Grade 9 Math Exam

mono

1

to determine the are of a composite figure

1) break it up into simple shapes 2)find the area of each shape 3)add or subtract all of the areas to find total

with addition or subtraction, there are only 2 possibilities when removing brackets

1) if there is no sign before the bracket or a plus sign, then simply drop the brackets and everything is the same 2)if there is a subtraction sign before the bracket and the sign of every thing inside, is the opposite

rearranging formulas

1)what do you need to do to isolate the variable 2) write new formula

co-interior angles have a sum of

180

sum of interior angle of a triangle is

180

the sum of interior angles

180(n-2)

bi

2

tri

3

opposite angles in a parallelogram is

360

the sum of interior angles of a quadrilateral is

360

power of a power law

a power can be written as a single power by multiplying the exponents

power

a product of identical factors and there is 2 parts a base and a exponent

linear system

a set of 2 or more linear systems considered at the same time

to find perimeter of a composite figure

add the distances around the outside of the figure

to subtract polynomials

add the opposite polynomials

maximum volume for a given surface are of a square based prism

always occurs when the prism is a cube

interior angle

angle formed on the inside of a polygon

exterior angles

angle formed on the outside of a geometric shape by extending one or more sides

alternate angles

are equal

corresponding angles

are equal

standard form

ax+by+c=0, to convert to y intercept form isolate y so that y is positive

the diagonals of a parallelogram

bisect each other

the median of a triangle

bisects its area

Pythagorean theorem

c represents length of the hypotenuse and longest side of a right angle triangle , a and b represent two other sides c2= a2+b2

rectangles with the same perimeter

can have different dimensions and contain different areas

rectangles with the same area

can have different dimensions and contain different perimeter

polygon

closed figure made up of line segments

two angle whose sum is 90 are

complementary angles

degree of polynominal

degree of highest term

when two lines intersect the opposite angles are

equal

when solving equations with brackets

expand to remove bracket, collect like terms, solve for variable

lines with negative slop

fall to right

adding/ subtracting fractions...

find the common denominator and then add/subtract

optimizing the area means

finding dimensions with max are for a given perimeter

exponent of 0

gives a answer of 1

exponent of 1

gives the same number

the height of a triangle formed by joining the midpoints of two sides is

half the height of the original triangle

slope of a parallel line

have the same slope

equiangular

having all angles equal

exponent

how many bases is multiplied

base

identical factor

like terms have

identical variables (count the exponents with the variable)

exponents with fractional base law

if there is a exponents on a fraction then you have to give the exponent to both the numerator and denominator

the sum of exterior angles

is 360

outliers

is different then then rest of the data

slope of a perpendicular line

is the negative reciprocal

to solve a one step equation

isolate the variable by performing the opposite operation

to subtract polynomials

it is easiest to pretend there is a 1 outside the bracket, so you can remove the bracket

for a rectangular prism with a fixed volume to have minimal surface area

it must be a cube

for a rectangles with a fixed area to have max perimeter

it must be a square

for a rectangles with a fixed perimeter to have max area

it must be a square

to multiply fractions...

just multiply the top and bottom to get the new fraction, then simplify

first difference of a

linear relation is constant non linear is not constant

converting mixed numbers

multiply denominator by the whole number and add the numerator

distributive property tells us to

multiply each term inside the bracket by the term outside the bracket

whatever is outside bracket

multiply it with whats inside the bracket

when distributing

multiply the monominal by each term in the polynomial, multiply numerical coefficient, apply exponents laws,

to divide fractions...

multiply the second ones reciprocal and then simplify

when multiplying or dividing algebraic expressions

multiply/divide number by number and variable by variable

odd number of negative factors=

negative answer

the maximum volume for a cylinder, with a fixed surface area

occurs when its height equals its diameter

the minimum surface area for a cylinder, with a fixed volume

occurs when its height equals its diameter that is h=d or h=2r

term

one quantity in an algebraic expression

a line segment joining the midpoints of two sides of a triangle is

parallel to the third side and half as long

midpoint

point that divides line segment in to 2 equal parts

vertex

point where two or more sides meet

even number of negative factors=

positive answer

joining the midpoints of the side of any quadrilateral

produces a parallelogram

dependent

relies on independent

independent

relies on nothing

to add polynomials

remove bracket and collect like terms

lines with positive slope

rise to right

slope of the line

rise/run, m= y1-y2/x1-x2

when volume is maximized the surface are can be found using

sa= 6pieR2 and the height will be twice the value of r or 2r

find an equation for a line given the slope and a point

substitute m into the equation and the point to isolate for b

check a solution by

substituting the variable and seeing if the right side equals the left

degree of term

sum of the exponents

adjacent angles are

supplementary

two angles whose sum is 180 are

supplementary angles

like terms

terms that have the same variable and the same exponent

median

the lines segment joining a vertex of a triangle to the midpoint of the opposite side

coefficient

the multiplier placed immediately before the variable in a term

dimensions of a rectangles with optimial areas depends on

the number of sides to be fenced. if fencing is not required on all sides, a greater area can be enclosed

rate of change

the relationship between two quantities that are changing, this is also slope

to find a pattern in first difference

the values of the independent variable must change by a constant amount

if only 3 sides of the rectangles are fenced

then the area will be twice that of a square fenced by the same amount

bisect

to divide into two equal parts

partial variation

two number that vary by different numbers

direct variation

two number that vary by the same thing

find an equation for a line given 2 points

use m=y1-y2/x1-x2 to find m then use the find an equation given slope and a point way to find b

to solve multi step equations

use samdeb 1)get rid of the constant term on the same side of the variable with subtraction/ addition 2)isolate the variable by multiplying/ dividing the coefficient

when surface area is minimized the volume can be found using

v=2pieR3 and the height will be twice that value or 2r

cube

v=s3 sa=6s2

quotient law

when dividing powers with the same base, subtract the exponents to write the quotient as a single power

product law

when multiplying powers with the same base, add the exponents to write the product as a single power

simplifying

write the numerator and denominator as a product of factors, then erase common factors and you will get the result.

vertical lines

y=a a= x intercept m= undefined

horizontal lines

y=b m=0

slope, y intercept form

y=mx+b m=slope, b= y intercept