Maths calculator Flashcards
What does invarient mean
after a transformation the properties of objects that do not change
what would be invarient for an enlargment and what would not
the angle would be invarient as it has not changed but the length would not as it has either got bigger or smaller
what does speed equal
distance/time
It takes a bus 90 minutes to travel 42 miles work out the average speed of the bus
42/1.5=28
How do you calculate distance
speed x time
Tiegan walked for 7 hours at an average speed of 2.8 miles per hour how many miles did tiegan walk
7 x 2.8=19.6
How do you work out time
distance/speed
cameron completed a 74km race at an average speed of 11.84 work out how long he took
74/11.84=6.25=6 hours and 15 mins
What does modal mean
most common
A bus travels from brook lane to 8 turville road in 15 mins with an average speed of 31kmph how many km did it take
0.25 x 31=7.75
How do you work out the gradient
for y-axis=highest number-lowest number
for x-axis=highest number-lowest number
gradient=difference for y-axis/difference for x-axis
How do you find the position of the median value
number of data points+1 /2
How do you find the position of the median value and then find the median in a group frequency table
number of data points+1 /2 whatever number you get add up the frequencys till you get to the number and look at what it’s asking for e.g. the number of children and whatever number you have got like 13 look across to what group that corresponds to
How do you know how to find exterior angles
exterior angles in a polygon add up to 360 degrees
each exterior angle of a polygon is 40 degrees,how many sides does it have?
360/40=9
What do you do if the angles in an exterior angle don’t add up to 360
the biggest one is most likely a reflex angle so you have to minus 180 degrees
What is the equation for pressure
force/area
What is the equation for force
area x pressure
What is something to be careful of when they ask to measure the area
sometimes they give height measurements aswell for area it is only length x width
What is the first circle theorem
angles in a segment are equal
What is the second circle theorem
The angle substended by an arc at the centre is twice the angle subtended at the circumference
What is the third circle theorem
The angle at the circumference in a semicircle is a right angle
What is the fourth circle theorem
opposite angles in a cyclic quadrilateral add up to 180 degrees
what is the fifth circle theorem
The angle between the tangent and the radius at a point on a circle is 90 degrees
What is the sixth circle theorem
2 tangents that meet at a point are the same length
What is the seventh circle theorem
The perpendicular line from the centre of a circle to a chord bisects the chord
What does the perpendicular chord bisect theorem mean
if the missing angle is on the same line as a length that runs across the center it is equal
AB and AC are tangents to a circle A=nothing,B=48,C=X work out the size of angle given that the theorem is the arc theorem
180-48=132
132/2=66
John is x years old,his sister is 16 and his brother is twice johns age all 3 siblings have a total age of 31.Write an equation and from the equation work out how old john is
x + 16 + 2x=3x+16=31
John = 5
5x-8
3x+5
What value of x makes these 2 expressions below equal
5x-8=3x+5 -3x
2x-8=5 +8
2x=13 /2
x=6.5
How do you solve an equation that is directionaly proportionate
In the equation add a k,if a=x you would add a=kx and try to work out k
R is directionally proportinate to t when R=112,T=35 work out R when T=25
112=K35 /35
112/35=3.2
3.2 X 25=80
what is the y-intercept of the equation:
y+17=12-2x
sub in 0 for x
y+17=12 -17
y=-5
What is the rule for working out the y-intercept in an equation
subsitute 0 in for x
How do you work out the co-ordiantes for the y-intercept in an equation
the x-axis is always 0 and the y-axis is the answer for y
How do you find the surface area for an object
work out each of it’s face area once you have them times each of them by 2 and add them together
what is the surface area of a cuboid box the measurments are:30,23,11
30 x 23=690
23 x 11=253
11 x 30=330
(2 x 690)+(2 x 253)+(2 x 330)=2546
What is the equation for volume
length x width x height
What unit of measurment do you measure volume in
cm cubed
In a container there is 120ml of water the height is 10cm the length is 8cm and the width is 5cm work out the depth of the water
120ml=120cm cubed
replace height with depth and add x for depth
120cm=8 x 5 x(x)
120cm=40 X(x) /40
3cm=x
g(x)=2x+9
h(x)=x sq -10
work out hg(x)
h(g(x))=(g(x sq)) -10, substitute g into h
(2x+9)sq -10
(2x+9)sq+(2x+9)sq -10
4xsq+18x+18x+81-10
4x sq+36x+71
F(x)=2x+5
G(x)=5x+3
a)use this info to show gf(x)=10x+28
b)solve gf(x)=0
a)f(g(x))=2x(gx)+5
2x(5x+3)+5
10x +11
b)gf(x)=0
10x+11=0 -11
10x=-11 /10
x=-1.1
f(x)=4x+7,write an expression for f-1(x)
f(x)=4x+7
y=4x+7 -7
y-7=4x /4
y-7/4=x
f-1x=x-7/4
f(x)=9x-4 work out the value of f(3)
a)work out the value of f-1(23)=3
F(3)=9x-4
9(3)-4=23
f(3)=23
b)9x-4
f-1(x)=1/9x+4/9
f-1(23)=1/9(23)+4/9
23/9+4/9=27/9
27/9=3
Given that f-1(x)=x-7/6 find an expression for f(x)
f-1(x)=x-7/6
y=x-7/6 X6
y=6x-7 +7
y+7=6x
y=6x+7
f(x)=6x+7
g(x)=3x-5,write an expression for g-1(x)
y=3x-5 +5
y+5=3x /3
y+5/3
g-1(x)=y+5/3
change to x
g-1(x)=x+5/3
what is 106% 24.7kg
1.06 X 24.7kg=26.182
145% of a value is 5365kg what is the original value
1.45 x original=5365 /1.45
5365/1.45=3700kg
Ethan did a maths test and got 80 out of 92.5% correct,he also did an english test and got 18.75% correct out of 64 how much more did ethan get on his maths test than his english
92.5/100
0.925 X 80=74
18.75/100=0.1875
0.1875 X 64=12
74-12=62
Eastwood is paid 850 pounds a month and spends 68% of it and saves the rest how long will it take to save 4624
850 X 0.68=578
850-578=272
4624/272=17
whats the equation for a surface area of a sphere
4piR sq
A sphere has a surface area of 264m,work out the radius
264=4piR sq /4pi
=ans sq /sq
=4.58
What relationship does the diameter and the radius have
diameter is twice the length of the radius
A sphere has a diameter of 14x write an expression for the surface area of the sphere
4 X pi X (14x/2) sq
4 X pi X 196/4=4 cancels eachother out and turns to 1
1 X Pi x 196X s1=
196pix sq
What is the equation for the volume of a sphere
4/3pi (R)cubed
What relationship does a hemisphere and a sphere have
volume of a hemisphere=1/2 X volume of a sphere
the diameter of a hemisphere is 22cm work out it’s volume
1/2 X 4/3 X pi X (11)cubed=
2662/3 pi or 2787.6
What is the equation for working out the volume of a cylinder
pi x radius sq x height
A cylindraic jar is filled at a rate of 20ml per second,how long will it take to fill the jar,the raidus is 4cm and the height is 7cm
pi x 4sq x 7=112pi then re-arrange the rate formula to make time the subject
time=volume/rate
112/20=5.6
What is the equation for rate
volume /time
What relationship does a prism have with a cylinder
a prism is have the volume of a cylinder
How do you work out the volume of a cuboid
length x width x height
How do you find the volume of a prism
volume of cuboid-volume of cylinder
write 16 to the power of-1 as a fraction in it’s simplest form
1/16
What is the value of 64 to the power of 2/3
we have to find one of the indicies that paired up with a power would equal 64
2 to power of 6=64
6 to the sq root of 64=2
2 sq=4
Work out the value of 1000 to the power of -2/3
1/1000 to 2/3
1/(10)3 to 2/3=
1/10 to power of 2=
1/100 or 0.01
what does it mean if a line is parallel to another line
their gradients are the same
What is the rule for rationalising denominators
if denominator is a+b you have to multiply by a-b
if denominator is a-b you have to multiply by a+b
Rationalise the denominator of 4 sq root 5/by 3+sq root 5
original fraction X by 3- sq root 5/over 3-sq root 5=
4 sq root 5(3-sq root 5)/over 9-5=
4 sq root 5(3-sq root 5)/over 4 then simplify
5 sq root (3-sq root5)
Fully simplify 6w to the power of 8/2w to the power of 4
take away powers as it’s divide
=3w to the power of 4
Fully simplify 6 to the power of 2 X 7 to the power of 3
add powers together as it multiply
=42 to the power of 9
Fully simplify 6m to the power 8 X 3m to the power of -2
change the power of 8 over
6 X 3=18 m to the power of 8 X m to the power of -2=6
18m to the power of 6
fully simplify 7 to the sq root of 24
7 X the sq root of 24 then write the sq root as a multiplication factor
7 X sq root of 4 X 6
sq root of 4 is 2
7 X 2 X sq root of 6
14 X sq root of 6
Calculate sq root of 60/sq root of 5
60/5=12 find something that multiplies by a sq number to get 12
sq root 4 X sq root 3
2 x sq root 3
will lines share an equation if there lines have different gradients
if they have different gradients they will share an equation because it means they are not parallel
In a graph how do you find a solution
when the lines intersect find the values of x and then y
what is the value for sin 30
1/2
what is the value for sin 30
1/2
What is the value for sin 45
1/ sq root 2
What is the value for sin 60
sq root 3/2
what is the value for cos 30
sq root 3/2
What is the value for sin 45
1/ sq root 2
What is the value for sin 60
sq root 3/2
what is the value for cos 30
sq root 3/2
what is the value for cos 45
1/ sq root 2
what is the value for cos 60
1/2
what is the value for tan 30
1/sq root 3
what is the value for tan 45
1
what is the value for tan 60
sq root 3
solve sin30=14/x
sub in value
1/2=14/x X x
1/2 x =14 / 1/2
14/ 1/2=
what is sin
opp/hyp
what is cos
adj/hyp
what is tan
opp/adj
Find the length of the hypotenuse of a right angled triangle the angle is 60 degrees and the opposite length is 6cm
hyp=opp/adj=tan
tan60=sq root 3
sq root 3=6/x X x
sq root 3x=6 /sq root 3
x=6 /sq root 3
What does a U mean in a venn diagram
if something is an a or b
What does n mean in a venn diagram
the things in set a and set b
What does ‘ mean and give an example
it means in completion a’ and b would mean everything in set a and not in set b
