Mathematics practise english 2 pdf

 Answers and Explanations 1. 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. 2. 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. 3. e. If the class has x students and 5 students are absent, then x − 5 students are present: ᎏ x − 5 5 ᎏ 4. b. If the tank is ᎏ 1 3 ᎏ full, it is ᎏ 2 3 ᎏ empty. Let x = the capacity of the tank; ᎏ 2 3 ᎏ x = 16, so x = 16 ÷ ᎏ 2 3 ᎏ = 16 × ᎏ 3 2 ᎏ = 24. 5. c. Let x = the length of the ramp. Use the Pythagorean theorem to obtain the equation: x 2 = 12 2 + 16 2 = 144 + 256 = 400 x = ͙400 ෆ = 20 6. c. 48 half-pints = 24 pints. Since 8 pt. = 1 gal., 24 pt. = 3 gal., 3($3.50) = $10.50. 7. d. If x is replaced by the answer choices, only 2 and −3 make the expression true. (2) 2 + 2 − 6 = 0 (−3) 2 + −3 − 6 = 0 4 + −4 = 0 9 + −3 − 6 = 0 9 + −9 = 0 0 = 0 0 = 0 8. 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 9. e. Let x = the width of the room; 23x = 322; x = 322 ÷ 23 = 14. Perimeter = 23 + 14 + 23 + 14 = 74 feet. 10. a. The perimeter of the figure is x + 2y + 3x − y + 2x + 3y + 5x + y = 11x + 5y. 5x + y 3x − y 2x + 3 y x + 2y A = 322 square feet 23 feet a + b a + 2b 2a + b 2a Ramp 12 ft. 16 ft. B D A C – GED MATHEMATICS PRACTICE QUESTIONS– 445 11. d. Set up an equation with Oliver’s money as the unknown, and solve. Oliver = x, Henry = 5 + x, and Murray = 5 + x. Therefore, x + 2(5 + x) = 85 x + 10 + 2x = 85 3x + 10 = 85 3x = 75 x = 25 12. IF YOUR TAXABLE INCOME IS: But Not Your Tax At Least More Than Is 0 $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 $250 plus 7% of any amount above $7,500 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. 14. 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 n 2 = square of a number, and n 2 + n + 4 = 60. 16. 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. 30 Hundreds of Dollars Baked Goods Groceries Dairy Produce Meat 25 20 15 10 5 C A B D – GED MATHEMATICS PRACTICE QUESTIONS– 446 18. e. Let x,2x, and 3x be the measures of the three angles. Then: x + 2x + 3x = 180 6x = 180 x = 180 ÷ 6 = 30 3x = 3(30) = 90 19. 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 ÷ 3 = 48 degrees 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 3 ᎏ 1 2 ᎏ or by ᎏ 7 2 ᎏ ; 2.94 ÷ ᎏ 7 2 ᎏ = 2.94 × ᎏ 2 7 ᎏ = 0.84. 21. d. Forty percent of the total expenses of $240,000 went for labor: 0.40($240,000) = $96,000. 22. d. To express a number in scientific notation, express it as the product of a number between 1 and 10 and a power of 10. In this case, the num- ber between 1 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 10 10 and 63,150,000,000 = 6.315 × 10 10 . 23. b. Slope = ᎏ x y 1 1 − − y x 2 2 ᎏ ; in this case, y 1 = 4, y 2 = 3, x 1 = 5, and x 2 = 0. Slope = ᎏ 4 5 − − 3 0 ᎏ = ᎏ 1 5 ᎏ . 24. e. 1 km = 1,000 m and 1 m = 100 cm. So 1 km = 100,000 cm and 1 km = 1,000,000 mm. 0 x y B (0,3) A (5,4) Operating Expenses 20% Raw Materials 33  % Labor 40% Net Profit 6  % 1 2 3 CBA D E C B A ЄA:ЄB:ЄC = 3:2:1 – GED MATHEMATICS PRACTICE QUESTIONS– 447 25. d. Let x = DC ឈ ៮ ៬ . Since ᭝ABE is similar to ᭝CED, the lengths of their corresponding sides are in proportion. ᎏ 6 x 0 ᎏ = ᎏ 8 4 0 8 ᎏ 48x = 80(60) = 4,800 x = 4,800 ÷ 48 = 100 100 feet is the answer. 26. e. Add the amounts given: 11 + 6 + 5 + 40 + 30 = $92. $100 − $92 leaves $8 for profit. 27. c. Let x = number of points scored by Josh, x + 7 = number of points scored by Nick, and x − 2 = number of points scored by Paul. x + x + 7 + x − 2 = 38 3x + 5 = 38 3x = 33 x = 11 28. c. Use the formula V = lwh. In this case, l = 5, w = 5, and h = h. Therefore, V = 5 × 5 × h = 25h and 25h = 200. 29. 29. d. Since 3 2 = 9 and 4 2 = 16, ͙12 ෆ is between 3 and 4. Only point D lies between 3 and 4. 30. 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 9 sq. ft. = 1 sq. yd., 450 sq. ft. ÷ 9 = 50 sq. yd. 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. ᎏ d fr o a ll n a c r s s ᎏ = ᎏ 1 x ᎏ = ᎏ y z ᎏ y( ᎏ 1 x ᎏ ) = ( ᎏ y z ᎏ )y ᎏ x y ᎏ = z 32. e. Replace the variables with their given values. (−2) 2 (32 − [−2]) = 4(34) = 136 33. e. Since ᎏ 1 4 ᎏ in. represents 8 mi, 1 in. represents 4 × 8 = 32 mi., and 2 in. represents 2 × 32 = 64 mi., ᎏ 1 8 ᎏ in. represents 4 mi. Then 2 ᎏ 1 8 ᎏ in. represent 64 + 4 = 68 mi. 10′ 15′ 25′ 20′ 012 ACBED 345 Profit ? Materials $40 Insurance $5 Misc. $6 Salaries $30 Taxes $11 60′ 48′ 80′ AB E CD – GED MATHEMATICS PRACTICE QUESTIONS– 448 34. c. Use the formula for the area of a triangle. A = ᎏ 1 2 ᎏ bh ᎏ 1 2 ᎏ (4)(8) = 16 35. c. Let x = height of steeple. Set up proportion: ᎏ le h n e g ig t h h t o o f f s o h b ad je o c w t ᎏ : ᎏ 2 x 8 ᎏ = ᎏ 6 4 ᎏ 4x = 6(28) = 168 x = 168 ÷ 4 = 42 ft. 36. 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 6 ft., the water forms a rectangular solid with dimensions 30 by 20 by 6. The volume of water is the prod- uct 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. 6 × 10 5 = 600,000 4 × 10 3 = 4,000 600,000 ÷ 4,000 = 600 ÷ 4 = 150 40. d. Let x = cost of lot and 3x = cost of house. x + 3x = 120,000 4x = 120,000 x = 120,000 ÷ 4 = 30,000 3x = 3(30,000) = $90,000 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) 42. a. Simply multiply: $8,000 × 0.13 × 5 = $5,200 43. e. Tr y −5 for x in each equation. Only option e is true when −5 is substituted for x. 12x = −60 12(−5) = −60 −60 = −60 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 45. a. Solve: x + (2x + 12) = $174 3x + 12 = $174 3x = $162 x = $54 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 2 adults’ tickets and 4 children’s tickets is $48. Write and solve an equation: 2x + 4(x − 6) = $48 2 x + 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. 3 ft. 30 ft. 20 ft. 8 units 4 units – GED MATHEMATICS PRACTICE QUESTIONS– 449 49. c. Find the amount of interest. For the time period, use ᎏ 1 9 2 ᎏ , which equals ᎏ 3 4 ᎏ , or .75. Multiply. $1,500 × 0.04 × 0.75 = $45. Add to find the amount paid back. $1,500 + $45 = $1,545. 50. c. Multiply 3 lb. 12. oz. by 6 to get 18 lb. 72 oz. Divide 72 oz. by the number of oz. in a pound (16) to get 4 lbs. with a remainder of 8 oz. Therefore, 18 lb. + 4 lb. 8 oz. = 22 lb. 8 oz. 51. a. If 80% of the audience were adults, 100% − 80% = 20% were children. 20% = .20, and 0.20(650) = 130 52. b. Let x = number of inches between the towns on the map. Set up a proportion: ᎏ 6 1 0 i m n. i. ᎏ = ᎏ 22 x 5 in m . i. ᎏ 60x = 255 x = ᎏ 2 6 5 0 5 ᎏ = 4 ᎏ 1 4 ᎏ 53. b. 4 ft. 3 in. = 3 ft. 15 in. − 2 ft. 8 in. = 1 ft. 7 in. 54. d. v = lwh; the container is 5 ft. long × 3 ft. wide × 2 ft. high. 5 × 3 × 2 = 30 ft. 3 55. d. The top of the bar for Wednesday is at 6 on the vertical scale. 56. e. The top of the bar for Monday is halfway between 4 and 6, so 5 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- urday. The difference between 17 gal. and 5 gal. is 12 gal. 57. d. The tops of the bars for Monday through Sun- day are at 5, 4, 6, 5, 14, 17, and 9. These add up to 60. 58. a. Let x = m∠OAB. OA ឈ ៮ ៬ = OB ឈ ៮ ៬ since radii of the same circle have equal measures. Therefore, m∠OAB = m∠OBA. x + x + 70 = 180 2x + 70 = 180 2x = 180 − 70 = 110 x = 110 ÷ 2 = 55 59. e. Let x = number of books on the small shelf, and x + 8 = number of books on the large shelf. Then, 4x = number of books on 4 small shelves, and 3(x + 8) = number of books on 3 large shelves. 4x + 3(x + 8) = 297 4x + 3x + 24 = 297 7x + 24 = 297 7x = 297 − 24 7x = 273 ÷ 7 = 39 60. a. 40 ft. = 40 × 12 = 480 in. 3 ft. 4 in. = 3(12) + 4 = 36 + 4 = 40 in. 480 ÷ 40 = 12 scarves. 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 compat- ible numbers, $100,000 out of $300,000 is ᎏ 1 3 ᎏ . A B O 70° 20 Number of Gallons Days of the Week Paint Sales at Carolyn’s Hardware M T W Th F Sa Su 18 16 14 12 10 8 6 4 2 – GED MATHEMATICS PRACTICE QUESTIONS– 450 . sides. 2a + a + b + 2a + b + a + 2b = 6a + 4b 9. e. Let x = the width of the room; 23 x = 322 ; x = 322 ÷ 23 = 14. Perimeter = 23 + 14 + 23 + 14 = 74 feet. 10. a. The perimeter of the figure is x + 2y. figure is x + 2y + 3x − y + 2x + 3y + 5x + y = 11x + 5y. 5x + y 3x − y 2x + 3 y x + 2y A = 322 square feet 23 feet a + b a + 2b 2a + b 2a Ramp 12 ft. 16 ft. B D A C – GED MATHEMATICS PRACTICE QUESTIONS– 445 11 large shelves. 4x + 3(x + 8) = 29 7 4x + 3x + 24 = 29 7 7x + 24 = 29 7 7x = 29 7 − 24 7x = 27 3 ÷ 7 = 39 60. a. 40 ft. = 40 × 12 = 480 in. 3 ft. 4 in. = 3( 12) + 4 = 36 + 4 = 40 in. 480 ÷ 40 = 12 scarves. 61. b.