Download ACT Math - Squarespace

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