Algebra (Equations)
48-61%of exam
QuadraticsFactoringLinesSystemsInequalitiesMethod Pickers
Functions
24-32%of exam
Number + Statistics
11-25%of exam
CorrelationResidualsTwo-Way TablesCenter + SpreadReal vs Irrational
Exam Skills
10-15%of exam
ModelingInterpret in ContextReference SheetShow Work
Quick Facts
- Exam
- Regents Algebra I
- Standards
- Next Generation Math
- Questions
- 35 in 4 parts
- Time
- 3 hours
- Pass
- Scale score 65
- Calculator
- Graphing allowed
- Reference sheet
- Provided
- Max credits
- 82 raw
Order of Operations
PEMDAS: Please Excuse My Dear Aunt Sally
ParenthesesExponentsMultiply/DivideAdd/Subtract
Factoring vs Formula
Factoring
- Nice integers
- Zero product
- Fast
Quadratic formula
- Any quadratic
- Uses discriminant
- Always works
Easy vs universal
Solve Quadratic How?
- Factors easily→Factor + zero product(Fastest)
- a = 1, b even→Complete the square(Clean)
- Will not factor→Quadratic formula(Always works)
- Need only roots→Graph x-intercepts(Calculator)
- x^2 = number→Square root both sides(Two roots)
- Need vertex→Vertex form / -b/2a(Min or max)
Quadratic Core
- Standard form
- y = ax^2 + bx + c
- Quadratic formula
- x = (-b +/- root) / 2aReference
- Discriminant
- b^2 - 4ac
- Axis of symmetry
- x = -b / 2a
- Vertex x
- -b / 2a
- Vertex form
- a(x-h)^2 + k
- Vertex point
- (h, k)
- Zeros
- Where y = 0
Quadratic Formula
x = (-b +/- root b^2 - 4ac) / 2a
a, b, c from standard+/- gives two rootsInside = discriminant
Solve System How?
- One variable alone→Substitution(Plug in)
- Opposite coefficients→Elimination(Add equations)
- Answer choices given→Graph intersection(Calculator)
- Variables cancel false→No solution(Parallel)
- Variables cancel true→Infinite solutions(Same line)
Discriminant Rules
- b^2 - 4ac > 0
- Two real roots
- b^2 - 4ac = 0
- One real root
- b^2 - 4ac < 0
- No real roots
- Perfect square
- Two rational roots
- Not a square
- Two irrational roots
- Sum of roots
- -b / a
- Product of roots
- c / a
Factoring Patterns
- GCF first
- Pull common factor
- Diff of squares
- a^2 - b^2 = (a-b)(a+b)
- Perfect trinomial
- a^2 + 2ab + b^2
- x^2 + bx + c
- Multiply c, add b
- ax^2 + bx + c
- AC method / split
- Zero product
- Each factor = 0
- Complete square
- Add (b/2)^2
Linear Forms
- Slope
- (y2 - y1)/(x2 - x1)
- Slope-intercept
- y = mx + b
- Point-slope
- y-y1 = m(x-x1)
- Standard form
- Ax + By = C
- y-intercept
- b, where x = 0
- Parallel
- Same slope m
- Perpendicular
- Negative reciprocal slope
- Horizontal
- Slope = 0
Systems + Inequalities
- Substitution
- Plug one into other
- Elimination
- Add to cancel variable
- Graphing
- Solution is intersection
- No solution
- Parallel, no cross
- Infinite solutions
- Same line
- Flip sign
- Divide by negative
- Dashed line
- Strict < or >
- Solid line
- <= or >=
Line Equation
y = mx + b: slope m, intercept b
m = rise/runb = where x is 0+m up, -m down
Linear vs Exponential
Linear
- Add constant
- Constant rate
- Straight line
Exponential
- Multiply constant
- Constant ratio
- Curved growth
Add vs multiply
Which Function Type?
- Equal y differences→Linear(Constant rate)
- Constant y ratio→Exponential(Multiply)
- Equal 2nd differences→Quadratic(Parabola)
- Add same each step→Arithmetic / linear(Common d)
- Multiply each step→Geometric / exponential(Common r)
- U-shaped graph→Quadratic(Vertex)
Function Basics
- f(x) notation
- Output for input x
- Domain
- Allowed x inputs
- Range
- Possible y outputs
- Function test
- One y per x
- Vertical line test
- Graph crosses once
- Avg rate of change
- (f(b)-f(a))/(b-a)
- x-intercept
- Root, where y = 0
- Discrete
- Separate plotted points
Slope
Slope = rise over run
Rise = change in yRun = change in xUp-right positive
Domain vs Range
Domain
- Inputs x
- Read left-right
- Allowed values
Range
- Outputs y
- Read bottom-up
- Resulting values
x in vs y out
Exponential Models
- General form
- y = a * b^x
- a value
- Initial amount
- b > 1
- Growth factor
- 0 < b < 1
- Decay factor
- Growth rate r
- b = 1 + r
- Decay rate r
- b = 1 - r
- Constant ratio
- Equal y multiples
Exponential
y = a times b to the x
a = startb > 1 growsb < 1 decays
Discrete vs Continuous
Discrete
- Separate points
- Countable items
- No connecting
Continuous
- Solid curve
- Any value
- Connected graph
Dots vs line
Sequences
- Arithmetic
- Add common difference d
- Arithmetic nth
- a_n = a_1 + (n-1)d
- Geometric
- Multiply common ratio r
- Geometric nth
- a_n = a_1 * r^(n-1)
- Recursive
- Uses previous term
- Linear pattern
- Arithmetic sequence
- Exponential pattern
- Geometric sequence
Transformations
- f(x) + k
- Shift up k
- f(x) - k
- Shift down k
- f(x - h)
- Shift right h
- f(x + h)
- Shift left h
- -f(x)
- Reflect over x-axis
- a * f(x)
- Vertical stretch a
- f(-x)
- Reflect over y-axis
Correlation vs Causation
Correlation
- Move together
- Measured by r
- Pattern only
Causation
- One causes other
- Needs experiment
- Not from r
Linked vs causes
Statistics
- Mean
- Sum / count
- Median
- Middle of ordered data
- Correlation r
- Range -1 to 1
- r near 1
- Strong positive linear
- r near 0
- Weak / no linear
- Residual
- Actual minus predicted
- Good fit
- Random residual scatter
- Two-way table
- Counts by categories
Mean vs Median
Mean
- Average value
- Sum / count
- Shifted by outliers
Median
- Middle value
- Order first
- Resists outliers
Average vs middle
Number + Quantity
- Rational
- Fraction of integers
- Irrational
- Non-repeating decimal
- Rational +/- rational
- Stays rational
- Rational + irrational
- Becomes irrational
- Closure
- Stays in same set
- Units / accuracy
- Match real context
Common Traps
Zero vs no solution
x = 0 is a value ≠ No solution means none
Slope vs intercept
m is the slope ≠ b is the y-intercept
Domain vs range
Domain is x inputs ≠ Range is y outputs
Add vs multiply exponents
Same base multiply: add ≠ Power of power: multiply
Vertex vs zeros
Vertex is turning point ≠ Zeros are x-intercepts
Correlation vs causation
r shows a pattern ≠ Pattern is not cause
Scale score vs percent
65 is scale score ≠ Not raw percent correct
Last Minute
- 1.Passing = scale score 65, not percent
- 2.35 questions, Parts I-IV, 3 hours
- 3.Graphing calculator and straightedge allowed
- 4.Reference sheet given at back
- 5.Quadratic: (-b +/- root b^2-4ac)/2a
- 6.Axis and vertex: x = -b/2a
- 7.Discriminant b^2-4ac: + two, 0 one
- 8.Slope m = (y2-y1)/(x2-x1)
- 9.Linear adds; exponential multiplies y = a*b^x
- 10.Define variable, write equation first
- 11.Show all work on constructed-response
- 12.Interpret slope, zeros, vertex in context
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