MATH CHEAT SHEET (HIGH SCHOOL)


Unless you’re an accountant, an engineer or a math teacher, you’ve probably long forgotten some of the so-called higher math taught in high school.

In high school, your child will start thinking more theoretically in math class. With the basics and the more practical uses of math under their belts, they’ll start to expand their general mathematical understanding onto different planes. Geometry and trigonometry are major components of higher math.

Because it’s unlikely you use sines and cosines to balance your checkbook, you’ve probably forgotten much of what your student will be studying. Here are a few tips to get your mathematical motor running again.

Polygon Properties
Regular—all angles are equal and all sides are the same length. Regular polygons are both equiangular and equilateral.
Equiangular—all angles are equal.
Equilateral—all sides are the same length.

Names
Sides Names
N N-gon
3 Triangle
4 Quadrilateral
5 Pentagon
6 Hexagon
7 Heptagon
8 Octagon
10 Decagon
12 Dodecagon

Perimeter Formulas
The perimeter of any polygon is the sum of the lengths of all sides.
Set: a = side 1
b = side 2
c = side 3

Square = 4a
Rectangle = 2a + 2b
Triangle = a + b + c
Circle = 2 π r (where π = 3.141592 … and r = radius)

Area Formulas
Square = a2
Rectangle = ab
Triangle = ½ (bh) (where b = base h = height)
Parellelogram = bh
Circle = π r2

Phythagorean Theorem
The Pythagorean Theorem has many uses. You can use it to verify whether or not a triangle is a right triangle or you can use it to find the missing measures of sides.

a2 + b2 = c2

Where a and b are the two legs, and c is the hypotenuse, the side opposite the right angle.

Trigonometry
One of the many operations that function based on the right triangle, trigonometry focuses on the relationship between an angle and its sides. If one value of a right triangle is known—whether a side length or an angle degree—you can determine the rest of its values using the following trigonometric functions:

Functions
sine (sin) = opposite/hypotenuse
cosine (cos) = adjacent/hypotenuse
tangent (tan) = opposite/adjacent
cosecant (csc) = hypotenuse/opposite
secant (sec) = hypotenuse/adjacent
cotangent (cot) = adjacent/opposite

Worksheet
1.) Determine the area of a parallelogram with a base of 10 feet and a height of 2 feet.
2.) What is a square’s perimeter if one of its sides equals 4?
3.) If a circle has a radius of 5, what is its area?
4.) A right triangle’s a leg equals 16, and its b leg equals 12, what does its hypotenuse equal?
5.) Determine if this set of numbers equates to a right triangle. a = 9, b = 12, c = 15.
6.) Find the length of the missing side (a) for a triangle where b = 200 and c = 400.
7.) In a right triangle ABC, B = 55° 30', and b = 6.05. Find c and a.
8.) In each of the following right triangles of which two sides are given, compute the sin, cos, and tan of the angles A and B.
Express the results as common fractions.
(i). c = 41, a = 9.
(ii). c = 37, a = 35.
(iii). a = 24, b = 7.
9.) In a right triangle c = 6.3 and tan B = 1.2. Find a and b.
10.) a = 1.2, b = 2.3. Find A and c.

Answers
1.) 20 feet
2.) 16
3.) 78.54
4.) c = 20
5.) Yes, it is a right triangle. 92 + 122 = 152 OR 81 + 144 = 225.
6.) a = 346.4
7.) c = b/sin B = 6.05/sin 55°30' = 7.34. a = 4.16.
8.) (i). b = 40. So, sin A = cos B = 9/41, cos A = sin B = 40/41, tan A = 9/40, tan B = 40/9.
(ii). b = 12. So, sin A = cos B = 35/37, cos A = sin B = 12/37, tan A = 35/12, tan B = 12/37.
(iii). c = 25. So, sin A = cos B = 7/25, cos A = sin B = 24/25, tan A = 7/24, tan B = 24/7.
9.) a = 4, b = 4.8
10.) A = 27.55°, about 28°.
c = 2.6.


By Natalie Bauer