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ACT ACT-Math Exam Syllabus Topics:

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

                                          ACT American College Testing: Math Section Sample Questions:

                                          If

                                          anda = 4 and b = 8, which of the following could be true?

                                          • A. x < a
                                          • B. 4 < x < 8
                                          • C. None of the above
                                          • D. x > b
                                          • E. a < x < b
                                          Reveal Solution  Discussion  0

                                          Correct Answer: A  🗳️

                                          In the diagram above, ABC and DEC are right triangles, the length of side BC is 15 units, and the measure of

                                          is 60º.

                                          If

                                          is congruent to

                                          , what is the length of side DC?

                                          • A. √15 units
                                          • B. 15/2 × √3 units
                                          • C. 15√3 units
                                          • D. 15/2 units
                                          • E. 9 units
                                          Reveal Solution  Discussion  0

                                          Correct Answer: D  🗳️

                                          The number of decibels, d, produced by an audio source can be modeled by the equation:

                                          where I is the sound intensity of the audio source and K is a constant.
                                          How many decibels are produced by an audio source whose sound intensity is 1,000 times the value of K?

                                          • A. 100
                                          • B. 40
                                          • C. 10,000
                                          • D. 30
                                          • E. 4
                                          Reveal Solution  Discussion  0

                                          Correct Answer: D  🗳️

                                          In the diagram above, what is the sum of the measures of the

                                          ,

                                          and

                                          ?

                                          • A. 720º
                                          • B. 540º
                                          • C. 180º
                                          • D. Cannot be determined.
                                          • E. 360
                                          Reveal Solution  Discussion  0

                                          Correct Answer: E  🗳️

                                          Laura plans to paint the 8-foot-high rectangular walls of her room, and before she buys paint she needs to know the area of the wall surface to be painted. Two walls are 10 feet wide, and the other 2 walls are 15 feet wide. The combined area of the 1 window and the 1 door in her room is 60 square feet.
                                          What is the area, in square feet, of the wall surface Laura plans to paint?

                                          • A. 340
                                          • B. 390
                                          • C. 200
                                          • D. 400
                                          • E. 360
                                          Reveal Solution  Discussion  0

                                          Correct Answer: A  🗳️

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