ACT American College Testing: Math Section : ACT-Math Exam

  • Exam Code: ACT-Math
  • Exam Name: ACT American College Testing: Math Section
  • Updated: Jul 26, 2026
  • Q & A: 280 Questions and Answers

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ACT ACT-Math Exam Syllabus Topics:

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

                                          ACT American College Testing: Math Section Sample Questions:

                                          1. Let the function f be defined as f(x) = 5x 2 - 7(4x + 3).
                                          What is the value of f(3)?

                                          A) -33
                                          B) -26
                                          C) -18
                                          D) -75
                                          E) -60


                                          2. A car departs Little Rock, Ark., traveling to a baseball game located nine miles east and 12 miles north of the departure point. About how many miles is the game from the departure point?

                                          A) 63
                                          B) 3
                                          C) 15
                                          D) 21


                                          3. For what positive real value of k , if any, is the determinant of the matrix

                                          equal to k ? (Note: The determinant of matrix

                                          equalsad - bc .)

                                          A) 4
                                          B) 3
                                          C) There is no such value of k.
                                          D) 12
                                          E)


                                          4. In the diagram above, lines NO and PQ are parallel to each other and perpendicular to lines JK and LM. Line JK is parallel to line LM. If

                                          is 70º, what is the measure of

                                          ?

                                          A) 20º
                                          B) 90º
                                          C) 70º
                                          D) 110º
                                          E) 10º


                                          5. FILL BLANK
                                          The length of a rectangular prism is four times the height of the prism and one-third the width of the prism. If the volume of the prism is 384 in3, what is the width of the prism?


                                          Solutions:

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

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