Free Printable Bài kiểm tra Toán học

1.

Question 1: Simplify the polynomial $2x^2y - 4y^5 + 5x^4y - 7y^5 + x^3y^2 - 2x^2y$ to get:

a)

A. $5x^4y + 11y^5 + x^3y^2$ .

b)

B. $9x^4y - 11y^5 + x^3y^2.$

c)

C. $-5x^4y - 11y^5 + x^3y^2$ .

d)

D. $5x^4y - 11y^5 + x^3y^2$ .

2.

Question 2: The value of the polynomial $xy−2x2y2+x4yxy-2x^2y^2-x^4yxy+2x2y2−x4y$ at x = y = -1 is:

a)

A. 3.

b)

B. 1.

c)

C. 4.

d)

D. 0.

3.

Question 3: The quotient of the division $\frac{1}{9}x^3y^3 : (-3xy)^2$ is:

a)

A. $\frac{1}{81}$ .

b)

B. $-\frac{1}{81}$ .

c)

C. $-\frac{1}{81}xy.$

d)

D. $\frac{1}{81}xy$ .

4.

Question 4: The result of the product (2x + y)(2x - y) is:

a)

A. 4x - y.

b)

B. 4x + y.

c)

C. $4x^2 - y^2$ .

d)

D. $4x^2 + y^2$ .

5.

Question 5: Simplify the expression $(a + b)^2 - (a - b)^2$ to find the result:

a)

A. 4ab.

b)

B. -4ab.

c)

C. 0.

d)

D. $2b^2$ .

6.

Question 6: Given $B=(x^2+3)^2−x^2(x^2+3)−3(x+1)(x−1).$ Choose the correct statement.

a)

A. B < 12.

b)

B. B > 13.

c)

C. 12 < B < 14.

d)

D. 11 < B < 13.

7.

Question 7: Given xy² + 10x²y² - 15x³y = M.(5xy) What is the polynomial M?

a)

A. $y + 2xy - 3x^2.$

b)

B. $\frac{1}{5}y + 2xy - 3x^2$ .

c)

C. $-y + 2x^2y + 3x^2.$

d)

D. $5y + 2xy - 3x^2$ .

8.

Question 8: Perform the calculation $(5x^5y + 8x^3y^2) : 4x^2y$ :

a)

A. $x^3y + 4y^2$ .

b)

B. $\frac{5}{4}x^3y+2xy^{ }$ .

c)

C. $\frac{5}{4}x^4y^4 + 2xy^2$ .

d)

D. $13x^4y^3$ .

9.

Question 9: Ms. Hoa has x longan trees. The number of mango trees is 8 times the number of longan trees. The number of orange trees is y (trees) more than the number of mango trees. Write a polynomial (in simplified form) to calculate the total number of longan, mango, and orange trees in Ms. Hoa's garden.

a)

A. x + 2y.

b)

B. 2x + y.

c)

C. x + y.

d)

D. 9x + y.

10.

Question 10. Find x such that x³ + 3x² + 3x + 1 = 0.

a)

x = -1

b)

x = 1

c)

x = -2

d)

x = 0

11.

Question 11. What is the value of the expression Q = a² + b² given that a + b = 5 and ab = -3.

a)

Q = 25

b)

Q = 31

c)

Q = 16

d)

Q = -31

12.

Question 12. Given 3x² − xy + y² − M = x² + 2xy − 5y². The polynomial M in the given form is:

a)

2x² − xy + 4y².

b)

2x² + 3xy − 6y².

c)

2x² − 3xy − 6y².

d)

2x² − 3xy + 6y².

13.

Question 13. The polynomial 9x³ − 6x²y + 7x²y² + 7x²y² is divisible by which of the following monomials?

a)

9x³y.

b)

6x².

c)

7x³y².

d)

3xy².

14.

Question 14. Simplify (9x³y² − 6x²y³) ÷ (−3xy²) + (6x²y + 2x²) ÷ 2x² to find the polynomial degree:

a)

1.

b)

3.

c)

4.

d)

2.

15.

Question 15. Expanding the expression (x − 2y)³ gives:

a)

x³ − 3xy + 3x²y² + y³.

b)

x³ − 6x²y + 12xy² − 4y³.

c)

x³ − 6x²y + 12xy² − 8y³.

d)

x³ − 3x²y + 12xy² − 8y³.

16.

Question 16. Write the expression (x − 3y)(x² + 3xy + 9y²) in the form of the difference of two cubes:

a)

x³ + (3y)³.

b)

x³ + (9y)³.

c)

x³ − (3y)³.

d)

x³ − (9y)³.

17.

Question 17. Write the expression (x² + 3)(x² − 3) in the form of a sum:

a)

(x²)³ − 3³.

b)

(x²)³ + 3³.

c)

(x²)³ + 9³.

d)

(x²)³ − 9³.

18.

Question 18. Choose the correct form from the following options: (x − 3y)(x² + 3y + 9) = y² − 27.

a)

(a² − ab + b²)(a + b) = a² + b².

b)

(a² − ab + b²)(a + b) = a² − b².

c)

(b − 3y)(x² + 3y + 9) = 27 − y².

d)

(a² − ab + b²)(a + b) = a³ + b³.

19.

Question 19. Given x³ + 125 = (x + 5)(x² − x + 25). Choose the appropriate option to fill in the blank:

a)

5x.

b)

5x.

c)

10x.

d)

−10x.

20.

Question 20. The expansion of x³ − 27 is:

a)

(x − 3)(x² − 3x + 9).

b)

(x − 3)(x² + 3x + 9).

c)

(x − 3)(x² + 6x + 9).

d)

(x − 3)(x² − 6x + 9).

21.

Question 21. With x = −20, the value of the expression P = (x + 4)(x² − 4x + 16) − (64 − x³) is:

a)

16000.

b)

40.

c)

−16000.

d)

−40.

22.

Question 22. Analyzing the polynomial x³ + 4x² + 4x into factors gives us the result:

a)

x(x + 4)².

b)

2x(x + 2)².

c)

x(x + 2)².

d)

x(2x + 1)².

23.

Question 23. Factor the polynomial 2x − 4 + 5x² − 10x to get:

a)

(x − 2)(5x − 2).

b)

(x − 2)(5x + 2).

c)

(x − 2)(2 − 5x).

d)

(x + 2)(5x − 2).

24.

Question 23. Given a quadrilateral ABCD with A = 58°, B = 65°, C = 102°. What is the measure of angle D?

a)

122°

b)

78°

c)

135°

d)

115°

25.

Question 25. Given a right triangle ABC with a right angle at A, where BC = 15cm and AC = 12cm. What is the length of the line segment AB?

a)

4cm

b)

27cm

c)

81cm

d)

9cm

26.

Question 26. Given an isosceles right triangle MNP at M. Calculate the length of NP, knowing that MN = MP = 3dm.

a)

6dm

b)

18dm

c)

√18dm

d)

3dm

27.

Question 27. Given an isosceles trapezoid ABCD (AB//CD) with A = 70°. Which of the following statements is correct?

a)

C = 110°

b)

B = 110°

c)

C = 70°

d)

D = 70°

28.

Question 28. Given an isosceles trapezoid ABCD (AB//CD) with B= 90°. Which of the following statements is correct?

a)

A = 30°

b)

A = 150°

c)

C = 90°

d)

C = 150°

29.

Question 29. Given triangle ABC is right-angled at A. Let M, N, P be the midpoints of AB, BC, CA respectively. What condition does triangle ABC need to satisfy for rectangle AMNP to be a square?

a)

AB = 1/2 AC

b)

AB = AC

c)

AC = 1/2 AB

d)

B = 60°

30.

Question 30. Given trapezoid ABCD with AB//CD, the diagonals AC and BD intersect at O such that OA = OB, OC = OD. Find the false statement among the following statements?

a)

AC = BD

b)

BC = AD

c)

ABCD is an isosceles trapezoid

d)

Triangle AOD is isosceles at O

31.

Question 31. Given triangle ABC with three medians AI, BD, CE concurrent at G. Let M and N be the midpoints of GC and GB, respectively. What type of quadrilateral is MNED?

a)

Rectangle.

b)

Parallelogram.

c)

Isosceles trapezoid.

d)

Right trapezoid.

32.

Question 32. Write the ratio of the lengths of the line segments as follows: AB = 4dm, CD = 60cm.

a)

AB/CD = 1/15.

b)

AB/CD = 2/3.

c)

AB/CD = 3/2.

d)

AB/CD = 2/5.

33.

Question 33. Given triangle ABC with AD as the bisector of angle A. Please choose the correct statement.

a)

DC/DB = AC/AB.

b)

AB/AC = DC/DB.

c)

AB/DC = AC/DB.

d)

AD/DB = AC/AD.

34.

Question 34. Given the figure above, knowing that AD is the angle bisector of triangle ABC, please choose the correct statement. Calculate the lengths x and y of the line segments in the figure, knowing that the numbers in the figure are in cm.

a)

x = 12cm; y = 13cm.

b)

x = 14cm; y = 21cm.

c)

x = 14.3cm; y = 10.7cm.

d)

x = 15cm; y = 20cm.

35.

Question 35. The rhombus ABCD as shown in the figure below has BD = 20 cm. What is the length of OB?

a)

OB = 40 cm.

b)

OB = 20 cm.

c)

OB = 5 cm.

d)

OB = 10 cm.

36.

Question 36. The rhombus ABCD as shown in the figure below has angle BAD = 60°. What is the measure of angle BAC?

a)

BAC = 30°.

b)

BAC = 90°.

c)

BAC = 15°.

d)

BAC = 120°.

37.

Question 37. Quadrilateral ABCD is a parallelogram if:

a)

AC = BC.

b)

AB = CD, BC = AD.

c)

AB||CD.

d)

BC = AD.

38.

Question 38. Given the figure. Choose the incorrect statement:

a)

MQ||PN.

b)

I is the midpoint of MP.

c)

MN||PQ.

d)

MNPQ is a rhombus.

39.

Question 39. The parallelogram ABCD has B = 70°. What are the measures of the remaining angles of the parallelogram ABCD?

a)

C = D = 110°; A = 70°.

b)

A = D = 110°; C = 70°.

c)

A = C = 110°; D = 70°.

d)

A = C = D = 70°.

40.

Question 40. Given parallelogram ABCD with AB = 3 cm, AD = 5 cm, ∠BAD = 60°. What are the lengths of side BC and the measure of ∠BCD?

a)

BC = 3 cm and ∠BCD = 60°.

b)

BC = 3 cm and ∠BCD = 120°.

c)

BC = 5 cm and ∠BCD = 60°.

d)

BC = 5 cm and ∠BCD = 120°.

41.

Question 41. Which of the following properties does a rectangle **not** have?

a)

A rectangle has two equal diagonals.

b)

A rectangle has two adjacent sides equal.

c)

A rectangle has four right angles.

d)

A rectangle has two diagonals that bisect each other at the midpoint of each diagonal.

42.

Question 42. An plans to install LED lights to decorate the staircase of his house in the shape of a parallelogram ABCD as shown in the picture. An measured AB = 5 m, AD = 1.2 m, the length of LED light wire An needs to use is:

a)

6.2 m.

b)

12.4 m.

c)

6 m.

d)

10 m.

43.

Question 43. Given a right triangle with a hypotenuse of 12 cm. What is the length of the median corresponding to the hypotenuse of that right triangle?

a)

12 cm.

b)

6 cm.

c)

24 cm.

d)

4 cm.

44.

Question 44. Given the rhombus IKGH as shown in the figure below, with IK = 10 cm; OI = 8 cm. What is the length of KH?

a)

KH = 18 cm.

b)

KH = 2 cm.

c)

KH = 6 cm.

d)

KH = 12 cm.

45.

Question 45. Given the rhombus IKGH as shown in the figure below, with IG = 48 cm; KH = 14 cm. What is the length of IK?

a)

IK = 50 cm.

b)

IK = 48 cm.

c)

IK = 14 cm.

d)

IK = 25 cm.

46.

Question 46. Let ABCD be a rectangle with O as the intersection point of the two diagonals. Choose the incorrect statement.

a)

AC = BD.

b)

AB = CD; BC = AD.

c)

OA = OB.

d)

OC > OD.

47.

Question 47. What is the criterion for the quadrilateral below to be a rhombus?

a)

A quadrilateral with 4 equal sides.

b)

A quadrilateral with two diagonals that are perpendicular.

c)

A quadrilateral with two equal diagonals.

d)

A quadrilateral with two diagonals that bisect each other at their midpoints.

48.

Question 48. The rhombus ABCD has two diagonals AC and BD intersecting at O, with AC = 5 cm and BD = 10 cm. What are the lengths of sides OC and OD respectively?

a)

10 cm and 5 cm.

b)

10 cm and 20 cm.

c)

2.5 cm and 5 cm.

d)

5 cm and 10 cm.

49.

Question 49. Given triangle ABC, let M, N, and P be the midpoints of AB, AC, and BC respectively. Knowing that AB = AC, what shape is quadrilateral ANPM?

a)

square.

b)

rectangle.

c)

rhombus.

d)

parallelogram.

50.

Question 50. The parallelogram MNPQ has ∠M = 90°, MP = NQ. What shape is MNPQ?

a)

isosceles trapezoid.

b)

rectangle.

c)

rhombus.

d)

square.

51.

Question 51. In the rectangle MNPQ, which segment is equal in length to segment MN?

a)

NQ.

b)

NP.

c)

PQ.

d)

QM.

52.

Question 52. The factorization of polynomial $x^2 + 2023x + x$ into factors is

a)

x(x + 2023)

b)

$x(x^2 + 2023x)$

c)

$x(x^2 + 2023x + 1)$

d)

$x(x^{ }+2023+1)$

53.

Question 53. Expression $x^3-3x^2y+3xy^2-y^3$ Write in the following format.?

a)

$(x + y)^3$

b)

$(x - y)^3$

c)

$(x - y)^2$

d)

$(x + y)^2$

54.

Question 54. Cho hình chữ nhật ABCD có AB = 8 cm và AD = 6 cm. Tính chu vi của hình chữ nhật này.

a)

28 cm.

b)

48 cm.

c)

14 cm.

d)

24 cm.

55.

Question 55. Given triangle ABC with AB = 5 cm, AC = 12 cm, and BC = 13 cm. Determine the type of triangle ABC.

a)

tam giác vuông.

b)

tam giác tù.

c)

tam giác đều.

d)

tam giác cân.

56.

Question 56.Given a rhombus PQRS with side length PS = 10 cm and angle P = 60°. Find the area of this rhombus.

a)

25 cm².

b)

100 cm².

c)

50 cm².

d)

75 cm².

57.

Question 57. Find the value of the expression P = x² + 4x + 4 when x = -2.

a)

P = 16

b)

P = 0

c)

P = 4

d)

P = 8

58.

Question 58. Given rectangle ABCD with AB = 8 cm and AD = 5 cm. The area of rectangle ABCD is:

a)

30 cm².

b)

60 cm².

c)

50 cm².

d)

40 cm².

59.

Question 59. Given rectangle EFGH with O as the intersection point of the diagonals. Then, choose the incorrect statement.

a)

EG = FH.

b)

EF = GH; FG = EH.

c)

OE = OF.

d)

OG < OH.

60.

Question 60. Given 4x² + 4xy + y² - N = 0. The polynomial N in the given form is:

a)

0.

b)

−4x² − 4xy − y².

c)

−4x² + 4xy + y².

d)

4x² + 4xy + y².

61.

Question 61: For the polynomial 3x^2 − 5x + 2 − (x^2 − 4x + 1), the value of this polynomial at x = 2 is:

a)

D. 11.

b)

C. 9.

c)

B. 7.

d)

A. 5.

62.

Question 62: Given a rectangle ABCD with AB = 8 cm and AD = 5 cm. Calculate the perimeter of this rectangle.

a)

B. 30 cm.

b)

C. 40 cm.

c)

A. 26 cm.

d)

D. 50 cm.

63.

Question 63: Given triangle ABC with AB = 6 cm, AC = 8 cm, and BC = 10 cm. Calculate the area of this triangle.

a)

D. 48 cm².

b)

A. 24 cm².

c)

B. 30 cm².

d)

C. 36 cm².

Bài kiểm tra Toán học

Total questions: 63

Worksheet time: 27hrs 35mins

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