Practice problems
Two families: by grade (1 through college) and by concept (counting through integrals). Problems only — work them out, then ask our tutor to check.
Grade 1
Counting, adding small numbers, and shapes.
Grade 2
Two-digit addition, subtraction, and skip counting.
Grade 3
Multiplication, division, and intro to fractions.
Grade 4
Long multiplication, factors, and area.
Grade 5
Decimals, fraction operations, and volume.
Grade 6
Ratios, percentages, and negative numbers.
Grade 7
Proportional reasoning, expressions, and probability.
Grade 8
Linear equations, Pythagoras, and exponents.
Grade 9 / Algebra I
Linear systems, inequalities, and functions.
Grade 10 / Geometry
Triangles, circles, and coordinate geometry.
Grade 11 / Algebra II
Quadratics, logs, and sequences.
Grade 12 / Pre-Calculus
Trigonometry, complex numbers, and limits.
SAT Prep
Mixed mid-difficulty SAT-style problems.
AP Calculus
Limits, derivatives, and integrals at AP level.
College / Linear Algebra & Beyond
Multivariable, linear algebra, and proofs.
Counting & Number Sense
The very beginning — recognizing quantity.
Addition
Combining quantities.
Subtraction
Taking away and finding differences.
Multiplication
Repeated addition and groups.
Division
Sharing equally and inverse of multiplication.
Fractions
Parts of a whole.
Decimals
Place value beyond the ones.
Percentages
Parts out of 100.
Ratios & Proportions
Comparing quantities.
Algebra Basics
Letters that stand for numbers.
Geometry
Shapes, sizes, and space.
Trigonometry
Triangles and the unit circle.
Limits
The doorway to calculus.
Derivatives
Instantaneous rate of change.
Integrals
Accumulation and area.