ISEE Upper Level (grades 9-12) Quantitative Reasoning

ISEE Upper Level Quantitative Reasoning focuses on developing advanced mathematical skills and problem-solving abilities for high school students.

Advanced Topics

Inequalities and Absolute Value

Comparing and Measuring Differences

Inequalities show how values compare, using signs like \( <, >, \leq, \geq \). Absolute value is the distance a number is from zero, always positive.

Solving Inequalities

The steps are similar to solving equations, but remember to flip the inequality sign when multiplying or dividing by a negative number!

Absolute Value in Real Life

Absolute value is used to measure distances, like how far a temperature is from freezing, regardless of direction.

Where You'll See This

Inequalities are great for budgeting ("I have less than $20 to spend"), and absolute value helps in tracking changes, like temperature drops.

Examples

  • Solve \( x - 4 > 3 \): Add 4 to both sides to get \( x > 7 \).

  • The absolute value of -6 is 6 because it's 6 units from zero.

In a Nutshell

Inequalities compare values, and absolute value measures how far a number is from zero.