ACT Math Sections:
Important things to note:
-Calculator is allowed (some, more complex, calculators are prohibited, esp. calculators with internet access &/or qwerty keyboards)
-5 Multiple choice questions, one more than the other subjects (20% guess chance)
-The ACT assumes a student knows (these topics will be indirectly tested): Order of Operations, (Module 5) Operations of Odd and Even Numbers (even * even= even, odd * even =even, odd * odd = odd), Signed numbers (negative and positive), Adding, subtracting, multiplying and dividing signed numbers, Two kinds of problems, basic problems (2+2) and word problems (Module 5, Module 6 (system of Equations):
Pre-Algebra 20-25%: “Questions in this content area are based on basic operations using whole numbers, decimals, fractions, and integers; place value; square roots and approximations; the concept of exponents scientific notation; factors; ratio, proportion, and percent; linear equations in one variable; absolute value and ordering numbers by value; elementary counting techniques and simple probability; data collection, representation, and interpretation; and understanding simple descriptive statistics.”
Order of Frequency:
- Number Problems (ALL)
- Multiples, Factors, and Primes (Module 5)
- Divisibility and Remainders
- Percentages, Fractions, and Decimals (Module 5 (Ratios))
- Ratios and Proportions (Module 5)
- Mean, Median, and Mode (Module 8)
- Probability (Module 8)
- Absolute Value (Module 6)
- Exponents and Roots (Module 6)
- Series (Module 5: Counting Principles and Permutations)
- A tutorial for divisibility that uses the equation n=qm + r where n is the dividend, q is the quotient, m is the divisor, and r is the remainder.
Elementary Algebra 15-20%: “Questions in this content area are based on properties of exponents and square roots, evaluation of algebraic expressions through substitution, using variables to express functional relationships, understanding algebraic operations and the solution of quadratic equations by factoring.”
Order or Ease:
- Substitution (Module 6)
- Simplifying Algebraic Expressions (Module 6)
- Writing Expressions and Equations (Module 6)
- Solving Linear Equations (Module 6)
- Multiplying Binomials
- I recommend that we teach them to FOIL (First, Outer, Inner, Last)
- This site can be used as a reference but I have a feeling that we can create our own FOIL worksheet relatively easily.
- Inequalities (Module 6)
Intermediate Algebra 15-20%: “Questions in this content area are based on an understanding of the quadratic formula, rational and radical expressions (Module 6), absolute value equations and inequalities (Module 6), sequences and patterns (Module 5), systems of equations, quadratic inequalities, functions, modeling, matrices, roots of polynomials, and complex numbers.”
Topics to know (No order of ease or frequency):
- Solving and Factoring Quadratic Equations (Module 6)
- Solving Systems of Equations (Module 6)
- Relationships between the Sides of an Equation (Module 6)
- Functions (Module 6)
- Matrices (No)
- This site has a good overview of matrices
- Here is a website that we can curate: http://cdn.kutasoftware.com/Worksheets/Alg2/Basic%20Matrix%20Operations.pdf.
- Logarithms (No)
- A simple explanation of logarithmic use in algebra and examples of how logarithms work.
Coordinate Geometry 15-20%: “Questions in this content area are based on graphing and the curves; graphing inequalities; slope; parallel and perpendicular lines; distance; midpoints; and conics.
Topics to know:
- Number Lines and Inequalities (Module 6)
- The (x,y) Coordinate Plane (Module 6)
- Distance and Midpoints (Module 7)
- Slope (Module 6)
- Parallel and Perpendicular Lines (Module 6)
- The Equation of a Line (Module 6)
- Graphing Equations (Module 6 (Linear))
- Conic Sections (No)
- This sight has an extensive overview of conic sections that we can use as an outline for teaching.
Planar Geometry 20-25%: “Questions in this content area are based on the properties and relations of plane figures, including angles and relations among perpendicular and parallel lines; properties of circles, triangles , rectangles, parallelograms, and trapezoids; transformations; the concept of proof and proof techniques; volume; and applications of geometry to three dimensions.”
Topics to know:
- Angles and Lines (Module 7)
- Triangles (Module 7)
- Polygons (Module 7)
- Circles (Module 7)
- Simple Three-Dimensional Geometry (Module 7)
Trigonometry 5-10%: “Questions in this content area are based on understanding trigonometric relations in right triangles; values and properties of trigonometric functions; graphing trigonometric functions; modeling using trigonometric functions; use of trigonometric identities; and solving trigonometric equations.”
Topics to know:
- SOHCAHTOA (No)
Annotated Resources for making worksheets:
- This website uses clear graphical designs to show the relations between an angle (x) and its adjacent, opposite, and hypotenuse sides in a right triangle—which is the basis of trigonometry. The site tells us that we can find angles using sine, cosine, and tangent (Sine = Oppostie/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent (or, SOHCAHTOA))
-The site also explains the relationship between sine/ cosine/ tangent and an angle 60°.
(Sin60 = √3/2, cos60 = ½, and tan60 = √3/1)
-This website also uses graphical representations of lines to aid in understanding sine, cosine, and tangent.
-The site also has worksheets on SOHCAHTOA which we might want to curate and use ourselves.
-This site has more sample questions that we can use tocreate SOHCAHTOA problems.
- Solving Triangles (No)
-This site shows students how to set up formulas using real numbers for opposite, adjacent, and hypotenuse lines.
-This site brings in angle/side theorems.
- Trigonometric Identities (No)
- Has a table of trigonometric identities for: reciprocals, Pythagorean Theorem, quotient, co-functions, even-odds, sum-difference, double angle, power-reducing/ half angle formulas, sum-to-product formulas, and product-to-sum formulas.
- Trigonometric Graphs (No)
- The site explains how to graph sine waves using one point in a quadrant.
- Site explains graphing and translating sine waves. The site uses relatively few graphics, but explains how to translate and graph trigonometric functions in detail.
- A resource for using degree to find amplitude and period of a trigonometric function. This has questions and answers.