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ACT 1-on-1 Curriculum Math: Geometry & Trigonometry ACT Math General Strategies • Write down your work! – Do not just go to your calculator to find the answer. Write it down. – If you work it out, you can review the steps to get the right answer if you make a mistake. • Pace yourself – It is easy to lose track of time on one problem. – Do not spend too much time on any one problem. • Read the questions carefully! – This is a way to avoid easy mistakes. • Pick & Plug – Use the answer choices to help you solve the problem. • Oddball Answers are OK – In math, many times the odd answer out is the correct one. • Assign Values to Variables – If a question has numerous variables, assign a consistent numerical value to help you solve it. ACT Math Number Lines and Inequalities — Coordinate Geometry • Number line questions generally ask you to graph inequalities. x≤1 x > -2 -3 0 3 -3 0 3 ACT Math Coordinate Plane – Coordinate Geometry • The coordinate plane consists of the xaxis and y-axis. • These axes intersect at the origin. • Points can be defined in parenthesis as (x-coordinate, y-coordinate) ACT Math Distance Formula — Coordinate Geometry • To find the distance between any two points, use this formula: Distance = 𝑥2 − 𝑥1 2 y + (𝑦2 − 𝑦1 )2 x O ACT Math Midpoint Formula — Coordinate Geometry y • To find the midpoint between two coordinate points, use this formula: Midpoint = x1 + x2 y1 + y2 , 2 2 x O ACT Math Slope Formula — Coordinate Geometry y • To find the slope of any line, use this formula: Slope = rise run y −y = x 2 − x1 2 1 x • O Slope-intercept form is: y = mx + b where m is the slope and b is the y-intercept ACT Math Parallel/Perpendicular Lines — Coordinate Geometry y • Positive slope goes down to up. • Negative slope goes up to down. • Parallel lines have identical slopes x O • Perpendicular lines have opposite inverse slopes. ACT Math Graphing Equations — Coordinate Geometry y • To shift a graph left or right, add inside the function’s argument • To shift a graph up or down, add outside the function’s argument x O ACT Math Coordinate Geometry • Work on the following Practice Problems from 61D: – – – – # 31 # 33 # 36 # 44 ACT Math Angles — Plane Geometry • Vertical angles are equal – • Isosceles Triangle— – • A straight line is 180° If the sides are the same, the corresponding angles are the same Transversals – Corresponding angles are equal ACT Math Right Triangles — Plane Geometry • Whenever you see a right triangle, remember: a2 + b2 = c2 c a b ACT Math Circles — Plane Geometry • Area of a Circle A = πr 2 . • Circumference of a circle C = 2𝜋𝑟 = 𝜋𝑑 ACT Math Circles — Plane Geometry y • Equation of a Circle x − h 2+ y − k 2= r2 • • (h,k) is the center of the circle r is the radius x O ACT Math Arc Length and Sector Area — Plane Geometry • Arc Length and Sector Area central angle = 360° arc length = circumference sector area area of circle ACT Math Parallelograms — Plane Geometry • Area of a Parallelogram Area= base x height h b ACT Math Triangles — Plane Geometry • Area of a triangle Area = ½ base x height h b ACT Math 3D Geometry — Plane Geometry • Volume Volume = Area x height For a prism, this is V = lwh • Surface Area SA = 2 𝑙 𝑥 ℎ + 2 𝑙 𝑥 ℎ + 2 𝑤 𝑥 𝑙 ACT Math Plane Geometry • Work on the following Practice Problems from 61D: – – – – – – – – – – – – # 13 # 17 # 18 # 23 # 25 # 28 # 29 # 30 # 45 # 46 # 48 # 51 ACT Math Trigonometry sin 𝐴 = 𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 cos 𝐴 = 𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 tan 𝐴 = 𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 ACT Math Trigonometry /Strategies Practice • Work on the following Practice Problems from 61D: – – – – # 22 # 49 # 58 # 59