Quantitative Reasoning
25%of exam
Algebraic Reasoning
25%of exam
Geometric & Spatial Reasoning
25%of exam
Probabilistic & Statistical Reasoning
25%of exam
Quick Facts
- Exam
- TSIA2 Math
- CRC test
- 20 questions
- Diagnostic
- 48 questions
- Time
- Untimed
- Pass
- CRC 950-990
- Alt pass
- Diagnostic level 6
- Calculator
- On-screen only
- Platform
- ACCUPLACER
PEMDAS
Parentheses, Exponents, Multiply, Divide, Add, Subtract
Left to rightMultiply and divide tieAdd and subtract tie
Part-to-part vs Whole
Part-to-part
- Group to group
- 3 to 2
- No total
Part-to-whole
- Group to total
- 3 of 5
- Sum parts
Groups vs total
Ratios & Proportions
- Unit rate
- Quantity per one unit
- Proportion
- Two equal ratios
- Cross-multiply
- ad = bca/b=c/d
- Part-to-part
- Compares two groups
- Part-to-whole
- Group over total
- Direct variation
- y = kx
CRC vs Diagnostic
CRC
- 20 questions
- Adaptive
- Scaled 950-990
Diagnostic
- 48 questions
- If routed
- Level per category
Classify vs profile
Percent & Money
- Percent change
- Change over original
- Discount
- Dollar reduction off price
- Sale price
- Original minus discount
- Simple interest
- I = P r t
- Percent of
- Multiply by decimal
- Markup
- Increase over cost
Number Sense
- Order of operations
- PEMDAS sequence
- Scientific notation
- Power-of-ten form
- Fraction ops
- Common denominator first
- Signed numbers
- Track negative signs
- Proportional estimate
- Scale known ratio
- Unit conversion
- Multiply by conversion factor
Format & Scoring
- CRC test
- 20 adaptive questions
- Diagnostic test
- 48 routed questions
- Benchmark
- CRC 950 to 990
- Level 6
- Diagnostic passing level
- Untimed
- No time limit
- Calculator
- On-screen only
Solve Picker
- One variable→Inverse operations(Isolate variable)
- Two equations→Elimination(Cancel a variable)
- Quadratic factors→Zero-product(Each factor zero)
- Messy quadratic→Quadratic formula(Use discriminant)
- Same base powers→Set exponents equal(Rewrite bases)
- Radical present→Square then check(Reject extraneous)
Algebra Moves
- Distributive
- a(b+c) = ab+ac
- Like terms
- Same variable and power
- FOIL
- First outer inner last
- Difference of squares
- a^2-b^2 = (a-b)(a+b)
- Factoring
- Product and sum
- Exponent rules
- Add when multiplying
Solving Equations
- Linear equation
- Isolate the variable
- Inequality
- Flip sign on negative
- System
- Substitute or eliminate
- Quadratic formula
- Use when unfactorable
- Zero-product
- Set each factor zero
- Literal equation
- Solve for one variable
Functions & Graphs
- Slope
- Rise over run
- Slope-intercept
- y = mx + b
- Point-slope
- y-y1 = m(x-x1)
- f(a)
- Substitute the input
- Exponential
- Repeated percent change
- Vertex form
- Shows turning point
Radicals & Rationals
- Simplify radical
- Remove square factors
- Rational expression
- Fraction of polynomials
- Undefined
- Denominator equals zero
- Radical equation
- Square, then check
- Common-base power
- Set exponents equal
- Absolute value
- Two cases split
SOH-CAH-TOA
Sine opposite, cosine adjacent, tangent opposite
SOH: sin O/HCAH: cos A/HTOA: tan O/A
Perimeter vs Area
Perimeter
- Distance around
- Linear units
- Add sides
Area
- Space inside
- Square units
- Multiply dimensions
Around vs inside
Geometry Picker
- Distance around→Perimeter(Circle circumference)
- Inside a 2D shape→Area formula(Square units)
- Inside a solid→Volume(Cubic units)
- Outside a solid→Surface area(Sum faces)
- Right triangle side→Pythagorean(a^2+b^2=c^2)
- Right triangle angle→SOH-CAH-TOA(Pick ratio)
2D Measurement
- Rectangle area
- length x width
- Triangle area
- half base x height
- Trapezoid area
- half (b1+b2) h
- Circle area
- pi r squared
- Circumference
- 2 pi r
- Perimeter
- Distance around figure
Scale Factor
Length k, area k squared, volume k cubed
Sides: kArea: k^2Volume: k^3
Surface Area vs Volume
Surface area
- Sum of faces
- Square units
- Covers outside
Volume
- Space filled
- Cubic units
- Base times height
Skin vs fill
3D Solids
- Prism volume
- Base area x height
- Cylinder volume
- pi r squared h
- Cone volume
- One-third cylinder
- Surface area
- Sum of all faces
- Cube volume
- Side cubed
- Rectangular prism
- length x width x height
Similar vs Congruent
Similar
- Same shape
- Scaled sides
- Area k squared
Congruent
- Same size
- Equal sides
- Rigid motion
Scaled vs identical
Right Triangle Trig
- Pythagorean
- a^2 + b^2 = c^2Right triangle
- Sine
- Opposite over hypotenuse
- Cosine
- Adjacent over hypotenuse
- Tangent
- Opposite over adjacent
- Similarity
- Same shape, scaled
- Scale factor
- Area scales k squared
Transforms & Coordinate
- Translation
- Slide, same size
- Reflection
- Flip over line
- Rotation
- Turn about point
- Dilation
- Resize by factor
- Distance
- Pythagorean on points
- Midpoint
- Average the coordinates
Probability
Or add cases; and multiply chances
Or: addAnd: multiplyComplement: 1 minus
Mean vs Median
Mean
- Sum over count
- Uses all values
- Outlier sensitive
Median
- Middle value
- Sort first
- Outlier resistant
Average vs middle
Data Picker
- Typical value→Mean(Sum over count)
- Outliers present→Median(Resistant center)
- Spread asked→IQR or MAD(Resists extremes)
- Chance of event→Favorable over total(Full sample space)
- At least one→Complement(1 minus none)
- Both events happen→Multiply(Independent events)
Center & Spread
- Mean
- Sum over count
- Median
- Middle when ordered
- Mode
- Most frequent value
- Range
- Max minus min
- IQR
- Q3 minus Q1
- MAD
- Average absolute deviation
Independent vs Dependent
Independent
- No influence
- Multiply directly
- With replacement
Dependent
- Probability changes
- Update denominator
- No replacement
Same odds vs changed
Data & Displays
- Box plot
- Five-number summary
- Scatterplot
- Two-variable association
- Frequency table
- Counts per category
- Categorical
- Groups or labels
- Quantitative
- Numerical measurements
- Sampling
- Representative subset
Probability
- Simple probability
- Favorable over total
- Complement
- 1 minus event
- Independent
- Multiply probabilities
- Dependent
- Update the denominator
- Compound
- Combine two events
- Equally likely
- Same-chance outcomes
Common Traps
Percent base
Divide by original ≠ Not the new value
Inequality flip
Negative multiply flips ≠ Positive keeps sign
Distribute fully
Multiply every term ≠ Not just first
Scale factors
Area uses k squared ≠ Volume uses k cubed
Undefined fraction
Denominator zero undefined ≠ Numerator zero is root
Radius vs diameter
Formulas use radius ≠ Diameter doubles radius
Passing score
950 is scaled ≠ Not percent correct
Last Minute
- 1.Percent change over original
- 2.Flip inequality on negative
- 3.Area uses square units
- 4.Volume uses cubic units
- 5.Circle formulas need radius
- 6.Median resists outliers
- 7.Probability favorable over total
- 8.Multiply independent event chances
- 9.Check radical equation solutions
- 10.950 scaled meets readiness
- 11.Diagnostic level 6 also passes
- 12.Test untimed; pace for accuracy
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