platonic solids and the name of each shape comes from the number of faces it has.The five platonic solids are tetrahedron‚ octahedron‚ cube‚ icosahedron‚ and dodecahedron. Each solid is made of regular polygons and the polygons of each solid are congruent. The topics that will be discussed in this paper are what are the five platonic solids‚ who classified the five shapes‚ their key features‚ the shapes similarities and differences‚ and examples in real life. The first topic is what the five
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[pic] ARMY PUBLIC SCHOOL AND COLLEGE‚ JHELUM CANT Paper: Statistics Pre- Board 2012 (Objective) Marks: 18 Time: 30 min Name: ………………………………………………………………………… Section: ………………… SECTION-A (18 Marks) | |Select the correct answer. Cutting or over writing is not allowed. | | | |If in a table all possible values of a random variable are given with their corresponding probabilities‚ then its
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Rearranging Formulae 7. Algebraic Fractions 8. Using Graphs 9. Quadratic Equations 10. Simultaneous Equations 11. Algebraic Proofs 12. Circle Theorems 13. Trigonometry – for triangles which are not right-angled 14. Vectors 15. Similar Triangles 16. Congruent Triangles 17. Scale Factors – for volumes & surface areas of similar shapes (2D or 3D) 18. Stratified Samples 19. Histograms 20. Tree Diagrams 21. Mixed Questions NC = non-calculator question
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22. Conditional- if it is a line then it contains at least two points Inverse- if it is not a line then it does not contain at least two points Converse- If it contains at least two points then it is a line Contrapositive- if it does not contain at least two points‚ then it is not a line 23. Conditional- If there are 3 noncollinear points‚ then there is exactly one plane Inverse- if there are not exactly 3 collinear points‚ then there is not exactly one plane Converse- if there is exactly one
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SOLUTION: First graph the points on a coordinate grid and draw the trapezoid. SOLUTION: The trapezoid ABCD is an isosceles trapezoid. So‚ each pair of base angles is congruent. Therefore‚ ANSWER: 101 2. WT‚ if ZX = 20 and TY = 15 SOLUTION: The trapezoid WXYZ is an isosceles trapezoid. So‚ the diagonals are congruent. Therefore‚ WY = ZX. WT + TY = ZX WT + 15 = 20 WT = 5 ANSWER: 5 COORDINATE GEOMETRY Quadrilateral ABCD has vertices A (–4‚ –1)‚ B(–2‚ 3)‚ C(3‚ 3)‚ and D(5‚ –1). 3. Verify
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are called parallel lines. Line segments can be used to create different polygons. As in Euclid’s third postulate‚ with any straight line segment‚ a circle can be drawn having the segment as radius and one endpoint as center. All the angles in a triangle add up to 180 degrees. An acute angle is less than 90 degrees. A right angle is 90 degrees; all right
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After choosing a topic randomly‚ students will have 5 minutes to prepare before presenting their explanation for 5 minutes. 1. State the definition of the limit and explain the requirements for a limit to exist. Also‚ explain the 3 main techniques to evaluate limits. (Keywords: limit‚ intend‚ left‚ right‚ general‚ notation‚ 3 requirements‚ NAG‚ table‚ diagrams‚ indeterminate form‚ conjugate‚ factoring‚ substitution) The limit of the function is the height that the function intends to reach
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[pic] A parallelogram is a quadrilateral in which pairs of opposite sides are parallel and are congruent. Opposite sides are parallel and equal in length‚ and opposite angles are equal (angles "a" are the same‚ and angles "b" are the same) NOTE: Squares‚ Rectangles and Rhombuses are all Parallelograms! Name the kind of parallelogram this figure displays? Example 1: [pic] |[pic] |A parallelogram with: | |
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This unit’s main goal was to use similar triangles to measure the length of a shadow. While using the variables D‚ H‚ and L‚ we have figured out a formula to measure a shadow’s length. In order to do this though‚ everyone had to learn the basic concepts of similarity‚ congruence‚ right triangles‚ and trigonometry. Similarity and congruence were two very important factors because they helped us learn about angles and the importance of triangles. Similarity was a key to find out how to use proportions
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statement: A horse has 4 legs. a. b. c. d. ____ If it has 4 legs‚ then it is a horse. Every horse has 4 legs. If it is a horse‚ then it has 4 legs. It has 4 legs and it is a horse. 2. What other information is needed in order to prove the triangles congruent using the SAS Congruence Postulate? a. b. ∠BAC ≅ ∠DAC AC ⊥ BD c. d. AB Ä AD AC ≅ BD 1 Name: ______________________ ____ 3. Assume all angles are right angles. What is the area of the figure? ID: A a. b. c. d. ____
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