---
title: 'Lazy Australian Takes the British GCSE Higher Maths Exam!'
source: 'https://youtube.com/watch?v=hyYP98RcZEo'
video_id: 'hyYP98RcZEo'
date: 2026-08-12
duration_sec: 2947
---

# Lazy Australian Takes the British GCSE Higher Maths Exam!

> Source: [Lazy Australian Takes the British GCSE Higher Maths Exam!](https://youtube.com/watch?v=hyYP98RcZEo)

## Summary

A YouTuber takes the 2018 Australian Year 11 mathematics past paper, which is equivalent to the British GCSE Higher Maths exam. He works through the questions in real-time, showing his working and commenting on the difficulty. The video concludes with his score and a reflection on his performance.

### Key Points

- **Starting the Exam** [00:19] — The creator starts the exam, noting it's been 4-5 years since he studied maths.
- **Question 1: Exponents** [00:49] — He solves the first question: 3^7 / 3^2 / 3^3 = 3^2 = 9.
- **Question 2: Substitution** [01:09] — He substitutes values into v^2 = u^2 + 2as to get v^2 = 36.
- **Question 3: Percentages** [02:06] — He works through a bonus distribution problem, calculating percentages and comparing shares.
- **Question 4: Rate Problem** [04:33] — He solves a rate problem: 5 taps fill a pool in 120 minutes, so 3 taps take 200 minutes.
- **Question 5: Estimation** [06:44] — He estimates the time for a plane to travel one mile at 213 mph, getting about 17 seconds.
- **Question 6: Simultaneous Equations** [09:28] — He solves simultaneous equations, finding x = 4.5 and y = -1.5.
- **Question 7: Geometry** [10:47] — He calculates the area of a shaded region in a semicircle, getting pi/8.
- **Question 8: Trigonometry** [13:39] — He recalls that tan 45° = 1 and solves for x in a simple equation.
- **Question 9: Box Plot** [14:55] — He constructs a box plot for train delays, noting the distribution is not linear.
- **Question 10: Factorizing** [18:42] — He factorizes expressions, including 50 - 2y^2 = 2(5 - y)(5 + y).
- **Question 11: Percentage Change** [19:14] — He solves a percentage reduction problem, finding a 20% reduction.
- **Question 12: Circle Geometry** [21:16] — He uses circle geometry theorems to find an angle, getting 21 degrees.
- **Question 13: Transformations** [24:33] — He identifies a transformation as a rotation of 180 degrees.
- **Question 14: Exponents** [25:42] — He simplifies (16/81)^(3/4) to 8/27.
- **Question 15: Surds** [26:08] — He solves an equation involving surds, finding a + b + c = 0.
- **Question 16: Similar Shapes** [26:40] — He uses similarity ratios to find a length ratio of 3:10.
- **Question 17: Recurring Decimals** [28:23] — He solves a recurring decimal problem, getting 0.565656...
- **Question 21: Skipped** [32:23] — He skips question 21, finding it too difficult.
- **Question 22: Probability** [33:44] — He solves the final probability problem, finding the total number of pens is 45.
- **Final Score** [47:14] — He marks his paper and scores 72/80, which is 90%, a grade 8 or 9.

## Transcript

read the question this is so embarrassing god my math teacher is gonna be so so ashamed of this hey guys welcome back in today's video we're doing something a bit different and that is the
gcse exams for high level mathematics and i'm doing the 2018 past paper of australia's year 11 so it should hopefully not be too hard mathematics in high school but it has been like four or five years
now so i might have forgotten everything but let's give it a shot and see how i go so let's get started this is the 2018 paper and let's go
three to negative two over three over three okay not too odd so that's just three to the 7 minus 2 minus 3 which is three to the 7 minus 2 minus 3 which is 3 squared which equals to 9.
all right question 2. so work out the value of v okay so just subbing in numbers once again v squared equals to again v squared equals to 12 squared plus two times negative three
times eighteen which equals one four four four minus 6 times 18 equals to 48 108 144 minus 108 equals to 36
okay i hope that i don't make any mistakes because i'm doing this live and anyways let's see how it goes i can make s the subject so
squared s equals to v squared minus u squared on how many marks is that this is six marks already and i've spent just over a minute okay this doesn't seem very hard at all
but it gets harder we'll see company 40 of the bonus is shared equally between
three managers rest is shared between salesmen shed equally i'll get 25 percent more money they actually get so 2100 times 0.4 is the amount shared to
the managers which is uh 2 1 so 880 because 21 times 4 is 880 and that is between
3 m so the rest is 3 m so the rest is 2 1 0 times 0.6 which equals to 2 1 0 times 0.6 which equals to 1 to 60.
basic math but yeah that should add up to 2 100. yeah that should add up to 2 100. 2100 times 0.6 is 1260 divided by 7 four per person per salesman
done division without a calculator okay so
one there so 56 left over that's eight so 180 that's eight so 180 180 per salesman um now if it was just shared between two 10 people equally then
10 people equally then if 10 people equally he would get 210 pounds 30 over 180 is
well it's clearly not 25 but that's one over six so it's over six so it's how much is that now 16.67 percent yeah that's right so they did not
obviously get 25 percent more money so therefore therefore salesmen not correct
only on four minutes minutes if only three tabs are used so
if only three tabs are used so assuming five taps equally so
filled that means it would have filled um one fifth of the pool so cool so um how do we get it to three like it's pretty obvious but like i'm just trying to see if i can explain it
trying to see if i can explain it uh one fifth of the pool
in one minute it would fill 1 over 120 times 5 which is 720 1 over seven twenty three taps would fill three over seven
twenty which is one over uh to get that so that means it would
uh to get that so that means it would take hundred so three over six hundred
which is one over two hundred so that means it would be two hundred minutes means it would be two hundred minutes well i'm pretty rusty
school saw this they'd be pretty ashamed of me right now your working out okay so that was just or taps fill at the same speed
right now but like it's not an actual exam that's being marked so it doesn't a plane travels at a speed of 213 miles per hour just just use kilometers but i don't estimate the number of seconds it takes the plane to travel one mile
it takes the plane to travel one mile okay so okay so how many okay so to 13 miles in 3 600 seconds right so
in that one hour there's 60 minutes in one minute the 60 seconds so that would just be so we're dividing one mile okay
divided by 213 for the number of seconds oh another long division i didn't see a point of the test like it just doing stuff we did in year so long okay so that's one there
okay so that's one there two one three uh ten minus three is two one three uh ten minus three is seven two thirteen so that is we've got an estimate so that seems
about 17 seconds right because two times seven is fourteen times seven one two seven nine fourteen ninety one okay so just under 17 seconds
17 seconds so but it is very close so uh i don't know how many decimal places is two
that's understood overestimate uh so 17 seconds seconds and overestimate
[Music] is 16 point something
is less than 17. oh how do i explain this 213 times 17 is greater than 3600 but okay i'm not sure if that's what they're looking for but that's what i'm going to put okay way up
question six solve the simultaneous equation okay yeah this is what we learned in year seven australia wow i really wish i did i did high school in the uk now
so using the second equation we get x is equal to three y plus nine so five three y plus 9 plus y equals to 21. plus 9 plus y equals to 21. 15y plus 45 plus y equals 21.
16y equals to negative 24 y equals to negative 1.5 right okay and then that means x using that equation is equal to 4.5
using that equation is equal to 4.5 so double check 4.5 minus so double check 4.5 minus minus 4.5 is 9 yep minus 4.5 is 9 yep 5 times four point five check
point five equals to twenty two point five minus equals to twenty one yep okay so x equals to 4.5 y equals negative 1.5
equals to 4.5 y equals negative 1.5 oh the time
semicircle okay probably finding the area oh probably finding the area oh okay abs diameter ac is the arc okay
square okay area of square is easy okay area of square is easy which is just
20 squared area of shaded region
um so the r is pi r squared on four since we're taking a quarter only which is pi times 20 squared on four
pi times 20 squared on four and then i forgot area so that's not the shade region that is the quarter circle area of uh small
hemisphere the heaviest we have a semicircle semicircle series
it is pi r squared on 2 which is pi times 10 squared on 2. pi times 10 squared on 2. so area of shaded region remember we're trying to look for that pi of 8
pi of 8 area of shaded region is
that one minus that one so pi 20 squared on 4 minus 10 squared on 2 20 squared on 4 minus 10 squared on 2 which is pi 20 squared on which is pi 20 squared on 4 minus 20 we doubled that times four
and then times the bottom by four as well two times four so that is just pi 20 squared on it so
shaded on area square is then just get this over 20 squared so that is pi
over eight yep that next question
write down the exact value of 10 45 okay so oh my god i actually forgot this tan is this over that so tan 45 is one
60 0.5 work out the value of x oh x oh okay so well four over x equals to
4 equals to 0.5 x x equals to 8. i might have to do the a levels next time um
all right question nine how many questions are there questions are there so ten oh okay i think it will get so ten oh okay i think it will get harder
of minutes the trains were delayed correct to the minute okay the shortest delay of zero the longest delay was 42.
about the delays on monday huh so it's not linear so there were a lot here there were a lot lot short delays
42 so it was 42 is here i kind of forgot how to draw a box plot now um oh okay so now there's this uh okay
at 12. so that is 12. so that is here at four minutes delayed so that matches to this and what about
so that matches to this and what about 24 that is matching to 10-minute delay okay it looks kind of what we're looking for and then 36 so yeah because um each quarter right 0 12 24 36 48
0 12 24 36 48 36 is here at 20 minutes delayed okay so that is kind of the box plot i reckon i think that's how i do a box plot i kind of forgot
kind of forgot okay yeah what's that for
on monday with the distribution whoa uh whoa uh i don't know what can i say uh i don't know what can i say uh monday spread further apart
this is one of those bs questions that we kind of have to do in some last tests we kind of have to do in some last tests um on average um on average it was longer
max i mean roughly is still very similar question like this before mary says the longest delay on
tuesday was 33 minutes yup this means there must have been some delays between 25 and 30 minutes uh no
have been a lot of 33 minutes
in between 25 and 30. so there were a lot like at um this point and a lot of this point but none zero here i guess
it's just one over five x minus one one i don't know if it wants me to expand one over five x minus five yeah okay uh
factorize fully 50 minus two oh okay so 2 25 minus y squared 2 5 minus y five plus y yeah this isn't
as hard as i really expected it would be but question 11 now jack and say you work for coming out sauce boxes or breakfast cereal company idea switch over and do not change the price
the amount of serial in each box so who wants to her idea to yet by what percentage price okay so assume
price okay so assume 100 of cereal initially so now 125 for
125 for x is equivalent to x is equivalent to 100 for 100 for uh y dollars
so in this case we reduce we divide by 1.25 percent to match what we're looking for and x divided by
one point two five x okay so percentage okay divide by 5 over 4 so it is 0.8 which is
80 right so this is if we flip that up equals to 4 over 5x which equals to zero point eight x so um twenty percent reduction
discount would be at 80 so it's a 20 reduction
abc points on circumference circle o d a is tangent to circle a okay circle geometry let's go kind of forgot the formulas but angle b a e
a e is 56 cbo is 35 cba cbo cbo okay cao what's ca okay so this
cao what's ca okay so this is what we're looking for
to opposite angle what's the formula what's the this angle is equal to that angle i remember remember so bca equals two
56 degrees uh tangent angle too strong that but that's 56 that's 35.
uh okay crap now i was not right in thinking now i was not right in thinking ah okay okay so b-o-a equals to 2 times
56 equals to 1 1 2. equals to 1 1 2. angle at center
those two angles okay i can't be bothered like writing up the theory first so that those two are 180 minus one one two on two since those two are equal because radii are equal
like it's only three marks so uh 68 on two equals to 34 out okay i did so angle sum
okay i did so angle sum b c bac is equal to 180 equals to 56 plus 35 plus 2 times 34 plus 2 times 34 plus cao
oh i can't believe i'm not allowed to calculate it calculate it plus three times 35 approximately so plus three times 35 approximately so 103 plus cao
because angle some of that and there you go transformation that maps triangle a to triangle oh
i remember how to do this i mean it's just
rotate 180 what was the single transformation though
i don't know times one and rotate don't know how to what the other platform platform never done it before
81. so yeah this is not too hard 16 on 81 to the power 3 on 4 is equal to 2 to the power of 4 on 3 to the power of 4 to the power of 3 on 4 which equals to
cancer 2 to the power 3 and 3 to the power 3 equals to 8 127 uh yeah that has working so work out the value of a plus b plus c
value of a plus b plus c okay so plus c is equal to 10 times together which is
times one on root three which equals two one so a plus b one so a plus b plus c equals two zero
15 three solid shapes a b and c are similar surface area is for surface areas b looks like a square ratio of volume oh
looks like a square ratio of volume oh okay yeah okay yeah so it's a cube yeah that's a square proportion two and five
and uh length ratio of shape b to volume machine c is 27 so it's three cubed c is 27 so it's three cubed and four cubed
and four cubed is that right four times four yeah yeah of c okay so height
height b to c is equal to 3 to 4 because 3 cubed and 4 cubed so that means a to c is equal to
this is it would just make it easy 15 to twenty which equals two times three so six to fifteen is six to twenty which is equal to
written as that okay so this is equal to zero two five six five six five six dollars
five six five six five six dollars which equals to
zero five six okay it's been a while since i did this
so that is how does this work
exon 100 okay okay so that is yeah so these two are equal equate these two now
so just comparing these two equations to get this let's do x to get this let's do x 99x on 100
99 plus five times 5.6 on four nine five which should i'm going to bother calculating one twenty seven four nine five assuming what i've done
right okay we're 30 minutes in there okay we're 30 minutes in there my throat is pretty dead though
my throat is pretty dead though [Music] 21. uh oh is a triangle
what oh oh p to p m looking for um all right
o and and b how the heck do i do this i did by ariel i did by ariel now
m is the midpoint of a b opm apn are straight lines if it has a and b in the result then i'm going to be very annoyed
i'm going to draw another line through this ends up oh
don't know this one i just put a big f here and we'll just skip it for now and move on to the last question which is question 22 and we're 45 minutes in so
in a box there are three more blue pens and green pens in the box there are more than 12 pens in the box
the same color as 27 on 55 work out the number of ring pens on the box okay this is very doable so let's say there's n pens in box you know n is greater than 12 and let's
say there's b blue pens
and we also know we can remove these from the equation we can we know that from the equation we can we know that um b equals to three plus g green so
green so let's start with n minus b to b equals to n plus three b equals to n plus three on two uh g is equal to
uh n minus n plus 3 on 2 which is n on 2 minus n minus 3 on 2 okay so
n minus 3 on 2 okay so it takes two pens in the same color b and g so that would be our second simultaneous
is uh blue and blue or green and green so uh blue and blue or green and green so let's say it's blue and blue first
then we have uh so n plus three on two on n and the second one is green as well n minus one and there's one less so n
plus one on two this is blue and this is blue and green is
so this first one and second one so this gives us and this is all over two n n minus 1 plus
n squared minus 8 n plus 15 equals 2 okay so that's good to n squared to [Music] minus four n plus 18
okay so what are the 10 and 11 so that's only possibility n times n minus 1 is a number like 10 and 11
equals to so that means which is yeah 110 so that means which is yeah 110 55 times 2 so you get 55 times 2 so you get n is 11. so 121
n is 11. so 121 minus 22 plus 9 is
huh i must have done some oh okay on four yeah yeah one yeah okay yeah on two yeah so that equals two
the 2 is still there so 220 which is equal to 2755 n is equal to 11 wait what the heck
than 12 pence in the box huh so what else 55
times 3 is 165 uh 5 and 2. so 5 11. um what else could it be
harder than the first few questions that's for sure
so 55 let's see so it can be 11 10 unless the top is divisible by 11.
eight so squared plus eight that's divisible by eleven divisible by eleven what could that be
ah so there's more than 12 pins in the box so
what okay so it has to be 11 and 12 but then there's a 5 there as well
20 so 44 and 9 oh sorry 44 and 45 oh sorry 44 and 45 could that be it that probably is it so
and n minus 1 is 44. so 45 squared is equal to 4 times 5 plus 25 45 squared is equal to 4 times 5 plus 25 so 22 5 minus 2 that's why i have so much minus 2 times minus
so much minus 2 times minus 90 plus 9 90 plus 9 okay over 45 times 44 so 9 times 220 times four at the bottom
because i forgot that in the equation so
so yeah the two's there so 1 so 1 18 1980 times two is that right
203 five one one nine three five plus nine nine one nine four on one nine four on 1980 is that
it's just on the half that seems about right so does this equal to 27 on 55
so what is the factor here 1944 divided by 36. ah this is four five five yeah 180 oh it does work one four is four of those yep 54. sweet so n is 45
54. sweet so n is 45 and that was found from it has to be a of 5 and 11 105 and 1 and 11 and the difference is one and it wasn't it was more than 12 so n is 45 that means
means the number of green is the number of green is uh n minus 3 on 2 which is
but that's 21. so that just leaves the last question which i didn't get which is question 21. ah
that's a and that is b and i want the ratio
i'm gonna guess two to three but it i mean so that's the last one last question i think i got most of the rest um when i didn't get um i did finish uh question 17
which was just subbing these two numbers into the equation and finding solving for the two unknowns a and b so two equations two unknowns you can get that and 18 was some graphing so one of them
i drew the graph and one of them i put a negative sign in there and 19 was yeah a function manipulation and
another function manipulation and 20 was just uh factorizing and rationalizing the denominator done uh i'll just go and mark it now and
double check the answers with my marking sheet that i have here and work marking sheet that i have here and work out what it is
answer's right i'll like mark it correct because like um in terms want us to lay it out and i've never done it before but right then i'm just going to assume that i can do the working out for
um if i actually did know how to do it so our answer is nine yep six or minus six holy f
read the question this is so embarrassing oh my god my math teacher is going to be so
so so ashamed of this
yeah which is correct so in total out of eighteen lost five minus one minus one minus one is 72 out of 18.
get back and quickly check what is that good or bad i actually do not know but i'm gonna see what like the average mark on it is and
yeah let's get back to it okay so doing a little bit of digging um i later found out that the 72 out of 80 is 90 and that is roughly either a grade 8 or a grade 9
mathematics the grade 8 is 85 plus and grade 9 is 90 plus plus demonstrates creative use of relevant mathematics to solve an or use of mathematics to provide an answer to an ambiguous problem
the questions and i lost a few marks and silly mistakes don't know if this isn't like a formal grade or anything but i just based on a rough estimate and
guide from like some teaching educated guesses by teaching experts it says but uh do let me know what you guys got similar gcses and like let me know if there was anything wrong with like
the way i marked it or the way i gave myself a grade in the end you guys want to see more of this kind of format of videos later on in the definitely let me know in the comments if you want me to do some other exams
i might have a girl at the a levels next time or some american sats and give that a try or maybe i'll just redo my uh hsc mathematics that might be in one of the later videos so yeah hopefully you enjoyed the video
big thumbs up down below and i hope to see you guys up down below and i hope to see you guys in the next one