Grade 7 math practice

A. Rational Numbers

1. Add and subtract rational numbers
2. Multiply and divide rational numbers
3. Order of operations with rational numbers
4. Compare and order rational numbers

B. Exponents and Scientific Notation

1. Powers with negative bases and zero exponents
2. Scientific notation
3. Square roots of fractions and decimals

C. Percent and Finance

1. Percents greater than 100% and less than 1%
2. Commission, markup, tips and successive discounts
3. Simple and compound interest

D. Ratios and Proportional Reasoning

1. Ratios with three parts
2. Direct and inverse proportion
3. Scale drawings and maps

E. Introduction to Algebra

1. Writing expressions from words

F. Algebra

1. Simplify algebraic expressions
2. Solve multi-step equations
3. Equations from real-life problems
4. Inequalities (flipping the sign)
5. Use and rearrange formulas

G. Linear Relations

1. Linear relations: y = mx + b
2. Linear relations in real life

H. Sequences and Series

1. Arithmetic sequences: nth term
2. Sum of a sequence = average × number of terms
3. Geometric sequences (multiply each time)

I. Counting and Combinatorics

1. Factorials and arrangements
2. Arrangements of letters in a word
3. The choose operator (nCr)
4. Pascal's triangle

J. Factorials and Number Theory

1. Prime factors in n! (e.g. how many 2s in 45!)
2. Factorials, divisibility and digit puzzles

K. Geometry Theorems

1. Angle theorems: SAT, CAT, OAT, SAAT
2. Triangle theorems: SATT, EAT, ITT
3. Multi-step angle reasoning with reasons

L. Similar and Congruent Triangles

1. Similar triangles
2. Congruent triangles (SSS, SAS, ASA, AAS, RHS)
3. Ratio of areas of similar triangles

M. Circles and Cylinders

1. Circles, semicircles and composite shapes
2. Volume and surface area of cylinders

N. Geometry

1. Angles with parallel lines
2. Triangle angles: exterior and isosceles
3. Similar figures and scale factors
4. Parallel line theorems: F, Z and C patterns (TPT)
5. Points, lines, rays and segments
6. The Cartesian plane and the distance formula
7. Pythagorean theorem in 2D and 3D
8. Dilations and transformations on a grid

O. Contest Problems

1. Number and algebra puzzles (contest style)
2. Geometry puzzles (contest style)
3. Counting and probability puzzles (contest style)

P. Data and Probability

1. Probability with combinations (coins and choices)
2. Weighted means and data
3. Circle graphs
4. Probability: compound events and complements