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ACT ACT-Math Exam Syllabus Topics:

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

                                          ACT American College Testing: Math Section Sample Questions:

                                          Question 1

                                          If f(x) = 8x 2 - 10x + 5, then f(-4) = ?

                                          A. -3
                                          B. 173
                                          C. -173
                                          D. 50


                                          Question 2

                                          In the diagram above, line AB is parallel to line CD,

                                          measures 140º and

                                          measures 55º.

                                          What is the measure of

                                          ?

                                          A. 95º
                                          B. 40º
                                          C. 55º
                                          D. 135º
                                          E. 85º


                                          Question 3

                                          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. 158
                                          B. 122
                                          C. 132
                                          D. 55


                                          Question 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. 90º
                                          B. 70º
                                          C. 10º
                                          D. 20º
                                          E. 110º


                                          Question 5

                                          A box contains five blue pens, three black pens, and two red pens.
                                          If every time a pen is selected, it is removed from the box, what is the probability of selecting a black pen followed by a blue pen?

                                          A. 1/6
                                          B. 1/50
                                          C. 1/10
                                          D. 3/20
                                          E. 77/90


                                          Solutions:

                                          Question 1
                                          Answer: B
                                          Question 2
                                          Answer: E
                                          Question 3
                                          Answer: A
                                          Question 4
                                          Answer: D
                                          Question 5
                                          Answer: A

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