Expressions, Functions, Data
31-38%of exam
Linear Relationships
31-38%of exam
Non-Linear Relationships
31-38%of exam
Quick Facts
- Exam
- Algebra 1 EOC
- Assessment
- B.E.S.T. EOC
- Time
- 160 minutes
- Pass
- Scale 400
- Level
- Level 3
- Items
- 45-50
- Format
- Computer-adaptive
- Provider
- FLDOE
Exponent Rules
Add, Multiply, Subtract, Flip
Product: add exponentsPower: multiply exponentsQuotient: subtract exponentsNegative: reciprocal
Slope vs Rate of Change
Slope
- Rise over run
- Steepness of line
- Graph-based
Rate of Change
- Output per input
- Over an interval
- Formula-based
Graph vs interval
Model Picker
- Constant add each step→Linear model(y=mx+b)
- Constant multiply each step→Exponential model(y=a*b^t)
- Equal differences→Linear(Slope constant)
- Equal ratios→Exponential(Base constant)
- Simple interest→Linear growth(I=Prt)
- Compound interest→Exponential growth(A=P(1+r/n)^nt)
Exponent Rules
- Product of Powers
- Add exponents
- Power of a Power
- Multiply exponents
- Quotient of Powers
- Subtract exponents
- Negative Exponent
- Reciprocal of base
- Zero Exponent
- Equals one
- Power of a Product
- Apply to each factor
Achievement Levels
Level 3 starts at 400
L1: 325-378L2: 379-399L3: 400-417 passingL4: 418-434L5: 435-475
Function vs Relation
Function
- One output per input
- Passes vertical line test
- No repeated x with different y
Relation
- Any input-output pairs
- May repeat x-values
- Could fail vertical line test
One output vs any
Radicals & Rational
- Radicand
- Must be nonnegative
- Perfect square
- Pull out root
- Like radicals
- Add coefficients
- Rational expression
- Denominator nonzero
- Simplify rational
- Cancel common factors
- Extraneous root
- Check solution
Mean vs Median
Mean
- Average of values
- Sensitive to outliers
- Sum divided by count
Median
- Middle when ordered
- Resists outliers
- Splits data in half
Average vs middle
Function Basics
- Function
- One output per input
- Vertical line test
- At most once
- f(x) notation
- Output value
- Domain
- Input values
- Range
- Output values
- Interval notation
- Brackets include, parens exclude
Domain vs Range
Domain
- Input values
- x-values
- Independent variable
Range
- Output values
- y-values
- Dependent variable
Input vs output
Data & Stats
- Mean
- Average value
- Median
- Middle value
- Mode
- Most frequent
- IQR
- Q3 minus Q1
- Outlier
- Far from rest
- Scatter plot
- Bivariate data
- Correlation
- Association strength
- Causation
- One drives other
- Residual
- Observed minus predicted
- Margin of error
- Estimate range
Correlation vs Causation
Correlation
- Variables move together
- Association only
- Does not prove cause
Causation
- One variable drives other
- Direct cause and effect
- Requires evidence
Association vs cause
Inequality Flip
Negative multiply flips the sign
Add/subtract: no flipMultiply/divide negative: flipSolid line: includeDashed line: exclude
Expression vs Equation
Expression
- No equals sign
- Simplify or evaluate
- Represents a value
Equation
- Has equals sign
- Solve for unknown
- Both sides balanced
No equals vs equals
Line Form Picker
- Slope + intercept known→y=mx+b(Slope-intercept)
- Point + slope known→Point-slope(No b needed)
- Two intercepts known→Standard form(Ax+By=C)
- Lines parallel→Same slope(m1=m2)
- Lines perpendicular→Negative reciprocal(m1*m2=-1)
- Slope undefined→Vertical line(x=constant)
- Slope zero→Horizontal line(y=constant)
Linear Forms
- Slope
- Rise over run
- Slope formula
- (y2-y1)/(x2-x1)Formula
- Slope-intercept
- y=mx+b
- Point-slope
- y-y1=m(x-x1)
- Standard form
- Ax+By=C
- x-intercept
- y equals zero
- y-intercept
- x equals zero
- Parallel slopes
- Equal slopes
- Perpendicular slopes
- Negative reciprocals
Line Forms
Slope-intercept, point-slope, standard
y=mx+b: slope + y-inty-y1=m(x-x1): point + slopeAx+By=C: interceptsSwitch forms as needed
System Solver Picker
- Variable isolated→Substitution(Plug in)
- Coefficients align→Elimination(Add equations)
- Same slope, diff intercept→No solution(Parallel)
- Same line→Infinite solutions(Equivalent)
- Different slopes→One solution(Intersect)
- Inequalities system→Graph and shade(Overlap region)
Inequalities & Systems
- Inequality flip
- Negative multiply reverses
- Solid line
- Inclusive boundary
- Dashed line
- Strict boundary
- Substitution
- Isolate one variable
- Elimination
- Cancel a variable
- One solution
- Different slopes
- No solution
- Parallel, distinct
- Infinite solutions
- Same line
System Solutions
One, none, infinitely many
Diff slopes: one solutionSame slope diff intercept: noneSame line: infiniteCheck slopes first
Sequences & Modeling
- Arithmetic sequence
- Add common difference
- Explicit formula
- a1+(n-1)d
- Recursive rule
- Previous plus d
- Break-even
- Cost equals revenue
- Constraint
- Realistic domain
- Less than
- Subtract from quantity
Quadratic Forms
Standard: y-int, Vertex: max, Factored: roots
Standard: y-intercept cVertex: max or minFactored: zerosSwitch forms as needed
Linear vs Exponential
Linear
- Constant add each step
- Graph is a line
- y=mx+b
Exponential
- Constant multiply each step
- Graph is a curve
- y=a*b^t
Add vs multiply
Quadratic Form Picker
- Asked for zeros→Factored form(Roots visible)
- Asked max or min→Vertex form(Vertex visible)
- Asked y-intercept→Standard form(c is y-int)
- Completing the square→Standard form(Transform)
- Quadratic formula→Standard form(Plug in)
- Axis of symmetry→x=-b/2a(From standard)
Quadratic Forms
- Standard form
- y=ax^2+bx+c
- Vertex form
- y=a(x-h)^2+k
- Factored form
- y=a(x-r1)(x-r2)
- Axis of symmetry
- x=-b/2aFormula
- Vertex
- On axis of symmetry
- Zeros
- Set factors zero
- y-intercept
- Set x zero
- Discriminant
- b^2-4acFormula
- Opens up
- a positive
- Maximum
- a negative
Simple vs Compound Interest
Simple
- Linear growth
- I=Prt
- One rate applied once
Compound
- Exponential growth
- A=P(1+r/n)^nt
- Rate applied each period
Linear vs exponential
Factoring
- GCF
- Common factor first
- Trinomial x^2+bx+c
- Two numbers sum and product
- Difference of squares
- (a-b)(a+b)
- Perfect square trinomial
- a^2+2ab+b^2
- Sum of squares
- Not factorable
- Factor by grouping
- Pair and factor
Exponential & Finance
- Growth model
- y=a(1+r)^t
- Decay model
- y=a(1-r)^t
- Growth base
- b greater than 1
- Decay base
- 0 less than b less 1
- Simple interest
- I=Prt
- Compound interest
- A=P(1+r/n)^nt
- Simple growth
- Linear increase
- Compound growth
- Exponential increase
Absolute Value
- |u|=c
- Split u=c, u=-c
- |u|<c
- And compound
- |u|>c
- Or compound
- |u|=negative
- No solution
- Check solutions
- Extraneous possible
- Distance from zero
- Always nonnegative
Common Traps
Less than vs subtract from
'Less than' means subtract from ≠ 2n-6 not 6-2n
Inequality flip on negative only
Add/subtract: no flip ≠ Multiply/divide negative: flip
Association vs cause
Correlation moves together ≠ Causation drives change
Cancel factors not terms
Cancel common factors ≠ Never cancel individual terms
Sum of squares not factorable
Difference of squares factors ≠ Sum of squares does not
Extraneous roots
Squaring can add roots ≠ Check in original equation
Base 1 not exponential
b>1 means growth ≠ b=1 is constant, not exponential
Realistic domain in context
Context restricts domain ≠ Not always all reals
Last Minute
- 1.Weights: 31-38% each category
- 2.Passing: scale score 400 (Level 3)
- 3.160 minutes, break after 80
- 4.45-50 items, ~5 field-test
- 5.Computer-adaptive: difficulty adjusts
- 6.Scientific calculator + reference sheet
- 7.Negative multiply flips inequality
- 8.Cancel factors, not terms
- 9.Factored form for zeros
- 10.Vertex form for max/min
- 11.b>1 growth; 0<b<1 decay
- 12.Check for extraneous solutions
- 13.Correlation is not causation
- 14.Domain: inputs; Range: outputs
- 15.Less than means subtract from
- 16.EOC counts 30% of course grade
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