point‚ line‚ and plane. 2. “The ray through point P from point Q” is written in symbolic form as PQ. 3. “The length of segment PQ” can be written as PQ. 4. The vertex of angle PDQ is point P. 5. The symbol for perpendicular is . 6. A scalene triangle is a triangle with no two sides the same length. 7. An acute angle is an angle whose measure is more than 90°. 8. If AB intersects CD at point P‚ then a pair of vertical angles. APD and APC are 9. A diagonal is a line segment in a polygon connecting
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Math Exam Notes Unit 1 The Method of Substitution -Solving a linear system by substituting for one variable from one equation into the other equation -To solve a linear system by substitution: Step 1: Solve one of the equations for one variable in terms of the other variable Step 2: Substitute the expression from step 1 into the other equation and solve for the remaining variable Step 3: Substitute back into one of the original equations to find the value of the other variable Step
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Mock AIME Series Thomas Mildorf November 24‚ 2005 The following are five problem sets designed to be used for preparation for the American Invitation Math Exam. Part of my philosophy is that one should train by working problems that are more difficult than one is likely to encounter‚ so I have made these mock contests extremely difficult. The idea is that‚ once you become acclimated to them‚ the real AIMEs will seem easier‚ and you will approach them with justifiable confidence. Therefore‚ do not
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Geometrical Constructions (a) Bisector of line segment. (b) Division of a line segment into required number of parts/ proportional parts. (c) Perpendicular and parallel lines. (d) Bisection of an angle‚ trisection of a right angle/ straight angle. (e) Congruent angle. (f) To find the centre of an arc. (g) Regular polygons up to six sides with simple methods using T-square and setsquares. Point‚ Lines and Angles: Definitions of
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are coprime . A right triangle whose sides form a Pythagorean triple is called a Pythagorean triangle . The name is derived from the Pythagorean theorem ‚ stating that every right triangle has side lengths satisfying the formula a2 + b2 = c2 ; thus‚ Pythagorean triples describe the three integer side lengths of a right triangle. However‚ right triangles with noninteger sides do not form Pythagorean triples. For instance‚ the triangle with sides a = b
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arcs. The shorter arc is called the minor arc. SPHERICAL TRIANGLES A spherical triangle is that part of the surface of a sphere bounded by three arcs of great circles. The bounding arcs are called the sides of the spherical triangle and the intersections of these arcs are called the vertices of the spherical triangle. The angle formed by two intersecting arcs is called a spherical angle. Like a plane triangle‚ the spherical triangle has also six parts – three angles and three sides. The sides
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area of a hexagon using special right triangles‚ using trigonometry‚ breaking the hexagon into smaller polygons‚ and even show you how to construct one! So let’s get started‚ this hexagon has a radius of 6 cm‚ keep in mind that there are many different ways to do find the area of a hexagon. Use the formula 1/2asn meaning; ½ (apothem) (side length) (number of sides).You can put two radii (radii is a term for more than one radius) together and make a triangle. There is a problem we do not know the
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b)h h 2 b Volume of prism = area of cross section × length crosssection h lengt r 4 πr3 Volume of sphere = – 3 Surface area of sphere = 4 π r 2 1 Volume of cone = – π r2h l 3 h Curved surface area of cone = π rl r In any triangle ABC Area of triangle = 1 – 2 C ab sin C a b b a c Sine rule ––––– = ––––– = ––––– sin A sin B sin C A c B Cosine rule a2 = b2 + c2 – 2bc cos A The Quadratic Equation The solutions of ax2 + bx + c = 0‚ where a ≠ 0‚ are given by – b ± √ (b2 – 4ac)
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FORM 5 MATHEMATICS Chapter 3 TRANSFOMATION 111 NAME :__________________________________________ FORM 5 _________________________ 3.1 TRANSLATION (a) Base on the graph below‚ state the translation (i) A → A’ translation (ii) B → B’ (iii) C → C’ (iv) D → D’ (v) E → E’ (b) A Point P is located at coordinates (4‚3) on a Cartesian plane. P’ is the image of P under a translation
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area of cone = rl b hyp 1 3 h r opp adj = hyp cos opp = hyp sin opp = adj tan sin adj hyp tan or C opp hyp cos adj In any triangle ABC opp adj b a A B c a sin A Sine rule: b sin B c sin C Cosine rule: a2 = b2 + c2 – 2bc cos A Area of triangle = 1 2 ab sin C cross section lengt h Volume of prism = area of cross section length Area of a trapezium = r 1 2 (a + b)h a
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