AQA GCSE Maths June 2018 Paper 1 Foundation Walkthrough (24 May 2018)

AQA GCSE Maths June 2018 Paper 1 Foundation Walkthrough (24 May 2018)


Hello and welcome to mr. Tompkins EdTech and my series of walkthroughs for the AQA GCSE mathematics past papers. This
particular video is June 2018 paper one foundation tier. Now with a new
specification being new, grade 9 to 1 past papers are like gold dust and you
should not be watching this video unless you’ve already attempted to paper
yourself under test light conditions. If you haven’t, stop the video now and go
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and it makes it much easier for others to wade through all the YouTube dross and
find the good stuff. Also before attempting the actual past papers, make
sure you’ve gone through all the practice sets first. AQA produced four
sets of practice papers to help students prepare for the new GCSE exams and I
advise you to work through these before moving on to the actual past papers. Have
a look at this video series which gives full walkthroughs for AQA practice sets
one to four. If you don’t happen to have a copy yourself, you’ll find a download
link to the practice paper in the description below each video. Finally,
feel free to ask questions below. It would be helpful if you include a
question number and be as specific as possible. I really appreciate your
comments and feedback and I try to respond to these as quickly as I can –
especially around exam times. Okay, let’s get into it.
Welcome along to another past paper walkthrough from Mr. Tompkins EdTech.
Today we’re going to be looking at the AQA GCSE maths foundation tier paper one. It
was actually sat on the 24th of May 2018, although it does belong in the June set
of papers. Okay let’s get cracking! Question 1 – work out 1/2 times 5. Okay so
normally when we want to try it to try and find a fraction of a number we would
divide through by the number on the bottom and times through by the number
on the top but that doesn’t give us a whole number here in that case because 2
doesn’t divide into 5 nicely as a alternative approach I could rewrite 5
as 5 once and used the rules of fraction multiplication instead so top times top
equals 1 times 5 which is 5 bottom times bottom is 2 so 1/2 times 5 is the same
thing as 5 halves that’s a improper fraction isn’t it now to rewrite that as
a mixed number you’re looking at how many times 2 divides into 5 so what is 5
divided by 2 5 divided by 2 is 2 remainder 1 so the answer is 2 because
it goes in twice the remainder is 1 and the divisor was to wasn’t be divided by
2 the same thing as 2 and 1/2 it’s that one there question to circle the number
that is 5 less than minus 2 well the number 5 less than minus 2 is the same
thing as asking what is negative to take away 5 so 4 or 8 at negative 2 on the
number line and we’re going to subtract another 5 we’re going 5 more jumps
further in the negative direction that’s going to take me to negative 7 question 3 simplify 3 times a times 3
times a ok so what we want to do really is multiply like things with like things
so if I take that 3 and I multiply it by that 3 I’m gonna get 9 and if I take my
a and multiply it by my a I’m gonna get a times a is a squared so I end up with
9 a square three times three is nine eight times a
is a squared 9 a squared which is that one there
question four which shape is similar to shape X now similar in mathematics has a
very specific meaning it means exactly the same shape but one is an enlargement
of the other okay so have a look at my four possibilities you know some are
just clearly not right are they this one here a is clearly ridiculously stretched
out so that can’t be that one and similarly B is very dumpy looking they
think it’s gonna be that one so it’s gonna be C or D just by glancing at it
so if you measure this one on my kind of squares got no digits on it but you can
see it’s like six divisions from top to bottom and it is 12 divisions from one
point five one point to the other so it’s kind of half as tall as is wider
than it was twelve by six never look at C that is so let me just make a note is
that it was kind of six units that way and twelve units that way now I’m not
using a standard ruler here mine’s kind of a digital one but you could do it
with your own rule and use them in the millimeters on your own ruler probably
going to get different arts to me but that you should find that one is twice
as big as the other and if we have a look at this one in this direction it is
what’s that Oh ten twenty twenty four so it’s about twenty four in that direction
and in the other direction that’s around so again that one is about twice as wide
as it is tall so I’m thinking it’s probably see let’s just double check D
now if I check D that one is nine units from top to bottom and in the other
direction that is 16 units so in that one that one is not twice as big as it
so I think it’s going to be C because that one is in the same ratio as the one
at the top and that one isn’t so it’s gonna be C question five work out 20% of
14,000 okay so when you’re finding a percentage number on an on calculator
paper your you’ll starting with a hundred percent aren’t you so a hundred
percent is everything it’s the 14,000 now finding 10 percent is very easy I
could just divide my number by 10 so dividing 14,000 by 10 that is 1,400 but
we actually want 20 percent now you can make 20 percent by taking 2 lots of 10%
– lots of 10% it’s 20% I’d have to do the same on this side wouldn’t I if I
was going to do that though it balanced so – 10 % is 20% and to lots of 1,400 is
2,800 so 20% of 14,000 is going to be 2,800 question 6 a right 0.85 as a
fraction in its simplest form okay now this number is given as a
decimal so you know if you think about the place values of numbers the number
before the zero before the decimal point is units isn’t it now the 8 lies in the
tenths column and the 5 lies in a hundredths column so actually another
way of thinking about 0.85 is that you’ve got 85 100 which I can write down as a fraction
like that 85 100 now 85 ends in 5 and 100 ends in zero and that’s telling me I
can divide them both by 5 they got common divisor there of a knife
so if I could divide top and bottom by 5 and I’ll take another look and see if
there were any more so a fives into 85 go 17 times and fives into a hundred go
20 times so 17 over 20 now 17 is prime isn’t it so I can’t divide it down any
more than that it’s going to be that that’s my answer in its lowest terms 17
over 20 a windy today so that’s coming through on the microphone 6b right 5/8
as a decimal now it’s probably a good idea to remember what the eight side cuz
they’re quite quite common fractions to come up but let’s assume that you didn’t
remember what it was you can do this like a division actually five eighths is
the same thing as 5/8 so I could write 8 as my divisor and five as the number I
want to divide I need some extra zeros here I think so I’m going to make it
five point zero zero zero zero so 8 into 5 don’t go so kind of carry five over
into the next column function we write that bit more Spacey so I got a bit more
space to squeeze these extra numbers in space it out a little bit more so so 8
so if I don’t go 18 to 50 then if I’ve got remainder 5/8 times table 5/8 of 46
eights of 48 aren’t they so it goes in 6 times remainder 2 okay
eights into twenty eight sixteen twenty-four is bus isn’t it so it goes
in twice remainder eight times two 16 remainder is gonna be four then and then
finally eights into a 40 go five times don’t they exactly so
there is no remainder and I’ve got to the end of my decimal so my decimal
point started there my decimal answer is gonna start being the same place there
so the answer is 0.625 having said that I kind of knew it was 0.625 already
before I did the calculation because there’s a very common fraction and I do
a lot of math it’s kind of one that sticks in my head and it might be one
that you just want to remember the decimal conversion to and from eights
question seven a rectangular carpet measures 8 meters by 6 meters part of
the carpet is covered by a square rug of length 2 meters show that 1/12 of the
carpet is covered by the rug ok so what do we need to do here I think what we
need to do is we need to find the area of the square and we need to find the
area of the big rectangular coop here and then we need to express one as a
fraction of the other ok so the area of the square then is going to be white as
the square isn’t it so it’s 2 by 2 – x – 2 squared which is 4 meters squared and
the area of the rectangle is going to be those two sides multiplied together 8
times 6 8 6 is our 48 square meters okay and then so what expressing one as a
fraction of the other then so take in 4 and writing it as a fraction over 48 I
can see that 4 and 48 are both in the 4 times table so I can divide them both by
4 so 4 divided by 4 is 1 48 divided by 4
is 12 so therefore area of the square divided
by area of the car rectangle is equal to 4 over 48 which is the same thing as 1
over 12 we’re all done question 8 Sam Karlin Erik share 40 Suites Erik gets
the largest share what is the smallest possible number of Suites that Eric
could get so we’ve got Sam Karl and Eric and altogether their Suites add up to 40
that’s a pity it wasn’t the other way around because if it was what’s the
largest number of Suites that ever could get he would get one give one to each of
these guys and he’d get the rest it’s 38 so that would be 40 Suites all together
and Erik taken the largest amount but we’re not doing that we’re doing the
smallest amount so we need to find giving sweets to Sam and Karl in such a
way that Eric still gets the most but he gets the least most if you see what I
mean okay so if we divided 40 equally by three I know it doesn’t go because 40
isn’t in the three times table but let’s see what what number would be closed 40
divided by three what’s that then I know that 10 threes a 30 so 39 is 13 threes
so that is 13 remainder 1 and isn’t it okay so what if we give each of them 13
13 13 13 13 and that remainder one we also give to Erik as well so he gets the
extra one in that way he’s got more than the other two but it is very close to
them all getting the same amount and I think that then is going to be the
smallest possible number that Erik can get
question 9 the time in Rio is three hours behind London the time in New York
is five hours behind London what is the time in New York when it is 1:00 a.m. in
Rio hmm okay so he’s yellow so in London then we know that it is five hours
behind in New York and we know that it is so that is five hours behind isn’t it
and then in Rio it’s three hours behind so that is minus three so then we can
see from that that the distance in the times between New Yorker and in Rio is
gonna be the difference between those two then isn’t it so that is going to be
Rio’s gonna be two hours two hours ahead of New York or New York it’s going to be
two hours behind Rio okay so if it is 1 a.m. in Rio then it’s going to be 2 how
2 hours but behind that in New York so what is two hours before 1 a.m. be
midnight the 11:11 p.m. wouldn’t it the night before so it’s gonna be 11 p.m. question 10 here is a list of numbers
work out their median okay now to find the median you need to arrange the
numbers from smallest to biggest and then find the number in the middle okay
so I’m going to do that first I’m gonna go through my list and rearrange it so
I’ve got a 1 I’ve got two twos I’ve got a 3 I’ve got a four I’ve got 1 2 3 5 5 5
5 I’ve got a 6 and I’ve got an 8 ok so I
rearranged them from smallest to biggest now how many of them are there there are
1 2 3 4 5 6 7 8 9 10 numbers all together
so 10 numbers all together so my middle one you can find by adding one and
dividing by two so you’re a middle temper is your 10 plus 1 divided by 2 10
plus 1 is 11 divided by 2 that tells me my median is gonna be the 5.15 the 5th
and the 6th number so counting in 1 2 3 4 5 that’s my fifth number that’s my 6
member so my median is going to be kind of halfway between those two numbers
then isn’t it so halfway between 4 & 5 is a 4.5 ok so that’s my median 4.5 alternatively if you don’t like using
this n plus 1 over 2 thwe of working out where the median is you can’t kind of
come in from both ends so you can kind of say count in so 1 2 3 4 looks like
counting from both ends until you’re just left with one or two numbers in the
middle do it that way that also works okay 10 B says work out the mean so the
mean is going to be all those numbers added up divided by the total number of
numbers and I already know that there are 10 numbers because I counted them
earlier but what does my numbers add up to I’ve got 1 2 3
I’m just going to do that 1 3 5 8 12 17 22 27 33 41 so they add up to 41 there
were 10 numbers all together so dividing 41 by 10 just move the decimal point one
across it gives me 4.1 so my mean is 4.1 question 11 300 passengers go on a coach
trip each coach takes 50 passengers each passenger pays 25 pounds the table shows
the cost of four the coach company costs for each coach is 90 pounds for the
driver and 70 P per mile for the fuel each coach travels 200 miles work out a
total profit for the company that they make on this trip okay so we’ve got
oodles of information here we’ve got just make sure that we use it all up in
the right order okay so we want to work out the total profit now a profit is the
income that you’ve got coming in less your expenses that you’ve got going out
okay so we can try and work out those two things first work out the income
work out the expenditure and then subtract one from the other and that
will be the profit okay so just go write that down that profit equals income
minus expenditure so let’s work out the income first so how much money we’ve got
coming in so we’ve got three hundred passengers going on the trip each coach
takes 50 passengers and each passenger pays 25 pounds okay so we don’t need the
information about the the passengers yet 50 passengers in a coach but we do know
that we need to know that we’ve got 300 passengers paying 25 pounds each so that
is our total income then isn’t it it’s going to be equal to 300 passengers pay
in 25 pounds each okay so what’s 300 times 25 so what I can do is I can take
those two zeroes off there and put them on there instead and do three lots of
2500 which would be 7,500 so they’ve got 7,500 pounds coming in and what is our
expenditure then so that is going to be right that
properly now what have you got then so we’ve got each coach takes 50 passengers
how many coaches will need so i total number of coaches then it’s going to be
our 300 passengers divided by our 50 per coach so council that into that 30
divided by 5 is 6 so I’m going to need 6 coaches so we want six coaches not one
coach so if we’ve got six coaches we’re going to need six drivers six 9s are 54
so 690 s is going to be 540 okay and we are travelling how far we’re going we’re
going 200 miles so fuel per mile is 70 paper mile for
fuel for 200 miles then it’s going to be 200 lots of 70 P I’m going to convert
that 70 P into pence at 0.7 pence isn’t it so 200 times 0.7 that is or 200 lots
of 70 P to lots of 70 P 1 pound 40 times 100 that is going to be 14 pounds no 140
pounds isn’t it so it’s a hundred and forty pounds per coach for the 200 miles
at 70 p.m. I’ll okay sir but we’ve got six coaches so a hundred and forty times
six what’s that so that’s zero four six is a 24 Erik two one six is six plus two
is eight as 840 so it’s going to cost us 840
pounds in fuel so then the total cost it’s going to be those two things added
together so it’s going to be five hundred and forty plus eight forty
five hundred four is the cost for your six drivers and 840 is the cost of all
the fuel so adding those up eight forty and five forty zero eight and thirteen
1380 so then the profit is going to be income seven thousand five hundred
pounds – our expenditure of one thousand three hundred and eighty pounds so zero
can’t do that gotta borrow one so that’s four that becomes ten ten subtract 8 is
2 4 subtract 3 is 1 + 7 subtract 1 is 6 so the profit then is six thousand one
hundred and twenty pounds okay twelve a workout sixteen point four minus three
point nine two plus seven point eight ok so I’ve got two operations to perform
here I need to do the subtraction and the addition that actually occurred at
the six point four and a 7.8 together first and then do the subtraction or I
can subtract three point nine two from sixteen point four and add on 7.8
doesn’t really make any difference I think I’m gonna start with a subtraction
seen as most logical 16.4 subtract three point and nine two just gonna pop out
with an extra zero to make this attraction go a bit easier so zero take
away two I can’t do you’re gonna borrow one from there that makes it ten ten
subtract 2 is 8 3 subtract nine I can’t do so again going to borrow one from
there that makes it 13 13 subtract 9 is 4 5 subtract 3 is 2
and one subtract nothing is one so I get 12 pound 48 after the subtraction now I
need to add on 7.8 so I’m just going to continue from here I’m just gonna write
plus and put the 7.8 here just being careful to line it up in the right place
decimal point below decimal point and you can see I’ve padded it out again
with an extra zero just so I’ve got the right number of columns now we’re doing
addition this time so 8 plus 0 is 8 4 plus 8 is 12 so gonna write the 2 here
and I’m going to carry 1 to the next column 2 and 7 makes 9 plus 1 is 10 so
I’m going to put the 0 here and carry one into the next column and then I’ve
got 1 plus 1 which is 2 now my decimal point was here and here it’s going to be
here my answer 20 point 2 8 12 B workout 2,840 3.6 1/7 I’m going to do this
because the divisor is small it’s a single digit number I’m going to just
use short division to do this and so I’m gonna write my 7 on the outside and then
my 2 8 4 3 point 6 1 along there now you notice I’ve written them with nice lots
of space in between because I know I’m gonna have remainders to squeeze in so
if you write your numbers down with a bit of space and it doesn’t get too
crowded as you go through okay so let’s do the division then 7 goes into 2
doesn’t go 7 into 28 7 14 21 28 goes in 4 times exactly remainder 0 so 7s into 4
don’t go so that goes in zero times remainder all of those four sevens into
43 where are 6 7 2 42 so it goes in 6 times
remained a 1 so I’m gonna write a little one there 7 s into 16 that goes how many
times since the 16 goes twice so twice oops doodle right color twice
and remainder 2 and then finally 7s into 21 go three times remainder zero okay so
all done now that the decimal point was here so my decimal point is gonna be in
the same place here it’s gonna be four hundred and six point two three four oh
six point two three question 13 in a game too fair spin as a
spun if the numbers the arrow lands on are different the score is the higher
number and if the number the lack of the arrow lands on are the same then the
score is zero complete the table to show the possible scores so if they are
different it’s the highest number and if they’re the same it’s zero okay so we’ve
got the numbers for spinner al on one side and B of along the other so if I
get one on spinner a and two on spin of B then it’s to hire one of the
difference just going to be the higher one of the two it’s gonna be – if I get
one on a and 3 on B it’s gonna be the higher one and if it’s one on a and five
on B it’s going to be the higher one so it’s two two three five okay so I get
two on spinner a and two on spin of B then they are the same so it’s zero
forget – on a and 3 on B it’s the higher once it’s three and if it’s two and five
it’s gonna be the high one it’s five okay the next row four on spinner a if
it’s two unspinning B then four is higher so I’m gonna get four if it’s
four and two then four is higher if it’s four and three then four is higher and
if it’s 4 and 5 then 5 is higher and then the final row 6 on spinner a 6 is
higher than 2 so it’s 6 6 is higher than 2 so it’s 6 6 is higher than 3 so it’s 6
+ 6 is higher than 5 so it’s 6 okay so that’s my completed table write
down the probability that the score is an odd number
okay well probability is defined to be successful outcomes divided by total
outcomes now here the total number of outcomes
where each of the cells I’ve got in my possibility space we’ve got four results
on a and four results on B 4 times 4 gives me a square of size 16 so there
are 16 possible outcomes all together we want the possibilities that are odd
numbers okay so which one of these answers are odd 3 is odd 3 is odd 5 is
odd 5 is odd 5 odd okay so 4 is definitely not odd and 6 isn’t
and 2 isn’t what about 0 is 0 an odd number
well in fact zeros are quite curious in a minute it doesn’t really have a it’s
neither odd nor even I think so anyway we’ve got 5 odd numbers so the answer is
5 out of a total of 16 5/16 is the answer okay now the last part says the
same game is played using spinner C and D the numbers on C are shown the table
shows some of the possible scores okay what numbers are missing
okay well let’s work it out from the table first so if I got one on spinner C
and I don’t know what I’ve got one’s been a D but the answer was four well I
know got got I must have got a four then on spinner D look at this answer here if I got one on
spinner C then I must have got four on on spinner D at that point there because
four is bigger than one so it would be the four that was accepted now if I got
a zero here that means the numbers must have been the same so I must have been a
four there okay and in my next row I see if I got a seven there and in the end it
was a zero then I must have had a seven up there so seven and seven weeks zero
and then finally I’ve got eight down here overnight so if I’ve got seven on
one spinner and but my final arts was eight it must have been an eight up here
so right the missing numbers on spinner D we haven’t done that yet it’s been the
DS up here so it should be four four seven eight question 14 two people
working at the same rate will take six hours to paint a room 14 a says assume
that they all work at the same rate how long will it take three people to paint
the room hmm okay so let’s have a think about this I’ve got two people and
they’re painting for six hours to do the room so that means that all together
two times six is twelve so it takes 12 people hours to were to paint the room
okay so then if I increase my number of people to three people
I’ve not increased the amount of work that needs to be done it’s still going
to be twelve people hours to paint the room but I’ve got three people to do it
with now so if I take my 12 people hours and I divide it by my three people that
leaves me with four hours okay so it’s gonna take my three
people four hours to paint the room just make sure that I’m answering the right
question how long will it take three people to paint the room or take them
for ten hours okay in fact the third person works at a faster rate how does
this affect the time to paint the room okay so let’s have a think about this so
we’re assuming that each of these three people paint the same rate and that gave
us the answer of four hours but this is a super super fast person who can paint
more than his Duloc so actually what I’m doing is I’m increasing this divisor
slightly let’s see can he can work the same rate as one-and-a-half people then
I’ve got three and a half people working on the job so 12 divided by a slightly
larger number is gonna give me a slightly smaller finish time so the
amount of time it’s gonna take to finish the room he’s gonna go down a little bit
it’s going to decrease so how does this affect the time to paint the room the
time will decrease question 15 three a plus B equals 7 + 6 X + 8 y is equal to
40 show that 9 a plus 3 B has a greater value than 3x plus 4 y well we know that
3 a plus B is equal to 7 so what is 9 a plus 3 B equal to right and if you can
notice but 9 a is three times bigger than 3a and 3b is three times bigger
than B so this number here is gonna have to be three times bigger than that one
there isn’t it so seven threes then are going to be 21 so 9 a plus 3 B is gonna
have to twenty-one okay let’s have a look at the
other one we were told that 6x plus 8y was 40 and we now want to know about 3x
plus 4y what that is equal to now again notice here that I’ve got 6x here and 3x
here which is exactly half I’ve got 8y here and for y here which is
exactly half so then this one here is gonna have to be half again isn’t it
so if I’m dividing by two that’s the same thing as harvin isn’t it 6x divided
by 2 is 3 x 8y divided by 2 is 4 y so 40 divided by 2 gives me 20 so we can see
that 9a plus 3b is 21 and 3x plus 4y is equal to 20 so 9a plus 3 B is greater
than 3x plus 4y okay we’ve done it circle the point that lies on the line X
minus 3 is equal to 0 okay it’s becoming a bit of a weird form here
if I add 3 to both sides on this equation then I’m gonna get well those
two things are going to cancel out aren’t they and it’s just gonna leave me
with x equals 3 so this is the line X is equal to 3 any line of the form X is
equal to number is going to be a vertical line through that number so
it’s going to be like a straight line passing through 3 at any point along
that line is going to have an x coordinate of 3 and then the y
coordinate whatever it happens to be so at that point there must lie on this
line question 17 a is a negative odd number
circle the words to describe a squared okay so a is a negative odd number
sometimes it’s helpful to give some examples of that so if a is a negative
number and it’s odd it could be something like minus 3 or minus 5 or
minus 9 something like that okay so circle the words that describe a
squared so if I took those numbers minus 3 minus 5 minus 9 and I times them by
themselves they’re negative 3 times negative 3 3 times 3 is 9 and the
negative times a negative is positive so that’s positive 9
negative 5 times itself would be positive 25 and negative 9 times itself
would be positive 81 okay so circle the words that describe each
of these answers so they’re so the ones I got ended up being positive and odd
didn’t they because a negative times a negative is a positive so any number I
pick which is negative and square I’m going to get a positive number and they
all ended up being odd and that’s no coincidence either because if you take
any odd number and you times it by an odd number you get an odd number so it
doesn’t matter what my value of a was if it started out being negative an odd and
I square it I’m gonna end up with a positive and odd solution that’s that
one question 18 circle the ratio which is the same as a scale one centimetre
represents a one kilometer hmm one centimeter is one kilometer okay well I
know that there are a thousand meters in a kilometer so what’s that then so one
centimeter then is the same thing as 1,000 meters and I know that there are a
hundred centimeters in a one meter a thousand meters is going to be a
thousand lots of a hundred centimeters so this scale we have dot equal signs in
it they’re a ratio only so one centimeter goes with well that’s times
that by a hundred that’s adding another two zero zero so it’s one and then one
two three zeros already had plus another two zeros centimeters so what’s that
that’s a hundred thousand centimeters isn’t it
so one centimeter to a hundred thousand centimeters is to scale it’s that one on
the end question 19 circle the percentage that
is closest in value to one third okay now one third one third one third of a
whole number is one third one third of a hundred percent was one third of a
hundred percent 100 divided by three threes into 100 goes thirty three point
three three three three times don’t they okay it’s that one with a dot on the top
they put three points three with a dot on the top so that is going to be your
percentage one-third is going to be equivalent to 33 point sorry reoccurring
so which one of my answers is closest to that it’s gonna be out of these two here
so you’re not going to be these two can be closest to one of these two which one
it’s thirty three point three three three three bigger to thirty three point
three or thirty three point four well if I’ve got thirty three point three three
three three and I went around after one decimal place I’m going to be rounding
off after that number the very next digit is a three which
means I would need to round down so it rounds off or is closest to thirty three
point three question 20 work out route 1 to 1 minus 13 minus 5 times 2 all
squared okay so oh I’m gonna have big mass going on here on I brackets indices
division multiplication addition subtraction that’s actually the order
you need to do things okay so first up brackets got to deal
with this bit in here now the bit in there has got two operations going on as
well it’s got a multiply and a subtraction so just having a little mini
bit mass competition out of those two I need to do the multiplying before I do
the subtraction okay so working for this through I’m just going to leave
everything as it is until I get to that point in big mass okay and then I’m
gonna do that bit so I’ve got 13 minus 5 times 2 I’m gonna do the multiplying
first so that gives me 13 minus 5 times 2 is 10 and then I’m gonna do the
subtraction so that is equal to root 1 – 1 – 13 subtract 10 is 3 so it’s 3
squared right so next up is indices ok now I’ve got two indices to do here I’ve
got this one my 3 squared but this is also an index as well
this root sign they have the same way as well so got to do those next so what is
the square root of 121 well 11 times 11 is 121 so the square root of 121 is 11
minus 3 squared 3 squared is 9 ok so now I’ve just got subtraction left
to do is very simple God did subtract one of those from the other 11 subtract
9 is 2 okay answer is 2 looked horrible but as long as you follow the rules of
bitmask carefully you will get the right answer question 21 part a says reflect
the triangle in the line x equals 2 okay so we’ve got a triangle here what does
the equation x equals 2 look like or the line x equals 2 look like we talked
about this earlier any line that is of the form X is equal to number is going
to be a vertical line through that value so the line X is equal to 2 is this one
here just going to draw it on in cream so that’s my mirror line so I want to
reflect it in that line so want to do a reflection I like to
take each point in turn work how far away it is from the mirror lines that’s
one unit away so its image is going to be one unit away on the opposite side
there this point down here again ask one unit away from the mirror lines image is
going to be one unit on the other side it’s going to be there and then finally
I’ve got this point here now that is one two three units away from the mirror
line so the image is gonna be one two three units away it’s going to be there
once I got all the points I can join them all up to make my shape okay there
we go all done question 20 OMB says rotate the kite 90 degrees
anti-clockwise about zero zero okay so the point of rotation is given as this
point here that’s my point of rotation and anti-clockwise is the opposite way
that the clock is going it’s this way around you’ve always got a clock in your
exam room to have a look at so if you can’t remember just have a look at the
clock and work backwards so it’s that way around okay so we’re gonna take each
point and rotate it now you might find it easy to do with tracing paper so what
you can do is trace the four points then stick your pen tip where the center of
in rotation is and then turn it around 90 degrees that’s one way of doing it or
you can take each one of the points and just think it through so at that point
there is going to kind of rotate around to their that point there is I kind of
think in Night Moves so if you’re looking at this point here it’s one two
three units down and one two across from the centre of enlargement so I can from
the center of rotation so rotating that kind of L shape round is going to be one
two three one two it’s going to be up there
okay this point down here is one two three four units directly below so just
going to end up over there four units to the right and finally this point over
here is one to the left and three down so it’s going to be two down and three
to the right it’s gonna be here okay once you got your four corners again
it’s just matter join them up then with a ruler okay so it’s good just to do a
visual inspection at the end you know these transformations are not going to
change the overall shape so if your object and image look different than
you’ve probably made a mistake it’s not gonna squish it or stretch it in any way
they’re gonna look like identical congruent shapes that you’ve just
shifted around the page a little bit question 22 Anna plays a computer game
each game is a win or a loss she wins 3/4 of her first 24 games
she then wins her next 12 games for all 36 games work out the ratio of wins two
losses give your answer in its simplest form okay so she wins 3/4 of her first
24 games so what is 3/4 of 24 then so again we talked about this earlier the
fact if you could want to find a fraction of a number you divide through
by the denominator and you times through by the numerator so 24 divided by 4 is 6
4 goes into 24 6 times that’s the same thing as 3 times 6 and then 3 times 6 is
18 okay so she wins 3/4 of her first 24 games today is 18 wins
how many losses so she won 18 out of 24 that is going to be 6 losses isn’t it
18 wins six losses for those 24 games okay she then wins her next 12 games so
that’s 12 wins so all 36 games work out the ratio of wins two losses so wins two
losses we said she went 18 of the first 24 plus another 12 that gives us a total
of 30 wins and her losses were six so 32 six okay now it wants it in the simplest
form that is not the simplest one because 30 and six have a common divisor
that both in the six times table so dividing by six 30 divided by 6 is 5 and
6 divided by 6 is 1 so the ratio in its simplest form is 5 to 1 5 to 1 question
23 a solid shape is made from centimeters cubes here is the planned
side elevation and front elevation of the shape centimeter cubes are added to
make this cuboid how many cubes are added okay so can we piece it together
what we’ve got to Center to start with so the plan is the view from above isn’t
it okay so when we’re looking from above it looks like an L shape from the front
it looks like a solid block and from the side it looks like that
ok now I need to make a block which is 4 by 4 by 3 I’m gonna use the plan I’m
gonna build up from it okay so let’s have a look at the plan
these three blocks here if I’m looking from the front elevation I can see that
I’ve got four blocks in on top of each other so there are already four blocks
powered up here here and here okay because I’d be looking it from the front
I can see that that’s four and therefore so they can have four four
four in that plan now the next square here here look that’s gonna be this row
so there are actually one two three blocks piled up there so they’re going
to be three blocks already there and then the next two rows here and here are
they’re going to be this one and this one so they’re gonna have two blocks and
two blocks in each of those and then obviously I’ve got no blocks here here
here here here and here okay so to build this up to a cuboid which is four by
four by three I’m gonna have to top up each one of these columns from above so
they’re all equal to four so I’m gonna have to add on for each of these I’m
gonna have to add four to each of those four times six is going to be 24 blocks
that go in there okay these ones are all fine this one here
I’m going to have to add an extra one to to make four blocks and then these two
I’m gonna have to add 2 to each I’m gonna have to add two and two so that
gives me a total of 29 29 blocks to add to top that all up so how many cubes are
added I’m going to be adding 29 cubes question 24 divided 405 in the ratio of
4 to 11 they want to raid divide in the ratio 4 to 11 I’ve got four parts to
eleven parts which is four plus eleven that’s 15 parts altogether okay so if I
then divide 405 by my 15 parts it should tell me what the value of each part is
worth then so 15 in the 4 don’t go 15 into 40
twice to 15 to 30 so that ramier remainder of 10 so a hundred and five
15s into a hundred and five go seven times so that is 27 so each part is
worth 27 so if I take my ratio of 4 to 11 and I scale it up by a factor of 27 427’s times 2 by 4 is doubling and
doubling again so 27 doubled is 54 doubled again is a hundred and 108 and
then 11 times 27 10:27 s is going to be 270 so add another 27 to that as two
hundred and ninety seven to nine seven we can just double check I’ve got my
outright answer by adding those two up make sure I still got 405 and 7 9 is 5
carry 1-0 405 it does work so I’m going to have a hundred and three 108 and 297
it’s the height of zach is 1 point 8 6 meters he’s a big boy and high of Fred
is 1.6 meters right the height of sack as a fraction of the height of Fred give
your answer in its simplest form right the height of this of Zach as a fraction
of the height of Fred that means sexed height goes on the top and Fred’s height
goes on the bottom so it’s going to be one point eight six divided by one point
six now again we got decimals here which we can easily get rid of by multiplying
top and bottom by let’s do it by a hundred so what’s that mall that gives me that
will give me a hundred and eighty six over a hundred and sixty won’t it
there’s a top-heavy fraction right so we’re looking for common divisors now
160 and 186 Wow struggling to find a common divisor
bigger than two let’s just have it and see and have another look so that have
been 93 over 80 okay any kind of factors there again three you know seven no no I
can’t think of any more no I think that’s about as far as I’m going to get
with canceling down now it’s asking for the simplest form here so we cancel down
as far as we can now we could write it as a mixed number we could write as one
and thirteen over 80 but I don’t actually think that is any more simple
than this I prefer to leave my answers as top every fractions I think they’re
more useful so I’m going to leave it like that the point a which has
coordinates 0 2 and the point B which has coordinates 6 5 our points on a
straight line a b c d now we’re told that a B is equal to BC which is equal
to C D so let’s just mother on the diagram so these are all the same length
aren’t they these three sections work out the coordinates of D okay right so
we know a coordinate a we know coordinate B so we can work out how far
in that direction and how far in that direction is between those two points so
having a look at the x coordinates 0 to 6 tells me that the distance in the
direction of X is 6 and looking at the Y coordinates 2 & 5 tells me that the
distance in the Y coordinates 5 subtract 2 is 3 so from A to B we’re going 6
units along and we’re going to go through
units up okay now we want to work out the coordinates of D so we can either
work out C along the way by going six long as three up and another six long
and three up or we can double that up and go twelve along and six up okay I’m
going to do it in one jump because I’m a bit lazy don’t do things twice so twelve
along and six up from B so B has coordinates six five so if I go an extra
twelve along in the direction of X then six plus twelve is 18 and if I go I make
five in the direction of Y and if I go up another six then that’s gonna be five
plus six that’s gonna be eleven up okay giving me a coordinates 1811 for D guys
I said I could have done it in two jumps gone by C but 1811 I think that’s
slightly quicker way of doing it a coin is thrown 50 times it lands on heads 31
times write down the relative frequency it lands on heads
okay well relative frequency is defined to be successful trials tricycle meaning
it the thing that you’re looking for what happens divided by total trials so
how many times you tried it all together so successful trials over total trial so
here it landed on heads 31 times so in terms of this problem we had 31
successes and we had 50 trials all together so the relative frequency is 31
over 50 don’t be under any pressure to simplify probability questions you never
get any more marks for it and just might as well leave it as it is I don’t know I
sure you can cancel it balcony anyway let’s move on 8b Raj says the coin is
biased towards heads you use the date to give a reason why he might be correct
okay well we’ve got 31 out of 50 trials that was her heads
which is a bit more than what you would expect when you the theoretical
probability of getting heads is 1/2 so the expected successes would have been
1/2 times 50 or 25 and he’s reporting 31 here okay so we would expect 25 but he
got 31 okay so that is some evidence to suggest it might be biased it might just
be a lucky break though it’s not that far off 25 is it but anyway that’s what
we can write down so 5 lots of X plus 3 is less than 60 so this is an inequality
now you can just solve these exactly the same way you would an equation and so as
long as you can solve equations you can also solve inequalities mostly there is
one extra rule but we’ll get to that in a minute so 5 lots of X plus 3 is less
than 60 I can simplify both sides by dividing through by 5 so divide in the
left-hand side by 5 that’s going to cancel with that it’s going to leave me
with X plus 3 it’s less than and then 60 divided by 5 is 12 and then subtracting
3 from both sides then I’m going to be left with X is less than 9 okay so like
I say you can you can solve these exactly as you would an equation just
one thing to be careful of is dividing through by negative numbers because that
has that flips the sign around if you do that so either avoid dividing but
through by negative numbers or remember that if you do you’ll have to flip the
inequality sign round the other way the range of a set numbers is 15 and 1/4
the smallest number is negative 2 and 7/8 work out the largest number
so range if you remember is defined to be the largest value minus the smallest
so if we rearrange that move that over there look then the largest value is
going to be the range plus the smallest isn’t it so I’m going to find it by
adding my two fractions together so in this case it’s gonna be my range which
is 15 and a quarter plus my negative two and seven eighths and now adding a
negative is the same thing as taken away so that is the same thing as those two
things subtracted from each other I’m just going to write the most top-heavy
fractions now as well do that let’s do that
so fifteen fours are 60 plus one is 61 quarters so I’ve got 61 quarters minus 2
eights are 16 plus 7 are 23 to 23 eighths
okay so subtraction I need a common denominator so just doubling up those
two numbers there so we change it into an equivalent fraction over 8 so 61
times 2 is 122 eighths so 120 two eighths minus twenty three eighths so
subtracted numerators that’s going to give me 99 over 8 do we have to give it
in a certain form just says work out the largest number got 99 over 8 so write as
a mixed number well I eighths into 99 go 12 times 9 a
12-8 are 96 that goes in 12 times remainder 3 so it’s 12 and 3/8 again I
think 99 over 8 is probably a more useful number to deal with and would
still get you all the marks I think doesn’t say write as a mixed number but
however those will get you three marks Y is inversely proportional to X complete
the table okay so why is inversely proportional to
X that means Y is inversely proportional little fishie over 1 over X okay that’s
what that is saying mathematically now we can replace the little fishie symbol
with equals K so I’m going to rewrite that so y equals K over X where K is a
constant that we can then find okay now you can find the constant K if you’ve
got two values while your value of x and your value of y that go together now
we’ve got one of those in the table if we look at this table I’ve got two
numbers here that go together when X when X is 6 Y is equal to 4 so sub in x
equals 6 Y zip to 4 into my partial equation y equals K over X I should be
had to find out what K is so that becomes 4 equals K over 6
replacing Y for 4 and X 6 okay and just taking that 6 there cross multiplying up
there or multiplying both sides by 6 if you’d rather I’m going to get K is equal
to 24 on I okay so my complete equation then is going to be y equals K which
we’ve now found to be 24 over X okay so now this is my complete equation which I
can then go and find my other values so if x equals 12
then Y is 24 over x1 is 24 over 12 24 divided by 12 is 2 so when X is 12 Y is
2 and what about the other way around so if Y is 8 what is X okay so if 8 is
equal to 24 over X just cross multiplying these two just switching
them around and I’m gonna get x equals 24 over 8 24 divided by 8 is 3
so X is 3 when y is 8 once you’ve done a few of these proportional questions they
get very very formulaic they always give you they always start off by giving you
the rule that links Y and X you can then form your partial equation which
involves their constant K and then you’ll have a pair of values that you
can sub in to find what K is to complete the equation and then you can go on and
use your complete equation to find other values they’re always the same very very
formulaic questions and after you’ve done a few you should be good on them a
large rectangle is made up by joining three identical small rectangles as
shown now it’s not drawn at least then get you read around we’re told that the
perimeter of one small rectangle is 15 work out the perimeter of the large
rectangle hmm this looks like a job for algebra now let’s say that the width of
one of these rectangles is W now I could write L therefore the length but
actually if you look