SMRM

What is the decimal equivalent of 1/8?

0.125

What is the decimal equivalent of 1/5?

0.20

What is the decimal equivalent of 1/4?

0.25

What is the decimal equivalent of 1/3?

0.33

What is the decimal equivalent of 1/2?

0.5

What is 1^2?

1

sin^2 x + cos^2 x

1

Q2) What should you do to the exponents (i.e., do you add them, multiply them, etc.) when you perform the following functions on numbers in scientific notation? b) multiply two numbers in scientific notation

1) Can I visualize it? 2) Can I draw a picture, graph, or diagram of it? 3) Can I explain it to someone else in layman's terms? 4) Can I think of and describe real-life examples?

deci (d)

1/10 or 10^-1

What is 10^2?

100

pico (p)

10^-12

femto (f)

10^-15

centi (c)

10^-2

milli (m)

10^-3

micro (u)

10^-6

nano (n)

10^-9

deca (da)

10^1

tera (T)

10^12

hecto (h)

10^2

kilo (k)

10^3

mega (M)

10^6

giga (G)

10^9

What is 11^2?

121

What is 12^2?

144

What is 4^2?

16

What is 13^2?

169

Q5) All of the angles in any triangle must add up to

180 degrees

π radians

180 degrees

14^2?

196

15^2?

225

What is 5^2?

25

What is 6^2?

36

2π radians

360 degrees

What is 2^2?

4

What is 7^2?

49

Q4) How do you represent a small whole number, such as 5, in scientific notation?

5 × 10^0

What is 8^2?

64

What is 9^2?

81

What is 3^2?

9

Area of a triangle

A = 1/2bh

Area of a circle

A = πr 2

Q3) How do you simplify if you end up with a number such as 0.05 x 10^-2 or 220 x 10^12

A number such as 0.05 x 10-2 can be simplified by moving the decimal to the right or to the left to achieve the correct arrangement with only one digit prior to the decimal. The mnemonic LARS can be used to remember that moving to the Left requires adding to the exponent and moving to the right requires Subtracting from the exponent.

cos(theta)

A/H

secant(theta)

A/H

cotangent(theta)

A/O

Pythagorean Theorem

A^2 + B^2 = C^2

Circumference of a circle

C = πd or C = 2πr

Graphs as Answer Choices: Often, the four answer choices for a question will be four different graphs. When asked to choose or predict a graph, ask yourself the following three questions. 1) Does the y-value start high or term-82low?

Does the y-value start high or low? In other words, when the graph first begins, is the value represented on the y-axis large or small? ASK YOURSELF: "Is it most logical at the beginning of this experiment or trial for this value to be high (i.e., at its max value) or for it to be low (i.e., at its minimum value)?

What is important to remember about Estimating Square Roots?

Find one you know that is just more than the number you are taking the square root of, and one that is just less. The answer will be in between those two. For example, the square root of 72 is estimated by saying that 82 is 64 and 92 is 81. Seventy-two is approximately in the middle of 64 and 81, so the square root of 72 is about 8.5. 1) Can I visualize it? 2) Can I draw a picture, graph, or diagram of it? 3) Can I explain it to someone else in layman's terms? 4) Can I think of and describe real-life examples?

For fractions where the numerator is larger, create a compound fraction. What is an example of this?

For example, 13/5 becomes 2 3/5 or exactly 2.60. It is surprising how often students get stuck because they forget this simple tool. One AAMC practice question results in an original answer of 16/81. Eight out of ten students get stumped at that point because they can't reduce this fraction and it's not one of the answer choices. However, if you remember to estimate, you could simply round it to 16/80, which simplifies to 4/20, or 1/5th . 1) Can I visualize it? 2) Can I draw a picture, graph, or diagram of it? 3) Can I explain it to someone else in layman's terms? 4) Can I think of and describe real-life examples?

cosecant(theta)

H/O

Recognizing Linear vs. Non-Linear Relationships:

If two variables are both in an equation, and one of them contains an exponent, log, ln, or root, the graph of either variable vs. the other will yield a non-linear graph. However, if BOTH variables contain the exact same math (i.e., both are cubed, or both are square rooted), the graph of one versus the other will be linear.

Graphs as Answer Choices: Often, the four answer choices for a question will be four different graphs. When asked to choose or predict a graph, ask yourself the following three questions. 3) What is the sign of the y-axis?

Is the value on the y-axis always positive, always negative, or is it both? This will help you decide whether your graph should start above or below the x-axis, and if you expect it to ever cross the x-axis.

tan(theta)

O/A or sin(theta)/cos(theta)

sin (theta)

O/H

Surface Area of a sphere

SA = 4πr 2

Mantissa and Exponent Part

The number part of scientific notation (i.e., 2.0) is called "the mantissa." The exponent part (i.e., x 10^4) is called "the power" or "the exponent."

How many radians are in one circle?

There are approximately 6 radians in one circle. Thus, if something is rotating at 12 rad/s, you know that it is making roughly two revolutions per second.

Volume of a sphere

V = 4/3πr 3

Graphs as Answer Choices: Often, the four answer choices for a question will be four different graphs. When asked to choose or predict a graph, ask yourself the following three questions. 2) What is the slope?

What does the slope represent? (i.e., on a displacement vs. time graph the slope is equal to velocity; on a velocity vs. time graph it is equal to acceleration, etc.) ASK YOURSELF: Should the slope be positive or negative? Should it be linear or non-linear?

To change from an obscure unit to the standard SI units:

make the number the mantissa in scientific notation and add the appropriate power: 650nm = 650 x 10-9m700Mw = 700 x 106W 1) Can I visualize it? 2) Can I draw a picture, graph, or diagram of it? 3) Can I explain it to someone else in layman's terms? 4) Can I think of and describe real-life examples?

To convert from degrees to radians

multiply the degrees by π radians/180° 1) Can I visualize it? 2) Can I draw a picture, graph, or diagram of it? 3) Can I explain it to someone else in layman's terms? 4) Can I think of and describe real-life examples?

To convert from radians to degrees

multiply the radians by 180°/π radians. 1) Can I visualize it? 2) Can I draw a picture, graph, or diagram of it? 3) Can I explain it to someone else in layman's terms? 4) Can I think of and describe real-life examples?

What is important to remember when the denominator is larger?

try the "high/low" method. Change the denominator to one digit higher and to one digit lower. In most cases, this will yield at least one familiar fraction. For example, 3/7 is changed to 3/6 and 3/8. It is thus a little less than 0.5, say 0.45. Similarly, 7/13 is changed to 7/12 and 7/14. Thus it is a little more than 0.5. 1) Can I visualize it? 2) Can I draw a picture, graph, or diagram of it? 3) Can I explain it to someone else in layman's terms? 4) Can I think of and describe real-life examples?

Commit to memory the following approximate decimal equivalents related to the sin and cosine of common angles:

√2 = 1.4; √3 = 1.7; √2/2 = 0.7; √3/2 = 0.9