Free Printable Math 9 SELF LEARNING ASSESSMENT (2ND Quarter)

1.

1. The quantity whose value does not change is called ______________________.

a)

variable

b)

constant

c)

equation

d)

coefficient

2.

The statement “y varies directly as x” is an example of what type of variation?

a)

Direct

b)

Inverse

c)

Joint

d)

Combined

3.

“The circumference (c) of a circle is directly proportional to its radius (r)” is translated as __________.

a)

c = kr

b)

k = cr

c)

c = k/r

d)

r = k/c

4.

Where does a direct variation starts?

a)

x axis

b)

y axis

c)

origin

d)

vertex

5.

The following statements are true about Direct variation except:

a)

The ratio of two variables is constant.

b)

As one variable increases, the other variable increases.

c)

The product of the two variables is constant .

d)

Every decrease in one variable corresponds to a decrease in another variable.

6.

What equation represents table of values above?

a)

$y\ =\frac{1}{2}x$

b)

y = 2x

c)

y=2x²

d)

$y=\frac{1}{2}x^2$

7.

If w varies directly as z and w = 18 when z = 9, what is the constant of variation?

a)

2

b)

9

c)

18

d)

36

8.

c varies directly as d, and c = 45 and d= 9. Find the value of c when d = 13.

a)

55

b)

60

c)

65

d)

70

9.

If k is constant of variation, which of the following equations is an example of inverse variation

a)

y = kx

b)

$y=\frac{x}{k}$

c)

$y=\frac{k}{x}$

d)

$k=\frac{y}{x}$

10.

What is the value of the constant in the equation $y=\frac{2}{3}x$ ?

a)

2

b)

3

c)

$\frac{2}{3}$

d)

$\frac{3}{2}$

11.

The speed of a car as compared to the time it travels is an illustration of what type of variation?

a)

Direct

b)

Inverse

c)

Joint

d)

Combined

12.

p varies inversely as q and p = 12 when q = 6. What is the equation of variation?

a)

p = 36q

b)

p = 72q

c)

p = 36/q

d)

p = 72/q

13.

u varies inversely as v and $u=\frac{3}{4}$ when $v=\frac{5}{6}$ . Find the constant of variation.

a)

$\frac{4}{5}$

b)

$\frac{5}{8}$

c)

$\frac{18}{12}$

d)

$\frac{18}{24}$

14.

If 12 men can dig a pond in 8 days, how long will it take 24 men to dig the pond?

a)

2 days

b)

4 days

c)

8 days

d)

16 days

15.

m varies jointly as b and c, and m = 42 when b = 2 and c = 3. Find the constant of variation.

a)

6

b)

7

c)

14

d)

21

16.

m varies jointly as b and c, and m = 42 when b = 2 and c = 3. What is the value of m when b = 3 and c = 5?

a)

15

b)

100

c)

105

d)

150

17.

What is the equation of variation if z varies jointly as x and y and z = 65 when x = 10 and y = 13?

a)

z = 2xy

b)

$z=\frac{2x}{y}$

c)

$z=\frac{xy}{2}$

d)

$z=\frac{x}{2y}$

18.

If z varies jointly as x and y and z = 65 when x = 10 and y = 13. What is the value of z when x = 14 and y = 5?

a)

15

b)

35

c)

70

d)

140

19.

Translate into mathematical equation: w varies jointly as n and the square root of p and inversely as the square of t?

a)

$w=\frac{knp}{t}$

b)

$w=\frac{knp^2}{t^2}$

c)

$t=\frac{knp}{w}$

d)

$w=\frac{kn\sqrt[]{p}}{t^2}$

20.

If r varies inversely as t, what happens to r if t is doubled?

a)

halved

b)

doubled

c)

quadrupled

d)

no changes

21.

x varies inversely as y and y varies inversely as z. Describe the relationship between x and z.

a)

x varies inversely as z

b)

x varies directly as z

c)

x is equal to the value of z

d)

x and z do not change its value

22.

h is directly proportional to the square of b and inversely proportional to the cube of d. If h = 6 when b = 4 and d = 2, what is the value of h when b = 6 and d = 3?

a)

1

b)

4

c)

6

d)

8

23.

The number of days required to construct a boat varies directly as the number of boats to be built and inversely as the number of people doing the job. If 8 people required 12 days to build 16 boats, how long will it take 15 people to build 50 boats?

a)

6 days

b)

20 days

c)

36 days

d)

40 days

24.

What is the value of a nonzero number raised to zero exponent?

a)

0

b)

1

c)

2

d)

undefined

25.

Which of the following expression is equivalent to m⁵+ m^-3?

a)

m^{5 - 3}

b)

$\frac{m^5}{m^3}$

c)

m⁵-m³

d)

$m^5+\frac{1}{m^3}$

26.

Express $ab^{\frac{2}{3}}$ to radical form.

a)

$a\sqrt[3]{b^2}$

b)

$\sqrt[3]{ab^2}$

c)

$\sqrt[]{ab^3}$

d)

$a\ \sqrt[]{b^3}$

27.

What is the index in the expression $\sqrt[]{5^3}$ ?

a)

125

b)

5

c)

3

d)

2

28.

What is exponential form of the radical expression?

a)

$x^{\frac{2}{5}}y^{\frac{3}{5}}$

b)

$x^{\frac{2}{5}}+y^{\frac{3}{5}}$

c)

(x² y³)⁵

d)

$\left(x^2y^3\right)^{\frac{5}{5}}$

29.

The process of removing the radical sign in the denominator is called_____________________.

a)

denesting

b)

decomposition

c)

factorization

d)

rationalization

30.

Which of the following is the simplest form of $\sqrt{50}$ ?

a)

$2\sqrt{5}$

b)

$5\sqrt{2}$

c)

$5\sqrt{10}$

d)

$10\sqrt{5}$

31.

Which of the following method(s) is/are used to simplify radical expression?

a)

Removing the perfect nth root.

b)

Reducing the index to the lowest possible order.

c)

Rationalizing the denominator.

d)

All of the above

32.

What is the conjugate of the denominator in the expression $\frac{\sqrt{2}+\sqrt{3}}{3-\sqrt{2}}?$

a)

$\sqrt{2}-3$

b)

$\sqrt{3}+\sqrt{2}$

c)

$3+\sqrt{2}$

d)

$\sqrt{2}+\sqrt{3}$

33.

Which of the following is the same as the expression above?

a)

$5a^2b^2\sqrt{b}$

b)

$\left(25a^5b^2\right)^{\frac{1}{2}}$

c)

$25a^4b^5$

d)

$25\left(a^4b^2\right)^{\frac{1}{3}}$

34.

What is the simplified expression of $\sqrt{48x^5}$ ?

a)

$4x\sqrt{3x}$

b)

$4x^2\sqrt{3x}$

c)

$4x^3\sqrt{3x}$

d)

$4x^4\sqrt{3x}$

35.

To rationalize the expression $\frac{6}{\sqrt{12}}$ , what term should be multiplied to the numerator and denominator?

a)

$\sqrt{2}$

b)

$\sqrt{3}$

c)

$\sqrt{4}$

d)

$\sqrt{6}$

36.

Express $\frac{6}{\sqrt{3}}$ in simplest form.

a)

$2\sqrt{3}$

b)

$\frac{\sqrt{3}}{2}$

c)

$\frac{2}{\sqrt{3}}$

d)

$\frac{2\sqrt{3}}{3}$

37.

What is the $\frac{\sqrt[]{5}}{\sqrt[4]{5}}$ in simplest form?

a)

$\frac{\sqrt[]{5}}{5}$

b)

$\frac{\sqrt[4]{5}}{5}$

c)

$\sqrt[]{5}$

d)

$\sqrt[4]{5}$

38.

What is the sum of the radicals $4\sqrt{6},\ 3\sqrt{6}\ and\ \sqrt{6}?$

a)

$7\sqrt{6}$

b)

$8\sqrt{6}$

c)

$12\sqrt{6}$

d)

$13\sqrt{6}$

39.

Perform the indicated operation and simplify: $\sqrt{75}+\sqrt{27}-\sqrt{48}$

a)

$\sqrt{3}$

b)

$3\sqrt{3}$

c)

$4\sqrt{3}$

d)

$5\sqrt{3}$

40.

Multiply and simplify: $\sqrt{2}\left(\sqrt{6}+\sqrt{8}\right)$

a)

$2\sqrt{3}+8$

b)

$2\sqrt{3}-8$

c)

$2\sqrt{3}+4$

d)

$2\sqrt{3}-4$

41.

If $\sqrt[]{x}=5$ , what is the value of x?

a)

9

b)

16

c)

25

d)

36

42.

What is the resulting value of $\frac{\left(2m^{\frac{3}{4}}\right)^3}{\left(4m^{\frac{1}{4}}\right)^3}$ when m = 16?

a)

64

b)

32

c)

16

d)

8

43.

Perform the indicated operation:

(4a³ b²)(3a^-4 b³)?

a)

$\frac{12b^5}{a}$

b)

12ab⁵

c)

$\frac{a}{12b^5}$

d)

$\frac{ab^5}{12}$

44.

Express $\left(3\sqrt{7}+2\sqrt{3}\right)^2$ into expanded form?

a)

$10\sqrt{7}+4\sqrt{3}$

b)

$25\sqrt{7}+12\sqrt{21}+4\sqrt{3}$

c)

$75+12\sqrt{21}$

d)

$63\sqrt{7}+12\sqrt{21}+12\sqrt{3}$

45.

What is the simplest form of the radical expression?

a)

b)

c)

d)

46.

What is the extraneous root of the equation $\sqrt{\ 5-x}-1\ =x?$

a)

1

b)

-1

c)

4

d)

-4

47.

Solve the radical equation $\sqrt{\ 5x+11}=x+3$ .

a)

-2

b)

1

c)

Both A and B

d)

no solution

48.

Translate the statement into radical equation, “The square root of seven more than a number is equal to five more than a number.”

a)

$\sqrt{\ x+7}=\ x+5$

b)

$\sqrt{x}+7=x+5$

c)

$\sqrt{7}+x\ =\ x\ +5$

d)

$\sqrt{\ x+7}=\sqrt{\ x+5}$

49.

“The square root of seven more than a number is equal to five more than a number.” What is the number?

a)

-9

b)

-6

c)

-3

d)

-2

50.

The length, width and height of a rectangular box are $\sqrt[3]{2xy},\sqrt[3]{4xy},\sqrt[3]{27xy}$ cm. respectively. What expression will represent the volume of the box?

a)

xy

b)

$6\sqrt[3]{xy}$

c)

$xy\sqrt[3]{6}$

d)

6xy

Math 9 SELF LEARNING ASSESSMENT (2ND Quarter)

Total questions: 50

Worksheet time: 57mins

Similar Resources on Wayground