First time solving a GCSE maths paper!

This is my first time trying all the questions from a GCSE maths Paper 1H on the spot. GCSE (General Certificate of Secondary Education ) is an exam for high school students in the UK. I mostly teach algebra and calculus at a community college here in the US and It will be interesting to see how the standardized tests are from different countries. This math test includes solving inequality, quadratic equations, rational equations, geometry, probability, and stats problems. If I make any mistakes in this video, please let me know and I will make correction videos! Enjoy

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#math #algebra #mathbasics
0:00 Solving the GCSE paper 1H June 2022 for the first time
1:30 Q1 Solving an inequality
2:04 Q2 Prime factorize 124
3:25 Q3 A ratio problem
7:29 Q4 Scientific Notation
11:00 Q5 A hexagon & a pentagon problem
13:54 Q6 Graphing a parabola & solving a quadratic equation by using the quadratic formula
18:07 Q7 Finding the ratio of the identities of two cubes
21:10 Q8 Approximating the mean from a frequency table
26:07 Q9 **Sorry, I got this one wrong
30:46 Q10 **Cumulative frequency (but I don't know)
39:25 Q11 An algebraic ratio problem
40:55 Q11 Convert 0.117171717... to a fraction
47:30 Q12 Three circles on a right-angled triangle
50:14 Q14 Finding the gradient on a curve & area under the speed graph
54:10 Q15 (a) Vector problems
1:03:03 Q15 (b)
1:07:23 Q16 A probability question with a Venn diagram
1:16:43 Q17 Directly proportional & inversely proportional
1:20:44 Q18 Simplifying a rational and negative exponent problem
1:23:16 Q19 Solving a rational equation
1:28;24 Q20 Equation of a tangent line to a circle
1:33:55 Q21 **I messed up!
Correction to Q21

[uyangapuujee]

I sat this paper, the last question gives me flashbacks 💀

[bprpmathbasics]

Don’t ask a calculus teacher to do a cumulative frequency graph 😆

[bprpmathbasics]

So far I got Q9, Q10, and Q21 wrong.
How many marks did I get?

[evanpoole]

that question 21 is probably the most notorious gcse maths problem ever made

[harley_]

I actually sat this paper when doing my GCSE’s, by then I had been watching a lot of your videos and they helped me gain confidence in my abilities. I ended up getting a grade 8 (second highest grade and roughly equivalent to a high A/low A*) so thank you

[Andromeda]

So glad I got to see you take this paper, I helped teach a class who would take this exam! It was the first paper out of COVID, so was an interesting time for teaching staff! That last question made it into national news, at it wasn't well received! You should consider looking at an Edexcel A-level Maths Paper 1 or Paper 2, these are pure papers (Stats and Mechanics are in Paper 3) and are the exams you would take in college to qualify for university. For context our curriculum goes GCSE>AS>A-Level>Uni! - If you do ever do an Alevel paper, do note there is a formula booklet that would be with it!

[ievastrolyte]

I think the American system is taught way differently and in the uk we are trained for more of these type of questions because some of the questions were severely over complicated.

[mikejackson]

Petrol is what we call gasoline in the UK.

[ingiford]

For number 9, you can make it easier, by placing the top 'area' of the square into the hole and figure out the surface area of the bottom piece and add just the 4 x4 extra walls

[danielaltmann]

Amazing video - U should try and do a additional maths paper (used for gcse students who have done their GCSE early) since its more basic calc and stuff like that it would be quite interesting idk.

[ethaniac]

Can we all take a moment to appreciate the effort that BPRP puts into his videos!

[harryslaughter]

As a maths teacher in the UK, I would recommend trying the A-Level Mathematics and/or A-Level Further Mathematics (for advanced students) papers. A-Level qualifications are for 18 year old students (pre-university) and therefore include calculus, complex numbers, linear algebra etc. GCSEs are for 16 year old students so are generally more basic and focus on fundamentals. Great video! :)

[cigmorfil]

For the vectors length ratios, you can use simulator triangles as the vectors are multiples of each other.

Thus you have
DE : DF = 1 : (3.5-1)[1]
= 1 : 2.5
= 2 : 5

[1] As EF is 3.5 times the length DE, and as FDE are on a straight line, DF must be 3.5 less the DE part, ie 3.5-1.

[zhelyo_physics]

Excellent! Try the Further Maths A Level exam next! You will enjoy it! : ) Hope you are well!!

[jeffeloso]

For the last question it was easier to do the general case, using 6 equilateral triangles of side circle radius and the segment left over from subtracting the equilateral triangle from1/6th of the one of the circles. The result is that the required area is equal to the area of 4 equilateral triangles side Radius of circle, minus 2/3rd of the area of one of the circles.

[QuentinStephens]

I'm looking forward to seeing you do an A level paper. We also had AS levels in my day (40 years ago!) which were a step up again. I would also like to see you compare papers of the old O levels with today's GCSEs.

[HenrikMyrhaug]

Full explanation of question 10:
a) Cumulative means everything up to that point, so to find the cumulative frequency, you take the sums of the frequencies up to that point.
If the frequencies are
(2, 4, 5, 3, 2, 4), the cumulative frequencies are
(2, 6, 11, 14, 16, 20)
Conversely, the frequency values will be equal to the difference between each step in the cumulative frequency (with the first frequency being equal to the first cumulative frequency)

b) The cumulative frequency graph is a line graph, where you draw the cumulative frequency values as points at the end of each range, and connect the dots (with a smooth curve). Because the first value range is 0<x<50, and the cumulative frequency is 10, you draw a point at height 10 and at the end of the range, meaning at (10, 50). Same for the rest of the points.

c) Estimating the number of days the profit is less than a specific value means drawing a vertical line from the value on the X- axis, up to the graph, and a horizontal line from there to the Y- axis and reading off the Y-value of this line.
If your graph isn't smooth, or you do a simple mean estimation, you will get 37.5, but they probably designed the question such that if you draw a smooth graph, your estimated number of days will be lower. Therefore, you probably wouldn't get credit unfortunately.

d) Interquartile range is exactly what you said, and is estimated by drawing horizontal lines from 1/4 and 3/4 of the distance along the y- axis, seeing where those lines intersect with the graph you drew, and drawing vertical lines down from those points to the X- axis. The X-value of these vertical lines will be Q1 and Q3 respectively, so you take Q3-Q1 to find the interquartile range.

[shipmate]

Thanks, this is like a fun way for revision.

[ianfowler]

Q15. I think I heard you say that a and b are unit vectors. The arrows would have been appropriate. All vectors in R^2 and be represented by a single point if the initial point is the origin. (4, 5) and <4, 5> are 2 popular notations to represent these "algebraic vectors". So the vector joining A(2, 3) to B(6, 5) can be represented by the SINGLE vector AB = (6-2, 5-3) = (4, 2). Where the initial point is now at the origin (0, 0). So in R^2:

1) If 2 vectors are scalar multiples of each other, they are collinear and therefore any linear combination will still be collinear with the original 2. This pair forms a "linearly dependent" pair. -2(4, 1) + 3(8, 2) = (16, 4) = 4(4, 1). Any linear combination will always be stuck on this line.

2) If a and b are not collinear then they form an "independent pair" called a BASIS for R^2. This means that any other vector in R^2 can be expressed as a linear combination of the basis pair. If a and b are STANDARD unit basis vectors then a = (0, 1) and b = (1, 0). All Vectors in R^2 can now be expresses as a linear combination of the basis pair a and b. This still works for the non-standard basis pair, like (2, 3) and (-1, 4). But We usually express a basis pair as unit vectors on the co-ordinate axes.

AB and AC clearly have linear combinations that are scalar multiples. Therefore AB and CD must also be scalar multiples of each other and point in the same direction. Since they share a common point(A), then A, B, and C must be collinear.

Note: if vector CD = -3* vector EF, then they point in the opposite.directions and CD is 3 times longer than EF..

I used to reach all this stuff (also in R^3) in high school - for like 30+ years.Let me know if you want to know about non co-planar vectors and basis triplets in R^3.

[enterlessguy]

The x intercepts for question 6 are actually phi+1 and (-1/phi)+1, just for my fellow mathematicians !!! (Context: phi is the golden ratio which Is a constant in math, phi≈1.618... and phi is an element of Q')