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ACT ACT-Math Exam Syllabus Topics:

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

                                          ACT American College Testing: Math Section Sample Questions:

                                          Question 1

                                          Which of the following has the greatest value when x = -1/4?

                                          A. -3/8x
                                          B. x -1
                                          C. 1/81x
                                          D. 4x + 3
                                          E. 16x


                                          Question 2

                                          If

                                          , then when a = 8, b could be equal to:

                                          A. 7
                                          B. -2
                                          C. 8
                                          D. 6
                                          E. 4


                                          Question 3

                                          Mario plays basketball on a town league team. The table below gives Mario's scoring statistics for last season.

                                          How many points did Mario score playing basketball last season?

                                          A. 129
                                          B. 190
                                          C. 213
                                          D. 330
                                          E. 380


                                          Question 4

                                          A youth basketball program serves a total of 280 children who are either 11 or 12 years old. The sum of the children's ages equal 3,238 years.
                                          How many 12-year-old children are in the program?

                                          A. 132
                                          B. 122
                                          C. 158
                                          D. 55


                                          Question 5

                                          If graphed, which of the following pairs of equations would be parallel to each other?

                                          A. y = 3x + 3, y = -1/3x - 3
                                          B. y = 6x + 6, y = 6x - 4
                                          C. y = 5x + 5, y = 1/5x + 5
                                          D. y = 4x + 1, y = 1/5x + 5
                                          E. y = 2x + 4, y = x + 4


                                          Solutions:

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

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