Formulas needed for EOCT Arithmetic Sequences an a1 (n 1)d or Geometric Sequences an a1 (r )n1 an dn z (*z is the term before the 1st term or amount at time zero) * a1 must be the first term or amount at time 1 - not the amount at time zero! Recursive Formulas a1 id the first term an an1 (or x) d or r Linear Function f ( x) mx b Exponential Function f ( x) a0 (r )t *Where b is the y-intercept, original amount or amount at time zero. m is the slope. Where a is the original amount or amount at time zero and r is the growth factor. Financial Exponential Formula *Where P is the original amount or amount at time zero and r is the A P(1 r )t growth or decay rate. (1 r ) is called the growth or decay factor. Point – Slope Form of a linear equation: ( y y1 ) m( x x1 ) Where ( x1 , y1 ) is any point on the line and m is the slope. *Parallel lines have the same slope – Perpendicular lines have opposite reciprocal slopes. Pythagorean Theorem: a2 b2 c2 *use only on right triangles – a and b are the legs -c is the hypotenuse. Distance Formula: d ( x2 x1 )2 ( y2 y1 )2 *Also remember that distance = rate x time! You may need this for Unit Conversion! x x y y Midpoint Formula: 1 2 , 1 2 2 2 *Remember the short-cut to finding an endpoint given the midpoint and the other endpoint is to double the midpoint and subtract the given endpoint. Segment Partition Formula: (( x2 x1 )( a a ) x1 , ( y2 y1 )( ) y1 ) ab ab *Where the ratio given is a : b , ( x1 , y1 ) is the first endpoint, and ( x2 , y2 ) is the second endpoint. Circles *When asked to find whether a point is inside, outside, or on the circle; find the distance between the Center and the Point using the distance formula d ( y2 y1 )2 ( x2 x1 )2 and compare this to the radius of the circle. You may have to use the distance formula to find the radius as well. The distance must be equal to the radius of the circle for the point to be on the circle. Translation Slide Transformations ( x #, y ) Right ( x #, y ) Left ( x, y #) Up ( x, y #) Down Reflection Flip x axis ( x, y ) Change the sign of y y axis ( x, y ) Change the sign of x y x ( y, x) Swap both y x ( y, x) Swap and change signs of both Rotation Turn 90 CW or 270 CCW ( y, x) Change the sign of the x and swap coordinates 90 CCW or 270 CW ( y, x) Change the sign of the y and swap coordinates 180 either way ( x, y) Change the sign of both Transformations that will map a figure onto itself include reflections over the line(s) of symmetry and rotations by any multiple of an angle of rotational symmetry. To find the angle of rotational symmetry divide 360 by the number of vertices (or points) on the figure. Odd Function If ( x, y) is on the graph, then ( x, y) is on the graph. Graphically there is symmetry with respect to the origin (turn the graph upside down and it will look the same). Given the function rule all exponents will be odd. Even Function If ( x, y) is on the graph, then ( x, y) is on the graph. Graphically there is symmetry with respect to the y-axis (what is on the left side of the y-axis is identical to what is on the right side of the y-axis). Given the function rule all exponents will be even. Statistics Five Point Summary for Box Plots include Lower Extreme, Q1 , Median, Q3 , and Upper Extreme (Your calculator will calculate these for you! Enter the data under L1, hit 2 nd data and run 1 Variable Statistics.) *The Interquartile Range (IQR): Q3 Q1 Outlier Formula: Any number lower than Q1 1.5( IQR) Any number higher than Q3 1.5( IQR) Mean Absolute Deviation (MAD): Make a table X X X X To find the MAD find the mean of the third column. If you have a TI-36X Pro you can make this table on your calculator under L1, L2, and L3 and enter a formula under L3. Finding linear and exponential models of best fit (regression): Enter all of the x data under L1 and the y data under L2 in your calculator. -To run a linear regression on the TI -30XS Multiview, hit 2nd data and run 2 Variable Statistics. Look for a and b and put into the format y = ax + b. -To run a linear regression on the TI-36X Pro , hit 2nd data and run a linreg. Look for a and b and put into the format y=ax+b. -You can only find an exponential model if you have the TI-36X Pro. Hit 2nd data and go to menu option 9, expreg. Look for a and b. Put into the format y a(b) x . -Remember r is the correlation coefficient and tells us if our model is a good fit. The closer to 1 or -1, the stronger the correlation. The closer to 0, the weaker the correlation. -Correlation does not imply causation. -We use these models to make predictions about what will happen in between our data values (interpolation) or make predictions about what will happen in the future (extrapolation). Use your table feature on your calculator to help you answer these types of questions. Be able to tell whether data displayed in a dot plot is skewed left or right (the skew is in the direction of the tail or outlier), symmetric (evenly distributed), or bimodal (two modes). Rate of Change: Remember to use the slope formula m y2 y1 x2 x1 *You will need two points on the curve or function. These may be given to you, you may have to find them by plugging x values into a function rule, or you may have to pick them off of the graph. If given an interval over which to find the average rate of change, such as [0,4], remember that these are both x-coordinates. Linear functions have a constant rate of change. Exponential functions do not.
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