Free Printable 2nd PERIODIC TEST IN MATHEMATICS 9

1.

Which of the following does NOT define direct variation?

a)

A. As the quantity decreases, the other quantity also decreases.

b)

B. As the quantity increases, the other quantity also increases.

c)

C. As the quantity increases the other quantity decreases.

d)

D. The product of the constant value and independent variable is equal to the dependent variable.

2.

Which of the following situations shows direct variation?

a)

The age of a used car to its resale value.

b)

The number of laborers to the number of working days.

c)

The time a teacher spends checking papers to the number of students.

d)

The size of pizza slices to the number of persons sharing a whole pizza.

3.

Which of the following situations shows inverse variation?

a)

The total cost of goods to its quantity.

b)

The number of students to the number of chairs in a class.

c)

The salary of the laborers to the number of days he/she worked.

d)

The speed of wifi connection/signal to the number of connected gadgets.

4.

Which of the following graph represents direct variation?

a)

b)

c)

d)

5.

Which equation represents the statement “x varies directly as y”?

a)

A. x=k

b)

B. x=k/y

c)

C. y=kx

d)

D. y=k/x

6.

If y varies directly as x and y is 64 when x is 8. What is the constant of variation?

a)

A. 14

b)

B. 4

c)

C. 18

d)

D. 8

7.

If a varies directly as b and a = 14 when b = 20, what is the value of b if a = 35?

a)

A. 30

b)

B. 40

c)

C. 50

d)

D. 60

8.

Which statement is TRUE about the inverse variation y ∝ x?

a)

If y increases then x increases.

b)

If y decreases then x increases.

c)

If y decreases then x remains constant.

d)

none of these

9.

The density (D) of an object varies inversely as its mass (m). Which of the following symbol/s represent the variation?

a)

D = km

b)

D = k/m

c)

D > m

d)

D < m

10.

The cost c varies directly as the number n of pencils. Which equation represents the relationship between the variables?

a)

c = kn

b)

t = kn

c)

n = kc

d)

c = kn

11.

The speed r of a moving object is inversely proportional to the time travelled. Express the relationship as an equation.

a)

r = k/t

b)

t = kr

c)

r = kt

d)

rk = r

12.

If y varies inversely as x and y = 32 when x = 4. What is the constant of variation?

a)

A. 8

b)

B. 36

c)

C. 28

d)

D. 128

13.

If y varies inversely as x, and y = 15 when x = 9, find y when x = -3.

a)

5

b)

13

c)

35

d)

-135

14.

Which of the following is NOT a type of variation?

a)

Direct

b)

Equal

c)

Inverse

d)

Joint

15.

The equation, "the speed is inversely proportional to the time t" is written as _____

a)

s = k / t

b)

s = k : t

c)

s = kt

d)

s = t / k

16.

Which of the following describes an inverse variation?

a)

b)

c)

d)

17.

Find the constant of variation of:

a)

210

b)

10

c)

15

d)

100

18.

Which equation represents the statement “F varies directly as U and inversely as N”?

a)

F = kUC

b)

F = kCU

c)

F = kC

d)

F = kU/N

19.

a varies jointly as the product of b and c. If a = 24 when b = 8 and c = 2, find b when a = 48 and c = 4.

a)

b = -8

b)

b = -1

c)

b = 0

d)

b = 8

20.

Five men can finish painting the room in 4 days. How many days will 2 men finish the job?

a)

5 days

b)

6 days

c)

2 days

d)

10 days

21.

A car can travel a distance of 16 km for 5 liters of gasoline. How many liters of gasoline is needed if you wish to travel 40 km?

a)

10 liters

b)

12 liters

c)

12.5 liters

d)

15 liters

22.

The electrical resistance (R) of a wire varies directly as its length (L) and inversely as the square of its diameter (d). This is an example of a:

a)

Direct Variation

b)

Inverse Variation

c)

Joint Variation

d)

Combined Variation

23.

The area (A) of a triangle varies jointly as its base (b) and height (h). If the area is 20cm² when b=8cm and h=5cm, what is k?

a)

A. 2

b)

B. 1/2

c)

C. 5

d)

D. 8

24.

The number of hours (H) required to paint a fence varies inversely as the number of people (N) painting. If 4 people can paint the fence in 12 hours, how long will it take 6 people to paint it?

a)

4 hours

b)

6 hours

c)

8 hours

d)

10 hours

25.

Y varies directly as M and inversely as N. If Y=16 when M=8 and N=2, what is the equation of variation?

a)

Y = KMN

b)

Y = KM/N

c)

Y = KN/M

d)

Y = KNM

26.

What is true about ∛(8x⁶y⁹)?

I. The index is 3

II. The radicand is 8x⁶y⁹

III. The simplified form is 2x²y³

IV. It is a radical expression

a)

I

b)

I and II

c)

I, II and III

d)

All of the above statements.

27.

Shiela is working on a math problem that involves simplifying an expression. She needs to simplify $\frac{5 - m^0}{m + n^0}$

a)

½

b)

¼

c)

4

d)

2

28.

Lily is working on a project that involves simplifying expressions. She comes across the expression $5\sqrt{3} + 2\sqrt{75}$ . What is the simplified form of the given expression?

a)

$7\sqrt{75}$

b)

$10\sqrt{5}$

c)

$12\sqrt{7}$

d)

$15\sqrt{3}$

29.

Simplify $(x^{-6}y^2)^3$

a)

$\frac{y^6}{x^{18}}$

b)

$\frac{y^5}{x^9}$

c)

$x^6y^5$

d)

$x^{-6}y^2$

30.

Simplify $16x^0$

a)

4

b)

1

c)

16

d)

36

31.

Simplify (24a)2⁻³

a)

12a

b)

3a

c)

4a

d)

6a

32.

What is the value of $2m^3(m-7m^2)$ ?

a)

$2m^4-14m^5$

b)

$2m^4-7m^{15}$

c)

$2m^4-7m^{15}$

d)

$2m^6-14m^{15}$

33.

Change $(25x^3)^{\frac{2}{3}}$ in radical form.

a)

$\sqrt[3]{25x^3}$

b)

$\sqrt[3]{(25x^3)^2}$

c)

$\sqrt[3]{(25x^2)}$

d)

$25\sqrt[3]{x^2}$

34.

Simplify $7^0k^{-2}$

a)

$\frac{1}{k^2}$

b)

$\frac{7}{k^2}$

c)

$\frac{k}{7}$

d)

$7k$

35.

Simplify: $\frac{\sqrt{16x^2}}{\sqrt{4x}}$

a)

$2\sqrt{x}$

b)

$2x\sqrt{x}$

c)

$4\sqrt{x}$

d)

$4\sqrt{2x}$

36.

What is the simplified form of $\sqrt[3]{a^3b^5}$ ?

a)

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

b)

$b\sqrt[3]{b}$

c)

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

d)

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

37.

Simplify $\frac{15a^5b^3}{3a^2}$ .

a)

$5a^3b^5$

b)

$5a^5b^3$

c)

$5a^5$

d)

$5b^3$

38.

Simplify $\frac{2a^5}{a^{-3}}$ .

a)

$2a^2$

b)

$2a^8$

c)

$a^5$

d)

$5a^5$

39.

What is the simplified form of the expression of $\sqrt{25t^4}$ ?

a)

$5t^2$

b)

$25t^4$

c)

$t^2$

d)

5t

40.

Zac is organizing a science fair project where he needs to simplify the expression for the area of a rectangular garden he plans to plant. The area is given by $\sqrt{200ab^8}$ . What is the simplified expression for the area of the garden?

a)

3b^4√2a^8

b)

3b^4√2a

c)

10b^4√2a

d)

3a^4√2b

41.

Simplify: √3 - 6√3 + 8√3.

a)

7

b)

7√3

c)

3√3

d)

2√3

42.

What is √25 + √81 - 3√4?

a)

2

b)

-6

c)

6

d)

8

43.

What is the sum of 10√5 and √45?

a)

13√5

b)

19√5

c)

7√5

d)

11√5

44.

Evaluate: 5√12 - √27.

a)

7√5

b)

7√3

c)

10√3

d)

10√5

45.

Simplify: 2√3 · 2√6 · √2

a)

4√36

b)

10√5

c)

12√7

d)

24

46.

What is $(\sqrt{5} + 3)^{2}$ ?

a)

14 - 6√5

b)

10√5 + 3

c)

14 + 6√5

d)

15√3

47.

Elijah is helping his friend Isla with a math problem. They need to multiply √10x and √5 and express it in simplified form. What should be their answer?

a)

7√x

b)

10√5

c)

5√2x

d)

15√3

48.

Joel is working on his Science problem and needs to rationalize $\frac{8x}{\sqrt[]{2}}$ What should be his answer?

a)

2

b)

$4\sqrt[]{2x}$

c)

$4x\sqrt[]{2}$

d)

16

49.

Michael is organizing a charity event and wants to create gift bags for the attendees. He has a total of $\frac{\sqrt[]{7x^3}}{\sqrt[]{3x}}$ to distribute. How many items can he put in each gift bag?

a)

2x

b)

$2x^4$

c)

5x

d)

$10x^5$

50.

Mr. Cruz is planning to put a perimeter fence on his lot. What is the perimeter of a rectangular lot if its width is 4√20 cm and its length is 5√45 cm?

a)

46√5 cm

b)

23√5 cm

c)

40√5 cm

d)

20√5 cm

2nd PERIODIC TEST IN MATHEMATICS 9

Total questions: 50

Worksheet time: 42mins

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