Maths calculator Flashcards by Robert Foskett

What does invarient mean

after a transformation the properties of objects that do not change

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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

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what does speed equal

distance/time

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It takes a bus 90 minutes to travel 42 miles work out the average speed of the bus

42/1.5=28

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How do you calculate distance

speed x time

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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

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How do you work out time

distance/speed

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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

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What does modal mean

most common

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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

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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

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How do you find the position of the median value

number of data points+1 /2

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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

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How do you know how to find exterior angles

exterior angles in a polygon add up to 360 degrees

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each exterior angle of a polygon is 40 degrees,how many sides does it have?

360/40=9

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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

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What is the equation for pressure

force/area

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What is the equation for force

area x pressure

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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

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What is the first circle theorem

angles in a segment are equal

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What is the second circle theorem

The angle substended by an arc at the centre is twice the angle subtended at the circumference

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What is the third circle theorem

The angle at the circumference in a semicircle is a right angle

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What is the fourth circle theorem

opposite angles in a cyclic quadrilateral add up to 180 degrees

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what is the fifth circle theorem

The angle between the tangent and the radius at a point on a circle is 90 degrees

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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

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

Maths calculator Flashcards

(98 cards)