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Transcript
23 questions 14 plane geometry 9 coordinate geometry No proofs, theorems Common formulas and questions Most drawings are actually drawn to scale Easier to do process of elimination If there is no drawing and you are confused draw one Angles and lines Triangles Quadrilaterals Circles Lines form angles of 180˚ Two intersecting lines make four angles but they only have two different measures Two lines cut by a transversal make 8 angles but they still only have two different measures Vertical angles are opposite each other and are equal Supplementary angles add up to equal 180˚(linear pair) Three sided figure Sum of interior angles is 180˚ Isosceles triangle = two sides of equal length Equilateral triangle = all sides and angles of equal measure Right triangle = one angle of the triangle is 90˚ Pythagorean Theorem = a2 + b2 = c2 Pythagorean triple = three numbers that solve the Pythagorean theorem Area of a triangle = A = ½ bh 3, 4, 5 5, 12, 13 7, 24, 25 Any multiples of these Isosceles right triangles Angles are 45˚-45˚-90˚, sides are in the ratio 1:1:√2 or x:x:x√2 30˚-60˚-90˚triangles Angles are 30˚-60˚-90˚, sides are in the ratio 1:√3:2 or x:x√3:2x Angle measures are the same Sides are proportional Set up proportions to find the missing sides Four sided figures, sum of interior angles is 360˚ Square = four equal sides, four right angles A = s2, P = 4s Rectangle = four right angles A = lw, P = 2l +2w Parallelogram A = bh, P =2b +2h Trapezoid = two pairs of parallel sides = one pair of parallel sides A = ½ h(b1+b2) Radius = distance from the center of the circle any point on the circle Diameter = distance from one point on the circle to another going through the center Chord = line segment connecting two points on the circle that does not go through the center Tangent = line that only touches the circle in one distinct spot Circumference = distance around, C = 2πr Area = A = πr2 Graphing!!!!!!!!! Number-lines, inequalities Graphing on a coordinate plane Graphing inequalities on a number line Solve the equation as if there is an equal sign. If there is an equal to line under the inequality sign, there will be an closed or filled in circle If there is no equal to line under the inequality sign, the circle is open. A solid line denotes which numbers are solutions to the problem Cartesian grid or plane Few actual graphing questions on ACT, mostly you will use graphs to answer questions Use process of elimination to narrow down Is the answer in the right quadrant? Could the point be on the line? Slope intercept or Y-intercept formula Slope formula Midpoint formula Distance Formula Circles Ellipses Parabolas y=mx+b m is the slope b is the y intercept (y1-y2) m= --------- (x1-x2) x1+x2/2, y1+y2/2 d = √((x2-x1)2+(y2-y1)2 (x-h)2+(y-k)2=r2 Center of the circle is (h,k) r is the radius (x-h)2+(y-k)2 ----a2 Center ----- =1 b2 of the ellipse (h, k) 2a = horizontal axis width 2b = vertical axis width y=x2 They will give you a standard formula and ask you to put it into slope intercept They will give you points and ask you to find slope Find midpoints given two coordinates or find the missing coordinate if you know one and the midpoint Find distance between points They will give you an equation and ask you what shape it will be when graphed You can graph most of these on your calculator to solve Or you can estimate most of them Worksheets