GED Mathematics Practice Questions

C H A P T E R 45 GED Mathematics Practice Questions NOW IT’S time to put all that you have learned about mathematics and problem solving into practice In the following section, you will find 100 multiple-choice questions like those you will find on the GED Mathematics Test Directions Read the following questions carefully and choose the best answer for each question Some questions may refer to a figure, table, or graph Be sure to answer every question; you will not be penalized for incorrect answers Do not spend too much time on any one question so you can be sure to complete the questions in the allotted time Record your answers on the answer sheet provided on the following page Make sure you mark the answer in the circle that corresponds to the question Note: On the GED, you are not permitted to write in the test booklet Make any notes or calculations on a separate piece of paper 423 – LEARNINGEXPRESS ANSWER SHEET – Answer Sheet 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e 61 62 63 66 67 68 69 72 73 74 76 79 80 81 82 84 85 86 88 89 90 91 93 94 95 96 97 98 99 100 a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c For questions 64, 65, 70, 71, 75, 77, 78, 83, 87, and 92, see the answer grids that follow each question 425 d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e – GED MATHEMATICS PRACTICE QUESTIONS – Danny worked 40 hours and earned $6.30 per hour His friend Erica earned $8.40 per hour at her job How many hours would Erica have to work in order to equal Danny’s earnings for 40 hours? a 20 b 25 c 30 d 252 e Not enough information is given The gauge on a water tank shows that the tank is ᎏᎏ full of water In order to fill the tank, 16 gallons of water are added How many gallons of water does the tank hold when full? a 20 b 24 c 30 d 32 e 48 Question is based on the following figure Question is based on the following figure A mp Ra 12 ft D 16 ft B The number of students in a class is x One day, students were absent What fractional part of the class was present? x a ᎏ5ᎏ b ᎏᎏ x c ᎏᎏ x−5 x+5 ᎏᎏ x−5 ᎏᎏ x e At a luncheon, 48 half-pints of fruit juice are served What is the cost, at $3.50 per gallon, of these servings of fruit juice? a $6.00 b $7.00 c $10.50 d $12.50 e $15.00 Given the equation x2 + x − = 0, which of the following give(s) a complete solution of the equation? a b and −3 c −2 and d and e and −3 C ᭝ABC is a right triangle, and ៮៮៮ ൿ ៮៮៮ If the CD AB measure of ∠CAD = 40°, what is the measure of ∠DCB? a 10° b 20° c 40° d 50° e 90° d What is the length in feet of the ramp? a 13 b 17 c 20 d 24 e Not enough information is given 427 – GED MATHEMATICS PRACTICE QUESTIONS – Question 10 is based on the following figure Question is based on the following figure 3x − y a + 2b 2a + b 2a 2x + 3y x + 2y a+b 5x + y What is the perimeter of the figure? a 6a + b b 5a + 5b c 6a + 4b d 3a + 5b e 3a + 5b 10 What is the perimeter of the figure? a 11x + 5y b 10x + 5y c 11x + 4y d 9x − y e 8x + 3y Question is based on the following figure 11 Henry has $5 more than Oliver, and the same amount of money as Murray Together, they have $85 How much money does Oliver have? a $10 b $12 c $15 d $25 e Not enough information is given A = 322 square feet 23 feet A rectangular dining room has a floor area of 322 square feet If the length of the room is 23 feet, what is the perimeter? a 28 feet b 37 feet c 45 feet d 60 feet e 74 feet Question 12 is based on the following table This table gives the instructions that accompany an income tax form IF YOUR TAXABLE INCOME IS: At Least But Not More Than Your Tax Is $3,499 2% of amount $3,500 $4,499 $70 plus 3% of any amount above $3,500 $4,500 $7,499 $100 plus 5% of any amount above $4,500 $7,500 428 $250 plus 7% of any amount above $7,500 – GED MATHEMATICS PRACTICE QUESTIONS – 13 How much tax is due on a taxable income of $5,800? a $120 b $135 c $150 d $165 e $175 A bed and breakfast charges $48.00 per day for a double room In addition, there is 5% tax How much does a couple pay for several days’ stay? a $144.00 b $151.20 c $156.20 d $158.40 e Not enough information is given Question 16 is based on the following graph 30 Hundreds of Dollars 12 25 20 15 10 Baked Goods Groceries Dairy Produce Meat 16 By how many dollars the sales in the meat department exceed the sales in the dairy department? a $100 b $1,000 c $1,500 d $1,800 e $10,000 17 A box of cereal is priced at x cents per box A customer has a coupon for 15 cents off If the store reduces prices by doubling the value of each coupon, how much, in cents, does the customer pay for the box of cereal? a x − 15 b x − 30 c x + 15 d x + 30 e Not enough information is given Question 14 is based on the following figure A C B D 14 If ៮៮៮ is perpendicular to ៮៮៮ and m∠CBD = AC CB 125°, then m∠A equals a 15° b 20° c 35° d 45° e Not enough information is given 15 If the square of a number is added to the number increased by 4, the result is 60 If n represents the number, which equation can be used to find n? a n2 + = 60 b n2 + 4n = 60 c n2 + n + = 60 d n2 + 60 = 4n + e n2 + n = 64 429 – GED MATHEMATICS PRACTICE QUESTIONS – Question 21 is based on the following graph Question 18 is based on the following figure A Distribution of Expenses for Sales of $240,000 Ace Manufacturing Company ЄA:ЄB:ЄC = 3:2:1 B Labor 40% Raw Materials 33 % C 18 The measures of the angles of a triangle are in the ratio 3:2:1 What is the measure of the largest angle of the triangle? a 65° b 70° c 72° d 80° e 90° Operating Expenses 20% Net Profit % 21 How many dollars were spent for labor? a $4,800 b $9,600 c $48,000 d $96,000 e $960,000 22 The distance between two heavenly bodies is 63,150,000,000 miles What is the number expressed in scientific notation? a 631.5 × 108 b 63.15 × 109 c 6315 × 107 d 6.315 × 1010 e 6.315 × 10−10 Question 19 is based on the following figure E D C A B 19 If m∠1 = 36° and m∠2 = 2(m∠3), then m∠3 equals a 36° b 40° c 44° d 48° e Not enough information is given 20 Ms Klein bought pounds of beef and 3ᎏ1ᎏ pounds of chicken for $13.98 If the beef cost $2.76 per pound, what was the cost of the chicken per pound? a $0.72 b $0.80 c $0.84 d $0.87 e $0.92 430 – GED MATHEMATICS PRACTICE QUESTIONS – Question 23 is based on the following graph Question 26 is based on the following graph y A (5,4) B (0,3) Materials $40 Salaries $30 x Profit ? Taxes $11 23 What is the slope of the line passing through points A (5,4) and B (0,3)? a ᎏ1ᎏ 10 Insurance $5 Misc $6 c The graph shows what happens to each $100 taken in by a small business How many dollars out of each $100 taken in represent profit? a $5 b $6 c $7 d $7.5 e $8 27 Nick scored more points than Josh in a basketball game Paul scored points less than Josh in the same game If the three boys scored a total of 38 points, how many points did Josh score? a b c 11 d 14 e 15 28 b 26 A box in the form of a rectangle solid has a square base feet in length and a height of h feet If the volume of the rectangular solid is 200 cubic feet, which of the following equations may be used to find h? a 5h = 200 b 5h2 = 200 c 25h = 200 d h = 200 ÷ e h = 5(200) ᎏᎏ ᎏᎏ ᎏᎏ d e 24 kilometer = a 10 meters b 100 meters c 1,000 centimeters d 10,000 centimeters e 1,000,000 millimeters Question 25 is based on the following figure A 60′ B 48′ E 80′ D 25 C To measure the distance (DC) across a pond, a surveyor takes points A and B so that ឈ៮៬ is parAB ឈ៮៬ ឈ៮៬ ឈ៮៬ ឈ៮៬ allel to DC If AB = 60 feet, EB = 48 feet, and ED ឈ៮៬ = 80 feet, find DC a 72 ft b 84 ft c 96 ft d 100 ft e Not enough information is given 431 – GED MATHEMATICS PRACTICE QUESTIONS – Question 29 is based on the following figure A 29 B C D 33 E Which point on the number line represents the closest approximation to the square root of 12? a A b B c C d D e E On a road map, ᎏ1ᎏ inch represents miles of actual road distance The towns of Alton and Waverly are represented by points 2ᎏ1ᎏ inches apart on the map What is the actual distance, in miles, between Alton and Waverly? a 17 b 32 c 40 d 60 e 68 Question 34 is based on the following figure Question 30 is based on the following figure units 25′ 15′ 20′ units 10′ 30 31 The diagram represents a large living room What is the area, in square yards, of the room? a 16.6 b 33.3 c 45 d 50 e 450 If dollar is worth x French francs, what is the value, in dollars, of y French francs? a xy b ᎏxᎏ y c y ᎏᎏ x ᎏᎏ xy 34 What is the area, in square graph units, of the triangle? a b 10 c 16 d 32 e 48 35 At a certain time of day, a man feet tall casts a shadow feet in length At the same time, a church steeple casts a shadow 28 feet in length How high, in feet, is the church steeple? a 30 b 32 c 42 d 48 e 56 d e x + y 32 Evaluate y 2(4x − y) if y = −2 and x = a −18 b 18 c 86 d 96 e 136 432 – GED MATHEMATICS PRACTICE QUESTIONS – 97 Two sides of a triangle measure and 10 inches If the triangle is a right triangle, which of the following could be the measure, in inches, of the third side? a b c d 10 e 12 T SʈT 98 m∠1 = 77 The floor of a walk-in closet measures feet by feet If the ceiling height is feet, what is the volume in cubic feet of the closet? a 28 b 56 c 112 d 168 e 224 100 In a right triangle, the hypotenuse measures 15 inches If one leg of the triangle measures inches, which of following equations could be used to find the length of the other leg (x) in inches? a x = ͙15 + ෆ b x = ͙15 − ෆ c x = 15 − d x2 = 152 + 62 e x2 = 152 − 62 Question 98 refers to the figure below S 99 10 11 12 13 14 16 15 m∠10 = 95 Classify the figure containing interior angles 3, 6, 11, and 13 a scalene triangle b trapezoid c parallelogram d rectangle e square 444 – GED MATHEMATICS PRACTICE QUESTIONS – Answers and Explanations d If x is replaced by the answer choices, only and −3 make the expression true (2)2 + − = (−3)2 + −3 − = + −4 = + −3 − = + −9 = 0=0 0=0 c Danny earned a total of 40($6.30) = $252 To find the number of hours Erica would take to earn $252, divide $252 by $8.40 A a + 2b 2a + b 2a D a+b B c To find the perimeter of the figure, find the sum of the lengths of its sides 2a + a + b + 2a + b + a + 2b = 6a + 4b C c Since m∠ACB = 90° and m∠CAD = 40°, then m∠B = 180 − 90 − 40 = 50° In BCD, m∠CDB = 90° and m∠B = 50° Therefore, m∠DCB = 180 − 90 − 50 = 40 A = 322 square feet e If the class has x students and students are x−5 absent, then x − students are present: ᎏ5ᎏ b If the tank is ᎏ1ᎏ full, it is ᎏ2ᎏ empty Let x = the 3 capacity of the tank; ᎏ2ᎏ x = 16, so x = 16 ữ = 3 16 ì = 24 23 feet e Let x = the width of the room; 23x = 322; x = 322 ÷ 23 = 14 Perimeter = 23 + 14 + 23 + 14 = 74 feet 10 mp Ra 12 ft 3x − y 2x + 3y x + 2y 16 ft 5x + y c Let x = the length of the ramp Use the Pythagorean theorem to obtain the equation: x2 = 122 + 162 = 144 + 256 = 400 x = ͙400 = 20 ෆ a The perimeter of the figure is x + 2y + 3x − y + 2x + 3y + 5x + y = 11x + 5y c 48 half-pints = 24 pints Since pt = gal., 24 pt = gal., 3($3.50) = $10.50 445 – GED MATHEMATICS PRACTICE QUESTIONS – 14 11 d Set up an equation with Oliver’s money as the unknown, and solve Oliver = x, Henry = + x, and Murray = + x Therefore, x + 2(5 + x) = 85 x + 10 + 2x = 85 3x + 10 = 85 3x = 75 x = 25 12 A IF YOUR TAXABLE INCOME IS: At Least But Not More Than B C Your Tax Is $3,499 2% of amount $3,500 $4,499 $70 plus 3% of any amount above $3,500 $4,500 $7,499 D $100 plus 5% of any amount above $4,500 $7,500 c m∠CBD = 125 m∠ABC = 180 − 125 = 55 m∠A + m∠ABC = 90 m∠A + 55 = 90 m∠A = 90 − 55 = 35 15 c Let n = number Then n2 = square of a number, and n2 + n + = 60 $250 plus 7% of any amount above $7,500 16 30 Hundreds of Dollars d $5,800 − $4,500 = $1,300 Tax is $100 + 5% of $1,300 = 100 + 0.05(1,300) = 100 + 65 = $165 13 e You cannot compute the cost unless you are told the number of days that the couple stays at the bed and breakfast This information is not given 25 20 15 10 Baked Goods Groceries Dairy Produce Meat b Meat department sales = $2,500 Dairy department sales = $1,500 Difference = $1,000 17 b Because the coupon has double value, the reduction is 2(.15) = 30 cents The cost of the cereal is x − 30 cents 446 – GED MATHEMATICS PRACTICE QUESTIONS – 18 21 A ЄA:ЄB:ЄC = 3:2:1 Raw Materials 33 % Labor 40% B Operating Expenses 20% Net Profit % C e Let x, 2x, and 3x be the measures of the three angles Then: x + 2x + 3x = 180 6x = 180 x = 180 ÷ = 30 3x = 3(30) = 90 19 E D C 22 d To express a number in scientific notation, express it as the product of a number between and 10 and a power of 10 In this case, the number between and 10 is 6.315 In going from 6.315 to 63,150,000,000, you move the decimal point 10 places to the right Each such move represents a multiplication by 1010 and 63,150,000,000 = 6.315 × 1010 23 A d Forty percent of the total expenses of $240,000 went for labor: 0.40($240,000) = $96,000 y B d Let x = m∠3 and 2x = m∠2 m∠1 + m∠2 + m∠3 = 180 36 + 2x + x = 180 3x + 36 = 180 3x = 180 − 36 = 144 x = 144 ÷ = 48 degrees B (0,3) 20 c The beef costs 4($2.76) = $11.04 The chicken costs $13.98 − $11.04 = $2.94 To find the cost per pound of chicken, divide $2.94 by 3ᎏ1ᎏ or by 7 ᎏᎏ; 2.94 ÷ ᎏᎏ = 2.94 × ᎏᎏ = 0.84 2 A (5,4) x y −y b Slope = ᎏᎏ; in this case, y1 = 4, y2 = 3, x1 = 5, x1 − x2 4−3 and x2 = Slope = ᎏᎏ = ᎏ1ᎏ 5−0 24 e km = 1,000 m and m = 100 cm So km = 100,000 cm and km = 1,000,000 mm 447 – GED MATHEMATICS PRACTICE QUESTIONS – 25 A 60′ 28 c Use the formula V = lwh In this case, l = 5, w = 5, and h = h Therefore, V = × × h = 25h and 25h = 200 B 48′ E 29 29 A 80′ B C D E d Since = and = 16, ͙12 is between and ෆ Only point D lies between and 32 42 C D 30 d Let x = ឈ៮៬ Since ᭝ABE is similar to ᭝CED, the DC lengths of their corresponding sides are in proportion x 80 ᎏᎏ = ᎏᎏ 60 48 48x = 80(60) = 4,800 x = 4,800 ÷ 48 = 100 100 feet is the answer 10′ d Divide the floor space into two rectangles by drawing a line segment The area of the large rectangle = 20 × 15 = 300 sq ft The area of the small rectangle = 10 × 15 = 150 sq ft The total area of floor space = 150 + 300 = 450 sq ft Since sq ft = sq yd., 450 sq ft ÷ = 50 sq yd Salaries $30 Profit ? 15′ 20′ 26 Materials $40 25′ 31 c If you don’t see that you need to divide y by x, set up a proportion Let z = number of dollars needed to purchase y francs Taxes $11 Insurance $5 Misc $6 z dollars ᎏ ᎏ = ᎏᎏ = ᎏ ᎏ y francs x z y(ᎏ1ᎏ) = (ᎏyᎏ)y x y ᎏᎏ = z x e Add the amounts given: 11 + + + 40 + 30 = $92 $100 − $92 leaves $8 for profit 27 c Let x = number of points scored by Josh, x + = number of points scored by Nick, and x − = number of points scored by Paul x + x + + x − = 38 3x + = 38 3x = 33 x = 11 32 e Replace the variables with their given values (−2)2 (32 − [−2]) = 4(34) = 136 33 e Since ᎏ1ᎏ in represents mi, in represents × = 32 mi., and in represents × 32 = 64 mi., 1 ᎏᎏ in represents mi Then 2ᎏᎏ in represent 8 64 + = 68 mi 448 – GED MATHEMATICS PRACTICE QUESTIONS – 34 40 d Let x = cost of lot and 3x = cost of house x + 3x = 120,000 4x = 120,000 x = 120,000 ÷ = 30,000 3x = 3(30,000) = $90,000 units units 41 e Find the interest by multiplying the amount borrowed ($1,300) by the time period in years (1.5) by the interest expressed as a decimal (0.09) To find the amount paid back, the amount borrowed must be added to the interest $1,300 + ($1,300 × 0.09 × 1.5) c Use the formula for the area of a triangle A = ᎏ1ᎏbh ᎏᎏ(4)(8) = 16 42 a Simply multiply: $8,000 × 0.13 × = $5,200 43 e Try −5 for x in each equation Only option e is true when −5 is substituted for x 12x = −60 12(−5) = −60 −60 = −60 35 c Let x = height of steeple Set up proportion: height of objec t x ᎏfᎏ:ᎏᎏ = ᎏᎏ length o shadow 28 4x = 6(28) = 168 x = 168 ÷ = 42 ft 44 b When you subtract the check from the amount in the checking account, the result will be the current balance: $572.18 − c = $434.68 36 20 ft ft 45 a Solve: x + (2x + 12) = $174 3x + 12 = $174 3x = $162 x = $54 30 ft d As you can see from the figure, to find the area of the walkway, you need to subtract the area of the inner rectangle, (20)(30) sq ft., from the area of the outer rectangle, (26)(36) sq ft.: (26)(36) − (20)(30) sq ft 37 e Since the average depth of the pool is ft., the water forms a rectangular solid with dimensions 30 by 20 by The volume of water is the product of these three numbers: (30)(20)(6) = 3,600 ft.3 38 d Taken together, the pool and the walkway form a rectangle with dimensions 36 by 26 The total area is the product of these numbers: (36)(26) = 936 sq ft 39 c × 105 = 600,000 ì 103 = 4,000 600,000 ữ 4,000 = 600 ÷ = 150 46 c Let x = the price of an adult’s ticket and x − $6 = the price of a child’s ticket In the problem, the cost of adults’ tickets and children’s tickets is $48 Write and solve an equation: 2x + 4(x − 6) = $48 2x + 4x − $24 = $48 6x − $24 = $48 6x = $72 x = $12 47 c The median is the middle amount Arrange the amounts in order and find the middle amount, $900 48 b The mode is the number that occurs most often Only 14 occurs more than once in the data set 449 – GED MATHEMATICS PRACTICE QUESTIONS – urday The difference between 17 gal and gal is 12 gal 49 c Find the amount of interest For the time period, use ᎏ9ᎏ, which equals ᎏ3ᎏ, or 75 Multiply 12 $1,500 × 0.04 × 0.75 = $45 Add to find the amount paid back $1,500 + $45 = $1,545 57 d The tops of the bars for Monday through Sunday are at 5, 4, 6, 5, 14, 17, and These add up to 60 50 c Multiply lb 12 oz by to get 18 lb 72 oz Divide 72 oz by the number of oz in a pound (16) to get lbs with a remainder of oz Therefore, 18 lb + lb oz = 22 lb oz 58 A 51 a If 80% of the audience were adults, 100% − 80% = 20% were children 20% = 20, and 0.20(650) = 130 O 52 b Let x = number of inches between the towns on the map Set up a proportion: in ᎏmi 60 ᎏ B x = ᎏin i 225 ᎏ m 60x = 255 a Let x = m∠OAB ឈ៮៬ = ឈ៮៬ since radii of the OA OB same circle have equal measures Therefore, m∠OAB = m∠OBA x + x + 70 = 180 2x + 70 = 180 2x = 180 − 70 = 110 x = 110 ÷ = 55 x = ᎏ5ᎏ = 4ᎏ1ᎏ 60 53 b ft in = ft 15 in − ft in = ft in 54 d v = lwh; the container is ft long × ft wide × ft high × × = 30 ft.3 55 59 e Let x = number of books on the small shelf, and x + = number of books on the large shelf Then, 4x = number of books on small shelves, and 3(x + 8) = number of books on large shelves 4x + 3(x + 8) = 297 4x + 3x + 24 = 297 7x + 24 = 297 7x = 297 − 24 7x = 273 ÷ = 39 Paint Sales at Carolyn’s Hardware 20 18 Number of Gallons 70° 16 14 12 10 M T W Th F Days of the Week Sa 60 a 40 ft = 40 × 12 = 480 in ft in = 3(12) + = 36 + = 40 in 480 ÷ 40 = 12 scarves Su d The top of the bar for Wednesday is at on the vertical scale 56 e The top of the bar for Monday is halfway between and 6, so gal were sold on Monday The top of the bar for Saturday is halfway between 16 and 18, so 17 gal were sold on Sat- 61 b $130,000 (catalog sales) − $65,000 (online sales) = $65,000 62 b $130,000 + $65,000 + $100,000 = $295,000, which is about $300,000 Working with compatible numbers, $100,000 out of $300,000 is ᎏ1ᎏ 450 – GED MATHEMATICS PRACTICE QUESTIONS – 63 c 22 feet = 264 inches; 264 ÷ 5.5 = 48 65 58 64 ᎏ1ᎏ 58 / / / • • • • • / 0 / • • • • 1 1 • / 0 2 2 1 3 3 4 4 1 2 2 3 3 5 4 4 6 6 5 5 7 7 6 6 8 8 7 7 9 9 8 8 9 9 The coordinates of point A are (−3,0) The coordinates of point B are (3,2) Use the slope formula: y2 − y1 ᎏᎏ x2 − x1 Substitute and solve: 2−0 ᎏ(−3) 3− ᎏ = ᎏ2ᎏ, or ᎏ1ᎏ Substitute the values for x and y in the expression Then simplify 3(2 × − 5) + (3 + 4)2 = 3(3) + 72 = + 49 = 58 66 e Since the dimensions of Box A are half of the dimensions of Box B, the side lengths must be 3, 2, and 1.5 Next, find the volumes of the two boxes Use the formula V = lwh The volume of Box B is 72, and the volume of Box A is 72 is times larger than 12 67 d Set up a proportion: ᎏ5ᎏ = ᎏxᎏ, where x is the 100 number of children enrolled in the program 12 × 100 = 1,200, and 1,200 ÷ = 240 68 e Add the number of marbles to get the total number in the bag; 12 + + + = 25 Therefore, 25 is the number of possible outcomes Seven marbles are either blue or yellow Seven is 28 the number of favorable outcomes; ᎏ7ᎏ × ᎏ4ᎏ = ᎏ0ᎏ 25 = 28% 69 a Substitute for b and for n into the function Then, solve the equation C = $25.60(4) + $14(4)(3 − 1) = $102.40 + $112.00 = $214.40 451 – GED MATHEMATICS PRACTICE QUESTIONS – 70 375 71 1,040 40 / / / • • • • 0 0 1 1 1 2 2 2 3 3 4 4 5 5 6 6 7 8 9 • / • / / • • • • 1 2 2 3 3 4 5 5 6 6 6 7 7 7 8 8 8 9 9 9 Multiply $250 by 1.5, which equals $375 Set up the proportion and solve: x = the number of miles between the two landmarks ᎏᎏ 6ᎏ1ᎏ ᎏ=ᎏ 120 x 6ᎏ1ᎏ × 120 = 780 and 380 ÷ ᎏ3ᎏ = 1,040 The answer is 1,040 miles 72 d Separate the two inequalities into two inequalities, x < and −2 = x Choice d is the only graph that represents the inequalities There must be an open circle to represent that the is not included and a shaded circle to represent that the −2 is included 73 a Angle and the angle measuring 50° are corresponding angles Therefore, m∠4 = 50° 74 a Angle and the angle measuring 104° are supplementary; therefore, m∠3 = 180 − 104 = 76 As established in the previous problem, angle and the angle measuring 50° are corresponding angles, so m∠4 = 50° Angle 3, angle 4, and x are the interior angles of a triangle, so they equal 180°; 50 + 76 + x = 180, and so x = 54° 452 – GED MATHEMATICS PRACTICE QUESTIONS – 75 (−3, −1) 77 10 / / / • • • 0 1 −1 2 2 −2 3 3 −3 4 4 −4 5 5 −5 6 6 −6 7 7 8 8 9 9 • • −6 −5 −4 −3 −2 −1 The vertical line is parallel to the y-axis, and all of its points have the x-coordinate −3 The horizontal line is parallel to the x-axis, and all of its points have the y-coordinate −1 Therefore, the coordinates are −3 and −1 Quadrilateral ABCD is a trapezoid because it has one pair of parallel sides The bases are the parallel sides, AB and CD The height is 2.5 cm Use the formula for the area of a trapezoid A = ᎏ1ᎏ × (b1 + b2) × h 76 c Mean = average Add the scores and divide by the number of scores 78 + 86 + 82 + 81 + 82 + 77 = 486 486 ữ = 81 = ì (6 + 2) × 2.5 = ᎏ1ᎏ × × 2.5 = × 2.5 = 10 cm2 453 – GED MATHEMATICS PRACTICE QUESTIONS – 82 a Find 24% of $2,500 78 4.8 or 4.80 x 24 ᎏᎏ = ᎏᎏ 2,500 100 100x 60,000 ᎏ ᎏ = ᎏᎏ 100 100 x = 600 / / • • 0 0 1 1 1 / 20 2 2 / 3 3 4 4 5 5 6 6 7 7 2 8 8 3 3 9 9 4 4 5 5 6 6 7 7 8 8 9 9 • / • 83 ᎏᎏ 20 or ᎏ5ᎏ 100 • / ᎏᎏ ᎏᎏ, where x x is the cost Set up the proportion = of cans of yams; × = 24, and 24 ÷ = $4.80 79 d ft in = 69 inches Divide by 3: 69 ÷ = 23 inches Convert feet to inches, 23 in = ft 11 in 80 d Think of the space as two rectangles: 21 ft by 14 ft and 10 ft by ft (You can find the length of the missing side of the smaller rectangle by subtracting: 24 − 14 = 10.) Use the formula A = lw to find the area of each rectangle, and then combine to find the total area of the floor to be carpeted: 21 × 14 = 294, and × 10 = 70 Add the areas of the two rectangles: 294 + 70 = 364, so the Wrights will need to buy 364 square feet of carpeting 81 e x = one number and 3x + 12 = the other number, for the equation: x + 3x + 12 = − 20 4x + 12 = −20 4x = −32 x = −8 3(−8) + 12 = −12 • • • 0 1 • Clothing expenses take 5% of the Wrights’ pay Change 5% to a fraction to get ᎏ5ᎏ, which can 100 also be reduced to ᎏ1ᎏ 20 84 d Either locate each point on the grid and compare it to the line, or substitute the x and y values from each ordered pair into the equation: y = −ᎏ3ᎏx + −5 = −ᎏ3ᎏ(8) + −5 = −6 + −5 = −5 85 d The three numbers can be represented by x, x + 2, and x + Solve the equation: x + x + + x + = 90 3x + = 90 3x = 84 x = 28 The three numbers are 28, 30, 32 The question asks for the largest of these 454 – GED MATHEMATICS PRACTICE QUESTIONS – 91 b Add the times and multiply by cents: 19 + 24 + = 51 minutes; 51 × 09 = $4.59 86 e Similar triangles have the same angle measures Congruent triangles have the same angle measures and the same side lengths From the given information, you cannot know if the side lengths are the same, so you can conclude only that the triangles are similar 92 56 56 / / / • • • • 0 0 1 1 2 2 3 3 4 4 −1 5 −2 6 6 −3 7 7 −4 8 8 −5 9 9 87 (1,1) • −6 −5 −4 −3 −2 −1 −6 Let x represents the amount that Christian put in and 2x − 20 represents Maggie’s contribution Solve the equation x + 2x − 20 = 94 3x = 114 x = 38 Christian put in $38 and Maggie put in 94 − 38 = $56 Plot the points given in the problem and compete the parallelogram Remember that in a parallelogram, both pairs of opposite sides are equal and parallel 88 e The median time is the middle time There is no way of knowing how far behind the median the slowest runner was 89 b The steepest rise on the graph was from April 23 to April 30 The symbol indicates that it was in the Midwest 90 d The prices for the West Coast have been rising steadily by or cents each week On May 7, the price on the West Coast is a little beneath $1.80 If it rises or cents, it should be at about $1.82 by the following week The question gives no reason to expect a sudden decline in price or a sharp increase 93 d The number of games played is the total of the wins and losses, (20 + 15 = 35) Write the ratio 20 and simplify ᎏᎏ = ᎏ4ᎏ 35 94 b Use the Pythagorean theorem: 252 + 92 = c2: c = ͙252 + 92 = ͙625 + ෆ = ͙706 ෆෆ ෆ81 ෆ 95 b Use the order of operations −3 × 52 + 2(4 − 18) + 33 −3 × 25 + 2(−14) + 27 −75 + (−28) + 27 −76 455 – GED MATHEMATICS PRACTICE QUESTIONS – 96 e ᭝ABC is a right triangle, but you have no way of knowing which angle is a right angle, so eliminate choice a Regardless of the type of triangle, the sum of the measure of the interior angles of triangle must be 180° 97 c You can try each combination of sides in the Pythagorean theorem Only 6, 8, and 10 will work 62 + 82 = 102, 36 + 64 = 100, 100 = 100 99 e A closet is the shape of a rectangular solid To find the volume, multiply V = lwh 7(4)(8) = 224 cubic feet 100 e.Use the Pythagorean theorem If a2 + b2 = c2 and c is the hypotenuse, then b2 = c2 − a2 or x2 = 152 − 62 98 b A four-sided figure with only one pair of parallel sides is a trapezoid 456 – GED MATHEMATICS PRACTICE QUESTIONS – Glossar y of Terms: Mathematics a number used as a repeated factor in an exponential expression In 85, is the base number base 10 see decimal numbers binary system one of the simplest numbering systems The base of the binary system is 2, which means that only the digits and can appear in a binary representation of any number circumference the distance around the outside of a circle composite number any integer that can be divided evenly by a number other than itself and All numbers are either prime or composite counting numbers all whole numbers, with the exception of decimal a number in the base 10 number system Each place value in a decimal number is worth ten times the place value of the digit to its right denominator the bottom number in a fraction The denominator of ᎏ1ᎏ is 2 diameter a chord that passes through the center of a circle and has endpoints on the circle difference the result of subtracting one number from another divisible by capable of being evenly divided by a given number, without a remainder dividend the number in a division problem that is being divided In 32 ÷ = 8, 32 is the dividend even number a counting number that is divisible by expanded notation a method of writing numbers as the sum of their units (hundreds, tens, ones, etc.) The expanded notation for 378 is 300 + 70 + exponent a number that indicates an operation of repeated multiplication For instance, 34 indicates that the number should be multiplied by itself times factor one of two or more numbers or variables that are being multiplied together fractal a geometric figure that is self-similar; that is, any smaller piece of the figure will have roughly the same shape as the whole improper fraction a fraction whose numerator is the same size as or larger than its denominator Improper fractions are equal to or greater than base all of the whole numbers and negative numbers Examples are −3, −2, −1, 0, 1, 2, and Note that integers not include fractions or decimals multiple of a multiple of a number has that number as one of its factors 35 is a multiple of 7; it is also a multiple of negative number a real number whose value is less than zero numerator the top number in a fraction The numerator of ᎏ1ᎏ is odd number a counting number that is not evenly divisible by percent a ratio or fraction whose denominator is assumed to be 100, expressed using the % sign 98% is 98 equal to ᎏ0ᎏ perimeter the distance around the outside of a polygon polygon a closed two-dimensional shape made up of three or more line segments that are joined together positive number a real number whose value is greater than zero prime number a real number that is divisible by only two positive factors: and itself product the result when two numbers are multiplied together proper fraction a fraction whose denominator is larger than its numerator Proper fractions are equal to less than proportion a relationship between two equivalent c sets of fractions in the form ᎏaᎏ = ᎏdᎏ b quotient the result when one number is divided into another radical the symbol used to signify a root operation radius any line segment from the center of the circle to a point on the circle The radius of a circle is equal to half its diameter ratio the relationship between two things, expressed as a proportion real numbers include fractions and decimals in addition to integers reciprocal one of two numbers that, when multiplied together, give a product of For instance, since 3 ᎏᎏ × ᎏᎏ is equal to 1, ᎏᎏ is the reciprocal of ᎏᎏ 3 remainder the amount left over after a division problem using whole numbers Divisible numbers always have a remainder of zero integer 457 – GED MATHEMATICS PRACTICE QUESTIONS – one or two (or more) equal factors of a number The square root of 36 is 6, because × = 36 The cube root of 27 is because × × = 27 simplify terms to combine like terms and reduce an equation to its most basic form root (square root) a letter, often x, used to represent an unknown number value in a problem whole numbers 0, 1, 2, 3, and so on They not include negatives, fractions, or decimals variable 458 ... is its holding capacity? a 45 ft.3 b 37 ft.3 c ft.3 d 30 ft.3 e 10 ft.3 434 – GED MATHEMATICS PRACTICE QUESTIONS – Questions 55 through 57 are based on the following graph Question 58 is based... Monday? a gallons b gallons c 10 gallons d 11 gallons e 12 gallons 57 58 435 – GED MATHEMATICS PRACTICE QUESTIONS – Questions 61 and 62 refer to the following graph Question 64 refers to the following... four-sided figure with only one pair of parallel sides is a trapezoid 456 – GED MATHEMATICS PRACTICE QUESTIONS – Glossar y of Terms: Mathematics a number used as a repeated factor in an exponential expression