of bias; understand the role of randomization and a control group; and use simulation to model a sampling distribution and estimate a margin of error.

Perform compass-and-straightedge constructions: copy a segment and an angle; bisect a segment (perpendicular bisector) and an angle; construct a perpendicular and a parallel line; construct an equilateral triangle; and explain why each construction produces the intended figure.

Prove theorems about parallelograms (opposite sides and angles congruent, diagonals bisect each other) and prove that a given quadrilateral is a parallelogram, rectangle, rhombus, or square using side, angle, and diagonal properties.

Prove theorems about lines and angles (vertical angles, the angle relationships from parallel lines cut by a transversal) and about triangles (the angle sum is 180 degrees, the exterior angle theorem, the isosceles triangle base angles, and the midsegment theorem).

Represent and perform reflections, rotations, and translations using rules and the coordinate plane; recognize that rigid motions preserve distance and angle; and define congruence of two figures as the existence of a sequence of rigid motions mapping one onto the other.

Use the triangle congruence criteria (SSS, SAS, ASA, AAS, HL) to prove two triangles congruent, and use CPCTC (corresponding parts of congruent triangles are congruent) to justify further equal sides or angles.

Apply central angle, inscribed angle, chord, tangent, and secant relationships in a circle; compute arc length and sector area; and write and use the equation of a circle in the coordinate plane.

Use the distance, midpoint, and slope formulas to analyze figures; determine parallel and perpendicular lines from slope; partition a directed segment into a given ratio; and write equations of lines satisfying given conditions.

Perform dilations on the coordinate plane and describe their effect on lengths and angles; define similarity through a sequence of rigid motions and a dilation; and prove triangles similar using AA (and SAS, SSS similarity), then use proportions to find missing lengths.

Define the sine, cosine, and tangent ratios in a right triangle (SOHCAHTOA), use them with inverse trig functions to find missing sides and angles, apply the relationship between the sine and cosine of complementary angles, and solve angle-of-elevation and depression problems.

Use volume formulas for prisms, cylinders, pyramids, cones, and spheres; identify the two-dimensional cross sections of three-dimensional solids and the solids formed by rotating a region; and solve density problems combining volume with mass or population.