The ACT Math Subject Test is a standardized test that measures your mathematical skills and knowledge. The ACT Math test is designed to assess your knowledge of topics, as described in Table 1 and your ability to apply them in problem-solving situations.

Table 1: ACT Math Format

No. of QuestionsQuestion TypeTime LimitTime/Question
60Multiple-choice with 4 answer choices60 Minutes1 Minute

Table 2: Distribution of question types and skills you can expect to encounter on the ACT Mathematics test

Question TypesSubtopicsQuestion Distribution (approx.)
Pre AlgebraBasic operations using whole numbers, fractions, decimals, and integers,
Scientific notation,
Square roots,
Ratio, proportion, and percent,
Linear equations,
Ordering numbers by value,
Simple probability,
Simple descriptive statistics,
Data collection, representation, and interpretation,
12-15 questions (20 to 25%)
Elementary AlgebraSubstitution method for evaluating algebraic expressions,
Expressing functional relationships using variables
Understanding algebraic operations ,
Quadratic equations (with and without factoring)
9-12 questions (15 to 20%)
Intermediate AlgebraQuadratic formula,
Absolute value equations,
Quadratic inequalities,
Rational and radical expressions,
Systems of equations,
Complex numbers.
Polynomial roots
9-12 questions (15 to 20%)
Statistics and ProbabilityData collection methods 
Sample space
6-7 questions (8% – 12%)
Coordinate GeometrySlope,
Parallel and perpendicular lines,
Graphing (in the context of equations and graphs),
9-12 questions (15 to 20%)
Plane GeometryProperties of plane figures,
Properties of circles, triangles, rectangles, trapezoids, and parallelograms Proving basics and techniques,
Three-dimensional measurements
12-15 questions (20 to 25%)
TrigonometryTrigonometric identities,
Trigonometric functions (values and properties).
Graphing trigonometric functions.
Modelling using trigonometric functions,
Solving trigonometric equations
3-6 questions (5 to 10%)
FunctionsFunctions (definition, notation, representation, and application),
Linear functions,
Radical functions,
Logarithmic functions
7-9 questions (12% – 15%)
Integrating essential skillsRates,
Proportional relationships,
Surface area,
12-15 questions (20 to 27%)

Here are the ACT formulas students must know before taking the test this fall:

Table 3. Pre-Algebra

Scientific NotationScientific notation is a way of writing very large or very small numbers using powers of 10.
For example:
The number 3,500,000 can be expressed in scientific notation as 3.5 x 10^6. The number 0.000012 can be expressed in scientific notation as 1.2 x 10^-5.
Square RootsThe square root of a product: ?(ab) = ?a × ?b
The square root of a quotient: ?(a/b) = (?a) / (?b)
Ratio, proportion, and percentDirect and Indirect Proportion ( (a1/b1)=(a2/b2) and (a1a2 = b1b2)  
Ratio: The ratio of two quantities a and b can be written as a:b or a/b.    
Linear equationsy = mx + b

Table 4. Elementary Algebra

Elementary Algebra  The distributive property: a(b + c) = ab + ac
The commutative property: a + b = b + a, ab = ba
The associative property: (a + b) + c = a + (b + c), (ab)c = a(bc)
The identity property: a + 0 = a, a x 1 = a
The inverse property: a + (-a) = 0, a x 1/a = 1

Table 5. Intermediate Algebra: Linear Equations and Functions

Matrices:Matrix addition and subtraction: A + B = B + A, A – B = A + (-B)
Scalar multiplication: k(A + B) = kA + kB, (k + l)A = kA + lA ·      
Matrix multiplication: AB = C, where C[i,j] = ?k A[i,k]B[k,j]
Complex Numbers:The imaginary unit: i^2 = -1T
he complex conjugate of a+bi is a-bi
Addition and subtraction: (a+bi) + (c+di) = (a+c) + (b+d)i, (a+bi) – (c+di) = (a-c) + (b-d)i
Multiplication: (a+bi)(c+di) = (ac-bd) + (ad+bc)i
Division: (a+bi) / (c+di) = ((ac+bd)/(c^2+d^2)) + ((bc-ad)/(c^2+d^2))i  

Table 6. Statistics and Probability

MeanSum of the terms / the number of different terms
Average speedTotal distance / total time
ProbabilityProbability = Target outcomes / Total outcomes  

Table 7. Coordinate Geometry

SlopeSlope = y? – y? /  x? – x?
Slope-Intercept Formy=mx+b
Midpoint Formula(x?+x?) / 2, (y?+y?) / 2
Distance Formulad=?(x? – x?)² + (y? – y?)²
LogarithmsLog_b(x.y) = log_bx + log_by
Log_b{x/y} = log_bx – log_by

Table 8. Plane Geometry

RectanglesArea of Rectangle: area = length x width
Perimeter: 2l+2w
Volume: lwh a (h is the height of the figure)
TrianglesArea of Triangle: area = (1/2) (base) (height)
Pythagorean Theorem: a2 + b2 = c2
TrapezoidsArea: [parallel side a + parallel side b)/2]h
CirclesArea of Circle: ? * r²
Circumference = 2? * r
Length of an Arc: (2?r)(degree measure center of arc/360)
Equation of a Circle: (x – h)^2 + (y – k)^2 = r^2 where (h,k) are the center of the circle
CylinderVolume of a cylinder: ?r2h

Table 9. Trigonometry

SOH CAH TOAsin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent

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