Elementary Algebra - Problem Drill 01: Introduction to Elementary Algebra No. 1 of 10 Instructions: (1) Read the problem and answer choices carefully (2) Work the problems on paper as 1. Which of the following statements does not accurately describe algebra? (A) The generalization of arithmetic. (B) The study of relationships between sets. (C) The analysis of shapes and figures. (D) The use of symbols to find unknown values. (E) The study of patterns. Algebra is the generalization of arithmetic. Algebra is the study of relationships between sets. C. Correct! Geometry is the analysis of shapes and figures. Algebra uses symbols to find unknown values. Algebra involves the study of patterns. Algebra can be described in many ways: The generalization of arithmetic. The study of relationships between sets. The use of symbols to describe mathematical relationships. Finding unknown values. The study of patterns. However, geometry involves the analysis of shapes and figures. (C) The analysis of shapes and figures.
No. 2 of 10 Instructions: (1) Read the problem and answer choices carefully (2) Work the problems on paper as 2. What does the acronym VANG stand for? (A) Verbal, Analytical, Numerical, Geometric (B) Verbal, Analytical, Numerical, Graphical (C) Verbal, Alphabetical, Numerical, Graphical (D) Visual, Analytical, Numerical, Graphical (E) Visual, Alphabetical, Nouns, Geometric The G does not stand for Geometrical. Review the tutorial slides pertaining to the VANG method then try again. B. Correct! The correct meanings of the letters in VANG are Verbal, Analytical or Algebraic, Numerical, and Graphical. The A does not stand for Alphabetical. Review the tutorial slides pertaining to the VANG method then try again. The V does not stand for Visual. Review the tutorial slides pertaining to the VANG method then try again. Review the tutorial slides pertaining to the VANG method then try again. VANG is an acronym that refers to the four different ways that an algebraic situation can be represented: V = Verbal, A = Analytical (or Algebraic), N = Numerical and G = Graphical. (B) Verbal, Analytical, Numerical, Graphical
No. 3 of 10 3. Which of the following does not correctly describe the four components of VANG? (A) Verbal with words (B) Analytical with symbols (C) Numerical with numbers (D) Guess with educational guess (E) Each description is correct. V stands for verbal, which means that words can be used to describe an algebraic situation. A stands for analytical or algebraic, which means that symbols can be used to describe an algebraic situation. N stands for numerical, which means that numbers can be used to describe an algebraic situation. D. Correct! G stands for graphical, not guessing, which means that graphs can be used to describe an algebraic situation. Review the tutorial slides pertaining to the VANG method then try again. VANG is an acronym that refers to the four different ways that an algebraic situation can be represented: V = Verbal, A = Analytical (or Algebraic), N = Numerical, and G = Graphical. A verbal description uses words to explain the relationships between sets. An analytical description uses symbols to form expressions and equations. A numerical description uses numbers, and often it uses tables of numbers. A graphical description uses charts or graphs. (D) Guess with educational guess
No. 4 of 10 4. Algebra is the study of patterns. What numbers come next in the following pattern? 3, 7, 11, 15,, (A) 4, 8 (B) 16, 17 (C) 17, 19 (D) 19, 23 (E) 21, 27 The next two numbers are 4 and 8 more than the last term, 15. The pattern is that each term is 4 more than the previous term, but 16 and 17 would be the numbers if each term were 1 more than the previous term. The pattern is that each term is 4 more than the previous term, but 17 and 19 would be the numbers if each term were 2 more than the previous term. D. Correct! The pattern is that each term is 4 more than the previous term, so the next two terms are 15 + 4 = 19 and 19 + 4 = 23. The pattern is that each term is 4 more than the previous term, but 21 and 27 would be the numbers if each term were 6 more than the previous term. The pattern contains the numbers 3, 7, 11, 15. The pattern is that each term is 4 more than the previous term. So, the next two numbers in the sequence are 15 + 4 = 19 and 19 + 4 = 23. (D) 19, 23
No. 5 of 10 5. Which algebraic expression represents two less than three times a number? (A) 3n 2 (B) 2n 3 (C) 3 2n (D) 2 3n (E) n 6 A. Correct! Three times a number is 3n, and two less than means to subtract 2. This expression represents three less than two times a number. This expression represents two times a number less than three. This expression represents three times a number less than two. This expression represents three times two less than a number. The verbal expression two less than three times a number can be represented by an algebraic expression as follows: two less than three times a number two less than 3n two less than 3n 3n 2 The correct expression is 3n 2. (A) 3n 2
No. 6 of 10 6. Given 2n 3 = 19, use the cover-up method to find the value of n. (A) n = 8 (B) n = 11 (C) n = 16 (D) n = 20 (E) n = 22 Substituting n = 8 into the original equation returns a false mathematical statement. B. Correct! Substituting n = 11 into the original equation returns a true mathematical statement. Substituting n = 16 into the original equation returns a false mathematical statement. Substituting n = 20 into the original equation returns a false mathematical statement. Substituting n = 22 into the original equation returns a false mathematical statement. The cover-up method can be used as follows: 2n 3 = 19 Cover up 2n, since it contains the variable. 3 = 19 The box must represent 22, so: 2n = 22 Cover up n. 2 = 22 This means that the box must represent 11, so n = 11. (B) n = 11
No. 7 of 10 7. Algebra can be described as the generalization of arithmetic. From the following examples, what generalization can you make? 2 11 = 11 2 13 19 = 19 13 3 a = a 3 (A) No matter which two numbers are multiplied, the product is always the same. (B) The order in which numbers are added does not affect the sum. (C) The order in which numbers are multiplied does not affect the product. (D) The order in which numbers are multiplied affects the product. (E) The order in which number are divided does not affect the quotient. The product changes depending on which numbers are multiplied. Although this statement is correct, the examples deal with multiplication and not addition. C. Correct! All of the examples show that when the same two numbers are multiplied, the results are equal even if the numbers are in different order. All of the examples show that when the same two numbers are multiplied, the results are equal even if the numbers are in different order. Therefore, the order does not affect the product. This is an incorrect statement regarding division and the examples deal with multiplication. All of the examples show that when the same two numbers are multiplied, the results are equal even if the numbers are in different order. (C) The order in which numbers are multiplied does not affect the product.
No. 8 of 10 8. How is a term different from an expression? (A) A term consists of several expressions, joined by + and. (B) A term consists of several expressions, joined by and. (C) An expression consists of several terms, joined by + and. (D) An expression consists of several terms, joined by and. (E) There is no difference between terms and expressions. An expression consists of one or several terms, joined by + and, not the other way around. When several expressions are joined by and, the result is usually not a term. C. Correct! An expression consists of one or more terms, joined by + and. If several terms were joined by and, the result would be another term. Review the definitions of term and expression then try again. Expressions consist of one or more terms connected by addition and/or subtraction. All of the following are terms: 2x, 17, 4k The following are all examples of expressions: 3x 2 + x 2x 17 4 k 2x + 17 4k (C) An expression consists of several terms, joined by + and.
No. 9 of 10 9. The solution of an equation is. (A) Always an even number. (B) Usually not greater than 10. (C) Always positive. (D) The value of the variable for which the equation is true. (E) The value of the variable for which the equation is false. Review the definition for the solution of an equation then try again. Review the definition for the solution of an equation then try again. Review the definition for the solution of an equation then try again. D. Correct! The solution of an equation is the value of the variable for which the equation is true. Review the definition for the solution of an equation then try again. The solution of an equation is the value of the variable for which the equation is true. (D) The value of the variable for which the equation is true.
No. 10 of 10 10. Which of the following strategies will be most helpful to your success with algebra? (A) Make a lot of random guesses. (B) Relate new topics to something you already learned. (C) Never practice. (D) Copy your answers from a friend. (E) Beat yourself up when you answer a question incorrectly. Educated guesses may help, but random guesses are typically not very helpful. B. Correct! Figuring out how two topics relate will increase your understanding of both topics. Practice is a key to doing well in algebra. Cheating is not the best way to succeed. You may get some answers correct by copying your friend s work, but you will not learn a thing about algebra. Believing in your ability to learn the material is necessary for success in most endeavors. You can help yourself succeed in algebra by practicing, making connections between new topics and things you already know, being persistent, and believing in yourself. (B) Relate new topics to something you already learned.