ACT Math PD for Teachers

Prepared for Sylacauga City SchoolsBy: Delynn Bouldin

Curriculum & Assessment SpecialistSTIAchievement Services

Quick Review

The Mathematics TestThere are 60 questions and a 60 minute time limit on this test.

Pre-Algebra/Elementary AlgebraPre-Algebra (23%). 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.Elementary Algebra (17%). 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.

Intermediate Algebra/Coordinate Geometry

Intermediate Algebra (15%). Questions in this content area are based on an understanding of the quadratic formula, rational and radical expressions, absolute value equations and inequalities, sequences and patterns, systems of equations, quadratic inequalities, functions, modeling, matrices, roots of polynomials, and complex numbers.

Coordinate Geometry (15%). Questions in this content area are based on graphing and the relations between equations and graphs, including points, lines, polynomials, circles, and other curves; graphing inequalities; slope; parallel and perpendicular lines; distance; midpoints; and conics.

Plane Geometry/Trigonometry

Plane Geometry (23%). 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.

Trigonometry (7%). 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.

Remember, Science and Math Go Hand-in-Hand!

The Science Test includes…

Data Representation (38%). This format presents graphic and tabular material similar to that found in science journals and texts. The questions associated with this format measure skills such as graph reading, interpretation of scatter plots, and interpretation of information presented in tables, diagrams, and figures.

Research Summaries (45%). This format provides descriptions of one or more related experiments. The questions focus on the design of experiments and the interpretation of experimental results.

Conflicting Viewpoints (17%). This format presents expressions of several hypotheses or views that, being based on differing premises or on incomplete data, are inconsistent with one another. The questions focus on the understanding, analysis, and comparison of alternative viewpoints or hypotheses.

• Questions have 5 answer choices.

• Many of the “simpler” problems are near the beginning---but, you may have to think back to 7th grade for how to do them.

• There may be more than one way to solve a problem. THINK about what is being asked before you start crunching numbers.

More Reminders About the Math Test:

• Read the question and decide how you will solve it. DO NOT read the answer choices until you have completed your calculations—unless plugging in the answers is faster.

• On questions that involve more than one step, partial answers are commonly used as distractors.

• The problems should not involve long calculations. If your are trying to find the square root of 934, you have probably done something incorrectly.

• Sometimes you can’t figure out how to approach a problem quickly. Mark it, skip it, and come back to it! Use your time to get every “easy” question correct.

More Reminders About the Math Test:

Now, We’ll Charge Forward.

But, remember the parable of the sower from Matthew 13:

“A farmer went out to sow his seed. 4 As he was scattering the seed, some fell along the path, and the birds came and ate it up. 5 Some fell on rocky places, where it did not have much soil. It sprang up quickly, because the soil was shallow. 6 But when the sun came up, the plants were scorched, and they withered because they had no root.7 Other seed fell among thorns, which grew up and choked the plants. 8 Still other seed fell on good soil, where it produced a crop—a hundred, sixty or thirty times what was sown.”

The things that I share with you are like this. And, so will it be with the students that some of you will share them with. Let’s strive to get a crop from as many seeds as possible.

What Skills Do Students Need for ACT Math?

Where do ACT Math questions come from?

119 out of 120 questions I have aligned so far came from Quality Core Algebra I and Quality Core Geometry standards! That is 99.17%.

If you teach from the Quality Core standards, you will:• Cover your Course of Study.• Prepare your students for EOC tests, which come from QC.• Prepare your students for the ACT, which comes from QC.

What formulas Are Worth Knowing?

Midpoint formula

Distance formula

Quadratic formula

Equation of a circle (x−h)2+(y−k)2=r2h and k are the x and y coordinates of the center of the circle.

Circumference of a circle

Area of a circle

Surface of a sphere A = 4

Volume of a sphere V =

Surface of a cylinder (2 • π • r²) + (2 • π • r • height)

Volume of a cylinder V = π • r² • height = ¼ • π • d² • height

Area of a Trapezoid

Surface of a cone SA = πr2 + πrl

Volume of a cone Vcone = 1/3 × b × h

Sum of interior angles of a polygon (n-2) × 180°

Each interior angle of a regular polygon (n-2) × 180° / n

Length Of Arc = (n◦/360◦) · 2πr

Area Of Sector = (n◦/360◦) · πr2

Sine = O/HCosine = A/HTangent = O/ACotangent = A/OSecant = H/ACosecant = H/O

What formulas Are Worth Knowing?

Problem Attack Strategies

• Remember: Do not read the answers until you have FINISHED your math---unless your strategy on that problem is to plug in answers.

• “Diagrams are not drawn to scale.” But, they usually are—or are at least close enough for estimating answers.

• When you see a right triangle, think either Pythagorean Theorem or direct proportions (like similar triangles).

Problem Attack Strategies

• If you see degree measures of 30, 45, or 60 in a right triangle, try using special right triangles.

• If you can reduce it, FOIL it, simplify it, or factor it---DO IT!

• When you see similar triangles, think about direct proportions.

• SohCahToa (though it is only 7% of the test)

• In the equation y = ax2 + bx + c, the a tells whether the U shaped graph opens up or down, and the c is the y intercept.

Problem Attack Strategies

• If you have complex numbers, treat i like any other variable. As a last step, change i2 to -1.

• The basic rules of exponents:1. The exponent tells how many times to use the number.2. A negative exponent means we divide.3. A fractional exponent means to take the nth root.

• Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, … Remember that 1 is not prime, and that 2 is the only prime number.

Problem Attack Strategies

• Know mean, median, mode and range. Watch for questions that ask you to determine the effect on a change in the data, or to find a weighted mean.

• Understand arithmetic and geometrical progressions.

• Watch for italicized words in the problem…especially if it is worded in a complicated and hard-to-understand manner. The italicized words may be all you need to figure it out!

Math in the Science Test

• Reading charts, tables, and graphs is critical!

• Students often must interpolate between data points/lines.

• Students must also compare data between two representations, or combine data from two representations.

• Students must learn to overlook “big word” nouns, and pay attention to what is happening. They can substitute cow, horse, or pig for the nouns….What is going on is the important part.

Now, let’s dig a little deeper…