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ACT ACT-Math Exam Syllabus Topics:

SectionWeightObjectives
Integrating Essential Skills20%- Combining multiple skills in complex problems
- Average and median calculations
- Area, surface area, and volume calculations
- Rates, percentages, and proportional relationships
Statistics & Probability15%- Measures of center and spread
- Probability calculations
- Bivariate data and scatterplots
- Statistical inference
- Data collection and representation
Geometry20%- Quilaterals and polygons
- Triangles (including right triangles)
- Coordinate geometry
- Circles and circular sectors
- Trigonometry (sine, cosine, tangent)
- Lines, angles, and planes
- 3D shapes and volume
Algebra20%- Rational and radical equations
- Exponential relationships
- Systems of equations
- Quadratic equations and inequalities
- Linear equations and inequalities
Number & Quantity12%- Real and complex number systems
- Vectors and matrices
- Quantities and units
- Integer and rational exponents
Functions20%- Linear, quadratic, and polynomial functions
- Modeling with functions
- Function transformations
- Exponential and logarithmic functions
- Function definition and notation

ACT American College Testing: Math Section Sample Questions:

1. The expression

is equivalent to:

A) 5/7
B) x + 5
C) (x + 5) / (x + 7)
D) (2x - 15) / (4x - 21)
E) -5 / (2x - 7)


2. The function m#n is equal to m 2 - n.
Which of the following is equivalent to m#(n#m)?

A) n 2 - m
B) (n 2 - m) 2 - m
C) (m 2 - n) 2 - n
D) -n
E) m2+ m - n 2


3. If g > 0 and h < 0, which of the following is always positive?

A) g × h
B) hg
C) g + h
D) g - h
E) |h| - |g|


4. Which of the following statements must be true whenever n, a, b, and c are positive integers such that n < a, c > a, and b > c?

A) a < n
B) b - n > a - n
C) n + b = a + c
D) 2n > a + b
E) b < n


5. If a + 3b = 37 and a - 3b = 19, then b = ___.

A) 3
B) 12
C) 24
D) 6


Solutions:

Question # 1
Answer: C
Question # 2
Answer: E
Question # 3
Answer: D
Question # 4
Answer: B
Question # 5
Answer: A

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