AQA Mathematics Module 5 Paper 2H (Calc) Unofficial Answers (10/06/2011)
Find paper 1H (non-calc) unofficial mark scheme here.
OK, crack on with question numbers, questions and answers - I'll try to keep up with editing the right answers to each question in here.
Even if you don't know the answer - a question (with number preferably) is great too, then I or someone else can answer it.
GO!
Question 01 - Given a square running through the centre points of a collection of identical circles arranged in a square (six circles per side), and the perimeter of square as 60:
Q: Calculate the radius of each circle.
A: 2.5
Question 15 - Given that: (5x + 9)/(6x^2 - 7x - 3) = 2/5
a)
Q: Show that a solution for x is -1.
A: Substitute x for -1, run through the calculation to end up with 2/5 as the answer.
b)
Q: Show that it can be shown as written as 4x^2 - 13x - 17=0
A: Multiply, rearrange, factorise, generally mess with until you end up with == 4x^2 - 13x - 17 = 0 (See method here.)
c)
Q: Solve the equation 4x^2 - 13x - 17
A: x1 = 4.25; x2 = -1
Question ? - Area of triangle
Q: Given sides of 7 and 10, with an angle of 53deg between, find the area. Give answer to appropriate accuracy.
A: 28
Question ? - Area of an isosceles (triangular) prism
Q: Given a triangular prism of base 6, height 4, and length 20 - find the area of the prism.
A: 240
Question ? - Sequences
Q: Given 8n - 52, for how many terms will the answer be less than 0?
A: 6
Question ? - Trial and improvement
Q: Given x^3 + 6x, use trial and improvement to gain an answer for x accurate to one decimal place.
A: 2.4
Question ? - Functions of sine; a sine graph is given
a)
Q: Draw y=3sin(x)
A: Start at (0,0), curve up to (90,3), back down to (180,0), keep curving to (270,-3), and back up to (360,0) - this is a stretch parallel to the y axis by a scale factor of 3.
b)
Q: Draw y=sin(x)+2
A: Start at (0,2), curve up to (90,3), back down to (180,2), keep curving to (270,1), and back up to (360,0) - this is a translation parallel to the y axis moving by 2 units 'upward'.
Question ? - Pi multiplied by these lengths tick box ("Is it Volume, Area, or Length?") Given a; b; c as lengths, and pi as a constant.
a)
Q: pi x a x b x c
A: Volume
b)
Q: pi(a + b)
A: Length
c)
Q: pi + a + b
A: Length
Question ? - Cosine values, and x values from cosine; given cos(60) = 0.5 and a cosine graph
a)
Q: Find another value of x where cos(x) = 0.5
A: 300
b)
Q: Find a value of x where cos(x) = -0.5
A: 120, or 240
^part b may have been the reverse, I don't remember! Answer was either -0.5 or 120, where the other was given.
Question ? - Trapezium
a)
Q: Given an area of 30, find possible values of a, b, and h
A: Anything where (a+b)/2 * h = 30. Huge range of possible answers, be nice on yourself with something like: 1, 2, 20 or 2, 3, 12 or 15, 15, 2.
b)
Q: Rearrange the given formula of a trapezium so that b is the subject
A: b = -a + 2A/h (See method here.)
Question ? - Solve for x
Q: Given (1/3)x - 4 = 1/2, work out the value of x.
A: 13.5 (See method here.)
Question ? - Triangles formed in circle from two tangents and radii.
Q: Find the value of the angle between the two radii formed from the two tangents (the smaller side).
A: 132deg
Question ? - Exterior angles in pentagon
Q: Given a regular pentagon, find the value of the exterior angle
A: 72deg
Question ? - Inequalities with graph
a)
Q: Draw the line y=3x-1 for -4<x<4.
A: Line should go from (-4,-13), through (0,-1) and up to (4,11)
b)
Q: Shade the region satisfied by the inequality y <= 3x - 1
A: Leaving a solid line, shade the region beneath the line drawn in part a.
Question [LAST] - Square and rectangle with algebraic sides; equal area
Q: Given a square with side length 3y - 2x and a rectangle with sides 2x and 3y + 2x, show that y is a multiple of x.
A: Reduce calculations to y = 2x (See method here.)
OK, crack on with question numbers, questions and answers - I'll try to keep up with editing the right answers to each question in here.
Even if you don't know the answer - a question (with number preferably) is great too, then I or someone else can answer it.
GO!
Question 01 - Given a square running through the centre points of a collection of identical circles arranged in a square (six circles per side), and the perimeter of square as 60:
Q: Calculate the radius of each circle.
A: 2.5
Question 15 - Given that: (5x + 9)/(6x^2 - 7x - 3) = 2/5
a)
Q: Show that a solution for x is -1.
A: Substitute x for -1, run through the calculation to end up with 2/5 as the answer.
b)
Q: Show that it can be shown as written as 4x^2 - 13x - 17=0
A: Multiply, rearrange, factorise, generally mess with until you end up with == 4x^2 - 13x - 17 = 0 (See method here.)
c)
Q: Solve the equation 4x^2 - 13x - 17
A: x1 = 4.25; x2 = -1
Question ? - Area of triangle
Q: Given sides of 7 and 10, with an angle of 53deg between, find the area. Give answer to appropriate accuracy.
A: 28
Question ? - Area of an isosceles (triangular) prism
Q: Given a triangular prism of base 6, height 4, and length 20 - find the area of the prism.
A: 240
Question ? - Sequences
Q: Given 8n - 52, for how many terms will the answer be less than 0?
A: 6
Question ? - Trial and improvement
Q: Given x^3 + 6x, use trial and improvement to gain an answer for x accurate to one decimal place.
A: 2.4
Question ? - Functions of sine; a sine graph is given
a)
Q: Draw y=3sin(x)
A: Start at (0,0), curve up to (90,3), back down to (180,0), keep curving to (270,-3), and back up to (360,0) - this is a stretch parallel to the y axis by a scale factor of 3.
b)
Q: Draw y=sin(x)+2
A: Start at (0,2), curve up to (90,3), back down to (180,2), keep curving to (270,1), and back up to (360,0) - this is a translation parallel to the y axis moving by 2 units 'upward'.
Question ? - Pi multiplied by these lengths tick box ("Is it Volume, Area, or Length?") Given a; b; c as lengths, and pi as a constant.
a)
Q: pi x a x b x c
A: Volume
b)
Q: pi(a + b)
A: Length
c)
Q: pi + a + b
A: Length
Question ? - Cosine values, and x values from cosine; given cos(60) = 0.5 and a cosine graph
a)
Q: Find another value of x where cos(x) = 0.5
A: 300
b)
Q: Find a value of x where cos(x) = -0.5
A: 120, or 240
^part b may have been the reverse, I don't remember! Answer was either -0.5 or 120, where the other was given.
Question ? - Trapezium
a)
Q: Given an area of 30, find possible values of a, b, and h
A: Anything where (a+b)/2 * h = 30. Huge range of possible answers, be nice on yourself with something like: 1, 2, 20 or 2, 3, 12 or 15, 15, 2.
b)
Q: Rearrange the given formula of a trapezium so that b is the subject
A: b = -a + 2A/h (See method here.)
Question ? - Solve for x
Q: Given (1/3)x - 4 = 1/2, work out the value of x.
A: 13.5 (See method here.)
Question ? - Triangles formed in circle from two tangents and radii.
Q: Find the value of the angle between the two radii formed from the two tangents (the smaller side).
A: 132deg
Question ? - Exterior angles in pentagon
Q: Given a regular pentagon, find the value of the exterior angle
A: 72deg
Question ? - Inequalities with graph
a)
Q: Draw the line y=3x-1 for -4<x<4.
A: Line should go from (-4,-13), through (0,-1) and up to (4,11)
b)
Q: Shade the region satisfied by the inequality y <= 3x - 1
A: Leaving a solid line, shade the region beneath the line drawn in part a.
Question [LAST] - Square and rectangle with algebraic sides; equal area
Q: Given a square with side length 3y - 2x and a rectangle with sides 2x and 3y + 2x, show that y is a multiple of x.
A: Reduce calculations to y = 2x (See method here.)
(edited 12 years ago)
Scroll to see replies
i'll try to state the quesitons i remember but im not sure what number they are.
Triangle question- find the area
Base-10?cm left side- 7cm angle of 53 degrees
half(7X10)sin53= 27.( something) which is rounded to 28
Triangular prism question
perpendicular H=4 Base= 6 Long section= 20
Volume= half(4X6) X20
=240
Perpendicular line equation= y=-3x+4
Graph- Shaded the region under the line and also just plot the points to draw the straight line
First question was the sqaure= 60cm^2 area Find the radius of the circles inside
Triangle question- find the area
Base-10?cm left side- 7cm angle of 53 degrees
half(7X10)sin53= 27.( something) which is rounded to 28
Triangular prism question
perpendicular H=4 Base= 6 Long section= 20
Volume= half(4X6) X20
=240
Perpendicular line equation= y=-3x+4
Graph- Shaded the region under the line and also just plot the points to draw the straight line
First question was the sqaure= 60cm^2 area Find the radius of the circles inside
(edited 12 years ago)
I got the radius one. Can some one explain the one which had the pi and then the three lengths and you had to decide if it was a length, cubic volume or square volume. I didn't know. I think I got about 107/140 if I don't get method marks. I just felt my a* slip away and I want to cry.
Original post by acceptingme
I got the radius one. Can some one explain the one which had the pi and then the three lengths and you had to decide if it was a length, cubic volume or square volume. I didn't know. I think I got about 107/140 if I don't get method marks. I just felt my a* slip away and I want to cry.
The first one was a volume because it was three lengths multiplied together, the other two were lengths because they were lengths added together,
Original post by RedUnited
The first one was a volume because it was three lengths multiplied together, the other two were lengths because they were lengths added together,
I got 2/3 there then. Ok I defo didn't do aswell as I thought I would. I just want to forget about it now. Hopefully on results day I get an A*. If not I'll just cry. I was really hoping on that A*.
Original post by RedUnited
The first one was a volume because it was three lengths multiplied together, the other two were lengths because they were lengths added together,
Nope, the middle one was area.
pi(3+4)
say, I can't remember the actual numbers, but as it was in brackets pi multiplies by both lengths. Two multiplications, thus area.
Question 15b I think
was show that (5x+9) / (6x^2-7x-3)=2/5 can be displayed as 4x^2-13X-17=0
so multiply out the fraction:
5x+9 = 2/5(6x^2-7x-3)
the times by 5
25x + 45 = 2 (6x^2-7x-3)
then multpily out bracket
25x + 45 = 12x^2-14x-6
then minus the 25x and 45 from left side to get:
12x^2 - 39x - 51 =0
and divide by three to get answer:
4x^2 - 13x -17 =0
that was quite a lot of working for only 2 marks!
was show that (5x+9) / (6x^2-7x-3)=2/5 can be displayed as 4x^2-13X-17=0
so multiply out the fraction:
5x+9 = 2/5(6x^2-7x-3)
the times by 5
25x + 45 = 2 (6x^2-7x-3)
then multpily out bracket
25x + 45 = 12x^2-14x-6
then minus the 25x and 45 from left side to get:
12x^2 - 39x - 51 =0
and divide by three to get answer:
4x^2 - 13x -17 =0
that was quite a lot of working for only 2 marks!
Original post by acceptingme
I got the radius one. Can some one explain the one which had the pi and then the three lengths and you had to decide if it was a length, cubic volume or square volume. I didn't know. I think I got about 107/140 if I don't get method marks. I just felt my a* slip away and I want to cry.
last year the grade boundary for an a* for 107/140 - so you could still get it
Original post by RedUnited
Sequence Question. For how many terms is the output of the sequence 8n-52 negative?
8n would have to be less than 52 so n less than 6.5. Therefore 1,2,3,4,5,6 - 6
8n would have to be less than 52 so n less than 6.5. Therefore 1,2,3,4,5,6 - 6
I got that tooo
Original post by FO12DY
Nope, the middle one was area.
pi(3+4)
say, I can't remember the actual numbers, but as it was in brackets pi multiplies by both lengths. Two multiplications, thus area.
pi(3+4)
say, I can't remember the actual numbers, but as it was in brackets pi multiplies by both lengths. Two multiplications, thus area.
Wouldn't that still be length because it would be l x pi + some other l x pi, which is just two lengths added together.
I put volume, area and length. But I have no idea. I really think I failed that paper. Hope the grade boundaries are low :'(
Original post by acceptingme
I put volume, area and length. But I have no idea. I really think I failed that paper. Hope the grade boundaries are low :'(
Well, you got that question right at least!
Original post by FO12DY
Well, you got that question right at least!
It's just upsetting because I know I made some stupid mistakes. I'm either gunna get a high A or a low A*. I'm banking on boundaries being low. I probably lots 35 all together between paper 1 and paper 2 in module 5 but I got high a* in the other two modules. I hope I get a nice examiner and he gives me some method marks.
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