Essential Skills Review
Math 9 PAT Key Concepts Summary
Master these essential skills for success on your Provincial Achievement Test
Chapter 1: Symmetry & Surface Area
Line & Rotational Symmetry
- Identify lines of symmetry in 2D shapes
- Determine order of rotational symmetry
- Create symmetric designs
Surface Area
- Right prisms and cylinders
- Composite 3D objects
- Using nets to calculate surface area
Surface Area Formulas:
Rectangular Prism: $SA = 2(lw + lh + wh)$
Cylinder: $SA = 2\pi r^2 + 2\pi rh$
Rectangular Prism: $SA = 2(lw + lh + wh)$
Cylinder: $SA = 2\pi r^2 + 2\pi rh$
PAT Tip:
Always check if you need to find surface area of composite objects by adding or subtracting areas.
Chapter 2: Numbers
Rational Numbers
- Compare and order rational numbers
- Add, subtract, multiply, divide fractions
- Convert between fractions, decimals, percents
- Solve problems with mixed numbers
Square Roots
- Perfect squares and square roots
- Estimate square roots of non-perfect squares
- Solve problems involving square roots
Example:
$\sqrt{50}$ is between $\sqrt{49} = 7$ and $\sqrt{64} = 8$So $\sqrt{50} \approx 7.1$
Chapter 3: Powers & Exponents
Exponent Laws
- Product law: $a^m \times a^n = a^{m+n}$
- Quotient law: $a^m \div a^n = a^{m-n}$
- Power law: $(a^m)^n = a^{mn}$
- Zero exponent: $a^0 = 1$ (where $a \neq 0$)
- Negative exponents: $a^{-n} = \frac{1}{a^n}$
Scientific Notation
- Express large and small numbers
- Operations with scientific notation
- Solve real-world problems
Scientific Notation:
$a \times 10^n$ where $1 \leq a < 10$ and $n$ is an integer
$a \times 10^n$ where $1 \leq a < 10$ and $n$ is an integer
Chapter 4: Scale Factors & Similarity
Similar Figures
- Identify similar polygons
- Calculate scale factors
- Find missing side lengths
- Solve problems using similarity
Transformations
- Dilations (enlargements/reductions)
- Scale factor relationships
- Area and perimeter changes
Remember:
If scale factor is $k$, then area changes by $k^2$ and volume by $k^3$.
Chapters 5 & 7: Polynomials
Polynomial Operations
- Add and subtract polynomials
- Multiply polynomials by monomials
- Multiply binomials (FOIL)
- Identify degree and number of terms
Factoring
- Factor out common factors
- Factor trinomials
- Factor by grouping
FOIL Example:
$(x + 3)(x + 5) = x^2 + 5x + 3x + 15 = x^2 + 8x + 15$
Chapter 6: Linear Relations
Slope & Y-Intercept
- Calculate slope using two points
- Identify y-intercept from graph or equation
- Write equations in slope-intercept form
- Graph linear equations
Linear Patterns
- Extend number patterns
- Write equations from tables
- Solve pattern problems
Slope Formula:
$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{\text{rise}}{\text{run}}$
Slope-Intercept Form: $y = mx + b$
$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{\text{rise}}{\text{run}}$
Slope-Intercept Form: $y = mx + b$
Chapters 8 & 9: Linear Equations & Inequalities
Solving Linear Equations
- One-step and multi-step equations
- Equations with variables on both sides
- Equations with fractions
- Word problems leading to equations
Linear Inequalities
- Solve one-variable inequalities
- Graph solutions on number lines
- Write inequalities from word problems
Important:
When multiplying or dividing by a negative number, flip the inequality sign!
Chapter 10: Circle Geometry
Circle Properties
- Radius, diameter, circumference
- Central and inscribed angles
- Chords and arcs
- Circle theorems
Problem Solving
- Find missing angles
- Calculate arc lengths
- Apply circle theorems
Circle Formulas:
Circumference: $C = 2\pi r = \pi d$
Area: $A = \pi r^2$
Circumference: $C = 2\pi r = \pi d$
Area: $A = \pi r^2$
Chapter 11: Data Analysis & Statistics
Measures of Central Tendency
- Calculate mean, median, mode
- Determine which measure is most appropriate
- Analyze data sets
Data Collection & Bias
- Identify sources of bias
- Evaluate sampling methods
- Interpret graphs and charts
- Probability calculations
Remember:
Mean is affected by outliers, median is not. Mode is the most frequent value.
Quick Reference for PAT Success
Test-Taking Strategies
- Read questions carefully
- Show all work clearly
- Check answers when possible
- Manage your time wisely
- Use estimation to verify
Common Mistakes to Avoid
- Sign errors with negative numbers
- Forgetting to flip inequality signs
- Order of operations mistakes
- Confusing area vs. perimeter
- Not simplifying final answers
Key Formulas to Memorize
- $a^m \times a^n = a^{m+n}$
- $(x + a)(x + b) = x^2 + (a+b)x + ab$
- $m = \frac{y_2 - y_1}{x_2 - x_1}$
- $A = \pi r^2$, $C = 2\pi r$
- $SA_{cylinder} = 2\pi r^2 + 2\pi rh$
Problem-Solving Steps
- Understand: What is being asked?
- Plan: What strategy will you use?
- Solve: Work through the problem
- Check: Does your answer make sense?
- Communicate: Show your reasoning