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1.

Given the differential equation dP/Dt=5P

A) Find the general solution for P to the differential equation

B)Find the particular solution for P to the differential equation given P(0)= 418

a)

A) P=Ce^5t

B) P= 5e^418t

b)

A) P=Ce^5t

B) P= 418e^5t

c)

A) P=Ce^t

B) P= 418e^t

d)

A) P=Ce^10t

B) P= 418e^10t

2.

The population of the little town of Scorpion Gulch is now 1000 people. The population is presently growing at about 5% per year.

Find the general solution.

a)

P=.05e^1000t

b)

P=1000e^5t

c)

P=1000e^.05t

d)

p=lne^1000t

3.

Y is proportional to the difference of x and z

a)

y= x-z

b)

y= k(z-x)

c)

y= k(x-z)

d)

y= z-x

4.

dy/dx = 2x/e^2y find the general solution

a)

y = ln (2x/2 + C)

2

b)

y = ln(2x/2)+c

c)

y = e^2x+c

d)

y = mx+b

5.

2. Solve the differential equation

𝑑𝑦/𝑑𝑡 =3𝑡²/𝑦 with initial condition

𝑦(2) = 0.

a)

𝑦 = ln(15t)

b)

𝑦 = 16t³

c)

𝑦 = (2𝑡³− 16)^1/2

d)

𝑦 = (2𝑡³−16)

6.

dy/dx= x √y

Find the general solution

a)

√y = ln|4x| + c

b)

√y = (x)^-1 + c

c)

2y^1/2= ln|x| + c

d)

1/2y^1/2= ln|x| + c

7.

y varies jointly with x and the square of z

a)

y= kxz²

b)

y= kx√z

c)

y= kxz

d)

kx²z

8.

what would the sign of the square root after finding c be given the initial condition g(1)= -5

a)

positive

b)

negative

9.

Dy/dx= tanx+15x2+e^x+1/x

a)

y= -ln|sinx| + 5x³ + e^x + ln|x| + c

b)

y= secxtanx + 5x³ + e^x + ln|x| + c

c)

y= -ln|cosx| + 5x³ + e^x + ln|x| + c

d)

y= sec²(x) + 5x³ + e^x + ln|x| + c

10.

dp/dy = (4y)^-1find the general solution

a)

p= 1/5y^5/4 + c

b)

p= 1/4ln|4y| + c

c)

p= 1/8y² + c

d)

p= 1 + c

4y

11.

y is proportional to the product of z and the square root of x

a)

y= z(x²)

b)

y= kz(x²)

c)

y= kx√z

d)

y=zkx

12.

dy/dx = 4x/y. Suppose y(0)=1

The particular solution is

a)

B

b)

C

c)

D

d)

E

13.

Find the particular solution for y if dy/dx = 2x√y and y = 4 when x = 3.

a)

2√y = x² + C

b)

y = (x² + 25)²/4

c)

y = (x²/2-5/2)^1/2

d)

y = x⁴/4

14.

State what type of variation the equation represents.

a)

Direct

b)

Inverse

c)

Joint

d)

None

15.

State what type of variation the equation represents.

a)

Direct

b)

Inverse

c)

Joint

d)

None

16.

If x varies inversely as v, and x = 35 when v = 3, find x when v = 15.

a)

7

b)

9

c)

5

d)

21

17.

What is the constant (k) in this inverse variation?
y = 400/x

a)

x

b)

y

c)

400

d)

Not enough information given

18.

If x=2,y=27; when x=6,y=9; find y when x =3

a)

9

b)

18

c)

3

d)

27

19.

x is directly proportional to y,but inversely proportional to z. x=⅙, for y=5 and z=9, find x when y=6 & z =⅕.

a)

9

b)

3y/10z

c)

6

d)

5

20.

T varies directly as the square root of p and inversely as the square of g. This joint variation can be written as

a)

$T\propto pg$

b)

$T\propto\frac{p}{\sqrt{g}}$

c)

$T\propto\frac{p}{g}$

d)

$T\propto\frac{\sqrt{p}}{g^2}$

21.

The relations between variables T,w,x is $T\propto\frac{x^2}{w}$ . It is given that T=32 when x=4 and w=6. Express T in terms of w and x.

a)

$\frac{12x^2}{w}$

b)

$\frac{3x^2}{w}$

c)

$\frac{x^2}{12w}$

d)

$\frac{24x^2}{w}$

22.

Given that $m\propto\sqrt{p}$ and m= 10 and p=4. Find the value of p if m= 35.

a)

7

b)

9

c)

49

d)

81

23.

Given that $y\propto\frac{1}{\left(x+2\right)^n}$ and $y=\frac{1}{2}$ when n = 2 and x = 2. Find the value of n when y = 1 and x = 6

a)

$\frac{1}{8}$

b)

$\frac{1}{2}$

c)

1

d)

2

24.

Given S varies inversely as the square of T and S = 36 when $T=\frac{1}{2}$ . Express S in terms of T.

a)

$S=\frac{9}{T^2}$

b)

$S=\frac{36}{T^2}$

c)

$S=\frac{36}{T^2}$

d)

$S=\frac{72}{T^2}$

25.

Table 1 shows the value of p, q and r.

Given that $p\propto\frac{p}{\sqrt{2r}}$ , calulate the value of m

a)

1

b)

2

c)

4

d)

8

26.

Suppose p varies directly as r, and p varies inversely as t.
t = 20 when p = 4 and r = 2.
Find t when r = 10 and p = -5.

a)

80

b)

-80

c)

4

d)

-20

27.

The relationship between variables K, L and M is shown in the equation $KL^2\ =\ \sqrt{M}$ . State the relationship of K, L and M in words.

a)

K varies directly as square of L and inversely ad square root of M

b)

K varies directly as square root of M and inversely as square of L

c)

K varies directly as square of M and inversely as square root of L

d)

K varies directly as square root of L and inversely as square of M

28.

Table 1 shows the value of p, q and r.

Given that $p\propto\frac{p}{\sqrt{2r}}$ , calulate the value of m

a)

1

b)

2

c)

4

d)

8

29.

Write the equation for the table given.

a)

y = 1/3x

b)

y = 3x

c)

y = 1/2x

30.

Suppose y varies directly as x.
If y = 22.5 when x = 15, find y when x = 20.

a)

1.5

b)

337.5

c)

30

d)

16.875

31.

The amount of money earned on a job is directly proportional to the number of hours worked. If $70.00 is earned in 5 hours, how much money is earned in 22 hours of work?

a)

$2

b)

$308

c)

$1.57

d)

$265

32.

Y varies directly with x, and y is 84 when x is 16. Which equation represents this situation?

a)

y=1344x

b)

y=100x

c)

y=5.25x

d)

y=4/21x

33.

The number of hours to paint a house varies inversely with the number of painters working. A 2400-square foot house can be painted in 27 hours by 6 painters. How many painters would need to work in order to paint the house in 18 hours?

a)

8 painters

b)

10 painters

c)

9 painters

d)

11 painters

34.

Suppose p varies directly as r, and p varies inversely as t.
t = 20 when p = 4 and r = 2.
Find t when r = 10 and p = -5.

a)

80

b)

-80

c)

4

d)

-20

35.

Find the distance between J and K.

a)

8.2

b)

7.7

c)

9

d)

10.2

36.

Find the length of the missing side.

a)

17 cm

b)

22 cm

c)

15 cm

d)

13 cm

37.

Which letter matches the coordinate (4, -6)?

a)

G

b)

Z

c)

K

d)

None of the above

38.

On the coordinate plane, which line is the y-axis?

a)

Horizontal Line (Side to Side)

b)

Vertical Line (Up and Down)

39.

What letter is at (7, -6)?

a)

D

b)

L

c)

X

d)

There is no letter at those coordinates.

40.

What is the value of x in the right triangle shown?

a)

16cm

b)

18cm

c)

24cm

d)

√674cm

41.

The pythagorean Theorem ONLY works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

42.

What is the opposite of squaring a number?

a)

divide

b)

multiply

c)

fractions

d)

square root

43.

Find the diameter of the circle.

a)

5 units

b)

4 units

c)

12.2 units

d)

7.5 units

44.

Find the length of the side CD.

a)

9 units

b)

√34

c)

√5

d)

3 units

45.

Find the length of the side WV.

a)

2.38 units

b)

2.73 units

c)

√2 units

d)

2.83 units

46.

The __ - axis is vertical in the coordinate plane.

a)

X

b)

Y

c)

Z

d)

None of the above

47.

How many quadrants are in a coordinate plane?

a)

1

b)

2

c)

3

d)

4

48.

Which letter matches the coordinate (4, -6)?

a)

G

b)

Z

c)

K

d)

None of the above

49.

What is the ordered pair for point A?

a)

( 2, 0)

b)

( 0 , 2)

c)

(0, -2)

d)

(-2,0)

50.

What is the ordered pair for point T?

a)

(3, 3)

b)

(3, -3)

c)

(-3, -3)

d)

(- 3, 3)

51.

The coordinates for the origin in the coordinate plane are________?

a)

(1,1)

b)

(0,0)

c)

(0,1)

d)

(1,0)

52.

what shape does this make

a)

rectangle

b)

parallegram

c)

trapizoid

d)

square

53.

The Pythagorean Theorem ONLY works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

54.

The Pythagorean Theorem is
a² + b²+ c²

a)

false

b)

true

55.

What is the distance between the two points?

a)

6.3

b)

6.5

c)

6.7

d)

16

56.

Find the distance between J and K.

a)

8.2

b)

7.7

c)

9

d)

10.2

57.

Find the length of the missing side.

a)

17 cm

b)

22 cm

c)

15 cm

d)

13 cm

58.

Which letter matches the coordinate (4, -6)?

a)

G

b)

Z

c)

K

d)

None of the above

59.

On the coordinate plane, which line is the y-axis?

a)

Horizontal Line (Side to Side)

b)

Vertical Line (Up and Down)

60.

What letter is at (7, -6)?

a)

D

b)

L

c)

X

d)

There is no letter at those coordinates.

61.

What is the value of x in the right triangle shown?

a)

16cm

b)

18cm

c)

24cm

d)

√674cm

62.

The pythagorean Theorem ONLY works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

63.

What is the opposite of squaring a number?

a)

divide

b)

multiply

c)

fractions

d)

square root

64.

Find the diameter of the circle.

a)

5 units

b)

4 units

c)

12.2 units

d)

7.5 units

65.

Find the length of the side CD.

a)

9 units

b)

√34

c)

√5

d)

3 units

66.

Find the length of the side WV.

a)

2.38 units

b)

2.73 units

c)

√2 units

d)

2.83 units

67.

The __ - axis is vertical in the coordinate plane.

a)

X

b)

Y

c)

Z

d)

None of the above

68.

How many quadrants are in a coordinate plane?

a)

1

b)

2

c)

3

d)

4

69.

Which letter matches the coordinate (4, -6)?

a)

G

b)

Z

c)

K

d)

None of the above

70.

What is the ordered pair for point A?

a)

( 2, 0)

b)

( 0 , 2)

c)

(0, -2)

d)

(-2,0)

71.

What is the ordered pair for point T?

a)

(3, 3)

b)

(3, -3)

c)

(-3, -3)

d)

(- 3, 3)

72.

The coordinates for the origin in the coordinate plane are________?

a)

(1,1)

b)

(0,0)

c)

(0,1)

d)

(1,0)

73.

what shape does this make

a)

rectangle

b)

parallegram

c)

trapizoid

d)

square

74.

The Pythagorean Theorem ONLY works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

75.

The Pythagorean Theorem is
a² + b²+ c²

a)

false

b)

true

76.

What is the distance between the two points?

a)

6.3

b)

6.5

c)

6.7

d)

16

My work

Total questions: 76

Worksheet time: 11hrs 24mins

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