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ACT ACT-Math Exam Syllabus Topics:
| Section | Weight | Objectives |
|---|---|---|
| Geometry | 20% | - Circles and circular sectors - Quilaterals and polygons - 3D shapes and volume - Trigonometry (sine, cosine, tangent) - Lines, angles, and planes - Coordinate geometry - Triangles (including right triangles) |
| Integrating Essential Skills | 20% | - Combining multiple skills in complex problems - Rates, percentages, and proportional relationships - Area, surface area, and volume calculations - Average and median calculations |
| Number & Quantity | 12% | - Quantities and units - Integer and rational exponents - Real and complex number systems - Vectors and matrices |
| Algebra | 20% | - Systems of equations - Exponential relationships - Rational and radical equations - Linear equations and inequalities - Quadratic equations and inequalities |
| Functions | 20% | - Modeling with functions - Function definition and notation - Linear, quadratic, and polynomial functions - Function transformations - Exponential and logarithmic functions |
| Statistics & Probability | 15% | - Probability calculations - Data collection and representation - Bivariate data and scatterplots - Statistical inference - Measures of center and spread |
ACT American College Testing: Math Section Sample Questions:
1. The equation |2x - 8| + 3 = 5 has 2 solutions.
Those solutions are equal to the solutions to which of the following pairs of equations?
A) 2x - 5 = 5 -2x - 5 = -5
B) 2x - 8 = 2 -2x - 8 = 2
C) 2x - 8 = 2 - (2x - 8) = 2
D) 2x - 8 = 2 - (2x - 8) = 8
E) 2x - 8 = 8 - (2x - 8) = 8
2. If graphed, which of the following pairs of equations would be parallel to each other?
A) y = 5x + 5, y = 1/5x + 5
B) y = 3x + 3, y = -1/3x - 3
C) y = 4x + 1, y = 1/5x + 5
D) y = 6x + 6, y = 6x - 4
E) y = 2x + 4, y = x + 4
3. The scatterplot above shows the speeds of different runners over time.
Which of the following could be the equation of the line of best fit?
A) S = -t + 25
B) S = -1/2 × (t - 20)
C) S = -1/2 × (t - 10)
D) S = -2 × (t - 15)
E) S = 2 × (t + 15)
4. A store prices a coat at $85. During a sale, the coat is sold at 20% off. After the sale, the store raises the price of the coat 10% over its sale price.
What is the price of the coat now?
A) $68.00
B) $18.70
C) $74.80
D) $93.50
E) $61.20
5. If y = - x 3 + 3 x - 3, what is the value of y when x = -3?
A) 18
B) -35
C) 33
D) 15
E) -21
Solutions:
| Question # 1 Answer: C | Question # 2 Answer: D | Question # 3 Answer: D | Question # 4 Answer: C | Question # 5 Answer: D |
