Algebraic reasoning
Solve equations and represent quantitative relationships.
OpenCLT Quantitative Reasoning
Build the quantitative sequence from exact arithmetic and algebraic models to geometry, data and conditional reasoning. In each lesson, reproduce the worked reasoning before attempting a fresh problem independently. The core section has forty questions in forty-five minutes, and standard practice should be completed without a calculator. Use simple exact values, diagrams and substitution to keep your work checkable. Once untimed reasoning is reliable, rehearse mixed sets: moving among models is different from repeating the same operation. The practice score records accuracy on these original questions; it does not convert automatically into an official scaled score.
Updated October 2, 2026
What to study
- algebra
- geometry
- data reasoning
How to approach the section
- Define the unknown, units and restrictions before translating a relationship into an equation.
- Keep fractions and radicals exact; substitute solutions into the original expression and reject values outside its domain.
- Use given geometry properties rather than visual estimates; distinguish radius/diameter and length/area/volume.
- For sets and data, name the denominator or sample, account for overlap and preserve the direction of conditional statements.
Common mistakes
- Applying a percentage to the wrong baseline or forgetting a fixed charge in a rate model.
- Squaring or multiplying an equation without checking extraneous or forbidden values afterward.
- Inventing equality from a drawing or reporting square units for a length.
- Treating a conditional rule as its converse or an observed association as a proved cause.
Geometric reasoning
Reason with shape properties and measurement.
OpenQuantitative logic and data
Analyze patterns, sets and data relationships.
Open