**Test for Admission to Catholic High Schools (TACHS):**

**(P = 4s)**

of rectangle = twice the length plus twice the width

**(P = 2L + 2W)**or twice the base plus twice the height (P = 2b + 2h)

Circumference = Pi times the diameter **(C =**** πD**) or Pi times twice the radius

**(C =**

*2π*r)Pythagorean Theorem: **a ^{2} + b^{2} = c^{2}**

Area = the stuff inside a flat 2-dimensional object; what you would measure if you painted it; square units (ft^{2}, m^{2}, etc)

of a square = 4 times the length of a side **(P = 4s)**

of rectangle = length * width (**A = LW)** or base times height **(A = bh)**

of a triangle = half the base times the height **(A = ****0.5bh)**

of a circle = the radius squared, then times Pi **(C = ***π*r^{2})

^{3}, m

^{3}, etc)

=the area of a face * the height

for rectangular solids = length * width * height **(V = L W h)**

Average = the sum of the numbers divided by the how many **(Average = sum / #)**

The sum of the angles in a triangle is 180^{O}.

The sum of the angles in a rectangle is 360^{O}.

^{O}.

4 quarts in a gallon, 3 feet in a yard, 100 centimeters in a meter, 1000 millimeters in a meter, 1000 meter in a kilometer

**Distance = rate * time** can also be included but is a specific version of a proportion. Anything that can be solved as d = rt can also be solved as a proportion. There are many types of problems that can be solved as proportions so there is no need to memorize a new formula, but it would be a good idea to understand how this formula relates to both proportions and graphing (y = mx + b) for the SHSAT.

**Adding Integers:**

**Subtracting Integers**: Subtracting a number is the same as adding a negative version of that number. Example: 5 – 1 = 5 + -1

**Multiplying and Dividing Integers:** Multiply or divide normally but answer is negative if unlike signs and positive if like signs. Example: -2 * -5 = +10

**Adding and Subtracting Fractions**: Find common denominator, then add or subtract numerators. Example: 1/2 + 1/4 = 3/4

**Multiplying Fractions:** Multiply across. Example: 1/2 * 1/2 = 1/4 (Half of a half is a quarter)

**Dividing Fractions:**Dividing by a fraction is the same as multiplying by the reciprocal. Example: 2/5 divided by 2 = 1/5

The **order of operations** always applies. Parentheses come first, then exponents, then multiplication or division (as you should see from above, they can be expressed as the same operation), then addition or subtraction (similarly, they can be expressed as the same operation). When in doubt about the order between multiplication and division or addition and subtraction, go left to right.

Division can be expressed as the division symbol, “/”, a fraction (and therefore a decimal less than 1 or percentage less than 100%), “per”, or raised to a negative exponent like 5^{-2} = 1/25

**SHSAT, HSPT Formula Sheet:**

**Sum = (n-2)*180**

**)**

^{O}Volume of Sphere = **(4/3)***π*r^{3}

**Multiplying Monomials:**Add the exponents. Example: x

^{3}* x

^{2}= x

^{5}

**Dividing Monomials:**Subtract the exponents. Example: x

^{3}/ x

^{2}= x

^{1}= x

Physics Regents: Physics Regents Reference Table (pdf)