Free Printable CÂU HỎI TRẮC NGHIỆM TOÁN HỌC LỚP 8 (7,0 điểm)

1.

Which of the following expressions is a monomial?

a)

A) 3x² + 2y

b)

B) 5xy²

c)

C) 4x+y+z

d)

D) x²–y²

2.

What is the degree of the monomial 7a³b²c?

a)

5

b)

6

c)

7

d)

3

3.

Simplify the product of the monomials 4x²y and 3xy³.

a)

12x³y⁴

b)

7x³y⁴

c)

12x²y⁴

d)

12x⁴y³

4.

What is the degree of the polynomial 2x³y² + 4x²y³ – 5x⁴?

a)

A) 7

b)

B) 6

c)

C) 5

d)

D) 4

5.

If P(x,y)=3x²–4xy+y², what is the coefficient of the xy term?

a)

-4

b)

4

c)

3

d)

1

6.

Simplify the polynomial (x+2y)(x–2y).

a)

A. x² + 4y²

b)

B. x² - y²

c)

C. x² + y²

d)

D. x² - 4y²

7.

Which of the following is NOT a polynomial?

a)

A. x² + 2xy² - y

b)

B. x² + 1

c)

C. 1/x + x²

d)

D. 2x + 3

8.

Simplify the expression: (x² - 4x + 4)/(x² - 2x)

a)

(x - 2)/x

b)

(x - 2)/(x + 2)

c)

x/x²

d)

(x + 2)/(x - 2)

9.

Find the product: (2x²y - 3xy²).(x² - y²)

a)

2x⁴y - 2x²y³ - 3x³y² + 3xy⁴

b)

2x⁴y - 3xy² - 2x³y³ + 3xy⁴

c)

2x⁴ - 3xy² - 2x³y² + 3y⁴

d)

2x⁴ + 3x³y² - 2x²y³ + 3xy⁴

10.

Divide the polynomial 6x⁴y–3x³y³+x²y by the monomial x²y:

a)

6x³- 3xy + 1

b)

6x² + 3xy + 1

c)

6x²- 3xy + 1

d)

6x²y- 3x² + 1

11.

Simplify the expression: 2xy² - 3x²y³ - (-4xy)

a)

-24x³y³

b)

-24x³y³

c)

-24x³y³

d)

-24x⁴y⁴

12.

What is the coefficient of x²y³ in the polynomial 7x²y³ –5xy² + 4x³y–9

a)

7

b)

-5

c)

4

d)

-9

13.

Simplify the following algebraic fraction: $\frac{2x^2 - 8}{4x}$

a)

$\frac{x^2 - 4}{2x}$

b)

$\frac{x^2 - 2}{2}$

c)

$\frac{x + 2}{2}$

d)

$\frac{2x - 8}{x}$

14.

Which of the following expressions is equivalent to $\frac{x^2 - 9}{x + 3}$ ?

a)

x+3

b)

x-3

c)

x+9

d)

x-9

15.

Simplify the following complex fraction: $\frac{\frac{1}{x} + \frac{1}{y}}{\frac{1}{x} - \frac{1}{y}}$

a)

$\frac{x-y}{x+y}$

b)

$\frac{y}{x}$

c)

$\frac{x}{y}$

d)

$\frac{x+y}{x-y}$

16.

Analyze the numerator and denominator, then simplify the fraction: $\frac{x^2 - 9}{x^2 + 6x + 9}$

a)

$\frac{x-3}{x+3}$

b)

$\frac{x+3}{x-3}$

c)

$\frac{1}{x+3}$

d)

$\frac{1}{x-3}$

17.

Find the length of the diagonal of a rectangle if the length and width are 8 cm and 6 cm, respectively.

a)

12 cm

b)

14 cm

c)

10 cm

d)

5 cm

18.

Find the least common denominator (LCD) of the fractions: $\frac{1}{x^2 - 4}$ and $\frac{1}{x^2 - 1}$

a)

$x^4 - 5x^2 + 4$

b)

$(x-1)(x+1)(x-2)(x+2)$

c)

$(x-1)(x+1)$

d)

$(x^2-1)(x^2-4)$

19.

What is the length of the hypotenuse of a right triangle with the two legs measuring 6 cm and 8 cm respectively?

a)

10 cm

b)

12 cm

c)

14 cm

d)

16 cm

20.

Which of the following is a Pythagorean triplet?

a)

(9, 12, 16)

b)

(6, 8, 11)

c)

(5, 12, 13)

d)

(7, 24, 26)

21.

Subtract the following fractions: $\frac{x-(x-1)}{x^2-1} - \frac{1}{x+1}$

a)

$\frac{x-(x-1)}{x^2-1}$

b)

$\frac{1}{x-1}$

c)

$\frac{x-1}{x^2+1}$

d)

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

22.

If the area of a square is 144 cm², what is the length of its diagonal?

a)

12 cm

b)

12 $\sqrt{2}$ cm

c)

24 cm

d)

24 $\sqrt{2}$ cm

23.

In a right triangle, if one leg is 15 cm and the hypotenuse is 25 cm, what is the length of the other leg?

a)

10 cm

b)

30 cm

c)

20 cm

d)

35 cm

24.

Which quadrilateral always has two diagonals that are perpendicular to each other?

a)

Rectangle

b)

Rhombus

c)

Trapezoid

d)

Parallelogram

25.

In a rhombus, if the lengths of the two diagonals are 10 cm and 24 cm respectively, what is the area of the rhombus?

a)

120 cm²

b)

240 cm²

c)

480 cm²

d)

360 cm²

26.

Which of the following statements is true for all trapezoids?

a)

Both diagonals are equal.

b)

Both bases are parallel.

c)

Opposite angles are equal.

d)

Angles at the base are equal.

27.

Calculate the product of the following fractions:

a)

$\frac{x+4}{x-3}$

b)

$\frac{x+4}{x+3}$

c)

$\frac{x-4}{x-3}$

d)

$\frac{x+4}{x-3}$

28.

If a quadrilateral has two pairs of adjacent sides that are equal but no sides are parallel, what type of quadrilateral is it?

a)

Square

b)

Rhombus

c)

Rectangle

d)

Trapezoid

29.

In a square, if the length of a side is s, what is the relationship between s and the diagonal d?

a)

Ad = s√3

b)

Bd = s√4

c)

Cd = s√5

d)

d = s√2

30.

Solve the following equation for x: $\frac{3}{x-2} + \frac{5}{x+2} = \frac{8}{x^2-4}$

a)

x=0

b)

x=2

c)

x=-2

d)

x=±2

31.

Which of the following is a trapezoid?

a)

A quadrilateral with all sides equal

b)

A quadrilateral with only one pair of parallel sides

c)

A quadrilateral with opposite sides parallel and equal

d)

A quadrilateral with all angles equal

32.

If $\frac{a^2-b^2}{a-b}=x$ , find x.

a)

a+b

b)

a-b

c)

$\frac{a+b}{2}$

d)

ab

33.

Which property is true for all parallelograms?

a)

The two diagonals are perpendicular.

b)

The two diagonals bisect each other at the midpoint of each diagonal.

c)

The two diagonals are equal.

d)

The two diagonals bisect each other at the midpoint of each diagonal.

34.

If the opposite sides of a quadrilateral are equal, then that quadrilateral is:

a)

Rhombus

b)

Rectangle

c)

Trapezoid

d)

Parallelogram

35.

Simplify the following expression: $\frac{x-2}{2+x}$ $\frac{x-1}{x}$ $\frac{1}{x+2}$ $\frac{x+2}{x}$

a)

$\frac{x-2}{2+x}$

b)

$\frac{x-1}{x}$

c)

$\frac{1}{x+2}$

d)

$\frac{x+2}{x}$

36.

In a rectangle, the length is twice the width. If the perimeter is 36 cm, find the area.

a)

54 cm²

b)

72 cm²

c)

108 cm²

d)

24 cm²

37.

A parallelogram has one angle of 60°. What are the measures of the other three angles?

a)

60°, 120°, 120°

b)

60°, 60°, 120°

c)

60°, 90°, 90°

d)

120°, 120°, 120°

38.

Which of the following expressions is equivalent to $\frac{3}{x} + \frac{5}{y}$ ?

a)

$\frac{3y+5x}{xy}$

b)

$\frac{3x+5y}{xy}$

c)

$\frac{8}{xy}$

d)

$\frac{8}{x+y}$

39.

Simplify the following complex fraction: $\frac{2x+3y}{4}$ $\frac{2y+3x}{4}$ $\frac{2x+3y}{xy}$ $\frac{2y+3x}{xy}$

a)

$\frac{2x+3y}{4}$

b)

$\frac{2y+3x}{4}$

c)

$\frac{2x+3y}{xy}$

d)

$\frac{2y+3x}{xy}$

40.

A quadrilateral has angles of 90°, 110°, and 70° respectively. What type of quadrilateral is it?

a)

Rectangle

b)

Square

c)

Trapezoid

d)

Parallelogram

41.

Find the area of a rhombus with diagonals measuring 10 cm and 24 cm.

a)

120 cm²

b)

130 cm²

c)

140 cm²

d)

150 cm²

42.

Find the value of x so that the following expression is undefined: $\frac{5}{x+3}$

a)

x=3

b)

x= -3

c)

x=0

d)

x=1

43.

In a parallelogram, if one angle is 70°, what is the measure of the adjacent angle?

a)

120°

b)

100°

c)

90°

d)

110°

44.

If $\frac{3x-9}{x^2-9}$ is simplified, what is the result?

a)

$\frac{3(x-3)}{(x-3)(x+3)}$

b)

$\frac{3}{x+3}$

c)

$\frac{3x-9}{x^2+9}$

d)

$\frac{3(x+3)}{x^2-9}$

45.

Solve the equation $\frac{x^2-1}{x-1} = 5$ for x

a)

x=1

b)

x=2

c)

x=3

d)

x=4

46.

In trapezoid ABCD, AB||CD. If the length of AB is 10 cm, the length of CD is 6 cm, and the height is 4 cm, find the area of the trapezoid.

a)

24 cm²

b)

40 cm²

c)

32 cm²

d)

16 cm²

47.

Find the value of x if: $\frac{4x-1}{2x+3} = \frac{2x-7}{x-5}$

a)

x=2

b)

x=4

c)

x=6

d)

x=8

48.

Triangle ABC is a right triangle at A. Let M be the midpoint of BC, D be the midpoint of AB, and E be the point symmetric to M through D. Given that BC = 4cm. What is the perimeter of quadrilateral AMBE?

a)

2cm

b)

6cm

c)

4cm

d)

8cm

49.

Given the lengths of the sides of a rectangle are 12cm and 5cm. What is the length of the diagonal?

a)

7cm

b)

13cm

c)

17cm

d)

19cm

50.

How does the area of a rhombus change if the length of each side is increased by 2 times?

a)

Remains unchanged

b)

Decreases by 4 times

c)

Increases by 2 times

d)

Increases by 4 times

51.

How does the area of a rectangle change if the length is doubled and the width is reduced by a factor of 4?

a)

Unchanged

b)

Decreased by a factor of 2

c)

Increased by a factor of 2

d)

Increased by a factor of 8

52.

Consider the quadrilateral ABCD with AB = AD, CB = CD, $\angle A = 100°$ , $\angle D = 60°$ . What is the measure of angle B?

a)

120°

b)

80°

c)

100°

d)

60°

53.

Let a be a positive number such that $a^2 + \frac{1}{a^2} = 7$ . What is the value of $a^3 + \frac{1}{a^3}$ ?

a)

18

b)

27

c)

9

d)

21

54.

60% of the students in the school are female. 40% of females and 80% of males in the school can swim. What is the percentage of students in the school who can swim?

a)

80%

b)

76%

c)

56%

d)

64%

55.

In a group of 80 students, 60 can swim, 54 can play chess, and only 10 do not know either. How many students know both swimming and chess?

a)

34

b)

24

c)

54

d)

44

56.

ABCD is a rectangle. Calculate the perimeter of ABCD if the area is 66cm^2 and $AB - BC = 5cm$ .

a)

34cm

b)

17cm

c)

48cm

d)

66cm

57.

ABCD is a rectangle. Calculate the perimeter of ABCD if the area is 66cm^2 and $AB - BC = 5cm$ .

a)

34cm

b)

17cm

c)

48cm

d)

66cm

58.

Quadrilateral ABCD has two diagonals that are perpendicular to each other. If AB = 16cm, BC = 14cm, and AD = 8cm, then CD =

a)

4cm

b)

3cm

c)

2cm

d)

1cm

59.

Hai hình vuông, mỗi cạnh 8m, được đặt sao cho một đỉnh của hình này nằm ở tâm của hình kia. Diện tích phần giao nhau là

a)

$48m^2$

b)

$16m^2$

c)

$32m^2$

d)

$8m^2$

60.

Cho ab + $b^2 / a^2$ - 3ab + 15b^2 = $1/3$ , tìm giá trị của $4a^2 / b^2$ .

a)

A. 25

b)

B. 64

c)

C. 49

d)

D. 36

CÂU HỎI TRẮC NGHIỆM TOÁN HỌC LỚP 8 (7,0 điểm)

Total questions: 60

Worksheet time: 30mins

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