Term 3 Flashcards
1cm^3=x mL
1m^3=y mL
x= 1 y= 1 000 000
what is the difference between capacity and volume?
volume: amount of space a solid occupies
capacity: amount an object can contain
volume formula for a cube?
V=s^3
s= side length
volume formula for a rectangle?
V=
l=length
b=breadth
h= height
volume formula for a cylinder?
V=(Pi)r^2
r= radius
volume formula for a cone?
V=1/3(Pi)r^2h
h= perpendicular height
volume formula for a pyramid?
v=1/3Ah
a=base area
h=perpendicular height
volume formula for a sphere?
V=4/3(Pi)r^3
volume formula for an prism?
V=Ah
A is cross sectional area
area formula for a square?
A=s^2
area formula for a rectangle?
A=lb
area formula for a triangle?
a=1/2bh
area formula for a circle?
A=(Pi)r^2
area formula for a parallelogram?
A=bh
area formula for a trapezium?
a=1/2h(a+b)
area formula for a rhombus?
A=1/2xy
where x and y are the diagonals
How do you find the area of a sector?
A=Q/360*(Pi)r^2
how do you find the area of an annulus?
A=(Pi)(R^2-r^2)
what is the formula for surface area of a cube?
SA=6s^2
surface area volume for rectangular prism?
SA=2lb+2lh+2bh
surface area formula of a cylinder?
SA=2(Pi)rh+2(Pi)r^2
surface area formula of a cone?
SA=(Pi)rl+(Pi)r^2
surface area formula or a sphere?
SA=4(Pi)r^2
Of the lathing sides of two similar figures are in the ratio m:n then?
the ratio of their surface areas is m^2:n^2
the ratio of their volumes is in the ratio m^3:n^3
what are the four tests for congruent triangles?
SSS
SAS
AAS
RHS
what sets similar figures apart from congruent figures?
similar figures are in the same shape but not necessarily the same size.
if two figures are similar the:
the matching sides are in the same ratio and matching angles are equal
a proportional statement is?
when the ratios of all the sides are written e.g. DE:AB=EF:BC=DE:AC
what are the three proofs for similar triangles?
three pairs of corresponding angles equal (equiangular) (AAA)
three pairs of corresponding sides in proportion (SSS)
two pairs of corresponding sides are in proportion and included angles are equal (SAS)
when rounding with significant figures what is the first significant figure?
he first non-zero digit.
zeroes at the end of a whole number or beginning of a decimal are not significant. what are they?
necessary placeholders.
when are zeroes significant?
when they are between non zero digits or zeroes at the end of a decimal.
how are numbers written in scientific notation expressed?
m*10^n
where m is a number between 1 and 10 and n is an integer.
what are the three types of decimals?
recurring (0.22222…)
terminating (0.2)
irrational ((root)2)
how do you express recurring decimals in fraction form. use 0.2222… as an example
let x=0.222... 10x=2.222... 9x=2 x=2/9
a rational number is?
any number that can be expressed as A/B where a and b are integers and b does not equal 0
irrational numbers are?
any number that is my rationale and cannot be expressed int he form a/b
what are the rules for multiplying and dividing surds? (3)
(|x)^2=x
|xy=|x*|y
|(x/y)=|x/|y
binomial products with surds is the same shit as with algebra
ya man
(a+b)^2=a^2+2ab+b^2
(a-b)^2=a^2-2ab+b^2
(a+b)(a-b)=a^2-b^2
how do you rationalize denominators?
you multiply the numerator and denominator by the surd that is the denominator.
if the denominator is something like (/x+4) then multiply it by the conjugate pair ie (/x-4)
a^m*a^n=?
a^(m+n)
a^m/a^n=?
a^m-n
(a^m)^n=?
a^mn
a^0=?
1
a^-n=?
1/(a^n)
(ab)^n=?
a^n+b^n
(a/b)^n=?
a^n/b^n
|a=?
a^1/2
n^|a^m=?
the nth root of a to the m
a^m/n
how is the gradient intercept form of a line written?
y=mx+b
where m is the gradient and b is the y intercept.
how are the x and y intercepts found?
let y=0 or x=0 respectively
what is the general form of a line?
ax+by+c=0
where a b and c are all integers and a is greater than zero
what is the intercept form of a line?
x/a+y/b=1
where a is the x intercept and b is the y intercept
make in general form, divide by c and simplify.
what are the 4 ways of working out the gradient of a line?
m=rise/run
m=tan (theta)
m=(y2-y1)/(x2-x1)
y=mx+b, m is the gradient.
what is the point gradient formula?
given p coordinates are (x1, y1)
y-y1=m(x-x1)
m is the gradient, p is a point on the line.
what is the two point formula?
m=(y2-y1)/(x2-x1)
what is the midpoint formula?
Midpoint=(x1+x2)/2,(y1+y2)/2
what is the distance formula?
AB=|(x2-x1)^2+(y2-y1)^2
what is the formula for he perpendicular distance from a point to a line?
(|ax1+by1+c|)/root(a^2+b^2)
what is a parabola?
an equation with a quadratic relationship; e.g. y=x^2.
when graphed makes a smooth curve.
what does the coefficient of x being positive or negative in a parabola change?
whether it is concave up (+) or concave down (-)
in the equation y=ax^2, what does a determine as a parabola?
as a decreases, the parabola becomes wider, as it increases the parabola becomes narrower.
in the equation y=ax^2+c, what effect does c have on the parabola?
the effect of c is to move the parabola up or down, and changes the y coordinate of the vertex.
in the equation y=(x-b)^2, what effect does b have on the parabola? why?
if b is negative, the parabola is moved right, of Positive the parabola moves left.
let y=0 (x-2)^2=0 root x-2=0 x=2
what is the general form of a parabola?
y=ax^2+bx+c where a b and c are real numbers and a doesn’t equal 0.
how do you find ye axis of symmetry in a parabola? two ways.
halfway through the two x intercepts OR x=-b/2a when there are no x intercepts.
what is the y min or y max?
the minimum (for concave up parabolas) or maximum (for concave down parabolas) value for y ie the y coordinate of the vertex.
how can the coordinates of the vertex be found using the completing the square method? use y=x^2+8x+5 as an example.
y=x^2+8x+5 y=(x^2+8x)+5 halve grouped stuff and raise it to the power of two. y=(x+4)^2+5 check it adds up to same as before. y=x^2+8x+~!16!~+5 there is an extra 16 so y=(x+4)^2 +5-16 y=(x+4)^2-11 therefor V=(-4,-11)
