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1.

What is the correct factorization of the polynomial 5y(x−1)−5x(1−x)?

a)

5(x−1)(x+y)

b)

(x−1)(5y+5x)

c)

5(y−x)(x−1)

d)

5(x+y)(x−1)

2.

With 5y(x−1)−5x(1−x), which statement is correct when changing the sign of the second term?

a)

Becomes 5y(x−1)+5x(1−x)

b)

Becomes 5y(x−1)+5x(x−1)

c)

Becomes 5y(1−x)+5x(x−1)

d)

Remains unchanged because it cannot change sign

3.

In 5y(x−1)−5x(1−x), factor out 5(x−1), what is the remaining expression?

a)

x−y

b)

y+x

c)

y−x

d)

x+y

4.

The regular quadrilateral pyramid has a lateral edge of 25 cm, and the base is a square ABCD with a side length of 30 cm. What is the area of the base?

a)

600 cm²

b)

750 cm²

c)

800 cm²

d)

900 cm²

5.

With a regular quadrilateral pyramid having a lateral edge of 25 cm and a base edge of 30 cm. What is the lateral surface area if the lateral edge is the edge of each lateral triangle?

a)

1800 cm²

b)

1200 cm²

c)

1500 cm²

d)

1000 cm²

6.

A regular quadrilateral pyramid has a lateral edge of 25 cm and a square base with a side length of 30 cm. What is the correct total surface area?

a)

2400 cm²

b)

1800 cm²

c)

2000 cm²

d)

2100 cm²

7.

The regular quadrilateral pyramid has a lateral edge of 17 cm, and the base is a square with a side length of 16 cm. What is the area of the base?

a)

180 cm²

b)

256 cm²

c)

200 cm²

d)

240 cm²

8.

In a regular quadrilateral pyramid with a lateral edge of 17 cm and a base edge of 16 cm, what is the lateral surface area if each lateral face is an isosceles triangle with a lateral edge of 17 cm and a base of 16 cm?

a)

480 cm²

b)

512 cm²

c)

400 cm²

d)

300 cm²

9.

For a regular quadrilateral pyramid: the lateral edge is 17 cm, and the base is a square with a side length of 16 cm. What is the total surface area?

a)

680 cm²

b)

800 cm²

c)

700 cm²

d)

736 cm²

10.

Solve the equation x²−4x=0. What is the correct value of the solution?

a)

Only x=0

b)

x=2 or x=−2

c)

x=0 or x=−4

d)

x=0 or x=4

11.

What is the production cost function C(x) = (2x + 5) / (x − 1) (million VND) for x > 1. What is the value of C(2)?

a)

9 million VND

b)

7 million VND

c)

8 million VND

d)

6 million VND

12.

With C(x) = (2x + 5) / (x − 1), what is the cost when producing x = 3 units?

a)

5.5 million VND

b)

6.0 million VND

c)

3.5 million VND

d)

4.5 million VND

13.

As x increases, what is the trend of C(x) = (2x + 5) / (x − 1)?

a)

Approaches 2

b)

Decreases to more than 4

c)

Increases without limit

d)

Approaches 0

14.

A vehicle travels a distance s (km) in a time t (hours). The average speed is s / t (km/h). Which statement is correct?

a)

After 3 hours, it travels 30t km

b)

If s = 100; t = 2 then v = 40 km/h

c)

The travel time is t (hours)

d)

The fraction is undefined at t = 0

15.

Calculate the average speed when s = 100 km and t = 2 hours.

a)

55 km/h

b)

40 km/h

c)

50 km/h

d)

60 km/h

16.

If a vehicle travels 30 km every hour, what is the distance after 3 hours?

a)

60 km

b)

120 km

c)

30t km

d)

90 km

17.

Expand the expression $(2a + 3b)^2$ using the appropriate identity.

a)

$4a^2 + 9ab + 9b^2$

b)

$4a^2 + 12ab + 9b^2$

c)

$4a^2 + 6ab + 9b^2$

d)

$2a^2 + 12ab + 3b^2$

18.

With a = 1; b = −2, what is the value of $(2a + 3b)^2$ ?

a)

0

b)

36

c)

4

d)

16

19.

To $(2a + 3b)^2$ equal 0, which condition is correct?

a)

2a + 3b = 0

b)

a = 1; b = −1

c)

a = 0; b = 0

d)

2a = 3b ≠ 0

20.

Let the expression B = (1/x + 3/(x+2)) − (1/x − 1/(x+1) + 3/(x+2)). What is the condition for B to be defined?

a)

any x, except x = 0

b)

x not equal to −1 and x not equal to −2

c)

x not equal to 0 and x not equal to −2

d)

x not equal to 0 and x not equal to −1

21.

With x = 0, what is the value of the expression B?

a)

Equal to 0

b)

Undefined

c)

Equal to −1

d)

Equal to 1

22.

Does the expression B take an integer value at x = −2?

a)

No, because B is always positive

b)

Yes, because the numerator is zero

c)

No, because the denominator is zero

d)

Yes, because 1/(x+1) = −1

23.

Consider the two monomials A = $3x^3yz$ and B = $−7y^3zx$ . Which statement is correct?

a)

Same degree 4 but cannot be added

b)

Cannot be added because of different variables

c)

Degree of A is 5

d)

Same form because they have 3 variables

24.

The degree of the monomial A = $3x^3yz$ is how much?

a)

4

b)

5

c)

6

d)

3

25.

Do the monomials A = $3x^3yz$ and B = $−7y^3zx$ have the same form?

a)

Yes, because they have the same degree of 5

b)

No, because the coefficients are different

c)

Yes, they have the same variables x, y, z

d)

No, because they contain different variables

26.

Let the expression M = $\frac{x^2+3}{x-2}$ − $\frac{3x}{x-2}$ + $\frac{x-1}{2-x}$ . What is the simplified form of M?

a)

2x − 1

b)

x + 2

c)

x − 2

d)

2 − x

27.

The conditions for the expression M = $(x^2+3)/(x−2)$ − $3x/(x−2)$ + $(x−1)/(2−x)$ are what?

a)

x is not equal to 2

b)

x is not equal to 1

c)

x is not equal to −2

d)

x is not equal to 0

28.

What is the value of M at x = 2025?

a)

2023

b)

0

c)

−2023

d)

2

29.

If M = 4, what is the value of x?

a)

−6

b)

6

c)

−4

d)

4

30.

Analyze the polynomial $x^2 - 6x + 9 - y^2$ into factors how?

a)

Split into a cubic polynomial

b)

Use the identity of the sum of squares

c)

Group terms and then use the difference of squares

d)

Cannot be factored further

31.

Analyze the polynomial $x^2 - 6x + 9 - y^2$ into factors.

a)

(x − y − 3)(x + y − 3)

b)

(x − y + 3)(x + y + 3)

c)

(x − y + 1)(x + y − 9)

d)

(x − y − 9)(x + y − 1)

32.

The value of $x^2 - 6x + 9 - y^2$ at x = 3, y = 3 is how much?

a)

18

b)

−9

c)

0

d)

9

33.

A regular triangular pyramid has a base edge of 10 cm and a height of 12 cm. What is the area of the base of the pyramid?

a)

25.0 cm²

b)

86.6 cm²

c)

43.3 cm²

d)

50.0 cm²

34.

With the given data, the height of an equilateral triangle with a side length of 10 cm is approximately how much?

a)

4.33 cm

b)

5.00 cm

c)

8.66 cm

d)

10.00 cm

35.

The pyramid above has a total surface area of approximately how much? (Knowing that the lateral edge is equal to the slant height of the isosceles triangle formed from the foot of the height)

a)

219.01 cm²

b)

130.00 cm²

c)

173.21 cm²

d)

86.60 cm²

36.

The volume of a triangular pyramid with a base edge of 10 cm and a height of 12 cm is how much?

a)

120.00 cm³

b)

219.01 cm³

c)

86.60 cm³

d)

173.21 cm³

37.

Let B = x^2 − y^2 − 2x − 2y. Factor B.

a)

(x − y + 2)(x + y − 2)

b)

(x − y)(x + y − 2)

c)

(x + y)(x − y − 2)

d)

(x − y − 2)(x + y + 2)

38.

What is the value of B at x = 2, y = −2?

a)

8

b)

−8

c)

4

d)

0

39.

At x = y = −1, B + $2y^2$ + 5 takes what value?

a)

Minimum value

b)

Maximum value

c)

Undefined

d)

Equal to 0

40.

A large square is divided into 4 parts: a small square with side x, a large square with side y (striped), and two rectangles with sides x and y. What is the total area?

a)

$(x + y)^2 - 2xy$

b)

$(x − y)^2 + 2xy$

c)

$x^2 + y^2 - 2xy$

d)

$x^2 + y^2 + 2xy$

41.

In the drawing, a large square with side length y consists of several parts: a small square with side length x that is striped, two rectangles with dimensions x×y that are not shaded, and the remaining area. What is the total area of the first three parts?

a)

$x^2 + xy + y^2$

b)

$x^2 + xy + 2y^2$

c)

$x^2 + 2xy + y^2$

d)

$2x^2 + xy + y^2$

42.

With x = 2 and y = 3, what is the total area of the small square and two rectangles of size x×y in square units?

a)

11 units

b)

12 units

c)

14 units

d)

13 units

43.

Let the polynomial A = $n^3 - 5n^2 + 4n$ . Which of the following values is correct regarding the divisibility of A?

a)

Divisible by 120

b)

Not divisible by 5

c)

Always divisible by 3

d)

Not divisible by 6

44.

Let A = $n^3 - 5n^2 + 4n$ = $n(n−1)(n−4)$ . Which conclusion is correct?

a)

A is always divisible by 3 for all n

b)

A is always divisible by 5 for all n

c)

A is always divisible by 6 for all n

d)

A is divisible by 6 for all integer n

45.

What is the condition for the expression B = $2/(x^2 − 5x − 6)$ + $(x − 1)/(x + 1)$ to be defined?

a)

x ≠ −1; x ≠ 6

b)

x ≠ 1; x ≠ −6

c)

x ≠ ±1; x ≠ 6

d)

x ≠ ±6; x ≠ 1

46.

Simplify B = $\frac{2}{x^2 - 5x - 6}$ + $\frac{x - 1}{x + 1}$ . What is the correct result?

a)

B = 1/(x − 6)

b)

B = 2/(x + 6)

c)

B = 2/(x − 6)

d)

B = (x + 1)/(x − 6)

47.

With x = 4, the value of B = $\frac{2}{x^2 - 5x - 6} + \frac{x - 1}{x + 1}$ is how much?

a)

−2/3

b)

2/3

c)

1/3

d)

−1/3

48.

To have B = 1/3 as above, what value of x satisfies this?

a)

x = 0 or x = 7

b)

x = 3 or x = 9

c)

x = 1 or x = 6

d)

x = −1 or x = 8

49.

A rectangular garden has a length of $2y^2 + 12 + xy$ (m) and a width of $2xy$ (m). What is the area of the garden in terms of x and y?

a)

$2y^2 + 12 + xy + 2xy$

b)

$2y^2·2xy + 12·xy$

c)

$(2y^2 + xy) + (12 + 2xy)$

d)

$(2y^2 + 12 + xy)(2xy)$

50.

Let the expression S = $4axy^3 + 24xy + 2ax^2y^2$ . Which of the following statements is true about the area of the garden represented by S (m^2)?

a)

$4axy^2 + 24xy + 2ax^2y^2$

b)

$4axy^3 + 24xy + 2ax^2y^2$

c)

$4axy^3 + 24x^2y + 2axy^2$

d)

$4axy^3 + 24xy^2 + 2ax^2y$

51.

If y = 2, then the value of S in the expression $S = 56x + 8x^2$ (m^2) is which statement correct?

a)

$56x^2 + 8x$

b)

$28x + 8x^2$

c)

$56x + 16x^2$

d)

$56x + 8x^2$

52.

If the area is 88 m^2 and y = 2, which statement is true about the equation relating $8x^2 + 56x - 88 = 0$ ?

a)

The equation $8x^2 + 56x - 88 = 0$ is correct

b)

$8x^2 + 56x - 88 = 0$ is incorrect

c)

The equation $8x^2 − 56x − 88 = 0$ is correct

d)

The equation $8x^2 + 56x + 88 = 0$ is correct

53.

Which positive integer value of x satisfies $8x^2 + 56x - 88 = 0$ is x = 2?

a)

Always false for all x

b)

True for x = 3

c)

True for x = 1

d)

True for x = 2

54.

A truck team plans to use x trucks of the same type to transport 120 tons of goods from A to B. At the start, they added 5 more trucks, with each truck carrying the same amount. Which statement is correct about the amount of goods each truck is supposed to carry as planned?

a)

120/x tons

b)

120/(x+5) tons

c)

x/120 tons

d)

120/(x−5) tons

55.

With the situation of adding 5 more trucks, what is the actual amount of goods each truck must carry?

a)

120/(x−5) tons

b)

120/x tons

c)

x/120 tons

d)

120/(x+5) tons

56.

The difference between the intended load and the actual load of each vehicle is which formula?

a)

120/(x+5) − 120/x

b)

120/x + 120/(x+5)

c)

120/(x−5) − 120/x

d)

120/x − 120/(x+5)

57.

If there are actually 10 vehicles, which statement is true about the difference between the intended load and the actual load of each vehicle being 5 tons?

a)

Affirmation is correct

b)

Affirmation is incorrect

c)

Incorrect when x = 15

d)

Correct when x = 5

58.

Which statement is true about the identity related to the square of the sum: $(-A - B)^2 = (A + B)^2$ ?

a)

True because the square removes the negative sign

b)

False because the negative sign affects the result

c)

True only when A and B are positive

d)

False only when A and B are negative

59.

What is the expression $(x + 2y)^2 - (x - 2y)^2$ ? Which statement is correct about the simplified result?

a)

Equal to $x^2 + 4y^2$

b)

Equal to 8xy

c)

Equal to 4xy

d)

Equal to $x^2 - 2xy + 4y^2$

60.

Identify the correct statement about a monomial that does not contain a variable.

a)

Cannot be a constant

b)

Can be a constant or a variable

c)

Is always any constant

d)

Is always a non-zero constant

61.

Which statement is correct about the number 0 in the context of monomials?

a)

0 is not a monomial

b)

0 is a monomial with a coefficient of 1

c)

0 is a valid monomial

d)

0 is a monomial of degree 1

62.

For the monomial $0x^2y^3$ . Which statement is correct?

a)

Is a monomial of degree 3

b)

Is not a monomial

c)

Is a monomial equal to 0

d)

Is a monomial of degree 5

63.

In the regular triangular pyramid I.ABC, which statement is correct?

a)

Face ABC is the base

b)

Face ABC is a lateral face

c)

IO is the height of the base

d)

Triangle ABC is right-angled at B

64.

In the regular triangular pyramid I.ABC, the most accurate statement about IO is.

a)

IO is the inscribed circle

b)

IO is the height of the pyramid

c)

IO is the median of the base

d)

IO is a lateral edge of the pyramid

65.

In the drawing, the length of the base edge AC is marked as 15 cm. Which conclusion is reasonable?

a)

The height of the pyramid is 15 cm

b)

The radius of the circle is 15 cm

c)

The perimeter of the base is 15 cm

d)

Edge AC is 15 cm long

66.

Consider the fraction x/(x+1). Which statement is correct about the domain?

a)

Defined only when x>0

b)

Not defined when x=1

c)

Not defined when x=−1

d)

Defined for all x

67.

With the fraction x/(x+1), what is the denominator?

a)

x

b)

x+1

c)

1−x

d)

x−1

68.

The value of the fraction x/(x+1) at x=0 is how much?

a)

−1

b)

1

c)

0

d)

Undefined

69.

Choose the monomial E= $−5xy^0$ . Which statement is correct?

a)

E has a variable of 0 and a negative coefficient

b)

The variable part is $xy^0$

c)

The degree of E is 1

d)

The coefficient of E is 5

70.

Consider the expression $(2x+\frac{1}{2})^3$ . Which statement is reasonable about the term containing $x^3$ when expanded?

a)

No x^3 appears

b)

The coefficient is 8

c)

The coefficient is 6

d)

The coefficient is 12

71.

What is the expression A(x) = $8x^3 + 3x^2 + \frac{1}{2} x + \frac{1}{8}$ ? When expanded, what do we get?

a)

$8x^3 + 3x^2 + \frac{1}{2} + \frac{x}{8}$

b)

$8x^3 + 3x^2 + \frac{1}{2} x + \frac{1}{8}$

c)

$8x^3 + 3x + \frac{1}{2} x^2 + \frac{1}{8}$

d)

$8x^2 + 3x^3 + \frac{1}{2} x + \frac{1}{8}$

72.

With x = $\frac{1}{2}$ , what is the value of A(x) = 8x^3 + 3x^2 + $\frac{1}{2}$ x + $\frac{1}{8}$ ?

a)

5/2

b)

3

c)

7/3

d)

8/3

73.

Find x so that A(x) = $8x^3 + 3x^2 + \frac{1}{2} x + \frac{1}{8}$ equals 0.

a)

x = 0

b)

x = −1

c)

x = 1/2

d)

x = −1/2

74.

Find x so that A(x) = $8x^3 + 3x^2 + \frac{1}{2} x + \frac{1}{8}$ equals 27.

a)

x = 5/4

b)

x = 1

c)

x = 3/2

d)

x = 2

75.

Let M = $\frac{x}{2−x} + \frac{−2}{x+2} − \frac{x^3}{4−x^2}$ . What are the conditions for M to be defined?

a)

x ≠ ±2

b)

x ≠ 2

c)

x ≠ −2

d)

x ≠ 0

76.

Simplify M = $x/(2−x) + (−2)/(x+2) − x^3/(4−x^2)$ . What is the result?

a)

M = 2x + 1

b)

M = 1 − x

c)

M = x − 1

d)

M = x + 1

77.

Calculate the value of M when x = 2025.

a)

M = 2024

b)

M = 2026

c)

M = 0

d)

M = −2024

78.

Calculate the value of x so that M = 3.

a)

x = 2

b)

x = 3

c)

x = 1

d)

x = 0

79.

Which statement is true about a monomial?

a)

A monomial must have a variable

b)

An integer is also a monomial

c)

Only positive numbers are monomials

d)

All integers are not monomials

80.

Select the incorrect statement about monomials.

a)

The degree of the monomial $4x^2y^3$ is 5

b)

The sum of two monomials is a monomial

c)

−7 is a monomial of degree 0

d)

A monomial has a coefficient that is a real number

81.

A cube-shaped block of wood with a side length of x (cm). A smaller cube with a side length of 12 cm is removed from a corner. What is the initial volume of the block of wood?

a)

3x^3 (cm^3)

b)

x^2 (cm^3)

c)

x^3 (cm^3)

d)

12x (cm^3)

82.

What is the volume of the small cube that has been cut out?

a)

12 cm^3

b)

1728 cm^3

c)

144 cm^3

d)

$12^2$ cm^3

83.

After removing a small cube with a side length of 12 cm, what is the volume of the remaining part?

a)

$x^2$ − 1728 (cm^3)

b)

1728 − $x^3$ (cm^3)

c)

$x^3$ + 1728 (cm^3)

d)

x^3 − 1728 (cm^3)

84.

What is the correct simplified result of the expression $2x^2 + 3x^2$ ?

a)

$5x^2$

b)

$6x^2 - x$

c)

$x^2$

d)

$4x + x^2$

85.

The expression 4x + x^2 can be simplified to which form?

a)

x + 4

b)

$6x^2 - x$

c)

$5x^2$

d)

x(4 + x)

86.

Simplify $3x^2 - 2x + 5 - x^2 + 4x - 2$ to which result?

a)

$2x^2 - x + 3$

b)

$2x^2 + x + 3$

c)

$2x^2 + 2x + 3$

d)

$6x^2 - x$

87.

Simplify $2x^2 + 3x^2 - x + x^2$ to which result?

a)

$5x^2 - x$

b)

$6x^2 + x$

c)

$5x^2 + x$

d)

$6x^2 - x$

88.

The fraction $\frac{x^2 - 9}{x + 3}$ can be simplified to which result, under appropriate conditions?

a)

x − 3, with x ≠ −3

b)

x + 3, with x ≠ 3

c)

x − 3, with x = −3

d)

x + 3, with x ≠ −3

89.

The value of the fraction $\frac{x^2 - 9}{x + 3}$ when x = −2 is how much?

a)

−1

b)

−5

c)

5

d)

1

90.

A rectangular board has a length of $x + 43$ cm and a width of $x + 30$ cm. Squares with a side length of $y^2 + 1$ cm are cut from each corner, and then it is folded into a box without a lid. What is the length of the box after folding?

a)

x − 2y^2 + 28 cm

b)

x − 2y^2 + 41 cm

c)

x + 43 − 2( $y^2 + 1$ ) cm

d)

x + 30 − 2(katex latex=$y^2 + 1$) cm

91.

For the open-top box, what is the width of the box after folding?

a)

x − 2y^2 + 28 cm

b)

x − 2y^2 + 41 cm

c)

x + 30 − 2(katex latex=$y^2 + 1$) cm

d)

x + 43 − 2( $y^2 + 1$ ) cm

92.

The volume of the remaining wood V of the block after carving a cube with a side length of 12 cm from a cube with a side length of x cm is given by which formula?

a)

V = $x^2$ − 1728 cm^3

b)

V = (x − 12)^3 cm^3

c)

V = $x^3$ + 1728 cm^3

d)

V = $x^3$ − 1728 cm^3

93.

The lateral area of a rectangular box in terms of x and y is 4xy^2 − 8y^4 + 130y^2 + 4x + 138 (cm^2). Which value is correct when x = 2, y = 1?

a)

276 cm^2

b)

68 cm^2

c)

264 $cm^2$

d)

270 cm^2

94.

Let x = 16, y = 4. What is the surface area of the rectangular box above in $cm^2$ ?

a)

1294 cm^2

b)

1282 cm^2

c)

1258 cm^2

d)

1310 cm^2

95.

A regular quadrilateral pyramid has a height of 14 cm, and its base is a square with a side length of 15 cm. Which statement is correct?

a)

The volume of the pyramid is 1,000 cm^3

b)

The lateral surface area of the pyramid is 476.4 cm^2

c)

The area of the base of the pyramid is 250 cm^2

d)

The slant height of the pyramid is 17.56 cm

96.

With a regular quadrilateral pyramid having a height of 14 cm and a base edge of 15 cm, what is the exact volume?

a)

1,050 cm^3

b)

1,125 cm^3

c)

1,000 cm^3

d)

750 cm^3

97.

The height of the pyramid above has the length of the lateral edge (measured from the apex to the apex of the base edge). What is the approximate value?

a)

17.56 cm

b)

19.00 cm

c)

17.32 cm

d)

18.03 cm

98.

Calculate the lateral surface area of a regular quadrilateral pyramid: base edge 15 cm, height 14 cm. Choose the closest approximation.

a)

500.0 $cm^2$

b)

525.6 cm^2

c)

476.4 cm^2

d)

450.0 $cm^2$

99.

Let y be the number of months borrowed, x be the amount paid each month. Which formula is suitable for the total principal and interest each month?

a)

x = 1600·y + r/12

b)

x = 1600/y + r/1600

c)

x = 1600/y + 1600·r/12

d)

x = 1600/y − 1600·r

100.

From the formula x = 1600/y + 1600·r/12, what is r in terms of x and y?

a)

r = 3(xy − 1600)/(400y)

b)

r = 3(1600 − xy)/400y

c)

r = (xy − 1600)/1200

d)

r = 12(x − 1600/y)/1600

101.

If each month you pay 20 million VND for 10 years, what is the approximate annual interest rate?

a)

4.0%

b)

5.5%

c)

4.5%

d)

5.0%

102.

A trapezoidal wall with a rectangular window. If the height is 3 m, the larger base is 8 m, the smaller base is 5 m, what is the area of the wall (excluding the window) when the window is 2 m × 1.5 m?

a)

19.5 m^2

b)

21.0 m^2

c)

22.5 m^2

d)

24.0 m^2

103.

A trapezoidal wall has a larger base of 8x, a smaller base of 4x, and a height of h. There is a rectangular window of 2x × 2h in the middle. What is the area of the wall (not subtracting the window)?

a)

6xh

b)

12xh

c)

8xh

d)

10xh

104.

With the wall above, what is the ratio of the area of the window to the total area of the wall (not subtracting the window)?

a)

2x/h

b)

h/(3x)

c)

x/h

d)

x/(3h)

105.

Assuming h = 2x. What portion of the entire wall (not excluding the window) does the area of the window occupy?

a)

2/3

b)

1/3

c)

1/2

d)

1/4

106.

If x = 3 m and h = 5 m, what is the actual area of the wall (after subtracting the window) in square meters?

a)

78

b)

72

c)

60

d)

90

107.

Let M = $\frac{x+3}{x-2}$ + $\frac{x-3}{x+2}$ − $\frac{2x^2 + 3x + 6}{x^2} \cdot \frac{1}{4}$ . What are the conditions for the expression M to be defined?

a)

x ≠ ±2

b)

x ≠ 0

c)

x ∈ ℝ

d)

x ≥ 0

108.

Simplify the expression M above. What is the correct result?

a)

3/(x+2)

b)

(x+3)/(x−2)

c)

(x−3)/(x+2)

d)

(x+2)/3

109.

What is the value of M when x = 3?

a)

1

b)

3/5

c)

5/3

d)

2/5

110.

For the integer values x belonging to {−1, 1, −3, −5}, which statement is true about the integrality of M?

a)

M is always equal to 0

b)

M is always negative

c)

M is always a fraction

d)

M takes integer values

111.

A large square has a side length of x + 5 (cm). Inside it, there is a smaller square with a side length of x − 2 (cm). What is the area of the remaining part of the large square?

a)

$(x+5)^2 + (x−2)^2$

b)

$(x+5)^2 − (x−2)^2$

c)

2(x+5)(x−2)

d)

$(x−2)^2 − (x+5)^2$

112.

Simplify the expression for the area of the remaining part above. What is the correct result?

a)

$(x+5−x+2)^2$

b)

7(2x+3)

c)

$(x+5)^2$

d)

$(x+5+x−2)^2$

113.

Let the fraction A = $\frac{x^2 + 4x + 4}{x - 2}$ . What is the condition for A to be defined?

a)

x ≠ 4

b)

x ≠ 0

c)

x ≠ 2

d)

x ≠ −2

114.

Let A = $\frac{x^2 + 4x + 4}{x - 2}$ . What is the value of A when x = 4?

a)

8

b)

20

c)

16

d)

12

115.

Let B = $\frac{x + 2}{3}$ and A = $\frac{x^2 + 4x + 4}{x - 2}$ . Calculate C = A : B.

a)

(x − 2)/(3(x + 2))

b)

(x + 2)/3 + (x − 2)

c)

3(x − 2)/(x + 2)

d)

(x + 2)/(3(x − 2))

116.

The fraction C = (x + 2)/(3(x − 2)) equals 1 when?

a)

x = 4

b)

x = −4

c)

x = 2

d)

x = 1

117.

In the morning, $8x^3y + 5x^6y^5 - 3x^5y^4$ was sold; in the afternoon, $x^6y^5 - x^5y^4$ was sold. What is the expression for the total amount of rice sold in the day?

a)

$7x^6y^5 - 4x^5y^4 + 8x^3y$

b)

$9x^6y^5 - 2x^5y^4 + 8x^3y$

c)

$6x^6y^5 - 4x^5y^4 + 8x^3y$

d)

$8x^6y^5 - 3x^5y^4 + 8x^3y$

118.

With x = 1, y = 2, what is the total amount of rice sold in a day?

a)

152

b)

160

c)

128

d)

144

119.

With x = 1, y = 2, how many bags of rice were sold in the afternoon?

a)

24

b)

28

c)

32

d)

36

120.

With x = 1, y = 2, what is the ratio of the number of morning sessions to the total number?

a)

1/2

b)

5/8

c)

2/3

d)

3/4

121.

A school plans to plant 100 green trees with x members, each person planting equally. How many trees is each member expected to plant?

a)

(x + 2)/100

b)

100x

c)

x/100

d)

100/x

122.

When starting to implement, add 2 more members. If still planting a total of 100 trees and dividing evenly, what is the new formula for the number of trees per person?

a)

(100 + 2)/x

b)

100/(x − 2)

c)

x/(100 + 2)

d)

100/(x + 2)

123.

What is the expression A = $6/(x^2 + 6x) + 1/(x + 6) + 5/x$ . What are the conditions for A to be defined?

a)

x ≠ 0 and x ≠ 6

b)

x ≠ 0 and x ≠ −6

c)

x ≠ −6 and x ≠ 6

d)

x ≠ 0 and x ≠ −3

124.

Simplify the expression A = $6/(x^2 + 6x) + 1/(x + 6) + 5/x$ by finding a common denominator, what result do we get?

a)

A = 1/x

b)

A = (x+5)/x

c)

A = 6/x

d)

A = 5/x

125.

Calculate the value of A when x = 2 with A = $6/(x^2 + 6x) + 1/(x + 6) + 5/x$ .

a)

A = 11/6

b)

A = 5/2

c)

A = 3

d)

A = 7/3

126.

With x = −3, the expression A = $6/(x^2 + 6x) + 1/(x + 6) + 5/x$ takes what value?

a)

Equal to 0

b)

Positive value

c)

Negative value

d)

Undefined

127.

Which of the following statements is false about a monomial?

a)

The degree of a monomial is the sum of the exponents

b)

The coefficient can be a fraction

c)

3x^2y + 5 is a monomial

d)

$\frac{5}{7}$ a^b is a monomial

128.

For the regular triangular pyramid S.ABC, AC = 6 cm, SH = 9 cm. What is the base of the pyramid?

a)

Triangle SBC

b)

Triangle ABC

c)

Triangle SAB

d)

Square ABCD

129.

In the pyramid S.ABC, point H is the perpendicular projection of S onto the base plane. Which statement is correct?

a)

SH is the height of the pyramid

b)

SA is the height of the pyramid

c)

SC is the height of the pyramid

d)

BC is the height of the pyramid

130.

With AC = 6 cm in equilateral triangle ABC, what is the length of side BC?

a)

BC = 9 cm

b)

BC = 3 cm

c)

BC = 6 cm

d)

BC = 12 cm

131.

In the regular triangular pyramid S.ABC, if SH = 9 cm, can the lengths of SA, SB, and SC be equal?

a)

SA = SB = SC are always different

b)

SA = SB = SC are not necessarily equal

c)

SA = SB = SC is 6 cm

d)

SA = SB = SC is 9 cm

132.

A tank contains x liters of water, and a tap drains at a rate of x/t liters/hour. Which statement is correct?

a)

x/t does not depend on t (time)

b)

x/t is an integer for all x, t

c)

x/t is always defined for any t

d)

x/t is an algebraic fraction when t is not 0

133.

The expression x/t is undefined when?

a)

when x is equal to 0

b)

when x is less than t

c)

when t is greater than 1

d)

when t is equal to 0

134.

Every hour, the faucet flows 40 liters, and after 4 hours, the water in the tank runs out. How much water was initially in the tank?

a)

100 liters of water

b)

160 liters of water

c)

140 liters of water

d)

120 liters of water

135.

Given the polynomial P = $5x^3 + 2x^2 - 5x^3 + x^2 + 3 - 3x^2$ . What is the degree of the polynomial P after simplification?

a)

degree 3 because $x^3$ remains

b)

degree 2 because $x^2$ remains

c)

degree 0 (constant)

d)

degree 1 because x remains

136.

What is the value of P(x) for all x after simplification?

a)

P(x) = 3

b)

$P(x) = x^2 + 3$

c)

P(x) = 0

d)

$P(x) = 3 - x^2$

137.

In the regular pyramid in the figure, which statement is correct about the height?

a)

MN is the height of the pyramid

b)

SQ is the height of the pyramid

c)

SA is the height of the pyramid

d)

SH is the height of the pyramid

138.

Let the polynomial R(x) = $x^2 - 2x + 1$ . Which statement is correct?

a)

R is a polynomial of degree 1

b)

R has degree 2

c)

R equals 0 when x = 1

d)

R simplifies to $x^2 + 1$

139.

The value of R(1) with R(x) = $x^2 - 2x + 1$ is how much?

a)

R(1) = −1

b)

R(1) = 2

c)

R(1) = 1

d)

R(1) = 0

140.

For the fraction $\frac{2x^2 - 8}{4x - 8}$ . What is the correct simplified value with x not equal to 2?

a)

(x − 4)/2

b)

(x − 2)/2

c)

(x − 2)/4

d)

(x + 2)/2

141.

Let the fraction A = $(x^2 − 4) / (2x − 4)$ . Which statement is correct about the domain of A?

a)

All real x are defined

b)

x ≠ 2 is defined

c)

x ≠ −2 is defined

d)

x ≠ 2 and x ≠ −2

142.

Simplify the fraction A = $(x^2 − 4) / (2x − 4)$ . What is the result?

a)

(x + 2) / (x − 2)

b)

(x − 2) / (x + 2)

c)

(x + 2) / 2

d)

(x − 2) / 2

143.

The value of the fraction A = $(x^2 − 4) / (2x − 4)$ at x = 0 is how much?

a)

1

b)

−1

c)

−2

d)

2

144.

A family travels 100 km in the residential area at a speed of x km/h and 240 km on the highway at a speed of 1.5x km/h. What is the expression for the total travel time?

a)

(100 + 240)/x

b)

100/(1.5x) + 240/x

c)

100/x + 240/x

d)

100/x + 240/(1.5x)

145.

In the above situation, how many hours is the travel time in the residential area?

a)

100/x

b)

240/x

c)

100/(1,5x)

d)

240/(1,5x)

146.

If x = 40 km/h is the speed in residential areas, what is the total travel time in hours?

a)

6.5 hours

b)

7.0 hours

c)

6.0 hours

d)

5.5 hours

147.

The speed on the highway is 50% greater than that on regular roads. If the speed on regular roads is x km/h, what is the speed on the highway?

a)

2x km/h

b)

x/1.5 km/h

c)

1.5x km/h

d)

0.5x km/h

148.

Simplify P = $(x^2 − 4) / [(x − 3)(x − 2)]$ . Which result is correct?

a)

(x + 2) / (x − 2)

b)

(x − 2) / (x − 3)

c)

(x − 3) / (x + 2)

d)

(x + 2) / (x − 3)

149.

The value of P = $(x^2 − 4) / [(x − 3)(x − 2)]$ at x = 4 is how much?

a)

8

b)

2

c)

6

d)

4

150.

A regular quadrilateral pyramid has a base edge of 120 cm, a height of 68.4 cm, and a slant height from the apex of 91 cm. Which statement is correct?

a)

The total surface area is 36240 cm²

b)

The base area is 140000 cm²

c)

Half the perimeter of the base is 21840 cm

d)

The volume of the pyramid is 328320 cm³

Page 1

Total questions: 150

Worksheet time: 1hrs 15mins

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