Free Printable Reviewer 24-25

1.

Which one refers to a polynomial equation in the form ax² + bx + c = 0 where a, b, c are real numbers and a ≠ 0?

a)

Quadratic Equation

b)

Quadratic Polynomial

c)

Quadratic Inequalities

d)

Linear Equation

2.

Janie has 4 less than 5 times the number of candy Brayden has. If c, represents the amount candy Brayden, which of the following shows how much candy Janie has?

a)

5c – 4

b)

4 – 5c

c)

5 ( 4 – c )

d)

4c + 5

3.

The solutions of the quadratic equation
x²-5x+6=0 are

a)

x=1 or x=-6

b)

x=3 or x=2

c)

x=-3 or x= 2

d)

x=-1 or x=6

4.

To complete the perfect square trinomial in the expression x²-22x+_____, we need to add

a)

11

b)

44

c)

121

d)

144

5.

In the quadratic formula, the expression

b²-4ac is called

a)

discrimination

b)

determinant

c)

discriminant

d)

none of these

6.

Solve the quadratic inequality:

$x^2-4x-5\le0$

a)

$-1\le x\le5$

b)

$-5\le x\le1$

c)

$x\ge5\ ,\ \ x\le-1$

d)

$x\le-5\ ,\ \ \ x\ge1$

7.

Solve Using the Quadratic Formula
x² + 4x - 40 = -8

a)

-10 & -4

b)

-4 & 10

c)

-8 & 4

d)

8 & -4

8.

Solve by the Extraction of Roots method: (x - 2) ² = 49

a)

9 or -5

b)

± 9

c)

± 5

d)

± 7

9.

Which of the following is NOT a method in solving a quadratic equation?

a)

Factoring

b)

Quadratic Formula

c)

Completing the Square

d)

Discriminant

10.

If the discriminant is equal to 121, then the nature of the roots is?

a)

real, irrational and unequal

b)

imaginary

c)

real, rational and unequal

d)

real and equal

11.

In the equation $x^2+\frac{x}{3}=\frac{2}{3}$ which is transformable into quadratic equation, What is the standard form in quadratic equation?

a)

$x^2+x+2=0$

b)

$x^2+x-2=0$

c)

$3x^2+4x-2=0$

d)

$3x^2+x-2=0$

12.

The length of the garden is 5 m longer than its width, and the area is 14 sq. m. What is the length of the garden?

a)

2 m

b)

5 m

c)

7 m

d)

9 m

13.

Which of the following variations produces pairs of numbers in which their ratio is a constant?

(45 seconds)

a)

direct variation

b)

inverse variation

c)

joint variation

d)

combined variation

14.

Which of the following statements is an example of direct variation?

(1.5 minutes)

a)

The number of hours (t) to finish the job to the number of men (m) working.

b)

The number of persons (p) sharing a pizza to the size (s) of the slices.

c)

The number of students (s) renting an apartment to the amount of money (m) that each of them will share for the rent.

d)

The amount of money (m) raised in a concert to the number of tickets (t) sold.

15.

If y varies directly as x and y = 48 when x = 4, what is the constant of variation?

(2 minutes)

a)

8

b)

12

c)

16

d)

24

16.

Which of the following variations has the product of two quantities as the constant?

(45 seconds)

a)

direct variation

b)

inverse variation

c)

joint variation

d)

combined variation

17.

What do you call a variation when more than one type of variation occurs in the same equation?

(45 seconds)

a)

direct variation

b)

inverse variation

c)

joint variation

d)

combined variation

18.

If W varies jointly as p, q, r and s, what is the equation for k?

(1.5 minutes)

a)

k = $\frac{W}{pqrs}$

b)

k = Wpqrs

c)

k = $\frac{pqrs}{W}$

d)

k = pqrs

19.

The density d of air varies inversely as the volume v of water in the atmosphere. What is the equation?

(1 minute)

a)

$v\ =\ \frac{k}{d}$

b)

$d\ =\ \frac{k}{v}$

c)

$v\ =\ \frac{d}{k}$

d)

$d\ =\ \frac{v}{k}$

20.

The volume of a cylinder V varies jointly as the height h and the square of its radius r. What is the equation?

(1.5 minutes)

a)

$V\ =\ khr$

b)

$V\ =\ \frac{k}{hr^2}$

c)

$V\ =\ khr^2$

d)

$V\ =\ \frac{hr^2}{k}$

21.

Q varies jointly as p and r and inversely as the cube of m. What is the equation?

(2 minutes)

a)

$Q\ =\ kprm$

b)

$Q\ =\ \frac{kpr}{m^{ }}$

c)

$Q\ =\ \frac{kpr}{m^2}$

d)

$Q\ =\ \frac{kpr}{m^3}$

22.

(PROBLEM SOLVING: DIRECT) The amount of paint (p) needed to paint the walls of a room varies directly as the area (A) of the wall. If 2 gallons of paint is needed to paint a 40 m² wall, how many gallons of paint are needed to paint a wall with an area of 100 m²?

Answer: (a) gallons

(5 MINUTES)

23.

Simplify. Assume that the variables/denominators, if there is any, are nonzero constants.

$a^4\cdot a^0$

a)

$1$

b)

$a^4$

c)

$a$

d)

$a^0$

24.

Simplify. Assume that the variables/denominators, if there is any, are nonzero constants.

$7^0+8^0+9^0$

a)

3

b)

1

c)

0

d)

24

25.

Simplify. Assume that the variables/denominators, if there is any, are nonzero constants.

$\frac{9^{-3}}{9^{-4}}$

a)

$\frac{1}{9}$

b)

$9$

c)

$9^7$

d)

$\frac{1}{9^7}$

26.

Simplify. Assume that the variables/denominators, if there is any, are nonzero constants.

$\left(\frac{3}{5}\right)^{-1}$

a)

$-\frac{5}{3}$

b)

$-\frac{3}{5}$

c)

$\frac{3}{5}$

d)

$\frac{5}{3}$

27.

Simplify. Assume that the variables/denominators, if there is any, are nonzero constants.

$\left(\frac{g^{-6}}{g^{-3}}\right)^{-2}$

a)

$\frac{1}{g^6}$

b)

$g^6$

c)

$g^{18}$

d)

$\frac{1}{g^{18}}$

28.

Simplify. Assume that the variables/denominators, if there is any, are nonzero constants.

$\frac{15n}{3n^2}$

a)

$5n$

b)

$\frac{1}{5n}$

c)

$\frac{n}{5}$

d)

$\frac{5}{n}$

29.

Simplify. Assume that the variables/denominators, if there is any, are nonzero constants.

$\frac{6k^{-2}m^3}{k^2m^5}$

a)

$\frac{6}{k^4m^2}$

b)

$\frac{6}{m^2}$

c)

$6k^4m^2$

d)

$\frac{6k^4}{m^2}$

30.

Simplify. Assume that the variables/denominators, if there is any, are nonzero constants.

$\frac{15n^{-4}p}{5n^{-4}p^{-1}}$

a)

$\frac{3}{n^8p^2}$

b)

$\frac{3}{p^2}$

c)

$\frac{3}{p}$

d)

$3p^2$

31.

Simplify. Assume that the variables/denominators, if there is any, are nonzero constants.

$\frac{2\left(a^6b^{-6}\right)^0}{a^{-4}b^3}$

a)

$\frac{2}{a^4b^3}$

b)

$\frac{a^4}{b^3}$

c)

$\frac{b^3}{a^4}$

d)

$\frac{2a^4}{b^3}$

32.

Write the exponential expression as radical.

$27^{\frac{2}{3}}$

a)

b)

c)

d)

33.

Write the radical as exponential expression.

a)

$a^{\frac{5}{4}}$

b)

$a^{\frac{4}{5}}$

c)

$a^{-\frac{4}{5}}$

d)

$a^{-\frac{5}{4}}$

34.

Write the given as a radical expression and simplify.

64^{\frac{1}{3}}

a)

4

b)

2

c)

16

d)

64

35.

Evaluate the expression:

$16^{\frac{3}{4}}$

a)

8

b)

16

c)

4

d)

32

36.

Evaluate the expression:

$36^{-\frac{1}{2}}$

a)

$-6$

b)

$6$

c)

$-\frac{1}{6}$

d)

$\frac{1}{6}$

37.

Evaluate the expression:

$81^{-\frac{3}{4}}$

a)

$-27$

b)

$\frac{1}{27}$

c)

$-\frac{1}{9}$

d)

$18$

38.

Perform the indicated operation $4\sqrt[]{x}-2\sqrt[]{x}$ .

a)

2

b)

4

c)

$2\sqrt{x}$

d)

$3\sqrt{x}$

39.

Find the difference: $\sqrt{12}-7\sqrt{3}$

a)

-5

b)

$-5\sqrt{3}$

c)

$6\sqrt{3}$

d)

$-3\sqrt{3}$

40.

Subtract: $9\sqrt{20}-\sqrt{80}$

a)

$8\sqrt{3}$

b)

$9\sqrt{4}$

c)

$14\sqrt{5}$

d)

$12\sqrt{20}$

41.

Perform the indicated operation: $4\sqrt{27}-2\sqrt{48}$

a)

$4\sqrt{3}$

b)

$2\sqrt{3}$

c)

$5\sqrt{5}$

d)

$16\sqrt{5}$

42.

Perform the indicated operation: $19\sqrt{8}-11\sqrt{2}$

a)

$8\sqrt{6}$

b)

$27\sqrt{2}$

c)

$8\sqrt{2}$

d)

$8\sqrt{8}$

43.

The product of $\sqrt{3}$ and $3\sqrt[3]{2}$ is equal to _____.

a)

$\sqrt[5]{6}$

b)

$\sqrt[6]{36}$

c)

$\sqrt[6]{6}$

d)

$\sqrt[6]{108}$

44.

What is the product of $\left(2\sqrt{5}+3\sqrt{2}\right)$ and $\left(2\sqrt{5}-3\sqrt{2}\right)$ ?

a)

$0$

b)

$2$

c)

1

d)

$16\sqrt{5}$

45.

What is the product when $\sqrt[3]{81a^5b^4}$ is multiplied by $\sqrt[3]{3a^2b}$ ?

a)

$9ab$

b)

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

c)

$3a^2b$

d)

$3a^2b\sqrt[3]{9ab^2}$

46.

Find the product: $\left(\sqrt{12}\right)\left(2\sqrt{3}\right)$

a)

$12$

b)

$6$

c)

$4$

d)

$2$

47.

What is the product of $\sqrt{3}\left(\sqrt{75}-\sqrt{3}+\sqrt{12}\right)$ ?

a)

$15$

b)

$17$

c)

$16$

d)

$18$

48.

Which of the following quadrilaterals has four right angles and 4 congruent sides?

a)

parallelogram

b)

rectangle

c)

rhombus

d)

square

49.

Which of the following is not a parallelogram?

a)

trapezoid

b)

square

c)

rhombus

d)

rectangle

50.

In a parallelogram, how would you describe the diagonals?

a)

They are congruent

b)

They bisect each other

c)

They are parallel

d)

They are perpendicular

51.

The figure PQRS is a rhombus. What is the value of y?

a)

-4

b)

-3

c)

3

d)

4

52.

The diagonals of a rectangle are

a)

parallel

b)

congruent

c)

perpendicular

d)

not congruent

53.

A square is a rectangle.

a)

Always

b)

Sometimes

c)

Never

54.

A rhombus is a parallelogram.

a)

Always

b)

Sometimes

c)

Never

55.

If PONS is a rectangle, PN = 2x - 5 and OS = 17. Solve for the value of x.

a)

6

b)

11

c)

12

d)

22

56.

Find x.

a)

103

b)

77

c)

83

d)

73

57.

The figure is a parallelogram.
Solve for x.

a)

7

b)

2

c)

0

d)

4

58.

If JOSE is a rhombus, JO = 3x - 5 and OS = 13 cm. What is the perimeter of JOSE?

a)

6 cm

b)

18 cm

c)

48 cm

d)

52 cm

59.

BCDE is square. Find CE.

a)

40

b)

90

c)

80

d)

20

60.

Given Rhombus TUVW. Find m∠2.

a)

62

b)

28

c)

90

d)

78

61.

If m∠B is 54° what is the m∠CDB?

a)

54°

b)

27°

c)

108°

d)

36°

62.

The sum of the interior angles of all quadrilaterals is ___ .

a)

90

b)

180

c)

270

d)

360

63.

If two figures are similar, the corresponding sides are ______________.

a)

equal

b)

congruent

c)

proportional

d)

none of these

64.

What is the similarity statement for the triangle pair?

a)

ΔXYZ~ΔNEW

b)

ΔXZY~ΔNWE

c)

ΔZYX~ΔENW

d)

ΔYZX~ΔNWE

65.

Are these two triangles similar? Which similarity criterion do you use to prove it?

a)

Yes, AA

b)

Yes, SAS

c)

Yes, SSS

d)

Not Similar

66.

Are these two triangles similar? Which similarity criterion do you use to prove it?

a)

Yes, AA

b)

Yes, SAS

c)

Yes, SSS

d)

Not Similar

67.

Are these two triangles similar? Which similarity criterion do you use to prove it?

a)

Yes, AA

b)

Yes, SAS

c)

Yes, SSS

d)

Not Similar

68.

Are these two triangles similar? Which similarity criterion do you use to prove it?

a)

Yes, AA

b)

Yes, SAS

c)

Yes, SSS

d)

Not Similar

69.

Are these two triangles similar? Which similarity criterion do you use to prove it?

a)

Yes, SSS

b)

Yes, SAS

c)

Yes, AA

d)

Not similar.

70.

If a line divides any two sides of a triangle in the same ratio then the line is ----------- to the third side

a)

parallel

b)

perpendicular

c)

co-incides

d)

none of the above

71.

Find the missing length.

a)

21

b)

18

c)

16

d)

24

72.

Find the missing length indicated.

a)

16

b)

8

c)

10

d)

14

73.

The figure is an example of a(n) _____.

a)

angle bisector

b)

perpendicular bisector

c)

median

d)

midsegment

74.

The dotted line represents a ____.

a)

median

b)

centroid

c)

midsegment

d)

midpoint

75.

Find the missing length.

a)

10

b)

21

c)

35

d)

9

76.

What is the ratio for Sine?

a)

Hyp/Opp

b)

Opp/Hyp

c)

Opp/Adj

d)

Adj/Opp

77.

What is the ratio for Cosine?

a)

Opp/Hyp

b)

Opp/Adj

c)

Adj/Opp

d)

Adj/Hyp

78.

What is the ratio for Tangent

a)

Opp/Adj

b)

Adj/Opp

c)

Opp/Hyp

d)

Hyp/Opp

79.

Choose the correct ratio.

a)

sin(37)=x/14

b)

cos(37)=x/14

c)

tan(37)=x/14

d)

sin(37)=14/x

80.

Find the length of side w.

a)

21.4 cm

b)

18.0 cm

c)

36.5 cm

d)

43.6 cm

81.

What is the length of side x?

a)

6.57 cm

b)

7 cm

c)

7.44 cm

d)

26.33 cm

82.

Find the length of side x.

a)

50.7

b)

50.1

c)

60.7

d)

61.0

83.

Find the measure of the indicated angle. Round to the nearest tenth.

a)

35.8°

b)

43.8°

c)

46.2°

d)

54.2°

84.

Find m∠N

a)

14

b)

65

c)

76

d)

53

85.

Find the measure of the indicated angle (?) round to the nearest tenth.

a)

9.4

b)

55.2

c)

20.15

d)

19.4

86.

Which law you are going to use to solve a triangle where given are the values of 3 sides?

a)

Law of Sines

b)

Law of Cosines

c)

both

d)

either

87.

Which law you are going to use to solve the given triangle?

a)

Law of Sines

b)

Law of Cosines

c)

both

d)

either

88.

Which law you are going to use to solve the given triangle?

a)

Law of Sines

b)

Law of Cosines

c)

both

d)

either

89.

Which equation you are going to use to find the unknown?

a)

$x^2=17^2+28^2-2x\cos114$

b)

$x^{ }=17^{ }+28^{ }-2\left(17\right)\left(28\right)\cos114$

c)

$x^2=17^2+28^2-2\left(17\right)\left(28\right)\cos114$

d)

$x^{ }=17^2+28^2-2\left(17\right)\left(28\right)\cos114$

90.

Which equation you are going to use to find the unknown?

a)

$\frac{7}{\sin39.4}=\frac{46.5}{\sin x}$

b)

$\frac{7}{\sin39.4}=\frac{x}{\sin46.5}$

c)

$\frac{x}{\sin39.4}=\frac{7}{\sin46.5}$

d)

$\frac{x}{\sin46.5}=\frac{39.4}{\sin7}$

Reviewer 24-25

Total questions: 90

Worksheet time: 2hrs 29mins

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