# Math 2

Flashcards by Jadéjah Robinson, updated more than 1 year ago Created by Jadéjah Robinson over 6 years ago
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### Description

Math 2 Syllabus for 2015 EOCs Transformations Triangles and Proofs Trigonometry Concepts of Algebra Interpret Functions Systems Special Functions Quadratics Statistics and Probability

## Resource summary

 Question Answer 4 units to the right ( x+4, y ) 8 units down ( x, y - 8 ) 2 units left and 4 units up ( x - 2 , y + 4 ) reflect over the y axis ( - x, y ) reflect over the x axis ( x, - y ) reflect over the line y=x ( y, x ) rotate 90 degrees cc ( -y, x ) rotate 180 degrees cc ( -x, y ) rotate 270 degrees cc ( y, - x ) A ( -2, 5), B (2, 4), C (3, -3) Rotate AB 270 degrees cc A' (5,2) B' (4,-2) A ( -2, 5), B (2, 4), C (3, -3) Rotate BC 90 degrees clockwise B' (4,-2) C' (-3,-3) A ( -2, 5), B (2, 4), C (3, -3) Rotate ABC across the line y=x A' (5, -2) B' (4, 2) C' (-3,3) A ( -2, 5), B (2, 4), C (3, -3) Translate AC 3 units left and 2 units down A' (-5, 3) C' (0, -5) A ( -2, 5), B (2, 4), C (3, -3) Translate ABC 2 units right and 1 unit up, then dilate by a factor of 2 A' (0, 12) B' (8, 10) C' (10, -4) A ( -2, 5), B (2, 4), C (3, -3) Dilate AC by a factor of 3 then rotate 90 degrees clockwise A' (15, 6) B' (-9, -9) (3y, -3x) A ( -2, 5), B (2, 4), C (3, -3) Translate AB up 2 units and down 2 units, then dilate by factor of 2, then rotate 270 degrees clockwise. A' (-4, 10) B' (4, 8) A'' (-10,-4) B''(-8, 4) Describe ( x-3, y+6 ) Translating 3 units left and 6 units up If A' was rotated 270 degrees cc what were the original points of A? A (2, -5) parent function of linear equation y = x direct variation y = kx E (-1, -3.5) F (4, -3) G (0, 1) H (-4, -2) Scale factor 0.5 Graph E (-1, -3.5) F (2, -1.5) G (0, 0.5) H (-2, -1) Classify Angle 2 and 4 Corresponding Angles Classify Angles 5 and 10 Alternate Interior Angles Classify Angles 14 and 15 Same Side Interior Angles Ana made a zip line for her tree house. To do this, she attached a pulley cable. She then strung the cable at an angle between the tree house and another tree. She made the drawing of the zip line at the left. The two trees are parallel. What is the measure of angle 1 and are angle 1 and the given angle same-side interior angles, alternate interior angles, or corresponding angles? a) 105 degrees b) Same-side interior angles Identify all numbered angles that are congruent to the given angle Angle 6: Vertical Angle 4: Corresponding Angle 2: Alternate Interior Find angle 1 AND 2 Angle 1: 76 degrees ( alternate interior) Angle 2: 180 degrees (same side interior) Find the value of x. Then find the value of each labeled angle x = 75 x+10 = 85 x+20 = 95 y = 110 y-40 = 70 Find the values of the variables. w = 59 x = 121 y = 59 v = 121 z = 53 Find the value of x. x = 24 Simplify. (n^4 - 2n -1) + (5n - n^4 + 5) 3n + 4 Simplify. (2x^2 - 9x +11) (2x + 1) 4x^3 - 16x^2 + 11x + 11 (y^2 - 4w^2) ^2 y^4 - 8y^2 + 16w^4 The bisectors of the angles of a triangle intersect in a point that is equidistant from the three sides of the triangle Incenter The lines that contain the altitudes, intersect in a point Orthocenter The medians of a triangle intersect in a point that is two-thirds the distance from each vertex to the midpoint of the opposite side Centroid The perpendicular bisectors of the sides of a triangle intersect in a point that is equidistant from the three vertices of the triangle. This construction is used to circumscribe a circle. Circumcenter A line that contains the midpoints of one side of a triangle and is parallel to another side passes through the midpoint of the third side Midsegment Midpoint formula [( x1+x2) /2, (y1+y2)/2] Mid-segment = _____ of third side 1/2 3rd side = _____ midsegments 2 A segment from the vertex to the midpoint of the opposite side. Median The perpendicular segment from a vertex to the line that contains the opposite side Altitude The point of intersection of two or more lines Point of concurrency Median in ABC CJ Altitude for AHB AH Intersection of altitudes Orthocenter Name the orthocenter Point Y Pythagorean Theorem c^2 = a^2 + b^2 Find x 3 *square root sign* 3 Find the value of y 8 *square root sign* 2 45 - 45 - 90 triangle Hypotenuse = leg times square root of two 30 - 60 - 90 triangle Hypotenuse = 2 times the short leg Long leg = short leg times the square root of 3 (5 * the square root of 2)^2 5^2 * (the square root of 2)^2 25 * 2 50 Equation of a circle r^2 = (x-h)^2 + (y-k)^2 Center: (h,k) Tangent opposite/adjacent Sine opposite/hypotenuse Cosine adjacent/opposite SOH - CAH - TOA SOH - CAH - TOA Used when trying to find the measure of one of the acute angles, given the lengths of the side Inverse Trigonometric Function The length of the hypotenuse of a 30 - 60 - 90 triangle is 9. Find the perimeter. 27/2 + 9/2 * the square root of 3 ______ ft = 1 mile 5280 2 miles 96 Distance formula the square root of: (x2 - x1)^2 + (y2 - y1)^2 To find the height of a pole, a surveyor moves 140 feet away from the base of the pole and then, with a transit 4 feet tall, measures the angle of elevation to the top of the pole to be 44 degrees. To the nearest foot, what is the height of the pole? 139 feet Equation for finding discriminant b^2 - 4ac Discriminant greater than 0: ___ solutions 2 solutions Discriminant equal to 0: ___ solutions 1 solution Discriminant less than 0: ___ solutions no real number solutions

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