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ACT ACT-Math Exam Syllabus Topics:

SectionWeightObjectives
Preparing for Higher Math57–60%- Statistics & Probability
  • 1. Basic statistical modeling
    • 2. Counting techniques and probability rules
      • 3. Data representation and interpretation
        • 4. Measures of central tendency and spread
          - Geometry
          • 1. Triangles, circles, and polygons
            • 2. Congruence, similarity, and measurement
              • 3. Surface area, volume, and trigonometric ratios
                • 4. Plane and coordinate geometry
                  - Algebra
                  • 1. Linear, polynomial, radical, and exponential equations
                    • 2. Systems of equations and inequalities
                      • 3. Modeling algebraic relationships
                        • 4. Quadratic expressions and functions
                          - Functions
                          • 1. Graph interpretation and transformation
                            • 2. Function definition and notation
                              • 3. Domain and range analysis
                                • 4. Linear, radical, polynomial, and logarithmic functions
                                  - Number & Quantity
                                  • 1. Real and complex number systems
                                    • 2. Vectors and matrices
                                      • 3. Ratios, proportions, and percentages
                                        • 4. Integer and rational exponents
                                          Integrating Essential Skills40–43%- Logical reasoning and estimation
                                          - Problem-solving in real-world contexts
                                          - Multi-step arithmetic and pre-algebra
                                          - Rates, averages, and unit conversion
                                          ModelingIntegrated throughout- Refine and evaluate model solutions
                                          - Apply models across all content domains
                                          - Create and interpret mathematical models

                                          ACT American College Testing: Math Section Sample Questions:

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

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


                                          2. In the diagram above, ABDE is a square and BCD is an equilateral triangle.

                                          If FC = 6√3 cm, what is the perimeter of ABCDE?

                                          A)

                                          cm
                                          B) 84 cm
                                          C)

                                          cm
                                          D)

                                          cm
                                          E) 60 cm


                                          3. If b3 = -64, then b 2 - 3b - 4 =:

                                          A) 0.
                                          B) -4.
                                          C) -6.
                                          D) 24.
                                          E) 28.


                                          4. FILL BLANK
                                          Point A of rectangle ABCD is located at (-3, 12) and point C is located at (9, 5).
                                          What is the area of rectangle ABCD?


                                          5. If the height of a cylinder is doubled and the radius of the cylinder is halved, the volume of the cylinder:

                                          A) becomes half as large.
                                          B) becomes twice as large.
                                          C) becomes four times larger.
                                          D) becomes four times smaller.
                                          E) remains the same.


                                          Solutions:

                                          Question # 1
                                          Answer: A
                                          Question # 2
                                          Answer: E
                                          Question # 3
                                          Answer: D
                                          Question # 4
                                          Answer: Only visible for members
                                          Question # 5
                                          Answer: A

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