Download CARPET

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