MATH EXAM GRADE 10 Flashcards
If the lines have the SAME slope but DIFFERENT y-int how many solutions are there and what type of lines is it
-Zero solutions
-lines are parallel
If the lines have DIFFERENT slope and DIFFERENT y-int how many solutions are there
-1 solution
If the lines have the SAME slope and the SAME y-int how many solutions are there
-Infinit solutions
Do you add or subtract if the coefficients sign are the same for elimination
subtract
Do you add or subtract if the coefficients sign are different for elimination
add
steps on how to find perpendicular bisector
- find the midpoint of the line segment
- find the slope of the line segment
- find the negative reciprocal of the slope
- sub the midpoint and the negative reciprocal into y=mx+b
steps on how to find the median
- find the midpoint of side opposite from the vertex
2.find slope using Midpoint and vertex
3.sub the slope and one known point that lies on the median into the equation y=mx+b to find “b”
steps on how to find altitude
- find slope of sides opposite from vertex
- find negative reciprocal of the slope
3.sub the vertex and negative reciprocal into y=mx+b
steps on how to find shortest distance
- find equation #1
2.find the negative reciprocal - use the negative reciprocal and the point to sub into y=mx+b
- use elimination or substitution to find the POI of the two lines
5.find the distance from the point P and the POI
if the first differences are constant the relation is….
linear
if the second differences are constant the relation is….
quadratic
How to find the y-int when doing first differences
take the equation and sub the x-int for x to solve for y
how to find first and second differences
start from the bottom and minus the y-int, and for second differences use the first difference results
if something is linear what form is it in and how many exponents does it have
form= y=mx+b
and there is an exponent of 1
if something is quadratic how many exponents does it have
2
if the a value is postive which way does the parabola open
upwards
if the a value is negative which way does the parabola open
downwards
when given somthing in vertex form what letters are the vertex
h and k and always switch the sign of h when graphing
when something is in vertex form how do you find the axis of symmetry
its the x value in the vertex
when given something in vertex form how do you graph it
plot the vertex and then use step pattern
when something is given in factored form what are the x-int
r and s
how do you find the axis of symmetry in factored form?
x=r+s/2
how to find the y-int/vertex of something in factored form
sub in the axis of symmetry (x) into the equation to find y
if the a value is negative is it a max or min
max
if the a value is postive is it a max or min
min
greater then 1 the parabola is vertically _________ by a factor of a
stretched
between 0 and 1 the parabola is vertically ___________ by a factor of a
compressed
if a=1 there is ______ vertical stretch or compression
no
how do you know if there is a reflection in the x-axis
if the “a” is negative, there is a reflection over the x-axis.
If the k value is positive the parabola is vertically translated k units ____
upwards
If the k value is negative the parabola is vertically translated k units ____
downwards
if h is greater then 0 it shifts _______
right
If h is less then 0 it moves h units ___
left
what is a parent function
y=xsquared
how to find the step pattern?
multiply a by the original step pattern (1,3,5)
when doing word problems involving vertex and factored form use vertex form if given _____
the vertex and another point
when doing word problems involving vertex and factored form use factored form if given _____
the x-int and another point
what is vertex form
y= a (x-h)squared + K
What is factored form
y = a (x-r) (x-s)
how do you expand polynomials
using FOIL
First
Outisde
Inside
Last
after multiplying each term collect and combine any like terms
how many terms is in a difference of squares
2
what is the difference between complex trinomials and simple trinomials
in simple trinomials a=1
what does a perfect square trinomial look like
asquared+2ab+bsquared
If D＞0 then….
there is 2 x-int (2 real roots)
If D=0 then…
There is 1 x-int ( 1 real root)
if D＜0 then…
There is 0 x-int (no real roots)
when do you use inverse when solving triangles
to find a missing angle
when do you use SOH CAH TOA
solving a missing side length
