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2300 2010 4310 square meters Add to find the total area. Answer: Arliss will tell the city contractor that the area of the pool is 4310 square meters. SKILL PRACTICE A community member has donated a small lot to be used as a parking lot for a public library and recreation center. The figure below shows the dimensions of the lot. 1. Which of the following expressions can be used to find the length of side x? (1) (2) (3) 50 3 50 602 602 6TH STREET PARKING LOT (4) 70 60 (5) 60 60 50 70 yd 60 yd 2. What is the perimeter of the parking lot in yards? 600 540 470 (4) 430 (5) 300 x 60 yd PROGRAM 33: Measurement (1) (2) (3) 60 yd 3. 50 yd Find the area of the parking lot in square yards. (Hint: The shape is a combination of a square and a rectangle.) (1) (2) (3) 16,800 15,500 14,400 (4) 11,900 (5) 10,800 P R O B L E M S O LV E R Connection Example: The Park family is planning to carpet their family room, which measures 18 feet by 24 feet. They will not need to carpet the fireplace hearth, a 3-ft-by-6-ft area centered on one of the 18-foot walls. How many square yards of carpet will they need? hearth When working with perimeters and areas on the GED test, it makes sense to sketch a diagram. This will help you visualize the measurements you know and solve for the missing measurement. 24 ft 6 ft CARPET 18 ft 3 ft Step 1. Sketch a diagram of the family room floor. Step 2. Figure the total area of the room (18 24 432 sq ft) and subtract the floor area covered by the hearth (3 6 18 sq ft): 432 sq ft 18 sq ft 414 sq ft. Step 3. Convert 414 square feet to square yards. (Remember, 9 sq ft 1 sq yd.) How many square yards of carpet do the Parks need? Answers and explanations start on page 318. 145 8Use substitution to solve for distance in this situation. Example: Krystin can run 7 miles per hour. At that rate, how far can she run in 30 minutes? (1) 2.1 miles (4) 15 miles Refer to the GED formulas (2) 3.5 miles (5) 21 miles page on page 340. (3) 14 miles You’re right if you chose (2) 3.5 miles. Remember, 30 minutes is equal to 12 or 0.5 hour. Since the rate is expressed in miles per hour, you must also express the time in hours. d rt d 7 0.5 d 3.5 miles Hint: On the GED Math Test, eliminate answer choices that aren’t reasonable. If Krystin can run 7 miles in 1 hour, she can’t run more than 7 in less than 1 hour. You can eliminate Choices (3), (4), and (5) using your common sense. 8Use substitution to find the total cost of a purchase. Example: Jamal finds pre-viewed videotapes in a bargain bin for $4.95 each. How much will 8 tapes cost? SKILL PRACTICE Choose the correct formula. Then solve by substitution. 1. 2. 3. Ashley Rose coaches a city league basketball team. She plans to take her players out for pizza after the final game. An individual pizza with salad and drink sells for $4.99. How much will Ashley Rose pay for 9 meals, not including tax and tip? 4. A small solar-powered aircraft flew 5.4 hours. If the aircraft averaged 30 miles per hour, how many miles did it travel? 5. Computer Warehouse offers the two payment plans shown below. Monique wants to buy a computer system that sells for $1499. During a winter storm, Tyrone averages 20 miles per hour in his delivery truck. After 45 minutes of driving, how far has he traveled? (Hint: Express time in hours. 45 minutes = 45/60 hour. Reduce to work with a simpler fraction.) Denzel wants to buy a used van for $7800. He plans to borrow the money from the credit union at 8% interest. To estimate the amount of interest he will pay, he uses the simple-interest formula. How much will he pay in interest if he borrows the money for 48 months? (Hint: Write time (t) in years.) PLAN A 5 Years 3% simple interest PROGRAM 34: Formulas c nr c 8 $4.95 c $39.60 Substitute and solve: PLAN B 3 Years 4% simple interest a. Under which plan will Monique pay the least amount of interest? b. If Monique chooses Plan A, how much will she pay in all for the computer system? 6. Find the total cost of 50 computer diskettes at $0.23 per diskette. 7. Compare the formulas for distance and total cost. How are they similar? Answers and explanations start on page 319. 155 You will need to be able to apply the right formula at the right time to do well on the GED Math Test. Always read each item carefully. If a geometric figure is described, you may be able to use a formula to solve the problem. Decide whether you need to solve for perimeter, area, or volume. Then select the correct formula. SKILL PRACTICE Answer each item using the formulas on page 156. 1. Which measurements do you need to find the area of a triangle? (1) side and length (2) height and width (3) length and width 2. (4) side and base (5) base and height (4) P 2l 2w (5) P 4s A cardboard box is 2 feet wide, 2.5 feet long, and 1 foot in height. Which formula can be used to find how much the box will hold? (1) A lw (2) V πr2h (3) P 4s 4. (4) V lwh (5) P 2l 2w A square fish pond measures 3 meters on one side. Which formula can be used to find the distance around the pond? (1) P 4s (2) P a b c (3) A bh TECHNOLOGY (4) A s2 (5) V s3 Connection A computer spreadsheet uses formulas. A formula can be assigned to a cell to perform a specific calculation. A cell is a box within a spreadsheet. Each cell is named using row and column headings, such as the shaded cell D2. PROGRAM 34: Formulas Noah wants to plant a vegetable garden in the rectangular space behind his garage. Which formula can be used to find out how many square feet of ground the garden covers? (1) A s2 (2) A lw (3) A 12 bh 3. The spreadsheet below can be used to figure out the cost of a catalog order. In cell D2, we write the formula B2*C2. (The sign tells the computer the entry is a formula. The symbol * means multiplication.) The computer will automatically multiply the number of model kits by the price per kit and show the answer $15.80 in cell D2. (2 7.90 15.80) 1 2 3 4 5 A Item Model Kits Paint Sets B Quantity 2 4 C Price Per Item $7.90 $3.75 D Cost $15.80 1. What formula could you write in cell D3 to find the cost of the paint sets? 2. What formula could you write in cell D4 to find the subtotal of D2 and D3? Use for addition. Answers and explanations start on page 319. 157 8Look how the formula is applied in solving for a leg measure in a right-triangle problem. Example: One leg of a right triangle measures 5 centimeters. The hypotenuse measures 13 centimeters. Find the length of the remaining leg. Use the Pythagorean relationship. Subtract 25 from both sides to isolate the variable. Find the square root of 144. c2 132 169 169 25 144 b a2 b2 52 b2 5 cm 25 b2 25 25 b2 b2 144 12 centimeters 13 cm b Answer: The missing measurement is 12 centimeters. Most right triangles do not have three measurements that can be written in whole numbers. Thus, the GED Math Test makes frequent use of a few special ratios. Watch for problems written using a 3:4:5 ratio. Look at the triangle to the right. Do you recognize the ratio? Each of the numbers in the ratio has been doubled. 10 6 8 Solve each problem. 1. 2. Find the missing side of these right triangles. leg a leg b a. 9 12 b. 10 c. hypotenuse 26 24 25 The legs of a right triangle each measure 8 inches. Choose the best estimate for the length of the hypotenuse. (1) (2) (3) (4) (5) Between 9 and 10 inches Between 10 and 11 inches Between 11 and 12 inches Between 12 and 13 inches Between 13 and 14 inches C A L C U L AT O R PROGRAM 35: Geometry SKILL PRACTICE Connection Use your calculator to find the square roots that you have not memorized. Example: While remodeling his kitchen, Ted needs to cut a piece of dry wall in the shape of a right triangle, to fit into a corner. The shorter sides of this piece measure 8 in and 11 in. What will the longest side measure to the nearest tenth of an inch? Step 1. Use the Pythagorean relationship, 82 112 c2. Calculator: 8 x2 1 1 x2 Step 2. Press the square root key ( ). The display reads Refer to page 338 of the Math Handbook for information on squares and the Casio® fx-260. 185. 13.60147 . Answer: Round the nearest tenth. The longest side will measure about 13.6 inches. Try this one: The legs of a right triangle measure 5 cm and 9 cm. Find the length of the hypotenuse to the nearest tenth of a centimeter. Answers and explanations start on page 321. 181 Answer Key PROGRAM 27: PASSING THE GED MATH TEST GED Practice, page 16 (5) $131 Press: 1 5 2 2 The display reads: GED Practice, page 22 You should have graphed the point with coordinates (4,1). y 5 4 9 4 3 2 131. 1 –5 GED Practice, page 17 (3) $1,428 Press: 2 3 8 6 The display reads: MATHEMATICS GED Practice, page 18 (5) $130 Press: 1 1 8 The display reads: 1 % 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 5 4 3 2 1 –5 –4 –3 –2 –1 0 –1 –2 –3 308 –4 –5 1 2 3 4 5 x 2 3 4 5 x –5 PROGRAM 28: NUMBER SENSE 7 M M MR 6 130. . 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 GED Practice, page 21 1.–4. You should have plotted the following points. y 1 1428. . 0 1 2 3 4 5 6 7 8 9 0 –3 GED Practice, page 20 Your grid may be slightly different. Remember, your answer can start in any column. For item 3, you do not have to show the leading 0 on the grid. 1. / 3/ 9/ 42. 5/ // 8 3. 0 / 0/ 7 4. 6 / 3/ 5 / / / 0 1 2 3 4 5 6 7 8 9 –1 –4 5 2 –2 –2 4 3 4 6 5 The whole-number part of the number is 6. The a fractional amount. The 1 represents 2 1 decimal 3 part 2 square root of 42 is between 6 and 7. . –3 –1 GED Practice, page 19 1. (4) $36 Press: 1 2 0 3 0 % 36. The display reads: 2. (3) between 6 and 7 M2 MC MR 4 M1 2 Press: ON 6.480740698 7 The 9 Creads: 8 display AC 0 –4 0 1 2 3 4 5 6 7 8 9 Your Approach to Learning Math Skill Practice, page 29 1. Your answer may vary. Sample answer: figuring the tip at a restaurant figuring out how much is left in the checking account buying groceries putting gas in the car shopping around to find the best price for pet supplies 2. Your answer may vary. Sample answer: d. I separate items into groups that cost about $10 and add them. 3. Your answer may vary. Sample answer: d. I move the decimal point to find 10%, double it to get 20%, and then round down to the nearest quarter. I figure the amount is pretty close to 15%. 4. Your answer may vary. Sample answer: d. I make a list of instructions, but I always ask my friend for landmarks that will help me know if I have gone too far or the wrong way. Understanding Our Number System Skill Practice, page 31 1. five hundred 2. six million 3. one thousand 4. four hundred million 5. sixty 6. nine hundred thousand 7. 5 8. 3 18 9. 100 ft 10. (4) John has done more than he has left to do. John has done 75%. If the whole job is 100%, John has 25% left to do. The only true statement is choice (4). Problem Solver Connection, page 277 Graph of the inequalities x < 2 or x > 3: MATHEMATICS 28 27 26 25 24 23 22 21 0 2 3 4 5 6 7 8 Skill Practice, page 279 1. 50 Each number is 7 greater than the number before. 2. 21 Add 2, then 3, then 4, and so on. 3. 6 Add 2, then subtract 1, add 2, subtract 1, and so on. 4. 36 Add 3, then 5, then 7, then 9, and so on. 5. 34 Each new number is the sum of the two numbers that came before. 6. To find the total cost (c), multiply the unit cost, or rate (r), by the number of bottles of glue (n): c nr. 7. To find the area (A), square the measure of the side (s): A s2. 8. To find the total water usage (U), multiply 50 gallons by the number of loads (n): U 50n. 9. To find the amount for shipping and handling (S), multiply the merchandise total (t) by 0.07 and add $5: S 0.07t 5. 10. $2000 Find $100 on the vertical scale and follow it over to a point on the line. The point is directly over the amount $2000 on the horizontal scale. OUTPUTS Skill Practice, page 281 1. a. 2x 1 b. input 0, output 1 input 1, output 3 input 2, output 5 input 3, output 7 c. 7 332 1 6 5 4 3 2 1 2. a. DOLLARS Skill Practice, page 277 1. (3) x > 4 3x 8 > 20 3x > 12 x>4 2. $8.90x ≤ $356 Let x (or any variable) equal the number of hours Mae works. If she works 40, the maximum number of hours, her pay will be 40($8.90), which equals $356. Set up the inequality so that the wage times the number of hours is equal to or less than $356. 3. (1) 48 > 12w Use the formula A lw. Substitute the known quantities: 48 12w. Finally, change the equation to an inequality to represent the problem: 48 > 12w. 4000 3600 3200 2800 2400 2000 1600 1200 800 400 0 0 1 2 3 4 5 6 7 8 9 10 QUILTS Your graph should be similar to this one. You should have two scales: one showing the number of quilts and the other showing the amount of revenue in dollars. b. $2400 Sheila’s cost for 10 quilts is $1600. Her revenue is 400(10), or $4000. Her profits after making and selling 10 quilts are $4000 $1600 $2400. Science Connection, page 281 The 6th generation will have 8 bees. The 7th generation will have 13. Skill Practice, page 283 1. (4,4) 2. (0,7) 3. (2,5) 4. (6,3) 9. y 6 J 5 3 2 1 L –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 x N –1 –2 –3 –4 –5 M –6 –7 10. No Point N has a negative value for x, and point P has a positive value for x. The points must fall in different quadrants. (Note: The signs for the y-coordinates also differ.) Skill Practice, page 285 1. y 7 6 5 4 3 2 1 –6 –5 –4 –3 –2 –1 1 –1 –2 –3 –4 –5 –6 INPUTS K 4 –7 1 2 3 4 (4,0) (5,5) (1,2) (6,5) 7 –7 0 5. 6. 7. 8. 2 3 4 5 6 7 x 3. (2) B Count over to 2 on the x-axis and down to 7 on the y-axis. 4. (4) 3 The fastest way to find slope is to count the number of spaces you need for the rise and the run and write a ratio. From point L, count up 9 spaces and 3 spaces to the right to reach point M. Write the ratio and express 9 3 in lowest terms: 3 1 . The slope is 3. 5. (4) 25 24 23 22 21 0 MATHEMATICS 6. 7. 8. 9. 10. 11. 12. 334 1 2 3 4 5 A closed circle shows that the number is included in the solution set. An open circle means that the number is not included in the solution set. (3) 4 and 2 You can solve by factoring the quadratic equation and setting each factor equal to zero: x2 2x 8 0, so (x 4)(x 2) 0. x40 x20 x4 x 2 You can also solve by substituting the numbers from the answer choices for x to see which solutions make the equation true. (2) K The slope of a vertical line is undefined. (The slope of a horizontal line is zero.) (3) $95 Sharon’s weekly costs are a function of the number of earrings she makes. Find 25 on the horizontal axis and move directly up to the corresponding point on the line. Read across to the scale. The point above 25 represents a cost of $95. (2) C 20 3n The fixed cost of $20 is added to the number of earrings multiplied by $3. (2) 3b 8 ≥ 29 Quickly substitute 10 for b in each answer choice, and you’ll find choice (2) is true. (4) between 10 and 11 Draw an imaginary right triangle with PQ as the hypotenuse. The lengths of the legs are 6 and 9. Use the Pythagorean relationship to find the length of the hypotenuse. c2 a2 b2 c2 62 92 c2 36 81 c2 117 c 117 Since 102 100 and 112 121, you know the hypotenuse must be between 10 and 11 units long. 3 (2) 2 Use the points P and Q and count the spaces for the rise and run. The rise is 9 and the run is 6. Write a ratio and express in lowest terms: 69 32 . Note: You do not have to use points P and Q. You can use any two convenient points on the line. You can also use the slope formula given on the GED formulas page, although this method tends to take more time. 13. (5) (3,4) Remember, the x-coordinate is the first number, and the y-coordinate is the second number. Substitute the numbers from the coordinates for the x and y variables in the equation. Only choice (5) makes the equation true: y 3x 5, and 4 3(3) 5. 14. (1) 3 and 1 You can solve by factoring the quadratic equation and setting each factor equal to zero: x2 2x 3 0, so (x 3)(x 1) 0. x30 x10 x 3 x1 You can also solve by substituting the numbers from the answer choices for x to see which solutions make the equation true. 15. (1) 5 Since you are asked to find one answer that is not in the solution set of the equation, and your answers are consecutive numbers, either 5 or 9 will be the correct choice. Substitute one of these two possibilities and you will know whether that choice or the only other possibility is correct. 16. (5) r 2l Only the love seat is one-half its regular price ( 12 ) when the recliner is purchased at its regular price (r). (2) 17. (2) 5 Use the formula for finding 61 slope from the GED formulas page. Let (1,2) (x1,y1) and (6,5) (x2,y2). Substitute and compare to the answer choices. 18. (3) [3(1)]2 (5 3)2 Find the coordinates for points M and N: M (1,3) and N (3,5). Use the formula for finding the distance between two points in a plane from the GED formulas page. Let M (x1,y1) and N (x2,y2). Substitute and compare to the answer choices. 19. (2) (4,2) Start at the y-intercept, 4, and use the slope to plot the points on the new line. Since the slope is 12 , move up 1 and 2 to the right. Continue the pattern until you intersect line g. 20. (5) y 5 By looking at the graph, we can see that for every point, y 5. For all choices but choice (5), we can substitute different values for x and get solutions where y does not equal 5. Alternate Math Formats, pages 295–296 21. and 22. y 5 4 3 2 1 –5 –4 –3 –2 –1 1 –1 –2 –3 –4 –5 2 3 4 5 x