Math: Geometry & Trigonometry ACT 1-on-1 Curriculum Math: Geometry & Trigonometry

ACT Math General Strategies Write down your work! Pace yourself 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.

Number Lines and Inequalities — Coordinate Geometry ACT Math Number Lines and Inequalities — Coordinate Geometry Number line questions generally ask you to graph inequalities. x > -2 x ≤ 1 -3 3 -3 3 Have them come up and do the example on the board.

Coordinate Plane – Coordinate Geometry ACT Math Coordinate Plane – Coordinate Geometry The coordinate plane consists of the x- axis and y-axis. These axes intersect at the origin. Points can be defined in parenthesis as (x-coordinate, y-coordinate)

Distance Formula — Coordinate Geometry ACT Math Distance Formula — Coordinate Geometry To find the distance between any two points, use this formula: Distance = x O y Put a point up and find the distance. Show students as well how this is based off the Pythagorean theorem—if they cannot remember the formula, have them draw a triangle and solve for the hypotenuse.

Midpoint Formula — Coordinate Geometry ACT Math Midpoint Formula — Coordinate Geometry x O y To find the midpoint between two coordinate points, use this formula: Midpoint =

Slope Formula — Coordinate Geometry ACT Math Slope Formula — Coordinate Geometry x O y To find the slope of any line, use this formula: Slope = Slope-intercept form is: y = mx + b where m is the slope and b is the y-intercept rise run = y 2 − y 1 x 2 − x 1

Parallel/Perpendicular Lines — Coordinate Geometry ACT Math Parallel/Perpendicular Lines — Coordinate Geometry x O y Positive slope goes down to up. Negative slope goes up to down. Parallel lines have identical slopes Perpendicular lines have opposite inverse slopes.

Graphing Equations — Coordinate Geometry ACT Math Graphing Equations — Coordinate Geometry x O 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 Explain this. Show an example as you do it.

ACT Math Coordinate Geometry Work on the following Practice Problems from 61D: # 31 # 33 # 36 # 44 Use problems from the sheet in your handout. You can assign one per student, cherry pick certain problems, or have them work through them all.

Angles — Plane Geometry ACT Math Angles — Plane Geometry Vertical angles are equal A straight line is 180° Isosceles Triangle— If the sides are the same, the corresponding angles are the same Transversals Corresponding angles are equal Also on transversals, hit the point that points on the same line equal 180⁰ and that the same side angles are supplementary as well.

Right Triangles — Plane Geometry ACT Math Right Triangles — Plane Geometry Whenever you see a right triangle, remember: a2 + b2 = c2 c Emphasize the need to make right triangles out of things. Show a problem like p. 169 #25, emphasizing that on any of these problems, you can make a right triangle with the radius (especially if the radius does not touch the line). a b

Circles — Plane Geometry ACT Math Circles — Plane Geometry Area of a Circle Circumference of a circle

Circles — Plane Geometry ACT Math Circles — Plane Geometry x O y Equation of a Circle (h,k) is the center of the circle r is the radius (x−h) 2 + (y−k) 2 = r 2 Emphasize the need to memorize this. There will be one question on the ACT that is based upon this form. If students know it, they can get it correct.

Arc Length and Sector Area — Plane Geometry ACT Math Arc Length and Sector Area — Plane Geometry Arc Length and Sector Area Arc length and sector area are proportional to the central angle. Make a ratio with it.

Parallelograms — Plane Geometry ACT Math Parallelograms — Plane Geometry Area of a Parallelogram Area= base x height b h

Triangles — Plane Geometry ACT Math Triangles — Plane Geometry Area of a triangle Area = ½ base x height h b

3D Geometry — Plane Geometry 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 Use problems from the sheet in your handout. You can assign one per student, cherry pick certain problems, or have them work through them all.

ACT Math Trigonometry sin 𝐴 = 𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 cos 𝐴 = 𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 tan 𝐴 = 𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 Walk through this by assigning values to the triangle.

Trigonometry /Strategies Practice ACT Math Trigonometry /Strategies Practice Work on the following Practice Problems from 61D: # 22 # 49 # 58 # 59 Use problems from the sheet in your handout. You can assign one per student, cherry pick certain problems, or have them work through them all.