ACT 1-on-1 CurriculumMath: Geometry & Trigonometry

ACT Math

• 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.

General Strategies

ACT Math

• Number line questions generally ask you to graph inequalities.

x > -2x ≤ 1

Number Lines and Inequalities — Coordinate Geometry

0 3-3 0 3-3

• 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)

ACT MathCoordinate Plane – Coordinate Geometry

ACT Math

• To find the distance between any two points, use this formula:

Distance =

Distance Formula — Coordinate Geometry

xO

y

ඥሺ𝑥2 − 𝑥1ሻ2 + (𝑦2 − 𝑦1)2

ACT Math

• To find the midpoint between two coordinate points, use this formula:

Midpoint =

Midpoint Formula — Coordinate Geometry

xO

y

൬x1 + x22 ,y1 + y22 ൰

ACT Math

• To find the slope of any line, use this formula:

Slope =

• Slope-intercept form is:

y = mx + b

where m is the slopeand b is the y-intercept

Slope Formula — Coordinate Geometry

xO

y

=

ACT Math

• Positive slope goes down to up.

• Negative slope goes up to down.

• Parallel lines have identical slopes

• Perpendicular lines have opposite inverse slopes.

Parallel/Perpendicular Lines — Coordinate Geometry

xO

y

ACT Math

• 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

Graphing Equations — Coordinate Geometry

xO

y

ACT Math

• Work on the following Practice Problems from 61D:

Coordinate Geometry

– # 31– # 33– # 36– # 44

ACT Math

• 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

Angles — Plane Geometry

ACT Math

• Whenever you see a right triangle, remember:

a2 + b2 = c2

Right Triangles — Plane Geometry

a

b

c

ACT Math

• Area of a Circle

• Circumference of a circle

Circles — Plane Geometry

A = πr2.

C = 2𝜋𝑟 = 𝜋𝑑

ACT Math

• Equation of a Circle

• (h,k) is the center of the circle• r is the radius

Circles — Plane Geometry

(x −h)2+( y −k )2=r2

xO

y

ACT Math

• Arc Length and Sector Area

Arc Length and Sector Area — Plane Geometry

central angle = arc length = sector area 360° circumference area of circle

ACT Math

• Area of a Parallelogram

Area= base x height

Parallelograms — Plane Geometry

b

h

ACT Math

• Area of a triangle

Area = ½ base x height

Triangles — Plane Geometry

b

h

ACT Math

• Volume

Volume = Area x height

For a prism, this is V = lwh

• Surface Area

SA =

3D Geometry — Plane Geometry

ACT Math

• Work on the following Practice Problems from 61D:

Plane Geometry

– # 13– # 17– # 18– # 23– # 25– # 28– # 29– # 30– # 45– # 46– # 48– # 51

ACT MathTrigonometry

=

=

=

ACT Math

• Work on the following Practice Problems from 61D:

Trigonometry /Strategies Practice

– # 22– # 49– # 58– # 59