College Algebra - Problem Drill 01: Introduction to College Algebra No. 1 of 10 Instructions: (1) Read the problem and answer choices carefully (2) Work the problems on paper as needed (3) Pick the answer (4) Go back to review the core concept tutorial as needed. 1. What type of equation has the variable in the denominator of an expression? (A) Linear (B) Polynomial (C) Quadratic (D) Radical (E) Rational Linear equations do not have a variable in the denominator. Polynomial equations do not have variables in the denominator. Review the definition of quadratic equations and try again. Review the definition of radical equations and try again. E. Correct! Rational equations have a variable in the denominator of a rational expression. The definition of a rational equation is an equation with the variable in the denominator of a rational expression. (E) Rational
No. 2 of 10 Instructions: (1) Read the problem and answer choices carefully (2) Work the problems on paper as needed (3) Pick the answer (4) Go back to review the core concept tutorial as needed. 2. What is the term for a combination of constants, operators, and variables representing numbers or quantities? (A) Equation (B) Expression (C) Function (D) Graph (E) Variable An equation is two expressions joined by an equal sign. B. Correct! An expression is a combination of constants, operators, and variables representing numbers or quantities. A function is a relation where each element of the first set corresponds to exactly on element of the second set. A graph is a method to describe the relationship between natural events by analyzing curves in a coordinate system. A variable is a symbol or letter used to represent an unknown quantity. The term for a combination of constants, operators, and variables representing numbers or quantities is expression. (B) Expression
No. 3 of 10 Instructions: (1) Read the problem and answer choices carefully (2) Work the problems on paper as needed (3) Pick the answer (4) Go back to review the core concept tutorial as needed. 3. Given the equation y = 2x + 1, find the y-values when x = 1, 2, and 4. (A) 3, 5, 9 (B) 1, 2, 5 (C) 3, 9, 5 (D) 2, 4, 8 (E) 4, 5, 7 A. Correct! You substituted x = 1, x = 2, and x = 4 into the equation to get y = 3, 5, and 9. Substitute x = 1, x = 2, and x = 4 into the equation to get the y-values. Substitute x = 1, x = 2, and x = 4 into the equation to get the y-values. Substitute x = 1, x = 2, and x = 4 into the equation to get the y-values. Substitute x = 1, x = 2, and x = 4 into the equation to get the y-values. Substitute x = 1, x = 2, and x = 4 into the equation y = 2x + 1. y = 2(1) + 1 = 2 + 1 = 3 y = 2(2) + 1 = 4 + 1 = 5 y = 2(4) + 1 = 8 + 1 = 9 (A) 3, 5, 9
No. 4 of 10 Instructions: (1) Read the problem and answer choices carefully (2) Work the problems on paper as needed (3) Pick the answer (4) Go back to review the core concept tutorial as needed. 4. Given the equation y = 3x 2, find the y-values when x = 1, 7, and 9. (A) 2, 8, 10 (B) 1, 19, 25 (C) -5, 1, 3 (D) -3, 15, 21 (E) 0, 15, 21 Substitute x = 1, x = 7, and x = 9 into the equation to get the y-values. B. Correct! You substituted x = 1, x = 7, and x = 9 into the equation to get y = 1, 19, and 25. Substitute x = 1, x = 7, and x = 9 into the equation to get the y-values. Substitute x = 1, x = 7, and x = 9 into the equation to get the y-values. Substitute x = 1, x = 7, and x = 9 into the equation to get the y-values. Substitute x = 1, x = 7, and x = 9 into the equation y = 3x 2. y = 3(1) 2 = 3 2 = 1 y = 3(7) 2 = 21 2 = 19 y = 3(9) 2 = 27 2 = 25 (B) 1, 19, 25
No. 5 of 10 Instructions: (1) Read the problem and answer choices carefully (2) Work the problems on paper as needed (3) Pick the answer (4) Go back to review the core concept tutorial as needed. 5. Tom has 6 more apples than Peter. Peter has twice the number of apples as John. Mike has 4 more apples than John. The number of apples Alex has is equal to the number of apples Mike and John have altogether. Find the relationship between the number of apples Alex and Tom have. (A) Alex has 2 apples less than Tom. (B) Alex has 2 apples more than Tom. (C) Alex has 3 apples less than Tom. (D) Alex has 3 apples more than Tom. (E) Alex has 10 apples more than Tom. A. Correct! You found the relationship between the number of apples Alex and Tom have. Write the given relations as equations to find the relationship between the number of apples Alex and Tom have. Write the given relations as equations to find the relationship between the number of apples Alex and Tom have. Write the given relations as equations to find the relationship between the number of apples Alex and Tom have. Write the given relations as equations to find the relationship between the number of apples Alex and Tom have. Suppose Tom, Peter, John, Mike, and Alex has t, p, j, m, and a apples, respectively. The given relations are as follows: t = p + 6 p = 2j m = j + 4 a = j + m Therefore, a = j + m = j + (j + 4) = 2j + 4 = p + 4 = p + 6 2 = t 2 Alex has 2 less apples than Tom. (A) Alex has 2 apples less than Tom.
No. 6 of 10 Instructions: (1) Read the problem and answer choices carefully (2) Work the problems on paper as needed (3) Pick the answer (4) Go back to review the core concept tutorial as needed. 6. Tom is five years older than Bill. Allen is twice as old as Tom. Mike is two years younger than Allen. Find the relationship between the ages of Bill and Mike. (A) Mike is seven year older than Bill. (B) Mike is eight years older than twice Bill s age. (C) Bill is seven years older than twice Mike s age. (D) Bill is seven year older than Mike. (E) Bill and Mike are the same age. Write the given relations as equations to find the relationship between the ages of Bill and Mike. B. Correct! You found the relationship between the ages of Bill and Mike. Write the given relations as equations to find the relationship between the ages of Bill and Mike. Write the given relations as equations to find the relationship between the ages of Bill and Mike. Write the given relations as equations to find the relationship between the ages of Bill and Mike. Suppose Tom, Bill, Allen, and Mike are t, b, a, and m years old, respectively. The given relations are as follows: t = b + 5 a = 2t m = a 2 Therefore, m = a 2 = 2t 2 = 2(b + 5) 2 = 2b + 8 Mike is eight years older than twice Bill s age. (B) Mike is eight years older than twice Bill s age.
No. 7 of 10 Instructions: (1) Read the problem and answer choices carefully (2) Work the problems on paper as needed (3) Pick the answer (4) Go back to review the core concept tutorial as needed. 7. What does the acronym VANG for? (A) Verbal, Analytical, Numerical, Geometric (B) Victor, Adam, Nathan, George (C) Vocal, Alphabetical, Numerical, Geometric (D) Verbal, Analytical, Numerical, Graphical (E) Visual, Auditory, Nautical, Gravitational D. Correct! V Verbal A Analytical N Numerical G Graphical (D) Verbal, Analytical, Numerical, Graphical
No. 8 of 10 Instructions: (1) Read the problem and answer choices carefully (2) Work the problems on paper as needed (3) Pick the answer (4) Go back to review the core concept tutorial as needed. 8. Find the intersection of the two lines y = x + 3 and y = -x + 1. (A) (-1, 2) (B) (1, -2) (C) (2, -1) (D) (-2, 1) (E) (1, 2) A. Correct! Thus, (-1, 2) is the point of intersection of the two lines. y = x + 3 = -x + 1 x + 3 = -x + 1 2x = -2 x = -1 y = (-1) + 3 = 2 The point of intersection of the two lines is (-1, 2). (A) (-1, 2)
No. 9 of 10 Instructions: (1) Read the problem and answer choices carefully (2) Work the problems on paper as needed (3) Pick the answer (4) Go back to review the core concept tutorial as needed. 9. Find the intersection of the two lines y = x + 8 and y = -x + 6. (A) (-1, -7) (B) (-1, 7) (C) (7, -1) (D) (-7, 1) (E) (1, 7) B. Correct! Thus, (-1, 7) is the point of intersection of the two lines. y = x + 8 = -x + 6 x + 8 = -x + 6 2x = -2 x = -1 y = (-1) + 8 = 7 The point of intersection of the two lines is (-1, 7). (B) (-1, 7)
No. 10 of 10 Instructions: (1) Read the problem and answer choices carefully (2) Work the problems on paper as needed (3) Pick the answer (4) Go back to review the core concept tutorial as needed. 10. Find the intersection of the two lines y = 2x + 3 and y = -x + 6. (A) (5, -1) (B) (-5, 1) (C) (5, 1) (D) (-1, 5) (E) (1, 5) E. Correct! Thus, (1, 5) is the point of intersection of the two lines. y = 2x + 3 = -x + 6 2x + 3 = -x + 6 3x = 3 x = 1 y = 2(1) + 3 = 5 The point of intersection of the two lines is (1, 5). (E) (1, 5)