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ACT ACT-Math Exam Syllabus Topics:

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

                                          ACT American College Testing: Math Section Sample Questions:

                                          1. The list of numbers 41, 35, 30, X, Y, 15 has a median of 25. The mode of the list of numbers is 15.
                                          To the nearest whole number, what is the mean of the list?

                                          A) 30
                                          B) 25
                                          C) 27
                                          D) 20
                                          E) 26


                                          2. Which of the following is the equation of a parabola whose vertex is at (5, -4)?

                                          A) y = (x - 5) 2 - 4
                                          B) y = (x + 5) 2 - 4
                                          C) y = x 2 - 29
                                          D) y = (x + 5) 2 + 4
                                          E) y = (x - 5) 2 + 4


                                          3. A spinner is divided into eight equal regions, labeled one through eight.
                                          If Jenna spins the wheel, what is the probability that she will spin a number that is less than four and greater than two?

                                          A) 1/8
                                          B) 1/2
                                          C) 3/4
                                          D) 9/32
                                          E) 3/8


                                          4. If g > 0 and h < 0, which of the following is always positive?

                                          A) g + h
                                          B) |h| - |g|
                                          C) g - h
                                          D) g × h
                                          E) hg


                                          5. 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) 10º
                                          C) 70º
                                          D) 90º
                                          E) 110º


                                          Solutions:

                                          Question # 1
                                          Answer: E
                                          Question # 2
                                          Answer: A
                                          Question # 3
                                          Answer: A
                                          Question # 4
                                          Answer: C
                                          Question # 5
                                          Answer: A

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