U1 AP Calc AB Oral Quiz

How do you multiply fractions, divide fractions, add fractions, subtract fraction, and solve fraction equations?

multiply fractions straight across,

divide fractions by flipping the second fraction and multiplying straight across

add fractions by using the butterfly method

subtract fractions with the butterfly

method, but you subtract the antennae instead

solve fractions by cross multiplying across the equal signs and then solving with factoring or SADMEP.

How do you find a fraction power (such as 8²/³? How do you find a negative power like 2-³?

You do a fraction power by taking the root of the bottom number and then the power of the top number (therefore 8²/³ = ³√8² = 2² = 4). You do a negative power by putting it on the bottom of the fraction and then powering it (therefore 2-³ = 1/2³ = 1/8)

What can x^a+b also be written as? What can xa-b also be written as? What can x^a*b also be written as?

x^{a+b} can be written as x^a * x^b,

x^{a-b} can be written as (x^a/x^b),

x^{a*b} can be written as (x^a)^b.

What is the formula for finding the area of a circle, a semicircle, a quarter-circle, a rectangle, a triangle, and a square? What is formula for the perimeter of a square and the circumference of a circle?

Area of a Circle = 𝜋𝑟²

Area of a Semicircle = ½ 𝜋𝑟²

Area of a Quarter-Circle= ¼ 𝜋𝑟²

Area of a Rectangle = length * width

Area of a Triangle = ½ * base * height

Area of a Square = side²

Perimeter of a square = 4 * the sides

Circumference of a circle = 2𝜋r

What is the formula for the surface area of a cube and a sphere? What is the formula for the volume of a cube, sphere, cylinder and cone?

Surface area of cube = 6𝑠²

Surface area of a sphere = 4𝜋𝑟²

Volume of a cube = 𝑠³

Volume of a sphere = 4/3 𝜋𝑟³

Volume of a cylinder = 𝜋𝑟²ℎ

Volume of a cone = 1/3 𝜋𝑟²ℎ

What is e the zero? What is the number e equivalent to (rounded to one decimal place)? Is e to the anything ever equal to zero? What is e to the anything always equal to?

e^0 = 1

𝑒^1 ≈ 2.7

e to the anything is never equal to zero.

e to the anything is always a positive number

What is ln 0? What is ln 1? What is ln(-#)? What can ln (a/b) (read as natural log of a times b) also be written as? What can ln a^r (read as natural log of a divided by b) also be written as? What can ln 𝑎) also be written as?

ln 0 = DNE

ln 1 = 0

ln(−#) = nonexistent

ln (𝑎 + ln 𝑏 = ln(𝑎𝑏)

ln 𝑎 − ln 𝑏 = ln a/b

𝑟 ln 𝑎 = ln 𝑎^r

What is the formula for finding the slope between two points? What are four formulas for the equation of a line?

Formula for the slope between two points = (𝑦² − 𝑦^1) / (𝑥² − 𝑥^1)

The four different equations for a line are:

Standard form = 𝐴𝑥 + 𝐵𝑦 = 𝐶, where A, B, and C are whole numbers

Point Slope Form = 𝑦 − 𝑦^1 = 𝑚(𝑥 − 𝑥^1)

Free Response Form = 𝑦 = 𝑚(𝑥 − 𝑥^1) + 𝑦^1

Slope Intercept Form = 𝑦 = 𝑚𝑥 + b

What can sec 𝑥 be algebraically simplified to? What about csc 𝑥 , tan 𝑥 , and cot 𝑥?

sec x = 1/cos x

csc x = 1/sin x

tan x = sin x/cos x

cot x = cos x/sin x

What is the difference between sec x and arccos x? What is the difference between csc x and arcsin x?

sec x is 1 over cosine and arccos is the opposite of cosine (it undoes a cosine in solving a problem). Csc x is 1 over sine and arcsine is the opposite of sine (it undoes a sine in solving problems). They are not related to each other at all

What is SOHCAHTOA? What is the Pythagorean theorem?

For SOHCAHTOA, first the opposite side is the one across from the angle 𝜃 and adjacent is the side touching the angle 𝜃 and hypotenuse is always across the right angle. Then,

sin 𝜃 = 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 / ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

cos 𝜃 = 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 / ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

tan 𝜃 = 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 / 𝑎𝑑𝑗𝑒𝑐𝑒𝑛𝑡

csc 𝜃 = ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 / 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒

sec 𝜃 = ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 / 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡

cot 𝜃 = 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 / 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒

Pythagorean Theorem is (𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡)² + (𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒)² = (ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒)²

When solving an equation how do you know if you have to use SADMEP or factoring? Explain what SADMEP means?

When solving equations, you will use SADMEP when the variable in the problem is only written once. And, you will use factoring when the variable is written more than one time

What is the opposite of adding, the opposite of multiplying, the opposite of squared, the opposite of cubed, the opposite of sin, the opposite of cos, the opposite of tan, the opposite of ln?

opposite of adding is subtracting.

opposite of multiplying is dividing.

opposite of squared is plus and minus square root.

opposite of cubed is cube root.

The opposite of sine is arcsine (sin^-1𝑥 in your calculator).

opposite of cosine is arccosine (cos^-1𝑥 in your calculator).

opposite of tangent is arctangent (tan^-1𝑥 in your calculator).

opposite of ln is e to the power

There are five things that you should be able to do in a calculator: find 𝑓(#), find where an equation equals 0, find the intersection of two graphs, find the derivative, find the integral. What do you do first for all of them? Then I will ask how you do each one.

push y=, type equation using x, T, theta, n

find f(#) type alpha, trace, choose equation then push 2nd quit, type x-value, graph, trace, type x-value

find the zero of an equation type the equation into 𝑦% and 0 into 𝑦!. Then type 2nd trace and

then 5 . Push enter and enter and then guess the x-value where the graph crosses the x-axis.

- To find the intersections of two graphs put one into 𝑦% and the other into 𝑦!. Then type 2nd trace

and then 5 . Push enter and enter and then guess the x-value it looks like the two graphs

cross at.

- To find a derivative, you push math 8 on the main screen.

- To find an integral, you push math 9 on the main screen

How do you know if numbers with parenthesis like (2, 7) are an interval or a point? What is the difference between a point and an interval?