A set of exam questions for 11th graders in mathematics

REPUBLICА TА'LIM MАRKАZI

11th grade

1. Solve the equation:

2. Find the largest value of the function in the following range - y = 8cos x- x + 8

3. At what value of b of the following integral is equal to 1?

4. The center line of an equilateral trapezoid drawn outside the circle is 5. Find the side of this trapezoid.

5. A two-sided angle at the base of a regular rectangular pyramid of size 36 45⁰ . Find the side of the base of the pyramid.

1. Find the value of the expression:

2. Find the largest value of the function in the following range: y = 16 tg x- 16 x + 4 +5

3. Find the value of the following integral:

4. The sides of a right rectangle drawn inside the circle are 12 and 16, respectively. Find the face of the circle.

5. The height of a regular rectangular pyramid is 6 cm, the apophema is 6,5 cm. Find the perimeter of the base of the pyramid.

1. Find the value of the expression: 11⁷ ̇ 25⁵: 275⁵

2. This f(x) = 2x²-1 abscissa on the graph of the function x₀=Show the equation of the experiment performed at the point 0.

3. Agar f(x) = tg2x if f  Calculate ().

4. Agar A (-3; у) and the distance between points V (5; -4) is 10 units, у find the

5. Find the volume of a cone whose circumference of the base is 8 and whose height is 9 cm.

1. Find the difference between the smallest common multiple of the numbers a = and b = and the largest common divisor.

2.                 y=6x+9 straight line у=х²+7 х-6 is parallel to the attempt of the function graph. Find the abscissa of the test point.

3. Agar f(x)=x³+ x-  va g(x) = 3x²+ x + if f  g  (x) find the smallest natural solution of the inequality.

4. and,) = 60⁰ . k at what value of (+ k ) vector is perpendicular to the vector?

5. The ratio of the faces of two spheres is 2. Find the ratio of the diameters of these spheres.

1. If so, sin²xWhat is the value of +?

2. Find the domain of the function:

y=

3. Material point S (t) = e^t+ cos t + 5 t acting on the rule of law. Of this point t=0 Find the velocity in

4. The side of an equilateral trapezoid is equal to 5, and the diagonal divides the midline into sections equal to 3 and 7. Find the face of the trapezoid.

5. The sides of a right triangular prism are 29 cm, 25 cm and 6 cm, and the side edge is equal to the greater height of the base. Find the size of the prism.

1. Calculate:;

2. If tg () =, find tg.

3. If and, find the function.

4. 3х+4у+ 7 = 0 and 3х+у-5 = 0 How far is the point of intersection of straight lines from the origin?

5. Drawn diagonally and perpendicular to the plane. The angle between the deflection and the plane is equal to, and the projection of the deflection in the plane is 30. Find the length of the perpendicular.

1. Calculate the value of the expression and when.

2. Solve the inequality:;

3. Find the product of the functions:;

4. In the figure, the perimeter of the triangle is 42 sm, the perimeter of the triangle 84 sm. if the face of the triangle is 44, find the face of the triangle ().

5. A telephone cable 15 m long was pulled from the ground by a wire 8 m high to a height of 20 m towards the house. Assuming that the wire is not hanging, find the distance from the wire to the house.

1., and which of the numbers is positive?

2. Calculate the following,.

3. Solve the equation:

4. One of the angles of the parallelogram is 150⁰ ga teng. It is perpendicular to the diagonal side of 6. Find the perimeter of the parallelogram.

5. The height of a regular rectangular pyramid is 24 and the side of the base is 14. Find his apophema.

1. Simplify.

2. Solve the inequality:.

3. What angle does the experiment with the abscissa from the point on the point make with the axis of the MOON?

4. If and vectors are given, and find the angle between the vectors.

5. Draw the inside of the cylinder on a regular rectangular prism. Find the ratio of the volume of the cylinder to the volume of the prism.

1. Find the initial function of the function passing through the point (6; 2).

2. Solve the equation.

3. and find the angle between the diagonals of the parallelogram made in the vectors.

4. The circumference AB of a circle is equal to its radius. From what angle does the AB water appear from an arbitrary point of the large AB arc?

5. Find the height of a regular tetrahedron of size 8.

1. Determine the inverse of the function.

2. At what interval values ​​of inequality is appropriate?

3. If and, what is the value of?

4. AVS triangular plane B₁ and C₁ intersects at points.

If AB₁: BB₁= 2: 3, BC = 15 cm, BC B₁C₁ if B₁C₁ find the length of the cut.

5. and if the vectors are perpendicular, what is the value of?

1. Calculate:

2. {a_n} What is the value of in arithmetic progression?

3. Find if and.

4. AB, AC, AD are mutually perpendicular to each other in pairs of straight lines. If BD = 9 cm, BC = 16 cm, AD = 5 cm, find the section length of the CD.

5. Find the base angle of an equilateral triangle with points and points.

Calculate 1..

2. If and if, what interval does the value of belong to?

3. Solve the equation:, if any.

4. Find the section length that separates the circle from the abscissa axis.

5. The side surface of a cylinder with a square diagonal cross-section is 64. Find its radius.

1. Find the sum of the zeros of the quadratic function.

2. Calculate.

3. Calculate the integral:

4. A circle is drawn inside an equilateral triangle with side 10 and base. Find the radius of the circle.

5. ABCD A₁ B₁ C₁ D₁ if the edge of the cube is 8 cm, AB₁C triangle perimeter and DAC₁ Find the face of the triangle.

1. Simplify.

2. At what values ​​of and the point of intersection of straight lines has a positive ordinate?

3. How many roots does the equation have in the interval?

4. At what values ​​of a (-1 <a <) it is possible to make a triangle from sections with lengths equal to 1 + a, 1-2a and 2, respectively?

5. and calculate the scalar product of the vectors.

1. Determine the growth interval of the function.

2. Simplify:

3. Solve the inequality, if any.

4. The point M is located at a distance of 60 cm from each third of a regular ABC triangle with side 40cm. Find the distance from the plane of the triangle ABC to the point M.

5. If the radius of the base circle of the sphere is 60 cm and the radius of the sphere is 75 cm, find the volume of the sphere.

1. The product of the roots of the equation

find:

2. Find the initial function of the function.

3. Solve the equation:

4. Acute angle 60⁰ the bases of an equilateral trapezoid equal to 1: 2. If the perimeter of the trapezoid is 50, find its large base.

5. The length of the circle drawn outside the regular hexagon is equal to. Find the face of this polygon.

At what values ​​of 1. is the inequality reasonable?

2. On the graph of the function, find the area bounded by the experiment and the coordinate axes at the point.

3. If so, calculate.

4. If the diagonals of a rhombus are 32 and 4 cm, find the cotangent of its large angle.

5. The side surface of a regular pyramid is 60% of the total surface area. Find the angle between the sides of the pyramid and the plane of the base.

1. Find the product of the roots of the equation:

2. The function is the initial function of the function, find the product of the function.

3. How many roots does the equation have in the cross section?

4. The bases of an equilateral trapezoid are 8 and 12. Its diagonals are mutually perpendicular. Find the face of an equilateral trapezoid.

5. is equal to the constructor of the cone and it forms an angle li with the plane of the base. Find the size of the cone.

1. Find the value of the expression:

2. Find the range of increase and decrease of the function.

If 3. is equal to, find the value.

4. If the side of a rhombus is 6 cm and the face is 18, find its obtuse angle?

5. The diagonal of a rectangular regular prism is 3,5 cm and the diagonal of the side prism is 2,5 cm. Find the size of the prism.

1. Describe and calculate in summary view.

2. and calculate the surface bounded by the function graphs.

3. If {a _n} - If the arithmetic is in progress, find.

4. One of the catheters of a right triangle is 12 cm, the hypotenuse is 6 cm larger than the other catheter. Find the face of a right triangle.

5. Four points are given. and find the cosine of the angle between the vectors.

1. Prove that the value of an expression is a rational number:

2. Solve the system:

3. Calculate:

4. The perimeters of two similar triangles are 18 and 36. The sum of their surfaces is 30. Find the face of a large triangle.

5. The radius of the base of the cylinder is 2 m and the height is 3 m. Find the diagonal of the arrow section.

1. Reduce the fraction:

2. The first term and denominator of geometric progression are known. Find what you have.

3. Find the largest and smallest value of the function in the range [-4; 1]:

4. The first side of a triangle x (х  ) cm, the second side is 4 cm shorter than it, and the third side is 4 cm longer than the first. Find the perimeter of this triangle.

5. The dimensions of a right-angled parallelepiped are 15 m, 50 m and 36 m. Find the edge of the hub that matches it.

1. Reduce the fraction:

2. Solve the inequality:

3. Calculate the integral:

4. The side of the rhombus is 4, the obtuse angle is 120⁰ ga teng. Find the face of the rhombus.

5. The radii of the truncated cone bases are 3 m and the height of 6 m is 4 m. Find the maker.

1. Simplify the expression:.

2. Solve the equation:

3. Calculate the integral.

4. The side of an equilateral triangle is b and the angle at the end is 2. Find the radius of the circle drawn inside it?

5. If each side of the cube is increased by 2 cm, its volume increases by 98 cm. What is the edge of the cube?

1. Find the area of ​​definition of the function:

2. Find the initial function if

3. Solve the equation:

4. Prove that a straight line does not intersect a circle.

5. How many sides are there in a regular polygon whose inner angles are equal to each other?

1. Prove that the value of the expression is divisible by 120.

2. Find the product of the functions:

3. Find the center of the circle given by the equation.

4. AOB angle 40⁰, BOC angle 80⁰. Find the angle between the bisectors of these two angles.

5. The mass of a regular octagonal wooden tile with a side of 3,2 cm and a thickness of 0,7 cm is 17,3 g. Find the density of the wood.

1. Solve the equation:

2. Calculate the velocity and acceleration of a material point moving at regularity at t = 2.

3. Find the face of the figure bounded by the following lines.

va x = e.

4. The upper ends of the vertical columns, spaced 3,4 m apart, are connected by a beam. If the heights of the columns are 5,8 m and 3,9 m, find the length of the beam.

5. A plane ABC intersects the AB and AC sides of a triangle and at points. If so, find the length of the BC section.

1. Find the smallest value of the following expression:

2. Find the angular coefficient of the experiment performed at a point on the graph of this function.

3. Find the range of values ​​of the function.

4. Find the distance between the points of intersection of the following (parabola) and (straight line).

5. All sides of a pyramid consist of regular triangles. If the full surface of the pyramid is equal to, find the distance between the centers of its sides.

1. Calculate:

2. If is equal to, calculate.

3. Find the range of values ​​of the function.

4. and the point of intersection of the lines lies in a circle whose center is at the origin. Find the radius of this circle.

5. The diagonal of a right-angled parallelepiped is 13 cm, the diagonals of the sides and cm. Find the volume of a right-angled parallelepiped.