ACT and SAT PrepMath

Strategies2013-2014

Hyman

ACT - Math

• 60 Minutes, 60 Questions

• Five Multiple Choice Answers

• Two Types of Questions: – Basic Math– Word Problems

What’s on the Test?Pre- and Elementary Algebra

Pre-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.

What’s on the Test?Intermediate Algebra and

Coordinate GeometryIntermediate 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.

What’s on the Test?Plane Geometry and

TrigonometryPlane 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.

Math Strategies

• Back-solving• Calculate

Wisely• Encourage

Your Inner Artist• Target Practice

Math Strategies: Backsolving

Backsolving is trying each answer option and seeing if it works. Although this may sound time-consuming, it comes in handy when trying to answer questions that have

numbers as answer options.

For instance, if you apply the number in option C to the problem and it is the

answer, you’re golden! If not, you should have more of an idea of which way to go

How Does it Work?Daniel arranged 4 bags and

put 40 marbles in the bags in such a way that each bag had 2 more marbles than the previous bag. How many marbles are there in the third bag?

a. 5b. 8c. 10d. 11e. 21

Apply the number in option C to the problem:

If there are 10 marbles in the

3rd bag, there should be 8 in the 2nd, 6 in the 1st and 12 in the 4th.

Hence:6+8+10+12=36

C is NOT your answer

Math Strategies: Plug It InUse this strategy for critical

thinking problems.

For example: (change ex)√√√

a>0 and b<0 What would (a*b)/b yield?

Your only options are either a positive or a negative number.

2169 c2169 c

Math Strategies: Calculate Wisely

Math questions on the ACT are designed to be answered within a minute, if that. They do not involve intense calculate. If you find yourself

reaching for a calculator so you can figure out the square root of 934, you probably made a mistake somewhere. No calculation on the test should be

THAT difficult.

On the other hand, please don’t waste your time calculating information that you already know. If you can’t figure out 2+2 by this point in your life,

then there may be some underlying issues.

Calculator Tips

• Don’t purchase a new calculator just for the ACT

or the SAT. Use the calculator that you know

and understand!• Make sure your calculator

has new batteries. You’d be in hot water if your

calculator died during one of those assessments!

Math Strategies: Visualize

Scribble space will be provided If you are having a hard time visualizing a

shape in your head, draw it out. Don’t waste time

making it perfect. No one will ever see your test

booklet except you. Do what you need to get the answer right: no more, no

less!

Do your figuring

here

• A

Visualization Example

In order to find the

length of a side, draw a

picture

Example:A ladder is

leaning against a 12

foot wall, and is 5 ft away from the base of the wall.

How long is the ladder?

12ft

5ft

Use the Pythagorean Theorem to determine this answer…

(a*a)+(b*b)=(c*c)(5*5)+(12*12)=(C*C)25+144=(C*C)169=(C*C)√169= √C13=C

The ladder is 13ft long

Math Strategies: Target Score

If you are looking to score a 19-23 on the Math Test, there is no need to look for shortcuts

because there is no need to race through the test. Focus on getting 32-39 questions right!

If you are looking to score a 27 or higher on the Math Test, you shouldn’t be working out

every question. Find quicker ways to answer questions because these faster methods will give you the time you need to make it to the

last few classes.

Math SubjectsMake sure you know….

Pre-Review Review

• Order or Operations(Please Excuse My Dear Aunt Sally)

• Odd numbers vs Even Numbers

• Positive Integers vs Negative Integersadding, subtracting, multiplying, dividing

Pre-Algebra

• Number Problems• Multiples, Factors, Primes• Divisibility and Remainders• Percentages, Fractions and Decimals• Rations and Proportions• Mean, Median and Mode• Probability• Absolute Value• Exponents and Roots• Series

Elementary Algebra

• Substitution• Simplifying Algebraic Expressions• Writing Expressions and Equations• Solving Linear Equations• Multiplying Binomials• Inequalities

Intermediate Algebra

• Solving and Factoring Quadratic Equations

• Solving Systems of Equations• Relationships between the Sides of

an Equation• Functions• Matrices• Logarithms

Coordinate Geometry

• Number Lines and Inequalities• The (x,y) Coordinate Plane• Distance and Midpoints• Slope• Parallel and Perpendicular Lines• The Equation of a Line• Graphic Equations• Conic Sections

Plane Geometry

• Angles and Lines• Triangles• Polygons• Circles• Simple Three-Dimensional Geometry

Trigonometry

• Solving Triangles• Trigonometric Identidies• Trigonometric Graphs• Sine, Cosine, Tangent