Final test in geometry (grade 8)

Department of Education Administration

municipal formation of the urban district "Usinsk"

Municipal autonomous educational institution

"Secondary school No. 3

with in-depth study of individual subjects" in Usinsk

Intermediate certification in geometry in the 8th grade of a secondary school.

Teacher

mathematicians

Rima Gafurbaevna

Khafizova

Usinsk

2019

SPECIFICATION OF CMM
for the final test in geometry in the 8th grade of a secondary school.

The final examination
is carried out in the form of a test.
Purpose of work
– the final work is intended to establish the level of mastery of the 8th grade geometry course.

3. Contents of the final work

determined on the basis of the following regulatory documents:

1. Federal state standard of basic general education.

2. Codifier of content elements and requirements (skills), compiled on the basis of the Mandatory minimum content of basic educational programs and Requirements for the level of training of secondary school graduates.

3. Educational and methodological set on geometry L.S. Atanasyan, V.F. Butuzov, S.B. Kadomtsev “Geometry” 8th grade: textbook for general education organizations. Enlightenment 2020.

4. Characteristics of the structure and content of the work

The geometry work includes 11 tasks of varying difficulty:

the first 8 tasks of the basic level; tasks 1-4 - a choice of answer, the next four tasks are also at a basic level; 5-8 - a short solution and record of the answer, the last two tasks - a detailed solution and answer.

The work is presented in four options.

5. Lead time

45 minutes are allotted to complete the entire work.

6. Evaluation of tasks and work in general.

Basic level tasks 1 - 4 are scored 1 point, 5-8 are scored 2 points, advanced level tasks 9 - 10 are scored 3 points.

The student’s performance as a whole is determined by the total score received by him based on the results of completing all tasks of the work.

The maximum score for the work is 18.

.
Option
1 Part 1:

1. One of the angles of the parallelogram is 24°. Find the greatest angle of the parallelogram.

1) 66° 2) 114° 3) 136° 4) 156°

2. In triangle ABC, the base AC is 18 cm, and the height drawn to it is equal to

7 cm. Find the area of the triangle.

1) 56 2) 63 3) 72 4) 84

3. The inscribed angle ABC of a circle with its center at point O is 37°. Find the central angle subtended by the same circular arc.

1) 18,5° 2) 40° 3) 74° 4) 124°

4. A circle with a radius of 8 cm is inscribed in a square. Find the area of this square.

1) 256 2) 196 3) 144 4) 64

5. The legs of a right triangle are 8 cm and 15 cm. Find the hypotenuse of the triangle.

6. Find the area of a rhombus if its diagonals are 8 cm and 6 cm.

7. Two tangents are drawn to a circle with a center at point O, intersecting at an angle of 76° at point P and touching the circle at points A and B. Find the value

angle AOB.

8. In a right triangle ABC ∟A = 30°, side BC = 4.5 cm. Find AB.

part 2

AC side

of triangle
ABC,
point
D
so that
AD
= 5,
DC
= 7. The area of triangle
ABC
is 60 cm².
Find the area of triangle ABD
.

10. In the trapezoid ABCD with bases BC = 9 cm and AD = 36 cm, a diagonal WD = 18 cm is drawn. Prove that the triangles VSD and AVD are similar.

Option 2

1 part

1. One of the angles of the parallelogram is 127°. Find the smallest angle of the parallelogram.

1) 27° 2) 53° 3) 36° 4) 63°

2. In triangle ABC, the base AC is 12 cm, and the height drawn to it is equal to

4 cm. Find the area of the triangle.

1) 16 2) 18 3) 24 4) 48

3. The central angle of a circle with its center at point O is 116°. Find the inscribed angle subtended by the same circular arc.

1) 58° 2) 40° 3) 74° 4) 64°

4. A circle with a radius of 6 cm is inscribed in a square. Find the perimeter of this square.

1) 36 2) 48 3) 24 4) 64

5. The legs of a right triangle are 24 cm and 7 cm. Find the hypotenuse of the triangle.

6. Find the area of a rhombus if its diagonals are 18 cm and 10 cm.

7. Two tangents are drawn to a circle with a center at point O, intersecting at an angle of 84° at point P and touching the circle at points A and B. Find the value

angle AOB.

8. In a right triangle ABC ∟A = 30°, AB = 13 cm. Find leg BC.

part 2

9. The bases of an isosceles trapezoid are 8 and 18, and its perimeter is 52. Find the area of the trapezoid.

10. In the trapezoid ABCD with bases BC = 6 cm and AD = 54 cm, a diagonal WD = 18 cm is drawn. Prove that the triangles BCSD and AVD are similar.

Option 3

1 part:

1. One of the angles of the parallelogram is 54°. Find the greatest angle of the parallelogram.

1) 66° 2) 114° 3) 126° 4) 156°

2. In triangle ABC, the base AC is 24 cm, and the height drawn to it is equal to

3 cm. Find the area of the triangle.

1) 36 2) 63 3) 72 4) 84

3. The inscribed angle ABC of a circle with its center at point O is 46°. Find the central angle subtended by the same circular arc.

1) 18,5° 2) 40° 3) 74° 4) 92°

4. A circle with a radius of 10 cm is inscribed in a square. Find the area of this square.

1) 256 2) 400 3) 144 4) 64

5. The legs of a right triangle are 16 cm and 12 cm. Find the hypotenuse of the triangle.

6. Find the area of a rhombus if its diagonals are 13 cm and 8 cm.

7. Two tangents are drawn to a circle with a center at point O, intersecting at an angle of 86° at point P and touching the circle at points A and B. Find the value

angle AOB.

8. In a right triangle ABC ∟A = 30°, side BC = 5.5 cm. Find AB.

part 2

AC side

of triangle
ABC,
point
D
so that
AD
= 5,
DC
= 9. The area of triangle
ABC
is 84 cm².
Find the area of triangle ABD
.

10. In the trapezoid ABCD with bases BC = 4 cm and AD = 36 cm, a diagonal WD = 12 cm is drawn. Prove that the triangles VSD and AVD are similar.

Option 4

1 part:

1. One of the angles of the parallelogram is 143°. Find the smallest angle of the parallelogram.

1) 37° 2) 53° 3) 36° 4) 63°

2. In triangle ABC, the base AC is 19 cm, and the height drawn to it is equal to

8 cm. Find the area of the triangle.

1) 16 2) 18 3) 24 4) 76

3. The central angle of a circle with its center at point O is 138°. Find the inscribed angle subtended by the same circular arc.

1) 58° 2) 69° 3) 74° 4) 64°

4. A circle with a radius of 12 cm is inscribed in a square. Find the perimeter of this square.

1) 36 2) 48 3) 96 4) 64

5. The sides of a right triangle are 20 cm and 15 cm. Find the hypotenuse of the triangle.

6. Find the area of a rhombus if its diagonals are 8 cm and 11 cm.

7. Two tangents are drawn to a circle with a center at point O, intersecting at an angle of 72° at point P and touching the circle at points A and B. Find the value of angle AOB.

8. In a right triangle ABC ∟A = 30°, AB = 19 cm. Find leg BC.

part 2

9. The bases of an isosceles trapezoid are 7 and 23, and its perimeter is 64. Find the area of the trapezoid.

10. In the trapezoid ABCD with bases BC = 3 cm and AD = 48 cm, a diagonal WD = 12 cm is drawn. Prove that the triangles VSD and AVD are similar.