Math 155 Course Review

Questions 1 - 38 can be used as a study plan for the midterm. All questions should be studied for the final exam.

Use the order of operations to find the value of theexpression.

1) 7(4 - 2)3 - 2(5 - 3)3

Objective: (5.2) Use the Order of OperationsAgreement

2) 52 - 25 5 2 + 9Objective: (5.2) Use the Order of Operations

Agreement

Solve the problem.3) A hill is at 500 feet above sea level, and a crater

next to it is at 254 feet below sea level. What isthe difference in height between the hill andthe crater?Objective: (5.2) Use the Order of Operations

Agreement

Reduce the rational number to its lowest terms.

4) 2135

Objective: (5.3) Reduce Rational Numbers

Perform the indicated operation(s). Where possible,reduce the answer to lowest terms.

5) 15

-16

79

Objective: (5.3) Add and Subtract Rational Numbers

Perform the indicated operations. If possible, reduce theanswer to its lowest terms.

6) 23

-16

45

-12

Objective: (5.3) Use the Order of OperationsAgreement with Rational Numbers

Solve the problem.7) Of the 648 people polled about gardening, 216

replied that they plant a garden. Whatfractional part of those polled, expressed inlowest terms, plant a garden?Objective: (5.3) Solve Problems Involving Rational

Numbers

Use a calculator with a square root key to find a decimalapproximation for the square root. Round the numberdisplayed as indicated.

8) 423 to the nearest thousandthObjective: (5.4) Simplify Square Roots

Simplify the square root.9) 2 300

Objective: (5.4) Simplify Square Roots

Perform the indicated operation. Simplify the answerwhen possible.

10) 5 25Objective: (5.4) Perform Operations with Square

Roots

11) 455

Objective: (5.4) Perform Operations with SquareRoots

12) 6 + 24Objective: (5.4) Perform Operations with Square

Roots

13) 18 - 8Objective: (5.4) Perform Operations with Square

Roots

Rationalize the denominator.

14) 75

Objective: (5.4) Rationalize Denominators

Perform the indicated operation. Simplify the answerwhen possible.

15) 2 - 5 128 - 2 72Objective: (5.4) Perform Operations with Square

Roots

Use properties of exponents to simplify the expression.Express answer in exponential form.

16) 33 3-5

Objective: (5.6) Use Properties of Exponents

Last Revised 201130

17) 55

53

Objective: (5.6) Use Properties of Exponents

Use properties of exponents to simplify the expression.Express answers in exponential form with positiveexponents only. Assume that any variables indenominators are not equal to zero.

18) 10x3y-5

2x7y-11

Objective: (5.6) Use Properties of Exponents

Perform the indicated operation and express the answer indecimal notation.

19) (8 108)(9 10-6)Objective: (5.6) Perform Computations Using

Scientific Notation

20) 3 104

15 10- 2

Objective: (5.6) Perform Computations UsingScientific Notation

Perform the indicated operation by first expressing eachnumber in scientific notation. Write answer in scientificnotation.

21) (220,000,000)(2,000,000,000)Objective: (5.6) Perform Computations Using

Scientific Notation

Evaluate the algebraic expression for the given value(s) ofthe variable(s).

22) x3 - 3x2 + 1 ; x = -2Objective: (6.1) Evaluate Algebraic Expressions

Simplify the algebraic expression.23) 6(2x - 1) - 8(x - 3)

Objective: (6.1) Simplify Algebraic Expressions

Solve and check the equation.24) -3y - 3 = -1 + 10y

Objective: (6.2) Solve Linear Equations

25) 4(2y - 2) = 7(y + 2)Objective: (6.2) Solve Linear Equations

Solve and check the equation. Begin your work byrewriting the equation without fractions.

26) 8x7

- x = x28

-94

Objective: (6.2) Solve Linear Equations ContainingFractions

Solve the proportion.

27) 23

=9x

Objective: (6.2) Solve Proportions

28) x - 65

=310

Objective: (6.2) Solve Proportions

Use a proportion to solve the problem.29) The ratio of a basketball player's completed

free throws to attempted free throws is 4 to 5.If she completed 8 free throws, find how manyfree throws she attempted. Round to thenearest whole number if necessary.Objective: (6.2) Solve Problems Using Proportions

Indicate whether the equation has no solution or is truefor all real numbers. If neither is the case, solve for thevariable.

30) 4x - 2(4 + 2x) = -8Objective: (6.2) Identity Equations with No Solution

or Infinitely Many Solutions

Let x represent the number. Use the given conditions towrite an equation. Solve the equation and find thenumber.

31) If 3 times a number is added to -8, the result isequal to 11 times the number. Find thenumber.Objective: (6.3) Use Linear Equations to Solve

Problems

Solve the formula for the specified variable.32) d = rt for t

Objective: (6.3) Solve a Formula for a Variable

2

Plot the point in the rectangular coordinate system.33) (-5, 4)

Objective: (7.1) Plot Points in the RectangularCoordinate System

Graph the equation. Select integers for x, -3 x 3.34) y = -2x + 5

Objective: (7.1) Graph Equations in the RectangularCoordinate System

35) y = x2 + 3

Objective: (7.1) Graph Equations in the RectangularCoordinate System

Use the x- and y-intercepts to graph the linear equation.36) x - 2y = -10

Objective: (7.2) Use Intercepts to Graph a LinearEquation

Calculate the slope of the line passing through the givenpoints. If the slope is undefined, so state. Then indicatewhether the line rises, falls, is horizontal, or is vertical.

37) (-19, -1), (-3, -13)Objective: (7.2) Calculate Slope

Graph the linear function using the slope and y-intercept.

38) y = 13x + 2

Objective: (7.2) Use the Slope and y-Intercept toGraph a Line

Express the percent as a decimal.

39) 310

%

Objective: (8.1) Express a Percent as a Decimal

Solve the problem.40) 75% of 24 is what number?

Objective: (8.1) Solve Applied Problems InvolvingSales Tax and Discounts

3

41) 19 is what percent of 50?Objective: (8.1) Solve Applied Problems Involving

Sales Tax and Discounts

42) 40% of what number is 98?Objective: (8.1) Solve Applied Problems Involving

Sales Tax and Discounts

43) A dress regularly sells for $117. The sale priceis $89. Find the percent decrease of the saleprice from the regular price.Objective: (8.1) Determine Percent Increase or

Decrease

The graph shows the level of subsidized daycare spendingin a foreign country for the period 1995-1999. Use thegraph to answer the question.

44) Find the percent increase in daycare spendingfrom 1997to 1998. Round to the nearestpercent.

Objective: (8.1) Determine Percent Increase orDecrease

The principal P is borrowed at simple interest rate r for aperiod of time t. Find the simple interest owed for the useof the money. Assume 360 days in a year and roundanswer to the nearest cent.

45) P = $160r = 8%t = 2 yearsObjective: (8.2) Calculate Simple Interest

The principal represents an amount of money deposited ina savings account subject to compound interest at thegiven rate. Find how much money will be in the accountafter the given number of years (Assume 360 days in ayear.), and how much interest was earned.

A = P 1 + rnnt

P = A

1 + rn

nt A = Pert

46) Principal: $9500Rate: 7.5%Compounded: monthlyTime: 4 yearsObjective: (8.3) Use Compound Interest Formulas

Solve the problem.47) A mother invests $9000 in a bank account at

the time of her daughter's birth. The interest iscompounded quarterly at a rate of 8%. Whatwill be the value of the daughter's account onher twentieth birthday, assuming no otherdeposits or withdrawals are made during thisperiod?Objective: (8.3) Use Compound Interest Formulas

Solve the problem.48) How much money should be deposited today

in an account that earns 5% compoundedquarterly so that it will accumulate to $6900 in2 years?Objective: (8.3) Calculate Present Value

Use dimensional analysis to convert the quantity to theindicated units. If necessary, round the answer to twodecimal places.

49) 13 yd to ftObjective: (9.1) Use Dimensional Analysis to Change

Units of Measurement

Convert the given measurement to the unit indicated.50) 5.49 m to cm

Objective: (9.1) Convert Units Within the MetricSystem

Use dimensional analysis to convert the unit indicated.51) 7 m to yd

Objective: (9.1) Use Dimensional Analysis to Changeto and from the Metric System

4

Select the best estimate for the measure of the givenquantity.

52) the length of a bedroom wallA) 4.2 m B) 4.2 mmC) 4.2 km D) 4.2 cm

Objective: (9.1) Understand and Use Metric Prefixes

Use the fact that a solid with a volume of 1000 cubiccentimeters has a capacity of 1 liter, along withdimensional analysis, to convert the given unit to the unitindicated.

53) 510.6 mL to cm3

Objective: (9.2) Use English and Metric Units toMeasure Capacity

Use dimensional analysis to convert the given square unitto the square unit indicated. Where necessary, round theanswer to two decimal places.

54) 13.1 ha to acresObjective: (9.2) Use Dimensional Analysis to Change

Units for Area

Selecting from milligram, gram, kilogram, and tonne,determine the best unit of measure to express the givenweight.

55) a pocket calculatorObjective: (9.3) Apply Metric Prefixes to Units of

Weight

Convert the given unit of weight to the unit indicated.56) 165 mg to g