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ACT ACT-Math Exam Syllabus Topics:

Section

Weight

Objectives

Integrating Essential Skills

40–43%

- Problem Solving

1. Multi-step word problems
2. Applied reasoning with arithmetic and algebra

- Graphical Interpretation

1. Reading and analyzing graphs and charts

- Mathematical Modeling

1. Translating real-world problems into equations
2. Interpreting algebraic and graphical representations

Preparing for Higher Math

57–60%

- Geometry

1. Coordinate geometry
2. Plane geometry (triangles, circles, polygons)
3. Transformations and symmetry

- Algebra

1. Quadratic expressions and functions
2. Polynomials and factoring
3. Linear equations and inequalities

- Functions

1. Linear, quadratic, and piecewise functions
2. Function notation and evaluation
3. Domain and range

- Number & Quantity

1. Real and complex number systems
2. Vectors and matrices (basic concepts)

- Statistics & Probability

1. Data interpretation
2. Probability fundamentals
3. Descriptive statistics (mean, median, mode)

ACT American College Testing: Math Section Sample Questions:

1. The measures of the length, width, and height of a rectangular prism are in the ratio 2:6:5.
If the volume of the prism is 1,620 mm3, what is the width of the prism?

A) 3 mm
B) 18 mm
C) 27 mm
D) 6 mm
E) 9 mm

2. 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) 27
B) 20
C) 25
D) 26
E) 30

3. A box in the shape of a cube has an interior side length of 18 inches and is used to ship a right circular cylinder with a radius of 6 inches and a height of 1 2 inches. The interior of the box not occupied by the cylinder is filled with packing material.
Which of the following numerical expressions gives the number of cubic inches of the box filled with packing material?

A) 6(18) 2 - 2π(6)(12)
B) 18 3 - π(12) 3
C) 6(18) 2 - 2π(6)(12) - 2π(6) 2
D) 18 3 - π(6) 2 (12)
E) 18 3 - π(6)(12) 2

4. If m < n < 0, then all of the following are true EXCEPT:

A) mn > 0.
B) m - n < 0.
C)

D)

E) -m < -n.