11. Sınıf Geometri 1. Dönem 3. Yazılı Test Soruları
11. Sınıf Geometri 1. Dönem 3. Yazılı Test Soruları, dersin temel geometrik kavramlarına odaklanır. Bu konular arasında doğruda nokta, düzlemde nokta ve doğru, uzayda nokta düzlem, çember ve yaylar, benzerlik ve oran gibi konular yer alır. Ayrıca, trigonometriye giriş, dik üçgenler ve trigonometrik fonksiyonlar da ele alınır.
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1. Soru: Bir çizgi üzerinde bulunan P, Q ve R noktalarının ardışık koordinatları sırasıyla (-4, 1), (2, 1) ve (5, -1) olduğuna göre, PQ ve QR doğrultularının eğimleri toplamı kaçtır?
a) -4/3
b) -1/2
c) 7/6
d) 3/4
Cevap: c) 7/6
Açıklama: İki nokta arasındaki eğimi hesaplamak için Δy/Δx formülünü kullanırız. PQ doğrultusunun eğimi (1-1)/(2-(-4)) = 0/6 = 0’dır. QR doğrultusunun eğimi (-1-1)/(5-2) = -2/3’dür. Bu durumda eğimlerin toplamı 0 + (-2/3) = -2/3 şeklinde hesaplanır.
2. Soru: ABCD bir paralelkenar olup, E noktası AB kenarının orta noktası ve F noktası da DC kenarının orta noktasıdır. AE doğrusu ile BF doğrusu kesiştiğinde oluşan açının ölçüsü kaç derecedir?
a) 45°
b) 60°
c) 90°
d) 120°
Cevap: c) 90°
Açıklama: Paralelkenarlarda karşılıklı açılar eşittir. ABCD paralelkenarında, ABE üçgeni ile CDF üçgeni birbirine benzerdir. Bu durumda, EAF ve BFD açıları birer birer bu benzerlik ilişkisini sağlar. AE doğrusu AB kenarının orta noktasından geçtiği için EAF açısı 90°’dir. Benzer şekilde, BF doğrusu DC kenarının orta noktasından geçtiği için BFD açısı da 90°’dir.
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25. Soru: Bir üçgende, a = 5, b = 12 ve c = 13 olmak üzere, cos(C) ifadesinin değeri kaçtır?
a) -1/3
b) -4/5
c) -5/12
d) -12/5
Cevap: b) -4/5
Açıklama: Kosinüs teoremi, bir üçgende kenar uzunluklarıyla açıların ilişkisini belirtir. c^2 = a^2 + b^2 – 2ab × cos(C) formülünü kullanarak cos(C) ifadesini bulabiliriz. Yerine a = 5, b = 12 ve c = 13 koyarsak, 13^2 = 5^2 + 12^2 – 2 × 5 × 12 × cos(C) elde ederiz. Bu denklemi çözerek cos(C) = -4/5 olduğunu buluruz.Certainly! Here are additional test questions on the topics covered in the 11th Grade Geometry 1st Term 3rd Written Exam:
1. Which of the following statements is true about a line and a plane in space?
a) A line lies entirely on a plane.
b) A line intersects a plane at exactly one point.
c) A line and a plane are always parallel.
d) A line and a plane may intersect at more than one point.
Answer: d) A line and a plane may intersect at more than one point.
Explanation: In three-dimensional space, a line can intersect a plane in various ways. It can intersect the plane at a single point, form a line segment within the plane, or lie entirely on the plane.
2. The radius of a circle is 8 cm. What is the circumference of the circle?
a) 16π cm
b) 32π cm
c) 64π cm
d) 128π cm
Answer: b) 32π cm
Explanation: The circumference of a circle is given by the formula C = 2πr, where r is the radius. Substituting the given radius (8 cm) into the formula, we get C = 2π × 8 = 16π cm.
3. In a triangle, if two angles measure 45° and 60°, what is the measure of the third angle?
a) 30°
b) 45°
c) 60°
d) 75°
Answer: d) 75°
Explanation: The sum of the angles in a triangle is always 180°. Therefore, the measure of the third angle can be found by subtracting the sum of the given angles (45° + 60° = 105°) from 180°: 180° – 105° = 75°.
4. Which of the following transformations preserves both shape and size?
a) Translation
b) Reflection
c) Rotation
d) Dilation
Answer: a) Translation
Explanation: A translation is a transformation that slides an object without changing its shape or size. The object maintains its orientation and all distances between points remain the same.
5. In a right triangle, the length of one leg is 8 cm and the length of the hypotenuse is 10 cm. What is the length of the other leg?
a) 2 cm
b) 4 cm
c) 6 cm
d) 8 cm
Answer: b) 4 cm
Explanation: In a right triangle, the Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. Let x be the length of the other leg. Using the theorem, we have 8^2 + x^2 = 10^2. Solving this equation, we find x = 4 cm.
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Please note that the format above includes only the questions, answer choices, correct answers, and brief explanations.Certainly! Here are more test questions on the topics covered in the 11th Grade Geometry 1st Term 3rd Written Exam:
6. In a square, what is the measure of each interior angle?
a) 45°
b) 60°
c) 90°
d) 180°
Answer: c) 90°
Explanation: In a square, all four interior angles are right angles, which measure 90° each.
7. Two triangles are congruent if they have:
a) The same shape but different sizes.
b) The same size but different shapes.
c) The same shape and the same size.
d) No relationship between their shapes and sizes.
Answer: c) The same shape and the same size.
Explanation: Two triangles are congruent if their corresponding sides and angles are equal in measure, indicating that they have the same shape and size.
8. In a parallelogram, opposite sides are:
a) Perpendicular
b) Congruent
c) Parallel
d) Intersecting
Answer: c) Parallel
Explanation: In a parallelogram, opposite sides are parallel, meaning they never intersect and have the same slope.
9. What is the area of a rectangle with length 12 cm and width 5 cm?
a) 17 cm²
b) 30 cm²
c) 60 cm²
d) 72 cm²
Answer: d) 60 cm²
Explanation: The area of a rectangle is given by the formula A = length × width. Substituting the given values, we get A = 12 cm × 5 cm = 60 cm².
10. Which trigonometric ratio represents the ratio of the adjacent side to the hypotenuse in a right triangle?
a) Sine (sin)
b) Cosine (cos)
c) Tangent (tan)
d) Cosecant (csc)
Answer: b) Cosine (cos)
Explanation: In a right triangle, the cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse.Certainly! Here are more test questions on the topics covered in the 11th Grade Geometry 1st Term 3rd Written Exam:
11. In a circle, what is the relationship between the radius and the diameter?
a) The radius is half the length of the diameter.
b) The radius is twice the length of the diameter.
c) The radius is equal to the length of the diameter.
d) There is no relationship between the radius and the diameter.
Answer: a) The radius is half the length of the diameter.
Explanation: The diameter of a circle is twice the length of its radius. Therefore, the relationship between the radius (r) and the diameter (d) can be expressed as d = 2r, or equivalently, r = d/2.
12. Which of the following statements about similar triangles is true?
a) Similar triangles have equal side lengths.
b) Similar triangles have equal angle measures.
c) Similar triangles have proportional side lengths.
d) Similar triangles have congruent angle measures.
Answer: c) Similar triangles have proportional side lengths.
Explanation: Similar triangles have corresponding angles that are congruent, but their side lengths are proportional. This means that the ratios of corresponding side lengths in similar triangles are equal.
13. The volume of a rectangular prism with length 6 cm, width 3 cm, and height 4 cm is:
a) 24 cm³
b) 36 cm³
c) 48 cm³
d) 72 cm³
Answer: b) 36 cm³
Explanation: The volume of a rectangular prism is given by the formula V = length × width × height. Substituting the given values, we get V = 6 cm × 3 cm × 4 cm = 72 cm³.
14. Which of the following transformations changes the size but preserves shape?
a) Reflection
b) Translation
c) Rotation
d) Dilation
Answer: d) Dilation
Explanation: A dilation is a transformation that changes the size of an object while preserving its shape. It involves scaling the object by a factor, either enlarging or reducing it.
15. In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. This is known as:
a) The Pythagorean theorem
b) The Law of Sines
c) The Law of Cosines
d) The Triangle Inequality theorem
Answer: d) The Triangle Inequality theorem
Explanation: The Triangle Inequality theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.Certainly! Here are more test questions on the topics covered in the 11th Grade Geometry 1st Term 3rd Written Exam:
16. Which of the following statements about a rhombus is true?
a) All sides are congruent.
b) Opposite angles are congruent.
c) Diagonals bisect each other at right angles.
d) All of the above.
Answer: d) All of the above.
Explanation: In a rhombus, all sides are congruent, opposite angles are congruent, and the diagonals bisect each other at right angles.
17. Two lines that are coplanar and do not intersect are called:
a) Perpendicular lines
b) Parallel lines
c) Skew lines
d) Intersecting lines
Answer: b) Parallel lines
Explanation: Parallel lines are coplanar lines that do not intersect. They maintain a constant distance between each other and have the same slope.
18. What is the sum of the interior angles of a hexagon?
a) 360°
b) 540°
c) 720°
d) 900°
Answer: b) 540°
Explanation: The sum of the interior angles of a polygon can be found using the formula (n-2) × 180°, where n represents the number of sides of the polygon. For a hexagon (6 sides), the sum is (6-2) × 180° = 4 × 180° = 720°. However, since we are looking for the sum of the interior angles, we need to subtract the exterior angles. A hexagon has six exterior angles, each measuring 360°/6 = 60°. Therefore, the sum of the interior angles is 720° – 360° = 360°.
19. Which transformation leaves an object unchanged?
a) Reflection
b) Translation
c) Rotation
d) Identity transformation
Answer: d) Identity transformation
Explanation: The identity transformation is a transformation that leaves an object unchanged. It preserves both the shape and size of the object.
20. In a right triangle, the ratio of the lengths of the two legs is 3:4. What is the ratio of the lengths of the legs to the hypotenuse?
a) 3:4
b) 4:5
c) 5:7
d) 7:9
Answer: b) 4:5
Explanation: In a right triangle, the ratios of the lengths of the legs to the hypotenuse are given by the Pythagorean triplets. The triplet (3, 4, 5) satisfies this condition, so the ratio of the lengths of the legs to the hypotenuse is 3:4:5.