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

2. 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.

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

4. 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)

5. 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.

6. 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 =

7. 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

8. 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.

9. 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.

10. 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.

11. 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.

12. 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

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

14. 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.

15. 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.

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

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

18. 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)

19. 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.

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

21. 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.