Title

Beginning Algebra
Tutorial 10: Practice Test on Tutorials 1 - 9

 Problems 1a - 1c: Replace ? with  < , > , or = .

 1a.  -5 ?  5 Answer: Since -5 is to the left of 5 on the number line, then -5 < 5.

 1b.  10 ?  5 Answer: Since 10 is to the right of 5 on the number line, then 10 > 5.

 1c.  |-5| ? |5| Answer: First of all, |-5| = 5. Next we have |5| = 5. Since both absolute values equal the same number 5, then  |-5| = |5| .

 Problems 2a - 2b:  Are the following statements true or false?

 2a.  - 4  >  4 Answer: Since - 4 is to the left of 4 on the number line, then - 4  <  4.  So, the above statement is false.

 2b.  - 4  <  - 4 Answer: Since - 4 is the same number as - 4 and the statement includes where the two numbers are equal to each other, then this statement is true.

 Problems 3a - 3c:  Write each sentence as a mathematical statement.

 3a.  5 is not equal to -5. Answer: Reading it left to right we get: 5 is not equal to -5

 3b.  -2 is less than or equal to 0. Answer: Reading it left to right we get: -2 is less than or equal to 0 -2  <  0

 3c.  7 is greater than 0. Answer: Reading it left to right we get: 7 is greater than 0 7  >  0

 Problems 4a - 4f :  List the elements of the following set that are also elements of the given set. {-½, 0, 5, , }

 4a.  Natural numbers  Answer: The numbers in the given set that are also natural numbers are {5, }

 4b.  Whole numbers  Answer: The numbers in the given set that are also whole numbers are {0, 5, }

 4c.  Integers  Answer:   The numbers in the given set that are also integers are {0, 5, }

 4d.  Rational numbers  Answer:   The numbers in the given set that are also rational numbers are {-1/2, 0, 5, }

 4e.  Irrational numbers  Answer: The number in the given set that is also an irrational number is {}

 4f.  Real numbers  Answer: The numbers in the given set that are also real numbers are {-½, 0, 5, , }

 Problems 5a:  Write the number as a product of primes.

 Problems 6a:  Write the fraction in lowest terms.

 Problems 7a - 7d:  Perform the following operations.  Write answers in the lowest terms.

 Problems 8a - 8b:   Evaluate.

 Problems 9a - 9b:  Write each phrase as an algebraic expression.  Let x represent the unknown number.

 9a.  The quotient of 7 and a number. Answer: The quotient of 7 and a number

 9b.  10 less than 2 times a number. Answer: 10 less than 2 times a number

 Problems 10a - 10b:  Write each sentence as an equation.  Let x represent the unknown number.

 10a.  The sum of 2 and 10 times a number is the same as 30. Answer: The sum of 2 and 10 times a number is the same as 30

 10b.  The product of 5 and a number is 2/3. Answer: The product of 5 and a number is 2/3

 11a.  -9 + (-10) Answer: -9 + (-10) = -19

 11c.  6.5 + (-1.2) + (-3.1) Answer: 6.5 + (-1.2) + (-3.1) =  5.3 + (-3.1) =  2.2

 Problems 12a - 12b: Simplify.

 12a.  -(-17) Answer: -(-17) = 17

 Problems 13a - 13b: Subtract.

 13a.  -15 - (-3) Answer: -15 - (-3) =  -15 + 3  = -12

 13b.  -1.5 - 2.5 Answer: -1.5 - 2.5 =  -1.5 + (-2.5) = - 4

 Problems 14a - 14c:  Multiply.

 14a.  (-5)(-12) Answer: (-5)(-12) = 60

 14b.  (3)(-5)(2) Answer: (3)(-5)(2) =  (-15)(2) = -30

 14c.  (-15)(0) Answer: (-15)(0) = 0

 Problems 15a - 15c: Divide.

 Problems 16a - 16b:   Simplify.

 Problems 17a - 17b:   Evaluate the expression.

 17a.    when x = 3 and y = -3. Answer:

 17b.   when x = 2 and y = -2 Answer:

 Problems 18a - 18b: Decide whether the given number is a solution of the given equation.

 18a.  Is 1 a solution to 3x - 1 = 4? Answer: Is 1 a solution?  Since we got a FALSE statement (2 does not equal 4), then 1 is not a solution.

 18b.  Is -3 a solution to 7 - x = 2x + 16? Answer: Is -3 a solution?  Since we got a TRUE statement (10 does equal 10), then -3 is a solution.

 Problem 19a:  Use a commutative property to write an  equivalent expression.

 19a.  3a + 2b Answer:   Using the commutative property of addition (where changing the order of a sum does not change the value of it), we get 3a + 2b = 2b + 3a

 Problem 20a:  Use an associative property to write an  equivalent expression.

 20a.  8(xy) Answer: Using the associative property of multiplication (where changing the grouping of a product does not change the value of it), we get  8(xy) = (8x)y

 Problems 21a - 21b:  Use the distributive property to find the product.

 21b.  8(2x + 3y +4z) Answer:

 Problems 22a - 22b: Write the opposite (additive inverse) and the reciprocal (multiplicative inverse) of each number.

 22a.  -10 Answer: The opposite of -10 is 10, since -10 + 10 = 0. The reciprocal of -10 is -1/10, since -10(-1/10) = 1.

 22b.  Answer: The opposite of 4/7 is - 4/7, since 4/7 + (- 4/7) = 0. The reciprocal of 4/7 is 7/4, since (4/7)(7/4) = 1.

 Problem 23a - 23c:   The bar graph below shows the profit a cd store made over the months of September through December of last year.   Use the graph to answer questions 23a - 23c.

 23a.  About how much was the profit in December?  Answer: The bar that associates with December is the fourth bar from the left.  The top of that bar is in between 20 and 25 on the vertical axis.  A good approximation is 22. The profit in December is about \$22000.     23b.  Which month had the lowest profit? Answer: It looks like October had the lowest profit.     23c.  What is the sum of the profits of October and November?  Answer: The bar that associates with October is the second bar from the left.  The top of that bar matches with 5 on the vertical axis. The bar that associates with November is the third bar from the left.  The top of that bar matches with 10 on the vertical axis. The sum of the profits of October and November would be 5,000 + 10,000 = \$15,000.

 Problems 24a - 24b: The line graph below shows last week's high temperatures in Fahrenheit.   Use the graph to answer questions 24a - 24b.

 24a.  How much was Monday's high temperature?  Answer: The point that matches with Monday on the horizontal axis also matches 85 on the vertical axis.  Monday's high temperature was 85 degrees Fahrenheit.   24b.  Which day had the highest high temperature?  Answer: It looks like Wednesday had the highest high temperature.

Last revised on July 25, 2011 by Kim Seward.