Mathematics practise english 2 pdf

To find the perimeter of the figure, find the sum of the lengths of its sides... You cannot compute the cost unless you are told the number of days that the couple stays at the bed and b

 A n s w e r s a n d E x p l a n a t i o n s

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:x−55

4 b If the tank is 13full, it is 23empty Let x = the

capacity of the tank;23x = 16, so x = 16 ÷23=

16 ×32= 24

5.

c Let x = the length of the ramp Use the

Pythagorean theorem to obtain the equation:

x2= 122+ 162= 144 + 256 = 400

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

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 + 3y

x + 2y

A = 322 square feet 23 feet

a + b

a + 2b

2a + b 2a

Ramp

12 ft.

16 ft.

B

D

A

C

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:

of any amount above $3,500

of any amount above $4,500

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 n2= square of a number,

and n2+ 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

Baked Goods

25 20 15 10 5

C

A

B

D

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 312or by

72; 2.94 ÷72= 2.94 ×27= 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 1010and 63,150,000,000 = 6.315 × 1010

23.

b Slope = x y1

1

−

−y x

2 2

; in this case, y1= 4, y2= 3, x1= 5,

and x2= 0 Slope = 45−−30= 15

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

y

B (0,3) A (5,4)

Operating Expenses 20%

Raw Materials

33  % Labor

40%

Net Profit

6  %

1 2 3

D E

C

B

A

A:B:C = 3:2:1

d Let x = DC  Since ABE is similar to CED, the

lengths of their corresponding sides are in

proportion

6x0= 8408

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 32= 9 and 42= 16,12 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.

d fr o a ll na c r s s = 1x= y z

y(1x) = (y z )y

x y = z

32 e Replace the variables with their given values.

(−2)2(32 − [−2]) = 4(34) = 136

33 e Since 14in represents 8 mi, 1 in represents 4 × 8

= 32 mi., and 2 in represents 2 × 32 = 64 mi.,

18in represents 4 mi Then 218in represent

64 + 4 = 68 mi

10 ′

15 ′

25 ′

20 ′

Profit

?

Materials

$40

Insurance

$5 Misc

$6

Salaries

$30

Taxes

$11

60 ′

48 ′

80 ′

E

C D

c Use the formula for the area of a triangle.

A = 12bh

12(4)(8) = 16

35 c Let x = height of steeple Set up proportion:

lehnegigthhtooffsohbadjeocwt:2x8= 64

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) =

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 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

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

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

3 ft.

30 ft.

8 units

4 units

49 c Find the amount of interest For the time

period, use 192, which equals 34, 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:

610imn.i. =22x5inm.i.

60x = 255

x = 26505= 414

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

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  = OB 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

A

B

O 70 °

20

Days of the Week

Paint Sales at Carolyn’s Hardware

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8

6

4

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