100+ Free Montana MAST Grade 8 Mathematics Practice Questions

The Number System

Know that numbers that are not rational are called irrational; understand informally that every number has a decimal expansion; know that rational numbers have decimal expansions that terminate in zeros or eventually repeat; convert a decimal expansion that repeats eventually into a rational number; use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line, and estimate the value of expressions (e.g., pi, square roots).

Expressions & Equations

Know and apply the properties of integer exponents to generate equivalent numerical expressions; use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p; use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large/very small quantities and to express how many times as much; perform operations with numbers expressed in scientific notation; graph proportional relationships interpreting the unit rate as slope; use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line; derive y = mx and y = mx + b; solve linear equations in one variable (one solution, infinitely many, no solution); analyze and solve pairs of simultaneous linear equations.

Functions

Understand that a function is a rule that assigns to each input exactly one output; compare properties of two functions each represented in a different way; interpret y = mx + b as defining a linear function; construct a function to model a linear relationship; determine the rate of change and initial value from a description or two (x,y) values; describe qualitatively the functional relationship between two quantities by analyzing a graph; sketch a graph that exhibits the qualitative features of a function.

Geometry

Verify experimentally the properties of rotations, reflections, and translations; understand congruence and similarity via sequences of transformations; describe the effect of dilations, translations, rotations, and reflections using coordinates; establish facts about the angle sum and exterior angle of triangles, parallel lines cut by a transversal, and the angle-angle criterion for similarity; explain a proof of the Pythagorean Theorem and its converse; apply the Pythagorean Theorem to determine unknown side lengths in two and three dimensions and the distance between two points; know the formulas for the volumes of cones, cylinders, and spheres and use them to solve problems.

Statistics & Probability

Construct and interpret scatter plots for bivariate measurement data; describe patterns such as clustering, outliers, positive/negative association, linear and nonlinear association; use the equation of a linear model to solve problems in the context of bivariate measurement data (interpret slope and intercept); construct and interpret a two-way table summarizing data on two categorical variables and use relative frequencies to describe possible association.