# General Curriculum Study Guide

## Test Design and Framework

The test design below describes general testing information. The framework that follows is a detailed outline that explains the knowledge and skills that this test measures.

### Test Design

Format | Computer-based test (CBT) |
---|---|

Number of Questions | 45 multiple-choice items, 1 open-response item |

Time | 2.5 hours testing time for Mathematics subtest 15 minutes additional time to complete a CBT tutorial |

### Mathematics Subtest Framework

Subareas | Range of Objectives | Approximate Test Weighting | |
---|---|---|---|

V | Numbers and Operations | 16–19 | 41% |

VI | Functions and Algebra | 20–22 | 22% |

VII | Geometry and Measurement | 23–24 | 18% |

VIII | Statistics and Probablility | 25–26 | 9% |

IX | Integration of Knowledge and Understanding | 27 | 10% |

#### Subarea V–Numbers and Operations

##### Objective 0016: Understand the number system and the concept of place value.

For example:

- Analyze the structures and properties of the base-10 and other numeral systems (e.g., expanded form of a number, visual representations of place value, numeration systems of ancient cultures).
- Recognize decimal expansions.
- Use scientific notation in the real world.
- Analyze differences in written English (e.g., level of formality, how dialects are used).
- Analyze procedures (e.g., rounding, regrouping) for estimation.
- Determine the reasonableness of estimates.
- Identify subsets of the real numbers (e.g., integer, rational, irrational) and their characteristics.

##### Objective 0017: Understand integers, fractions, decimals, percents, and mixed numbers.

For example:

- Understand the meanings and models of integers, fractions, decimals, percents, and mixed numbers and apply them to the solution of word problems.
- Analyze and convert among various representations of numbers (e.g., graphic, numeric, symbolic, verbal).
- Use number lines.
- Compare, sort, order, and round numbers.
- Recognize equivalent representations of numbers (e.g., fractions, decimals, percents).

##### Objective 0018: Understand and apply principles of number theory.

For example:

- Identify prime and composite numbers and their characteristics.
- Find the prime factorization of a number and recognize its uses.
- Demonstrate knowledge of the divisibility rules and why they work.
- Find the least common multiple (LCM) and greatest common factor (GCF) of a set of numbers.
- Apply the LCM and GCF in real-world situations.

##### Objective 0019: Understand operations on numbers.

For example:

- Understand the meaning and models of operations on numbers (e.g., integers, fractions, decimals).
- Analyze and justify standard and nonstandard computational algorithms and mental math techniques (e.g., by application of the arithmetic properties, such as commutative, associative, distributive).
- Evaluate the validity of nonstandard or unfamiliar computational strategies.
- Recognize and analyze various representations (e.g., graphic, pictorial, verbal) of number operations.
- Recognize relationships among operations (e.g., addition and subtraction, addition and multiplication, multiplication and exponentiation).
- Identify and apply the arithmetic properties and the transitive properties of equality and inequality.
- Apply the order of operations.
- Apply the laws of exponents.
- Demonstrate fluency in arithmetic computation, including operations on fractions.
- Interpret the concept of absolute value.
- Apply appropriate strategies (e.g., proportional thinking, ratios) to estimate quantities in real-world situations.
- Solve problems using arithmetic operations with various representations of numbers.

#### Subarea VI–Functions and Algebra

##### Objective 0020: Understand algebra as generalized arithmetic.

For example:

- Recognize and apply the concepts of variable, function, equality, and equation to express relationships algebraically.
- Manipulate simple algebraic expressions and solve linear equations and inequalities.
- Justify algebraic manipulations by application of the properties of equality, the order of operations, the number properties, and the order properties.
- Use algebra to solve word problems involving fractions, ratios, proportions, and percents.
- Identify variables and derive algebraic expressions that represent real-world situations.

##### Objective 0021: Understand the concept of function.

For example:

- Understand the definition of function and various representations of functions (e.g., input/output machines, tables, graphs, mapping diagrams, formulas).
- Recognize and extend patterns using a variety of representations (e.g., verbal, numeric, pictorial, algebraic).
- Identify and analyze direct and inverse relationships in tables, graphs, algebraic expressions and real-world situations.
- Use qualitative graphs to represent functional relationships in the real world.
- Translate among different representations (e.g., tables, graphs, algebraic expressions, verbal descriptions) of functional relationships.

##### Objective 0022: Understand linear functions and linear equations.

For example:

- Recognize the formula and graph of a linear function.
- Distinguish between linear and nonlinear functions.
- Find a linear equation that represents a graph.
- Analyze the relationships among proportions, constant rates, and linear functions.
- Interpret the meaning of the slope and the intercepts of a linear equation that models a real-world situation.
- Select the linear equation that best models a real-world situation.

#### Subarea VII–Geometry and Measurement

##### Objective 0023: Understand and apply concepts of measurement.

For example:

- Estimate and calculate measurements using customary, metric, and nonstandard units of measurement.
- Use unit conversions and dimensional analysis to solve measurement problems.
- Derive and use formulas for calculating the lengths, perimeters, areas, volumes, and surface areas of geometric shapes and figures.
- Determine how the characteristics (e.g., area, volume) of geometric figures and shapes are affected by changes in their dimensions.
- Solve a variety of measurement problems (e.g., time, temperature, rates, average rates of change) in real-world situations.

##### Objective 0024: Understand and apply concepts of geometry.

For example:

- Classify and analyze polygons using attributes of sides and angles, including real-world applications.
- Classify and analyze three-dimensional figures using attributes of faces, edges, and vertices.
- Analyze and apply geometric transformations (e.g., translations, rotations, reflections, dilations); relate them to concepts of symmetry, similarity, and congruence; and use these concepts to solve problems.
- Match three-dimensional figures and their two-dimensional representations (e.g., nets, projections, perspective drawings).
- Recognize and apply connections between algebra and geometry (e.g., the use of coordinate systems, the Pythagorean theorem).

#### Subarea VIII–Statistics and Probability

##### Objective 0025: Understand descriptive statistics.

For example:

- Use measures of central tendency (e.g., mean, median, mode) and spread to describe and interpret real-world data.
- Select appropriate ways to present data and communicate statistical information (e.g., tables, graphs, line plots, Venn diagrams).
- Analyze and interpret various graphic and nongraphic data representations (e.g., frequency distributions, percentiles).
- Compare different data sets.

##### Objective 0026: Understand and apply basic concepts of probability.

For example:

- Calculate the probabilities of simple and compound events and of independent and dependent events.
- Recognize and apply the concept of conditional probability.
- Recognize the difference between experimentally and theoretically determined probabilities in real-world situations.
- Apply knowledge of combinations and permutations to the computation of probabilities.

#### Subarea IX–Integration of Knowledge and Understanding

##### Objective 0027: Apply mathematical knowledge and reasoning to communicate multiple solutions in detail to a problem involving two or more of the following subareas: Numbers and Operations, Functions and Algebra, Geometry and Measurement, and Statistics and Probability.

- (Refer to objectives 0016 through 0026 and associated descriptive statements.)