Your test results have been recorded in the computer system. You responded correctly to 40 of the 40 questions. Your score is 100%.

The table below shows your answer, right or wrong, for each question. By clicking on any question number, you can see (a) the question, and (b) an explanation for arriving at its right answer.

A check mark, , indicates the question was answered correctly; a capital X indicates the question was answered incorrectly.

Objective 0005: Number and Quantity

Demonstrate knowledge of number systems, number representations, number operations, and basic number theory, including:

• recognizing, converting among, and ordering various representations of rational numbers (e.g., integers, fractions, decimals, powers)


• representing rational and irrational numbers on number lines and coordinate axes


• computing fluently with rational numbers, including applying order of operations


• solving multistep problems and estimating solutions to problems using a variety of number representations


• finding common factors and multiples of multidigit numbers


• recognizing and representing ratio concepts (e.g., proportions, unit rates, percents)


• applying ratio concepts and proportional reasoning to solve mathematical and real-world problems

Objective 0006: Algebra and Functions

Demonstrate knowledge of mathematical expressions, basic algebraic techniques, and the use of equations and inequalities to model and solve problems, including:

• applying properties of arithmetic to algebraic expressions


• solving one-variable equations and inequalities


• evaluating algebraic expressions for a given value of a variable


• recognizing equivalent versions of algebraic expressions


• recognizing the difference between an independent and a dependent variable


• analyzing and solving linear equations and systems of equations


• using variables and algebraic expressions to model and solve real-world problems

Objective 0007: Measurement and Geometry

Demonstrate knowledge of the principles and procedures of measurement, basic properties of two- and three-dimensional figures, and reasoning in geometry, including:

• solving mathematical and real-world problems involving area, surface area, and volume of two- and three-dimensional figures


• recognizing and representing polygons on a coordinate plane


• solving problems involving scale drawings


• applying the formulas for the circumference and area of a circle


• using facts about complementary, supplementary, vertical, and adjacent angles to solve multistep problems


• applying the concepts of similarity and congruence


• applying the Pythagorean theorem

Objective 0008: Statistics and Probability

Demonstrate knowledge of the collection, presentation, and interpretation of data, and of the fundamental properties of probability, including:

• displaying and interpreting data presented in a variety of formats (e.g., dot plots, histograms, circle graphs)


• using and interpreting measures of center (e.g., mean, median, mode) and spread (e.g., standard deviation, interquartile range, outliers) in context


• using random sampling to draw inferences about populations


• making inferences about populations that are based on comparisons of center, variability, and visual overlap of distributions


• interpreting scatter plots and estimating lines of fit for data involving two variables


• applying fundamental properties of probability to estimate the outcomes of events


• determining probabilities using various representations (e.g., Venn diagrams, tree graphs)