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33 Cards in this Set
- Front
- Back
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How do you find the gradient of a straight line? |
m=y₂-y₁/ x₂-x₁ |
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How do you find the distance between two points? |
Use Pythagoras √[(x₂-x₁)²+(y₂-y₁)²] |
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How do you find the midpoint of two points? |
[½(x₁+x₂), ½(y₁+y₂)] |
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What is the angle in a semicircle? |
The angle in a semi circle is always a right angle. |
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How do you find the equation of a circle given 3 points on the circle? |
Find the equation of two chords. Find the equations of the perpendicular bisectors. Where they cross is the centre. |
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What is the domain? |
The set of possible inputs for a function. |
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What is the range? |
The set of possible outputs for a function. |
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What is the discriminant? |
b²-4ac, positive=two roots, negative=no roots, zero=repeated root |
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How do you sketch inequalities? |
Draw the line of y=f(x). > or < then draw a dotted line. Otherwise draw a solid line. |
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What does the graph of y=1/x look like? |
An asymptote at both axis. In the top right and bottom left quadrants. |
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What does the graph of y= -1/x look like? |
An asymptote at both axis. In the top left and bottom right quadrant. |
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What does the graph of y=1/x² ? |
Asymptotes at both axis. The function is always positive. |
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What does the graph of y= -1/x² ? |
Asymptotes at both axis and always negative. |
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y=f(x)+a |
Vertical translation by a. |
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y=f(x+a) |
Horizontal translation by -a. |
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y=af(x) |
Stretch by scale factor a vertically. Multiply every y coordinate by a. |
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y=f(ax) |
Stretch by scale factor 1/a horizontally. Divide every x coordinate by a. |
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y= -f(x) |
Reflection in x-axis. |
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y=f(-x) |
Reflection in y-axis. |
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What is the choose function used for? |
Finding the number of ways of choosing r items from a group of size n, nCr. |
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What is nCr equal to? |
n!/r!(n-r)! |
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How does pascals triangle link to the choose function? |
The r term in the nth row of pascal’s triangle is given by (n-1)C(r-1). |
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What are the two unit vectors? |
i=(1,0) and j=(0,1). i is the x coordinate. j is the y coordinate. |
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What is differentiation by first principles? |
f’(x)=lim(h=>0) [f(x+h)-f(x)]/x+h-x |
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How do you use second order differentiation? |
Use it to check if a turning point is a minimum or a maximum. Plug the x-coordinate of the turning point into f’’(x). Positive=Min. Negative = Max. Zero=Tells you nothing, check by plugging in x-coordinates. |
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What is logax + logay? |
logaxy |
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What is logax-logay? |
loga(x/y) |
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What is loga(x)^k? |
klogax |
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What is loga(1/x)? |
-logax |
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What is logaa? |
logaa=1 |
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What is loga1? |
loga1=0 |
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How do you sketch y=ax^n? |
If you log both sides you get logy=nlogx+loga. Plot a graph of logy against logx. |
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How do you sketch y=ab^x? |
logy=loga + xlogb. Draw a graph of log y against x. |
