Math Flashcards
What are the decimals of 1/2 1/3 1/4 1/5 1/8
0.5 0.33 0.25 0.20 0.125
What do we do to fractions when the numerator is larger than denominator?
Create a compound fraction
13/5 becomes 2 3/5 or 2.60
For estimating fraction what should we do when the denominator is is larger than the numerator?
Use the “high/low” method.
Ex: turn 3/7 to either 3/6 or 3/8 thus it’s a little less than 0.5
What are the square roots for the numbers 1-15?
1^2 = 1 2^2= 4 3^2=9 4^2=16 5^2=25 6^2=36 7^2=49 8^2=64 9^2=81 10^2=100 11^2=121 12^2=144 13^2=169 14^2=196 15^2=225
When adding or subtracting numbers in scientific notation what do you do?
Rewrite so exponents are the same and them just add or subtract the numbers.
2.3510^3 + 8.5410^2 change this to 2.3510^3 + 85.410^3 and add or subtract
How do you multiply and divide scientific notation numbers?
Add exponents together and multiply the mantissas together. Same with dividing but you subtract exponents
How do you raise a number in scientific notation to a power?
(2. 3410^3)^2
2. 34^2 10^3^2
4. 910^9
How do you write a small number such as 5, in scientific notation?
?
What’s the sin and cos at 0 30 45 60 90?
Sin 0=0 30=1/2 45=sqrt2/2 60=sqrt3/2 90=1
Cos 0=1 30=sqrt3/2 45=sqrt2/2 60=1/2 90=0
What are the decimal values of sqrt2 sqrt3 sqrt2/2 and sqrt3/2
Sqrt2=1.4 Sqrt3=1.7 Sqrt2/2=0.7 Sqrt3/2=0.9
How is the cosecant, secant, and the cotangent related to cos, sin and tan?
They are the inverse of them SHO CHA TAO
Tan@=?
sin@/cos@
Sin^2X + Cos^2x=?
1
How would you solve for the area of a circle?
A=pi*r^2
If asked to solve for the circumference of a circle what would you do?
Use either C=pid or C=2pir
How would you solve for the ahead of a triangle?
area of triangle=1/2b*h
How would you solve for volume of a sphere?
Volume of a sphere=4/3pi*r^2
Solve for the surface areas of a sphere?
Surface area=4pi*r^2
What is Pythagoreans Theorem?
A^2 + B^2 = C^2
What must all the angles in a triangle add up to?
180 degrees
How would you convert from degrees to radians?
Pi radians = 180 degrees
Approximately how many radians are in 1 circle?
6 radians…. So if something is rotating at 12 rad/s you know that it is making two rev/s
How do you take the square root of a number in scientific notation?
Take the square root of the mantissa and divide the exponent by 2 or half it. Ex 1610^8 would be 410^4
For a equation regarding a graph, if two variables are both in an equation and one of them contains an ( exponent, log, ln, or root) the graph of one of those variables vs the other will yield what kind of graph?
Non Linear
Regarding to graphs, if the equation of the graph is comparing one variable vs the other and both contain the same math.. ie both variables are cubed or both are square rooted.. What kind of graph will it be?
Linear
What does the graph of y=x look like?
Linear line going through straight through the middle of the graph
What does the graph of y=1/x look like?
Looks like two quarter pipes one below the x axis on the negative side of the graph. And one above the x axis on the positive side
What does y=x^2 look like?
A parabola that crosses the y axis at 0
What does y=x^3 look like on a graph?
A half pipe but one of the sides is facing down
What does y= square root of x look like on a graph?
Looks like a little hill that starts from the 0 point on the graph
What does the y=lnx look like on a graph?
Looks like y= sqrt of x but it crosses the x axis and runs down the y portion of the graph
What does y=sinx look like on a graph?
Starts or crosses at the 0 0 point on the graph and looks like waves top of the wave goes up to 1 on the y axis
Y=cosx
Looks like y=sin of x but crosses the y axis at 1
X=1/2at^2
What would the x vs t graph look like or a vs t?
How about x vs a or a vs x?
Non linear
Linear
v=sqrt(2gh)
What would v vs g look like on a graph
g vs h?
v vs g non linear
g vs h linear
If 2 variables are on the same side of the equation and on the same side of the division line how are they related?
Inversely
If two variables are on the same side of the equation but on different sides of the division line, how are they related?
Directly
If two variables are on the opposite side of the equation but on the same side of the division line, how are they related?
Directly
If two variables are on opposite sides of the equation and on different sides of the division line, how are they related?
Inversly
- Does a constant force cause an object to accelerate faster?
- Can constant accel cause an object to move faster and faster? Explain
- Does a constant force cause it to travel at constant velocity? Explain.
- No, it will cause a constant (non-changing acceleration). Only a changing force will cause change in acceleration.
- Yes, constant accel is a measure of continuing increase in velocity per unit of time. Car 40 to 50 mph in 5 second, then from 50 to 60 mph in the next 5 seconds. Velocity is increasing, accel is constant.
- No, a constant net force will cause a constant accel therefore a change in velocity.
Can you accelerate a ball across a room horizontally by throwing it? Explain
No, to accelerate this object horizontally, an object creating the force must be in contact with it. Must be under the influence of a field force (eg, gravitational or electrical). In the vertical direction the ball is always accelerating due to the earths gravitational field.
Track the velocity of a ball thrown by a picture horizontally (ignore air resistance).
The only time the ball will be accelerating horizontally will be when the ball is in contact with the pictures hand. After release the horizontal velocity will remain constant until the ball hits the ground.
Track the velocity of a ball as it is shot from a cannon horizontally and then returns to the ground. ( include air resistance)
The canons velocity will decrease due to air resistance.
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