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ACT 1-on-1 Curriculum Math: Pre-algebra & Algebra

ACT 1-on-1 Curriculum Math: Pre-algebra & Algebra. ACT Math. Math Section at a Glance. 60 questions 60 minutes Three sections of questions: Pre-Algebra/ Elementary Algebra 24 questions Intermediate Algebra/ Coordinate Geometry 18 questions Plane Geometry/ Trigonometry

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ACT 1-on-1 Curriculum Math: Pre-algebra & Algebra

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  1. ACT 1-on-1 Curriculum Math: Pre-algebra & Algebra

  2. ACT Math Math Section at a Glance • 60 questions • 60 minutes • Three sections of questions: • Pre-Algebra/Elementary Algebra • 24 questions • Intermediate Algebra/Coordinate Geometry • 18 questions • Plane Geometry/Trigonometry • 18 questions Math Directions: DIRECTIONS: Answer each question and then plug in the matching bubble on your answer sheet. Do not stay on problems that you are struggling with. Answer the questions you know first; then go back complete the other problems as time permits. Calculators are allowed on this section of the test. Note that some of the problems can be answered without a calculator. Note: unless the questions explain something differently, assume the following. 1. Figures, graphs and charts may not be drawn to actual measurements. 2. Linear data, figures and shape are represented in a plane. 3. A straight, 180° line will be introduced as a line. 4. Arithmetic mean will be introduced as an average.

  3. ACT Math The Basics – Math • Concepts range from pre-algebra up to algebra II and trigonometry • There are only 4 trigonometry questions • Questions are generally in order of difficulty • To answer all questions, you need to work generally at a pace of one minute per question

  4. ACT Math General Strategies • Write down your work! • Do not just go to your calculator to find the answer. Write it down. • If you work it out, you can review the steps to get the right answer if you make a mistake. • Pace yourself • It is easy to lose track of time on one problem. • Do not spend too much time on any one problem. • Read the questions carefully! • This is a way to avoid easy mistakes. • Pick & Plug • Use the answer choices to help you solve the problem. • Oddball Answers are OK • In math, many times the odd answer out is the correct one. • Assign Values to Variables • If a question has numerous variables, assign a consistent numerical value to help you solve it.

  5. ACT Math Word Problems – Pre-Algebra/Elementary Algebra • Translate words into an equation or statement that you can solve.

  6. ACT Math Word Problems – Pre-Algebra/Elementary Algebra • 50 is what percent of 450? • 21 is 6 more than what number? • 8 is 5 less than half of what number? • 21 more than what number is five times the number?

  7. ACT Math Mean, Median, and Mode – Pre-Algebra/Elementary Algebra • Mean: • Mean is the average of a list of numbers. • Median • The middle number between a list of numbers is the median. • If the list has an even set of numbers, the median is the average of the two middle values. • Mode • The number that occurs the most in a list of numbers is the mode.

  8. ACT Math Primes, Multiples, and Factors– Pre-Algebra/Elementary Algebra • Primes: • A prime number is only divisible by one and itself. • Special rules: • 1 is not a prime number. • 2 is the only even prime number. • Factors: • Factors are numbers that you multiply together to get a product. • Multiples: • Multiples are formed by multiplying a given number by the counting numbers. • Greatest Common Factor (GCF) and Least Common Multiple (LCM) • Greatest common factor is the largest factor of a set of numbers. • Least Common Multiple is the smallest common multiple of a set of numbers.

  9. ACT Math Distance – Pre-Algebra/Elementary Algebra • For distance problems, remember that: Distance= Rate x Time • Use the given units to help on this. • Many will use miles and hours.

  10. ACT Math Measurements – Pre-Algebra/Elementary Algebra • For measurement questions, identify the units that are used. • You need to remember some basic conversions:

  11. ACT Math Absolute Value – Pre-Algebra/Elementary Algebra • Absolute value is the number of integers a number is away from zero. |-5| = 5 • For difficult absolute value questions, account for the positive and negative values of a variable when the variable is between the brackets.

  12. ACT Math Probability– Pre-Algebra/Elementary Algebra • Probability of x: • Combinations: For these problems, multiply the numbers provided by each other. • Permutations: For these problems, order matters. To find the answer, multiply the number of items by one less for each placement.

  13. ACT Math Exponents and Roots– Pre-Algebra/Elementary Algebra • Remember rules for simplifying expressions with exponents: • * = • = • = • = • =

  14. ACT Math Ratios and Proportions – Pre-Algebra/Elementary Algebra • Ratios are comparisons between two variables. • Solving Ratio Problems: • Write down both ratios as fractions, setting them equal to one another. • Verify that your units match on both sides of the equation. • Use cross-multiplication to solve the problem.

  15. ACT Math Series – Pre-Algebra/Elementary Algebra • Arithmetic sequences are separated by a common number, called a common term or difference. • Example: 28, 24, 20, 16 is a arithmetic sequence with a difference of -4. • Geometric sequences are separated by a common ratio that is either multiplied or divided by the previous number. • Example: 2, 6, 18, 54 is a geometric sequence with a ratio of 3.

  16. ACT Math Simplifying Algebraic Expressions – Pre-Algebra/Elementary Algebra • These test if you can simplify or manipulate algebraic expressions. • Remember the order of operations: PEMDAS. • Parentheses, Exponents, Multiplication and Division, Addition and Subtraction • Remember the distributive property. • A(b+c) = ab+ ac

  17. ACT Math Pre-Algebra/Elementary Algebra • Work on the following Practice Problems from 61D: • # 1 • # 3 • # 4 • # 5 • # 6 • # 14 • # 15 • # 16 • # 24 • # 27 • # 32 • # 35 • # 39 • # 43

  18. ACT Math System of Equations – Intermediate Algebra • System of equations provide a pair of equations with two variables for which you have to solve. • One way to solve for x is to add or subtract the equations to eliminate one of the variables. • Another way to solve for x is by substitution, where you solve for one of the variables and plug it into the other equation.

  19. ACT Math Solving & Factoring Quadratic Equations – Intermediate Algebra • Multiplying binomials: • Use FOIL to multiply binomials: First, Outer, Inner, Last. • Example: (x+5)(x-3) • Solving quadratics by factoring: • Factor x2+5x+6.

  20. ACT Math Functions – Intermediate Algebra • Functions are a way of restating y=ax+b as f(x) = ax+b. • To solve functions, you substitute x for some number or variable. • Example: f(x) = x2+2x-4. What is f(3)?

  21. ACT Math Inequalities – Intermediate Algebra • In an inequality, one of the sides of the equation is greater than the other. • Solve inequalities similar to the way you solve linear equations. • One note on solving inequalities: if you multiply or divide by a negative number, you must flip the sign.

  22. ACT Math Matrices – Intermediate Algebra • Matrix questions occasionally pop up on the ACT. • Adding and subtracting matrices: • To add or subtract matrices, add or subtract corresponding numbers. • Multiplying matrices: • Take the first row of the first matrix and the first column of the second matrix and multiply the corresponding numbers. • Determinant: • The determinant is found by subtracting the product of the diagonals.

  23. ACT Math Logarithms – Intermediate Algebra • The basic form of a logarithm: Logby = x means bx = y • Logarithmic identities: • Logb(xy) = Logbx + Logby • Logb(x/y) = Logbx - Logby • Logb(xd) = dLogbx

  24. ACT Math Intermediate Algebra • Work on the following Practice Problems from 61D: • # 10 • # 11 • # 12 • # 21 • # 34 • # 57

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