Directions: Translate these sentences into ML (mathematical language). Use letters as variables which are related to the words, and use a “let” statement to define your variables. For example: let F = Fred’s salary or let h = the number of hours. For sentences involving two unknown values, use two different variables.
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The combined salaries of James and Scott equal $970.
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Lisa worked 25 hours at $4 an hour, plus 10 more hours at $4.50 an hour to earn a total of $145.
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Larry is four times as old as his son Curly.
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Ten pounds less than sixty-seven pounds is fifty-seven pounds.
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Four more than five times a number equals one less than six times the same number.
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A woman worked a certain number of hours at $3 an hour and the same number of hours plus twenty more hours at $4 an hour, earning $150 all together.
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Calculate the number of feet in a measurement if you know the number of yards.
Objective 3 – Question Types
Solve different testing style question formats including those from CPT, SAT, OPT, and ACT.
Descriptions and Sample Questions for CPT Mathematics Tests
There are three ACCUPLACER CPT math tests: Arithmetic, Elementary Algebra, and College Level Math (CLM). Students begin math testing with either the Arithmetic or Elementary Algebra Test. The computer selects which test to present depending on how the student answers certain background questions. If the student obtains a high score on the Elementary Algebra Test, he/she will be able to take the CLM Test.
Arithmetic Test
This test measures your skills in three primary categories:
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Operations with whole numbers and fractions
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addition, subtraction, multiplication, division
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recognizing equivalent fractions and mixed numbers
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Operations with decimals and percent
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addition, subtraction, multiplication and division
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percent problems, decimal recognition
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percent equivalencies and estimation problems
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Applications and problem solving
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rate, percent and measurement problems
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geometry problems
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distribution of a quantity into its fractional parts
Elementary Algebra
There are three categories in the Elementary Algebra Test:
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Operations with integers and rational numbers includes:
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computation with integers and negative rationals
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use of absolute values
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ordering
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Operations with algebraic expressions:
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evaluation of simple formulas and expressions
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adding and subtracting monomials and polynomials
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evaluation of positive rational roots and exponents
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simplifying algebraic fractions
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factoring
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Equation solving, inequalities, and word problems including:
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solving verbal problems presented in algebraic context
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geometric reasoning
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the translation of written phrases into algebraic expressions
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graphing
College Level Math (CLM)
The CLM measures math skills from intermediate algebra through precalculus.
The categories covered include:
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Algebraic operations
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simplifying rational algebraic expressions
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factoring and expanding polynomials
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manipulating roots and exponents
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Solutions of equations and inequalities
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the solution of linear and quadratic equations by factoring
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expanding polynomials
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manipulating roots and exponents
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Coordinate geometry asks questions about
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plane geometry
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the coordinate plane, straight lines, conics, sets of points in
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a plane
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graphs of algebraic functions
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Application and other algebra topics asks about
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complex numbers
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series and sequences
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determinants, permutations
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combinations, fractions
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word problems
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Functions and trigonometry presents questions about,
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polynomial, algebraic, exponential, logarithmic
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trigonometric functions
Question Types
Generally there are three types of questions that appear on any standardized tests. These include procedural, conceptual, and application questions. Unlike the GED Mathematics Test, on the CPT students may also be expected to simply calculate an answer based on a quadratic equation. Students need to understand the basic structure of these questions and have the skills to respond appropriately.
Procedural questions require students to:
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Select and apply correct operations or procedures
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Modify procedures when needed
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Read and interpret graphs, charts, and tables
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Round, estimate, and order numbers
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Use formulas
Example
Body mass index (BMI) can be defined as BMI = 705 x w h2 where w is a person’s weight in pounds and h is the person’s height in inches. If Samuel is 68 inches tall and weighs 168 pounds, what is his body mass index?
Conceptual questions require students to:
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Recognize basic mathematical concepts
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Identify and apply concepts and principles of mathematics
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Compare, contrast, and integrate concepts and principles
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Interpret and apply signs, symbols, and mathematical terms
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Demonstrate understanding of relationships among numbers, concepts, and principles
Example
A total of p players came to practice. The coach divides them into 8 groups of z players for drills, but 5 players are left over. Which of the following equations expresses the relationship between the number of players out for practice and the number of players in each group?
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p = 5z + 8
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p = 8z + 5
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p = 5(z + 8)
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p = 8(z + 5)
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p = 5(8z + 5)
Application questions require students to:
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Identify the type of problem represented
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Decide whether there is sufficient information
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Select only pertinent information
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Apply the appropriate problem-solving strategy
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Adapt strategies or procedures
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Determine whether an answer is reasonable
Example
Cynthia is retiling her bathroom floor. She has determined that she will need 648 tiles. The tiles can be purchased for $0.43, or she can purchase them for $34.50 per box of 100 tiles. How much money would she save if she bought only whole boxes of tile instead of only individual tiles?
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$ 34.50
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$ 37.14
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$ 71.64
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$207.00
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$241.50
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