This Question Paper contains 8 Printed Pages. >t~ \t'{~~ ~2. ~0{:( Set No. of Quest ion Paper N-lO(E ) (JULY, 2011) 1 1 Time : 75 minutes] [Maximum Marks : 50 • Instructions : (1) There are 50 objective type questions in this part and all are com pulsory. (2) The questions are serially numbered from 1 to 50 and each carries 1 mark. (3) You are supplied with separate OMR sheet with the alternatives (A) 0 , (B)O, (C) 0 , (D) 0 against each question number. For each question,
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Difference Between Euclidean and Spherical Trigonometry 1 Non-Euclidean geometry is geometry that is not based on the postulates of Euclidean geometry. The five postulates of Euclidean geometry are: 1. Two points determine one line segment. 2. A line segment can be extended infinitely. 3. A center and radius determine a circle. 4. All right angles are congruent. 5. Given a line and a point not on the line, there exists exactly one line containing the given point parallel to the given
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1 SOME IMPORTANT MATHEMATICAL FORMULAE Circle : Area = π r2; Circumference = 2 π r. Square : Area = x2 ; Perimeter = 4x. Rectangle: Area = xy ; Perimeter = 2(x+y). 1 Triangle : Area = (base)(height) ; Perimeter = a+b+c. 2 3 2 Area of equilateral triangle = a . 4 4 Sphere : Surface Area = 4 π r2 ; Volume = π r3. 3 2 3 Cube : Surface Area = 6a ; Volume = a . 1 Cone : Curved Surface Area = π rl ; Volume = π r2 h 3 π r l + π r2 Total surface area = . Cuboid : Total surface
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Ch. 6 Formulas Name ___________________________ Sec. 6.1 (Triangles) 1. Law of Sines 1. ________________________ 2. You use the Law of Sines when you are given: 2. ________________________ (SSS, AAS,???) (2 pts.) 3. Area of a triangle when given 3. ________________________ SAS Sec. 6.2 (Triangles) 4. Law of Cosines 4. _______________________ 5. You use Law of Cosines when you are given: 5. _______________________
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spacecraft do not break apart during launch. Also forces applied to a spacecraft on return flights entering our earth atmosphere and how those forces act on it. 4. What type(s) of triangles is Pythagorean Theorem and sine, cosine, and tangent used for? Right Triangles 5. What type(s) of triangles can Law of Sines and Law of Cosines be used
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Name: _______________________________________ Date: _______________________ M8-U3: Notes #2 – Reflections Class: _______________________ A reflection is a transformation which ____________ the figure over a ________________________. This line is called the . Example 1: ΔABC is being reflected over the x-axis. Draw and label the image ΔA’B’C’. We can use an arrow to describe this reflection. ΔABC ΔA’B’C’ What are the coordinates of: A ________ A’ _________
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Volume of sphere = 4 3 Volume of cone = 3 Surface area of sphere = 4 1 3 h 2 Curved surface area of cone = 2 r l h r The Quadratic Equation The solutions of ax2 + bx + c = 0 where 0, are given by In any triangle ABC C b A Sine Rule a c x= B a b c = = sin A sin B sin C
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Right Triangles Word Problems with Illustrations and Solutions 1. Solve the right triangle ABC given that c = 18 cm and b = 9 cm. To find the remaining side a, use the Pythagorean Theorem: a2 + b2 = c2 a2 = c2 - b2 a2 = (18cm)2-(9cm)2 a2 = 324cm2 – 81cm2 a2 = 243cm2 a = 15.59cm 2. Ben and Emma are out flying a kite. Emma can see that the kite string she is holding is making a 70° angle with the ground. The kite is directly above Ben, who is standing 50 feet away. To the nearest foot, how many
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route she can choose? 1 of 7 International Kangaroo Mathematics Contest 2012 – Cadet B A (A) 900 m (B) 800 m (C) 700 m (D) 600 m (E) 400 m 8. The diagram shows two triangles. In how many ways can you choose two vertices, one in each triangle, so that the straight line through the vertices does not cross either triangle? (A) 1 (B) 2 (C) 3 (D) 4 (E) more than 4 9. Werner folds a sheet of paper as shown in the figure and makes two straight
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Empress Land Rules: Form four groups with four members in each. Therefore in total there should be 16. Take a piece of paper rip it into four pieces. Write one through four on the papers. Then fold them each into little pieces take a hat and shake it well and have one member from each group choose a number. Whatever number they choose is the number that their group will go in. there will be no yelling or shouting during another groups turn each team has 30 seconds to answer their question two
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