ISEE Upper Level Quantitative Reasoning

A comprehensive course to master the mathematical reasoning skills needed for success on the ISEE Upper Level exam.

Basic Concepts

Algebraic Thinking and Expressions

Algebra in Everyday Life

Algebra is like a math puzzle: you use letters to stand for numbers and then solve for them! This is super useful for figuring out unknowns.

What’s an Expression?

An expression is a combination of numbers, variables, and operations (no equals sign). For example, \( 3x + 7 \).

What’s an Equation?

An equation has an equals sign and shows that two things are the same. For example, \( 2y + 3 = 9 \).

Tricks for Simplifying

  • Combine like terms: \( 2x + 3x = 5x \)
  • Use properties: Distributive property helps expand or factor expressions

Why Learn This?

Algebraic thinking lets you describe real-life situations, like figuring out how many tickets you can buy with a set amount of money.

Everyday Algebra

Planning a party with a budget? Let’s say the cost is \( 5x + 12 \). If each pizza costs $5 and decorations are $12, you can figure out how many pizzas you can afford.

Examples

  • If \( x \) is the number of candies, and each costs $2, then \( 2x \) tells you the total price.

  • Solving \( 3x + 4 = 10 \) tells you how many items you can buy with $10 if each costs $3 and there’s a $4 fee.

In a Nutshell

Use variables and expressions to represent and solve real-world problems.

Key Terms

Variable
A letter or symbol that stands for a number.
Expression
A combination of numbers, variables, and operations without an equals sign.
Equation
A statement that two expressions are equal.