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

ACT-Math real exams

Exam Code: ACT-Math

Exam Name: ACT American College Testing: Math Section

Updated: Jul 15, 2026

Q & A: 280 Questions and Answers

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ACT ACT-Math Exam Syllabus Topics:

SectionWeightObjectives
Integrating Essential Skills40–43%- Mathematical Modeling
  • 1. Interpreting algebraic and graphical representations
    • 2. Translating real-world problems into equations
      - Problem Solving
      • 1. Multi-step word problems
        • 2. Applied reasoning with arithmetic and algebra
          - Graphical Interpretation
          • 1. Reading and analyzing graphs and charts
            Preparing for Higher Math57–60%- Algebra
            • 1. Linear equations and inequalities
              • 2. Polynomials and factoring
                • 3. Quadratic expressions and functions
                  - Number & Quantity
                  • 1. Real and complex number systems
                    • 2. Vectors and matrices (basic concepts)
                      - Functions
                      • 1. Linear, quadratic, and piecewise functions
                        • 2. Domain and range
                          • 3. Function notation and evaluation
                            - Geometry
                            • 1. Plane geometry (triangles, circles, polygons)
                              • 2. Transformations and symmetry
                                • 3. Coordinate geometry
                                  - Statistics & Probability
                                  • 1. Descriptive statistics (mean, median, mode)
                                    • 2. Data interpretation
                                      • 3. Probability fundamentals

                                        ACT American College Testing: Math Section Sample Questions:

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

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


                                        2. Which of the following is equivalent to (2 x + 6) / 4 times (6 x - 36) / (3 x + 9)?

                                        A) (12x 2 - 216) / (12x + 36)
                                        B) (x - 6) / 4
                                        C) x - 6
                                        D) (8x - 30) / (3x + 13)


                                        3. If 2(x - 14) = 22, then x = ___.

                                        A) 35
                                        B) 25
                                        C) 30
                                        D) 20


                                        4. Toby wants to find the volume of a solid toy soldier. He fills a rectangular container 8 cm long, 6 cm wide, and 10 cm high with water to a depth of 4 cm. Toby totally submerges the toy soldier in the water. The height of the water with the submerged toy soldier is 6.6 cm.
                                        Which of the following is closest to the volume, in cubic centimeters, of the toy soldier?

                                        A) 317
                                        B) 125
                                        C) 192
                                        D) 208
                                        E) 156


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

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


                                        Solutions:

                                        Question # 1
                                        Answer: C
                                        Question # 2
                                        Answer: C
                                        Question # 3
                                        Answer: B
                                        Question # 4
                                        Answer: B
                                        Question # 5
                                        Answer: B

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