Grade 8 math practice

A. Squares and Square Roots

1. Squares and square roots up to 50

B. Square Roots and Radicals

1. Square roots and cube roots
2. Estimate and compare square roots
3. Simplify square roots
4. Add and subtract radicals
5. Multiply radicals
6. The distributive property with radicals
7. Divide radicals
8. Rationalize the denominator: one term
9. Rationalize the denominator: conjugates
10. Add and subtract radical fractions: same denominator
11. Add and subtract radical fractions: different denominators

C. Exponents

1. Evaluate powers
2. Exponent laws: multiply and divide powers
3. Exponent laws: power of a power
4. Zero and negative exponents
5. Simplify with all the exponent laws
6. Simplify using a common base
7. Solve exponential equations
8. Fractional exponents and roots
9. Calculate in scientific notation
10. Contest problems with powers

D. Algebra: Expanding

1. The distributive property with variables
2. Multiply binomials

E. Systems of Equations

1. Solve systems by substitution
2. Solve systems by elimination
3. Systems of equations word problems
4. Systems with three variables

F. Geometry Theorems

1. Interior and exterior angles of polygons
2. Parallel lines and angles with algebra
3. Triangle theorems with algebra
4. Circle theorems

G. Probability

1. Independent and dependent events
2. Complements and "at least one"
3. Probability with combinations
4. Conditional probability and two-way tables
5. Expected value and fair games

H. Quick Review

1. Review: Heron's formula
2. Review: Equilateral triangles: height and area
3. Review: Section formula (dividing a segment in a ratio)
4. Review: Multi-step percent increase and decrease
5. Review: Average speed and upstream/downstream
6. Review: Simple and compound interest
7. Review: Prime factors in n! (e.g. how many 2s in 45!)
8. Review: Sum of a sequence = average × number of terms
9. Review: Arrangements of letters in a word
10. Review: The choose operator (nCr)
11. Review: Similar triangles
12. Review: Ratio of areas of similar triangles
13. Review: Multi-step angle reasoning with reasons
14. Review: Pythagorean theorem in 2D and 3D
15. Review: Volume and surface area of cylinders
16. Review: Linear relations: y = mx + b

I. Mixed Challenges

1. Mixed: radicals, exponents and equations
2. Mixed: geometry and algebra
3. Mixed: contest blend

J. Summit Challenges

1. Summit Challenges: Number and algebra
2. Summit Challenges: Geometry and measurement
3. Summit Challenges: Data, money and problem solving