# H.C.C.T.P. Highway Construction Careers Training Program. Entrance Exam. Study Guide

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1 H.C.C.T.P. Highway Construction Careers Training Program Entrance Exam Study Guide

2 Entrance Exam Study Guide How to use this study guide: This study guide is to prepare you for the math section on your entrance exam. The majority of the basic information is listed below. The exam will use this basic information in various ways to test your problem solving skills and your computational skills. Within each section there are brief explanations and problems worked out. Throughout the packet you will see hints and tips marked with a 'careful'. These 'careful' hints are to help you to avoid common mistakes. Good luck! Rounding/Place Values: The following represents the place value of individual digits. Millions Hundred thousands Ten Thousands Thousand s Hundred s Tens Ones Tenth s Hundredths Thousandths Ten Thousandth,34, Things to remember...the place value starts at 'ones' to the left of the decimal points and starts at 'Tenths' to the right of the decimal point. Steps for rounding:. Find the place value you are asked to round to.. Look to the digit to the right of the number. 3. If the digit is smaller than 5, leave your number alone. If the digit is greater than or equal to 5, add one to your number. 4. All the numbers to the right of the digit become O's. 7,7 rounded to the hundreds would be 7,700 because the in the tens place is smaller than 5. 7,7 rounded to the thousands would be 8,000 because the 7 in the hundreds place is larger than 5.

3 Basic Operations: Whole Numbers. Addition: Line up your place values and add in columns. Careful: make sure to carry over correctly. Ex. ) 54, Ex. ) 4, Subtraction: Line up your place values and subtract in columns. Careful: make sure to borrow correctly. Ex. 3) Ex. 4) Multiplication: Set up your problem in rows. Multiply the last digit in the bottom number with every number in the top. From there, multiply each subsequent digit in the bottom number with every number in the top. Careful: when you go from one digit to the next in the bottom number, make sure to add the correct number of 0's as place holders

4 4. Division: Set up your problem in long division format. When given the problem as A B...the number B goes on the outside of the division symbol and the number A goes underneath the division symbol. Go step by step seeing how many times the divisor 'number on the outside' goes into the dividend 'number on the inside'. Careful: Double check your multiplication and subtraction to avoid calculation mistakes R.Divide.Multiply Division Steps Does McDonalds Sell Cheese Burgers? Subtract 4.Compare 5.Bring down Basic Operations: Decimals Addition: First align the decimals in your numbers. Then add as you would with whole numbers. Careful: Make sure your decimals are lined up

5 Subtraction: First align the decimals in your numbers. Then subtract as you would with whole numbers. Careful: Make sure your decimals are lined up Multiplication: Multiply as you would whole numbers. The amount of numbers behind the decimal point in the problem, are the number of decimals in the answer. Careful: Do not align the decimals. Sample: X Division: Arrange the problem as long division. If there is a decimal in the divisor (number on the outside) move it to the right until the divisor is a whole number. The number of places the decimal was moved in the divisor is the number of places it should be moved in the dividend (number on the inside). Careful: Go slow and double check the multiplication and subtraction. Mixed Numbers/Improper fractions: An improper fraction is where the numerator (number on top) is larger than the denominator (number on the bottom). A mixed number is a combination of a whole number and a common fraction. Improper fraction: 3 Mixed Number: 3

6 To change from improper fraction to a mixed number: Turn the fraction into a long division problem. How many whole times the denominator can go into the numerator is the whole number of the mixed number and any remainder is the numerator of the common fraction. Change 5 4 to a mixed number. 6 R To change from a mixed number to an improper fraction: Multiply the denominator and the whole Number, and then add the numerator. This new value is the numerator of the improper fraction. Change 3 4 to an improper fraction Reducing Fractions: To reduce a fraction, divide both the numerator and denominator by the same value Addition/Subtraction: When adding or subtracting fractions or mixed numbers, they need to have a common denominator, meaning the same denominator. If the numbers do not already have a common denominator, you will need to multiply one or both fractions by a value so that the fractions have a common denominator. Careful: When you change the fraction by multiplying the denominator, make sure you multiply the numerator as well =

7 Multiplication: When multiplying improper or common fractions, you multiply the numerators and multiply the denominators. Try to reduce when possible. Careful: All mixed numbers must be changed to an improper fraction format prior to multiplication Negative Numbers Addition: Positive + Positive = Positive Negative + Negative = Negative Sum of a Negative and a Positive = Keep the sign of the larger and subtract = = (-) = -. + (-5) = 7 Subtraction: Negative Positive = Negative (Same as adding two negatives) Positive Negative = Positive (Same as adding two positives) Negative Negative = Negative + Positive (Keep the sign of the larger and subtract) = (-7) = (-4) = = (-3) = = -9 Multiplication/Division: Positive x/ Positive = Positive Negative x/ Negative = Positive Positive x/ Negative (or vice-versa) = Negative. 3 x 6 = x -3 = = -3

8 Percent to a decimal: Divide the percent by 00. Percent Change 3% to a decimal. 3% 00 =.3 Decimal to a percent: Multiply the decimal by 00. Change 0.04 to a percent x 00 = 4% Percent to a fraction: Change the percent to a decimal and then change to a fraction. Change 6% to a fraction Percent Proportion Problems: The formula for solving percent proportion problems is the following. part base percent 00 The percent is the value with a percent sign. The base value is the number after the word of and the part value is the new partial value. To solve, cross multiply. Cross multiplication involves multiplying the two numeric values that are diagonally from each other, then dividing by the third number. Careful: Do not try and reduce diagonally.. What is 5% of 4?. What percent is 78 of 80? x % % 00x 3, x is 7% of what number? 35 7 x 00 7 x 3,500 x

9 Order of Operations The order of operations tells us in which order to evaluate a mathematical expression. The order is the following.. Parenthesis. Exponents 3. Multiplication/Division (left to right) 4. Addition/Subtraction (left to right) The saying to remember the order of operations is Please Excuse My Dear Aunt Sally. Careful: When multiplication and division are next to each other in the expression, evaluate from left to right the same goes for addition and subtraction ( x + 3) x 8 x ( + 3) x (5) 6 8 x Graphs There are several things to keep in mind when answering questions in relation to a graph. Review the entire graph before answering any questions. Pay close attention to the labels and increments of the horizontal and vertical axis. For questions that ask you to analyze the graph, read all the options first before making your final choice Conversions Metric Conversions: Metric measurements are based on powers of 0. Kilo- means,000 Hecto- means 00 Deka- means 0 To convert Up- Divide by 0 Chart works around the ones place e.g. meter, gram or liter Deci- means /0 or 0. Centi- means /00 or 0.0 Down Multiply by Milli- means /000 or The saying to help remember metric conversions is King Henry Died Drinking Chocolate Milk (The is to help you remember the ones or units place).

10 . Convert 350 mm to m m. Convert.7 km to m m US Conversions: Unlike the metric system, the US system has various conversion facts that are not based on power on powers of 0. There are several conversion facts/values that would be beneficial to memorize. inches foot 3 feet yard 6 ounces pound 60 sec onds min ute 60 min utes hour When converting from a smaller unit to a larger unit, divide by the conversion value. Convert ft. to yards. ft yd 7 yd 3 ft When converting from a larger unit to a smaller unit, multiply by the conversion value. Convert.5 ft. to inches..5 ft in ft 30in

11 Plotting Points Number Line: The values on a number line increase moving to the right and decrease moving to the left. Negative numbers are to the left of 0 and positive numbers are to the right of 0. Coordinate Plane: The coordinate plane consists of two lines; one vertical (y-axis) and one horizontal (xaxis). The two axis meet at the point (0, 0) or the origin. The x-values are positive to the right of the origin and the y-values are positive about the origin. To Plot a Point: Any point has the format (x, y) where x is the x-coordinate, the amount to move in the horizontal direction and y is the y-coordinate, the amount to move in the vertical direction. If the x-value is positive move right, if it is negative, move left. If the y-value is positive, move up. If the y-value is negative move down. Plot the following points: A B C D (,5) (,7) ( 3, 4) (0,5) Geometric Figures Perimeter: Perimeter is the length around a shape. To determine the perimeter of any shape, find the sum of the sides. What is the perimeter of the following figure?

12 Area: The two- dimensional space a figure occupies. There are several formulas that determine area, depending on the shape. Rectangle: length x width Triangle : base height Circle : radius. If the base of a triangle is cm long and the height is 3 cm, what is the area of the triangle? A () (3) 8 cm. What is the area of the figure below? 4m 4m 9m 6m m m m Volume: The three- dimensional space a figure occupies. To determine volume, multiply volume, multiply the area the base and the height of the figure.. What is the volume of the figure below? 5 ft V 3 5 ft 3 ft 80 ft 3

13 Practice Problems WHOLE NUMBER PRACTICE. Round to the given place 5. Divide A) 3973 to hundreds A) B) to ten thousands B) Add 6. Evaluate each expression using A) the order of operations. B) A) 3 +5 (6-) C) Find the difference between B) and C) Multiply A) B) Applications A) Mr. Robinson drove from Los Angeles to Chicago. He drove 40 miles on Monday, 365 miles on Tuesday, and 38 miles on Wednesday. If the total distance is 850 miles, how much further does he have to drive? FRACTION PRACTICE. Reduce each fraction to lowest terms. 4 9 A) B) C) Write each improper fraction as a mixed number A) B) C) Write each mixed number as an improper fraction A) 5 B) 6 C) Add. Reduce your answers A) B) C)

14 5. Subtract 4 A) B) 9 C) Multiply. Reduce your answers A) B) C) Divide. Reduce your answers A) B) 5 4 C) Applications. A) Fred Thomson a nurse worked /3 hours of overtime on Monday, ¼ hours on Wednesday, /3 hours on Friday, and 6 ¾ hours on Saturday. If overtime pay is \$ per hour, what did Fred receive in overtime pay? B) The parents of Harper Junior High School choir members are making robes for the choir. Each robe requires 5/8 yards of material at \$8 per yard. How much will 4 choir robes cost? C) A fifteen foot board is cut into 3 ½ foot long pieces for a bookcase. After as many pieces as possible are cut, how long is the remaining piece? D) Gary Waller bought 7 ¾ acres to develop. He made a lake out of 7 /3 acres, then set aside ¾ acres for a park. How many /3 acre lots can he sell from remaining acreage? E) The number of box car loads shipped by one factory each day during the first week of February was ½, 3 ¼, ¾, 4, and 3 3/8. Determine the average number of box car loads shipped per day during this five-day period. F) A container with 54 cups of flour had the following amounts removed: ¼ cups, 3 ½ cups, ¾ cups, ½ cups, 3 /3 cups, and /3 cups. How much flour remains in the container?. Add or Subtract A) B) C) D) DECIMAL PRACTICE

15 . Multiply A) B) 3.8 C) Divide A) B) round to decimal places C) round to decimal places 4. Write as a decimal. Round to two decimal places. A) B) C ) Write as a fraction or mixed number. A) 0.45 B) 0.05 C) Applications A) Nancy buys a shirt for \$4.95 and a blouse for \$9.95. How much change will she receive from four \$0 bills? B) Lynn had \$43.9 in her checking account at the beginning of the month. During the month, she made deposits of \$00 and \$3.45. She wrote checks for \$74.95, \$4.5, \$8., \$30, and \$9.50. What is her balance at the end of the month? C) Lean ground round cost \$3.9/lb. What will a package weighting.8 pounds cost to the nearest cent? D) Eastern Phone Company charges \$0.53 for the first minute and \$0.9 for each additional minute for a phone call from Atlanta to Birmingham. How much would an 8-minute call cost? E)The utility bills for an apartment for a six- month period were \$6.50, \$45.83, \$ 79.7, \$83.46, \$7.60, and \$ Determine the average monthly billing for this period. F) Multiply thirty- three and eight hundredths by forty and seven tenths, and round the product to the nearest tenth. PERCENT PRACTICE. Write as a fraction. A) 6% B) 40% C) 75%. Write as a decimal A) 56% B) 3.9% C) 560% 3. Write as a percent. A).6 B).07 C) ¾ D) ¼

16 4. Solve the proportion. A)What is 0.7% of 485? B) 6% of 9.5 is what? C) 5 is what percent of 000? D) What percent of is 4? E) 4.8 is 5% of what? F) 78% of what is 3.9? 5. Applications A) If the interest rate on a charge card is ¼ % on the unpaid balance and your unpaid balance this month is \$3, how much interest will you pay this month? B) If the baseball team wins 78 of the 4 games that it plays, what percent has it lost? C) Jenkins Appliance has a washing machine regularly priced at \$350 on sale for \$ What is the discount rate? GEOMETRY PRACTICE. Find the perimeter of the following figures: 7 ft nnjhhjklkkkkk ½ ft. yd. 8 in ft. 3 ft 6 ft 8 ft 7 ¾ ft. 5 ft. 0 ft. A) B) C). Find the area of the following figures. 8 cm 8 cm 8 ft. yd. 8 in ft. 6 cm 0 ft. 0 ft. 4 ft. /3 yd. A) B) C)

17 Practice Problems Answer Key WHOLE NUMBER PRACTICE ANSWERS. A) 4000 B) A) 767 B) A) 356 B) 595 C) A),477,448 B) 3,745,78 5. A) 03 R B) 9 R9 6. A) 8 B) 3 C) 8 7. A) 683 miles FRACTION PRACTICE ANSWERS 7. A) B) C) A) 5 B) 9 C) A) B) C) A) B) C) A) B) 6 C) A) B) 0 6 C) A) B) C) A) 564 B) 5504 C) foot D) 5 lots 7 E ) 3 40 box car loads per day F ) 39 cups DECIMAL PRACTICE ANSWERS. A) 3.58 B) 6.58 C) 44 D) A) B) 38.6 C) A) 5.9 B) 4 C) A) 0.7 B) 0.03 C) A) B) C) 3 6. A) 58.0 B) C) D) 8.56

18 PERCENT PRACTICE 3 3. A) B) C) A).56 B).03 C) A) 6056 B) 0756 C) 7536 D) 5% 4. A) B) 5.07 C) 0.5% D) 00% E) 3 F) 5 5. A) B) 3.63% C) 5% GEOMETRY PRACTICE ANSWERS. A) 58 ½ B) 0 ft. C) 6 ft.. A) 96 cm B) 336 ft. C) 3 ¾ ft.

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