## Hiset Math

## About This Hiset Math Test

The Mathematics test assesses mathematical knowledge and competencies. The test measures a candidate’s ability to solve quantitative problems using fundamental concepts and reasoning skills. The questions present practical problems that require numerical operations, measurement, estimation, data interpretation, and logical thinking. Problems are based on realistic situations and may test abstract concepts such as algebraic patterns, precision in measurement, and probability. This test may contain some questions that will not count toward your score. The Mathematics test is calculator neutral. A calculator is not required, but if a test taker requests a calculator, the test center is required to provide access to one of the following: four-function or scientific calculator. Please refer to the state policies for the state in which you are testing. Some states have specified calculator type/model requirements. A test taker may not bring his or her own calculator to the testing center for use on the HiSET exam.

**Martin Luther King Jr.**

**Nikola Tesla**

## Math Hiset Exam

## The Test Framework

Some test questions require the use of formulas. The formulas needed to answer certain questions will be provided via a formula sheet. Test takers should know some formulas prior to testing. Some of these include: distance-rate-time, Pythagorean theorem, and quadratic formula.

### I. Numbers and Operations on Numbers

I. Numbers and Operations on Numbers 1. Use properties of operations with real numbers, including rational and irrational numbers. 2. Rewrite expressions involving radicals and rational exponents using the properties of exponents. 3. Solve problems using scientific notation. 4. Reason quantitatively and use units to solve problems. 5. Choose a level of accuracy appropriate to limitations on measurement. 6. Solve multistep real-world and mathematical problems involving rational numbers in any form and proportional relationships (settings may include money, rate, percent, average, estimation/rounding).

### II. Measurement/Geometry

1. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. 2. Know properties of polygons and circles, including angle measure, central angles, inscribed angles, perimeter, arc length and area of a sector, circumference, and area. 3. Understand and apply the Pythagorean theorem. 4. Understand transformations in the plane, including reflections, translations, rotations, and dilations. 5. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. 6. Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).

### III. Data Analysis/Probability/Statistics

1. Summarize and interpret data presented verbally, tabularly, and graphically; make predictions and solve problems based on the data. Recognize possible associations and trends in the data. 2. Identify line of best fit. 13 3. Find the probabilities of single and compound events. 4. Approximate the probability of a chance event, and develop a probability model and use it to find probabilities of events. 5. Use measures of center (mean) to draw inferences about populations including summarizing numerical data sets and calculation of measures of center. 6. Understand how to use statistics to gain information about a population, generalizing information about a population from a sample of the population.

### IV. Algebraic Concepts

1. Interpret parts of an expression, such as terms, factors, and coefficients in terms of its context. 2. Perform arithmetic operations on polynomials and rational expressions. 3. Write expressions in equivalent forms to solve problems. Factor a quadratic expression to reveal the zeros of the function it defines. 4. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 5. Solve quadratic equations in one variable. 6. Solve simple rational and radical equations in one variable. 7. Solve systems of equations. 8. Represent and solve equations and inequalities graphically. 9. Create equations and inequalities to represent relationships and use them to solve problems. 10. Rearrange formulas/equations to highlight a quantity of interest. 11. Understand the concept of a function and use function notation; interpret key features of graphs and tables in terms of quantities. Evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Write a function that describes a relationship between two quantities. 12. Understand domain and range of a function. 13. Write a function that describes a relationship between two quantities, including arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations, and translate between the two forms. 14. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 15. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate rate of change from a graph.

## Mathematics Process Categories

Each Process Category is further divided into Process Category Descriptors. The Process Category Descriptors are numbered under each Process Category as follows. A. Understand Mathematical Concepts and Procedures 1. Select appropriate procedures 2. Identify examples and counterexamples of concepts

## B. Analyze and Interpret Information

1. Make inferences or predictions based on data or information 2. Interpret data from a variety of sources C. Synthesize Data and Solve Problems 1. Reason quantitatively 2. Evaluate the reasonableness of solutions