Solution - FB 1 Math

Excel Review Center FB 1 - Math

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1. Use calculator

MODE 3:STAT 5:e^x

x y

0 1 AC 0.25 SHIFT 1STAT

2 0.5

ˆ7:Reg 4: x 4 days

2.

2 choices

1 2

x y 1 dx x 1 dy 0

x 1dx dy

x 1 y 1

Differentiate both sides

x 1dx dy

x 1 y 1

Reverse engineering: y 1.55

3. Use calculator

102

Just input the expression in your calculator

1 i 0

5.

2x 3 5y 2x 5y 3

4x 3y 71

Use calculator in MODE EQN

x 14 and y 5

6.

2

2

2x and 2x 2 the numbers

2x 2x 2 24

4x 4x 24

x x 6 0

x 2

so,

2x 4 and

2x 2 6

7.

M Miguel's present age

G Grandfather's present age

G 3 6 M 1 6M G 9

M G 68

Use calculator

M 11, G 57

8.

1 1

x 2 x 3 202 3

x 24

9.

7.61 6.95 6.95x

x 9.5%

10.

4h w

3

4wh 192 w w 192

3

w 12, h 16

11.

n d q 33

0.05n 0.10d 0.25q 3.30

n 3q 2d 3q 2d 3q 0

1d n n 2d

2Use calculator

n 18, d 9, q 6

12.

p n d

0.01p 0.05n 0.10d 1.44

0.16p 1.44

p n d 9

13. For how long did the plane fly at 115 mph speed?

1 2

1 2 1 2

1

2

total distance,d 555 miles

total time,t 5 hours

t t 5

d d 555 105t 115t 555

t 2 hours

t 3 hours

14.

I no. of chestnuts Ivan gathered

P no. of chestmuts Peter gathered

B no. of chestnuts Boris gathered

I 2P I 2P 0

B 2 P P B 2

I P B 26

Use calculator

I 12, P 6, B 8

15.

499 4 1 499 4 31997 1999

1 3

i i i i

i i 0

16.

n 1n 1

12 1

n

n

a a r

a 2 0.05 2

a 204.8

Thickness in inches:

204.8 0.05 204.85 inches

1 ft204.85 inches 17.1 ft

12 inches

17.

x speed in calm water

y speed of the water

d vt

Upstream:

100 x y 1.5

100 1.5x 1.5y

Downstream:

100 x y 1.25

100 1.25x 1.25y

Use calculator

x 73.33 mph

y 6.67 mph

18. Use calculator

MODE 3:STAT 2: A BX

x y

80 80 AC 250 SHIFT

110 140

ˆ1STAT 7:Reg 5: y 420

so,

420average profit per unit 1.68

250

19.

1 1tan 2x tan x4

x 0.281

20.

2

o

3sin 2 cos

30

21.

o

o

o

o

o

y ytan40 x

x tan40y

tan20x 23

ytan20

y23

tan40y 14.78 m

22.

y

x 23 m

20o

40o

x (3 + 0.015) km

6400km

6400km



2 2x 6400 3 0.015 6400

x 196 km

23.

o

o

s r

300 m r 30180

r 573 m

24.

1

1 2

2 2

1 2

Triangle 1 Triangle 2

b, h b 3 b, h b 3

A A 21

1 1b b 3 b b 3 21

2 2

b 3b b 3b 42

6b 42

b 7

so,

h 10, h 4

25.

2 2o i

2 2

V d d h4

1V 1 0.5

8

V 0.074

26.

3 3f i f i

3 3

4V V r r

34

3 2 79.59 cu.inch3

27.

3

1 1

2 2

1 2 2 1

3

1

1

1

V r

V r

r r 10 r 10 r

r27

343 10 r

r 3

28.

2 2

2 2

2

4x 4y 52 x y 13

x 13 y

x y 97

13 y y 97

y 4

so, y 16

29.

2 2 1

2 2 1

Extended three time its ownd length, so

k 1 3 4

x x k x x 1 4 1 2 11

y y k y y 4 4 4 2 20

so, 11, 20

30.

2 2

2 2

2

9x 9y 16

16x y

916 4

r r9 3

8diameter 2r

3

31.

2

2

y 2x 7x 5

x means the axis of symmetry is

vertical so,

D 7h x

2A 2 2

7x 4x 7

44x 7 0

32.

1 4

0 3

2 31A

1 22

2 1

3 0

1A 3 0 4 1 0 12 0 6 3 4 3 0

2A 15

33.

1

2

1

2

4x y 2 0 m 4

1x 2ky 1 0 m

2k1

m 4 2km

k 2

34.

6x 10y 5z 30 0

at x 0 and y 0 z 6

at x 0 and z 0 y 3

at y 0 and z 0 x 5

so,

1 1 1 1V xy z 5 3 6

3 2 3 2

V 15

35.

22V d h 4 h4 4

dV dh dV4 4 0.7

dt dt dtdV

8.8dt

36.

ln lny lny lnx

dy

dy dxy

lny y x

dy dy dxylny

ylny y x

ylnydy lnydy dx

xdy ylny

dx x 1 lny

37.

y 2x sin2x

y' 2 2cos2x

0 2 2cos2x

x2

38.

y 2x 3

dy 2dx 2 3.5 3.3

dy 0.4

39.

1 2x LL 3.2 0.4 0.4

x 1.2 m

40.

2

2

2

y 1 x

at y 10

10 1 x x 3

y 1 x

m y' 2x 2 3 6

41.

2

1

2

y 5

y 1

1 1y x

yx

1A xdy dy 2.47

y

42.

2

2 2

2

2

Perimeter, 800 2x 2y x 400 y

Area, A xy

A 400 y y 400y y

dA400 2y 0

dy

y 200

so,

A 400y y 400 200 200

1 hectareA 40,000 m 4 hectares

10,000 m

43.

5 6 7P 0.04289

18 17 16



44.

10 3C 120

45.

10 4P 5040

46.

r n rn r

5 8 5

8 5

P Cp q

2 2P C 1 0.124 12.4%

5 5

47. It forms a triangle connecting the three vector quantities (forces). Using cosine law,

2 2 2

o

20 30 40 2 30 40 cos

28.96

48.

2o

2

1s v t at

2

20 1 45 15 20s 15kph h

3600 2 20 / 3600 3600

1s km 167 m

6

49. Use calculator:

4n

n 1

3 2 112

50.

2

2

2

2

Reverse engineering

B. f x x 2x 2

f x 1 x 1 2 x 1 2

f x 1 x 2x 1 2x 2 2

f x 1 x 1 same as the given

51.

Total nurses after replacement:

n 2 0.51 2n

n 100

52. Using cosine law

2 2 ochord, x 20 20 2 20 20 cos150

x 38.6 cm

53. The gas station on the other road 1 km from the junction the shortest distance from one road to a gas station on the other road is the perpendicular distance from the gas station to the other road1 km from the junction.

Hence the shortest distance from one road to a gas station on the other road 1 km from the junction:

o1sin75 0.966 km

54.

o

20 12 32tan2 x

x tan212 12

tan xx tan

32 12

tan2 tan

26.57

so,

12x 24

tan

55.

Apothem is the radius of the inscribed circle

o2

o2

180A nr tan

n

180A 5 10 tan 363.3

5

56.

1 2

2

1A b b h

2

A 32 cm 6 cm 192 cm

57.

2

2

1V d h

3 4

1V 12 18 216

3 4

58.

interior exterior

o o

S 2S

n 2 180 2 360

n 6

59. Distance formula

2 2

2

2

13 3 8 y 7

169 25 y 14y 49

y 14y 95 0

y 19 and 5

60.

2

2

y 4y 12x 32 0

Cy Dx Ey F 0

D 12a 3

4C 4 1

latus rectum, LR 4a 12

61.

6x 15y 10z 30 0

at x 0 and y 0 z 3

at x 0 and z 0 y 2

at y 0 and z 0 x 5

so,

1 1 1 1V xy z 5 2 3

3 2 3 2

V 5

62.

t

3 2

2

3

13x 9y 4 m

31

slope of the tangent line, m 3m

so,

y x y' 3x

3 3x x 1

at x 1 y x 1

1,1 point of tangency

63. Divide the trapezoid into one rectangle and

2 right triangles. The height of the trapezoid

is 2 210 x . So, the area of the trapezoid

2 2

2 2

x choices

2 2

x 5

A 10 100 x x 100 x

dA d10 100 x x 100 x

dx dx

From choices: 10 2x

C. 20 10 2x x 5

dA d10 100 x x 100 x 0

dx dx

64. Total no. of possible outcomes = 6 x 6 = 36 Total no. of desirable outcomes = 5

(1,5), (2,4), (3,3), (4,2), (5,1)

5P

36

66.

x no. of boxes of screw A

y no. of boxes of screw B

z no. of boxes of screw C

x y z 24

300x 150y 50z 2200

6x 3y z 44

x y z 24

5x 2y 20

Trial and error:

if y 5 x 2 and z 17

Check :

300 2 150 5

17 50 2200

2200 2200

67.

x 3 3x 2

10 88x 24 30x 20

22x 44

x 2

so 2x 1 3



68.

x age of the boy

y age of his sister

2y 2 x 2 2x 3y 2

33

y 2 x 2 3x 4y 24

Use calculator

x 14 and y 10

69.

Rate of work:

1larger pipe

x 51

smaller pipex

1 148 1

x 5 x

x 93.6 min

70.

x y 40

4.5x 8.5y 6 40

Use calculator

x 25 and y 15

71.

2 2

2 2

2x 1 and 2x 3

2x 3 2x 1 40

4x 12x 9 4x 4x 1 40

8x 8 40

8x 32 x 4

2x 3 2 4 3 11

72.

3 21

5 xx 35

73.

n r 1 r 1n r 1

5 110 5 110 5 1

6 4

rth term C a b

5th term C x 2y

5th term 3360x y

74.

1

nS 2a n 1 d

2n

2600 2 3 n 1 22

n 50

75.

o

oo

x 6x 35

12 1 min

49 649 35 59.5

12 1 min

76.

5 6 6 180

77.

o

2 o2

o o

4sin40

4 xx 2.22

so, radius of the sector

R 8 x 10.22

10.22 80RA

360 360A 72.96

78. Using cosine law

2 2 2 o

2

150 300 x 2 300 xcos26

x 539.28x 67500 0

x 341.78

79.

1 m 2

22

3

LV A 4A A

6

2r 3 1 3V 4 d 20 4 2 20

6 4 3 4

V 18475.21 cm

80.

2

o

o o

2 o

o

o

R EA

180

E 180 3 180

10 3 18010

180

66

83.

2 11 1

2 1

y yy y x x

x x

1 1y 1 x 8

8 81

y 1 x 88

8 8y x 8

x 8y 0

84.

2x 3y 6 0

at x 0 y 2

at y 0 x 3

1 1A xy 2 3 3

2 2

85.

2

2

4x 256 0

x 64

x 8 and x 8

parallel lines

86.

2 2

n

n

1 1

x y 1

2x 2yy' 0

xm y'

y

slope of the normal line:

1 ym

m x

at 2,1

1m

2so,

y y m x x

1y 1 x 2

22y 2 x 2

x 2y

88.

A ab 8 6

A 48

89.

2 2 2 2

2

c a b 4 3e

a a 45

e4

91.

2 2

2 2 2

r a

x y a

x y a circle

92.

d sinx

lncosx tanxdx cosx

93.

y xlnx

1y' x 1 lnx

xy' 1 lnx

95. For a rectangle to have maximum area and minimum perimeter, it should be a regular polygon. Therefore, it’s a square and the ratio of the length of its sides is 1.

x

4 4

400



96.

2

2

2

x y 8 0

2xy x y' 0

at 2,2

2 2 2 2 y' 0

m y' 2

97.

2

2

t 0

y 16t 3000t 50000

dy dv 16t 3000t 50000

dt dt

v 3000

99.

2

1

x 42

x 0

88A ydx x 2 dx

3

100.

4

5/77 8 6

4

x x 4x dx 0

Solution - FB 1 Math

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