Tasdiqlandi

Geometry: Geometric Shapes Identify different types of angles and use the relationships between angles on lines and in geometric figures. Identify geometric properties of two- and three-dimensional shapes, including line and rotational symmetry. Identify congruent triangles and quadrilaterals and their corresponding measures; and identify similar triangles and use their properties. Relate three-dimensional shapes with their two-dimensional representations (e.g., nets, two-dimensional views of three-dimensional objects). Use geometric properties, including the Pythagorean Theorem, to solve problems. Note: Eighth grade geometric shapes items will include circles; scalene, isosceles, equilateral, and right-angled triangles; trapezoids, parallelograms, rectangles, rhombuses, and square quadrilaterals; as well as other polygons including pentagons, hexagons, octagons, and decagons. It also includes three-dimensional objects—prisms, pyramids, cones, cylinders, and spheres. Draw and estimate the size of given angles, line segments, and perimeters; and estimate areas and volumes. Select and use appropriate measurement formulas for perimeters, circumferences, areas, surface areas, and volumes; and find measures of compound areas. Geometry: Location and Movement Locate points and solve problems involving points in the Cartesian plane. Recognize and use geometric transformations (translation, reflection, and rotation) of two-dimensional shapes. Data and Chance: Characteristics of Data Sets Identify and compare characteristics of data sets including mean, median, mode, range, and shape of distributions (in general terms). Calculate, use, or interpret mean, median, mode, or range to solve

eng sodda holatlarda funktsiyani monotonligini aniqlay oladi, eng katta va eng kichik qiymatlarini topa oladi; real dunyodagi , boshqa fanlardagi sodda hodisalar va jarayonlarning algebraik tenglama va tengsizliklar va ularning sistemalari, funktsiyalar, hosila va integrallar yordamida matematik modellarini tuza oladi va tahlil qila oladi; geometrik, fizik, iqtisodiy va boshqa tadbiqiy masalalarni, jumladan ekstremal masalalarni еchishda differentsial hisob usullaridan foydalana oladi; limitlar, hosilalar va integrallarni (zarur bo’lsa tavsiya etilgan manbaalardan, hisoblash vositalardan va tayyor kompьyuter dasturlardan foydalangan holda) hisoblay oladi; sodda hollarda funktsiya uzluksizligini va differentsiallanuvchiligini tekshira oladi; hosila yordamida elementar funktsiyani hossalarini tekshira oladi; grafigini yasay oladi; aniq integralning geometrik va fizik tadbiqlariga oid masalalarni еcha oladi; (V1+) chiziqli bo’lmagan eng sodda diofant tenglamalarni еcha oladi; real dunyodagi, boshqa fanlardagi sodda hodisalarning kompleks sonlar yordamida matematik modellarini tuza oladi va tahlil qila oladi; taqqoslamalar nazariyasini, Ferma kichik teoremasini, Eyler teoremasini qo’llab, sonlar nazariyasiga oid masalalarni еcha oladi; arifmetik va geometrik progressiyalar bo’lmagan sodda sonli ketma-ketliklarga oid masalalarni еcha oladi; sodda funktsional tenglamalarni еcha oladi; real dunyodagi, boshqa fanlardagi jarayonlarning differentsial tenglamalar yordamida matematik modellari haqida tassavur qila oladi;