# ISEE Upper Level Math Review

Math skills are tested in the Quantitative Reasoning and Mathematics Achievement sections of the ISEE. The ERB follows the standards set forth by the National Council of Teachers of Mathematics (NCTM) to determine how the ISEE will test a student’s ability in mathematics. Students taking the Upper Level ISEE should be familiar with the following concepts, as stated by the ERB:

**Numbers and Operations **

- Understand numbers, relationships among numbers, meanings of operations, and relationships among operations
- Classify, perform operations on, make reasonable estimates of, and compare whole numbers, integers, rational numbers, irrational numbers, real numbers, and complex numbers
- Perform operations on matrices and vectors and compute combinations and permutations

**Algebra**

- Understand, represent, and analyze mathematical, algebraic, and graphical situations involving patterns, relations, and functions
- Understand relations and functions when presented as symbolic equations, graphs, and tables
- Model real‐world situations using symbolic equations and graphs
- Use symbolic manipulation to determine equivalent expressions, equations, and inequalities

**Geometry**

- Analyze characteristics of geometric figures
- Visualize and describe spatial relationships for geometric objects
- Classify and describe basic 2‐ and 3‐dimensional figures
- Understand and use coordinate grids, including transformations of geometric figures
- Understand the concepts of congruency, symmetry, and similarity

**Measurement**

- Develop, analyze, and use formulas for measurable attributes of objects
- Understand and use formulas for the area, surface area, and volume of geometric figures, including cones, spheres, and cylinders
- Make decisions about units and scales that are appropriate for problem situations involving measurement

**Data Analysis & Probability **

- Analyze, interpret, and make inferences about a set of data
- Understand and apply the concepts of probability
- Collect, display, interpret, and make predictions about a set of data
- Calculate mean, mode, median, range, standard deviation, and first and third quartiles of a set of data
- Calculate probabilities and expected values

**Mathematics Review**

Listed in the column to the right, you’ll find quick review guides for the 48 most important math topics tested on the ISEE Upper Level. Though you may be familiar with a concept, it would behoove you to review the information and complete the practice.

It is important to note that some of the concepts covered in this review are ones that you probably have never seen before. Do not worry if this is true. Instead, you should solidify your knowledge of familiar concepts, and then begin building your knowledge of the new concepts.

**Math Review Topics**

- Estimation & Rounding
- Number Types
- Mathematic Properties
- Order of Operations
- Arithmetic Word Problems
- Number Lines
- Fractions & Decimals
- Powers & Roots
- Scientific Notation
- Factors & Multiples
- Prime Numbers
- Ratios & Proportions
- Percentages
- Percent of Change
- Sequences
- Set Notation
- Fundamental Counting Principle
- Permutations
- Combinations
- Probability
- Distance, Rate, & Time
- Work Word Problems
- Simple & Compound Interest
- Mean, Median, Mode, Range, & Weighted Average
- Units of Measurement
- Operations on Algebraic Expressions
- Multiplying Polynomials
- Factoring Algebraic Expressions
- Balancing Algebraic Equations
- Absolute Value
- Direct and Inverse Variation
- Inequalities
- Systems of Linear Equations
- Linear Equations & Their Graphs
- Midpoint & Distance Formulas
- Linear Inequalities & Their Graphs
- Quadratic Equations and Their Graphs
- Function Notation
- Domain & Range
- Transformations on Functions
- Matrices
- Geometric Notation
- Types of Angles
- Triangles: Types and Rules
- Polygons: Angles, Perimeter, and Area
- Circles
- Solid Geometry: Surface Area and Volume
- Advanced Math: Matrix Multiplication, Standard Deviation, and Trigonometry