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GCSE Maths Revision

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Chittesh14
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#1
Report Thread starter 7 years ago
#1
Revision Sites for Maths GCSE:

https://www.khanacademy.org/
http://www.examsolutions.net/
https://mathswatchvle.com/
http://studymaths.co.uk/
http://www.bbc.co.uk/education/subjects/z6pfb9q
http://www.mrbartonmaths.com/
http://www.s-cool.co.uk/

Grade A/A*


  • Exponential Growth
  • Direct and Inverse Proportions
  • Surds (2)
  • Equations With Fractions
  • Equations With Graphs
  • Solving With Graphs
  • Transforming Graphs
  • Modelling Real Life Situations With Graphs
  • Quadratic Simultaneous Equations
  • Bearings
  • Area Scale Factor
  • Complex Surface Areas
  • Circle Theorem Proof
  • Arcs, Sectors, Segments
  • Congruent Triangles
  • 3D Coordinates
  • Pythagoras 3D
  • Volume Scale Factor
  • Sine Rule
  • Cosine Rule (Sides)
  • Cosine Rule (Angles)
  • Area Of A Scalene Triangle
  • 3D Trigonometry
  • Sine And Cosine Graphs
  • Tan Graphs
  • Transforming Trigonometry Graphs
  • Vectors (1+2)
  • Volumes Of Cones And Spheres
  • Histograms


Feel free to post questions that you need help on regarding these topics.
If you have any questions regarding questions that are from topics that have not been listed in this thread, feel free to post them too. Do not post the full solutions if you've got the answer to a question someone has asked. Also, please follow the TSR Rules and guide them to the answer to the question. However, if they are extremely struggling with the question after a few attempts, then you can give them the solution but annotate it and tell them how you got from step 1 to the last step -> solution.

01/03/2015 - I'm going to post questions from today and post their solutions 1 day after. Feel free to answer questions on here & post their answers, I'll tell you if they're correct or not. If they're wrong, you'll have to wait to see why you are wrong until the next day when I post the solutions & answer questions.

Spoiler:
Show
Direct And Inverse Proportion
01 - 03 - 2015
Questions:

1. M is directly proportional to L^3
When L = 2, M = 160.
(a) Find the value of M when L = 3
(b) Find the value of L when M = 120.

2. q is inversely proportional to the square of t.
When t = 4, q = 8.5
(a) Find a formula for q in terms of t.
(b) Caculate the value of q when t = 5.

3. The time, T seconds, for a hot sphere to cool is proportional to the square root of the surface area, A m^2, of the sphere.
When A = 100, T = 40.
Find the value of T when A = 60.
Give your answers correct to 3 significant figures.

4. y is directly proportional to the square of x.
x is directly proportional to the square root of z.
(a) Find a formula for y in terms of z and a constant of proportionality.
u is directly proportional to the square of v.
v is inversely proportional to the square root of w.
(b) Show that the product of u and w is constant.

Solutions will be posted tomorrow - 02/03/2015


Spoiler:
Show


Solving simultaneous equations where one
is linear and the other is quadratic

02-03-2015
Questions:

4. Solve these simultaneous equations.

(a)
x^2 + y^2 = 13 y = x + 1

(b)
x^2 + y^2 = 20 y = 2 - x

(c)
x^2 + y^2 = 34 y = 1 + 2x

5. Solve these simultaneous equations. Give your answers correct to 3 significant figures.

(a)
x^2 + y^2 = 20 y = x + 4

(b)
x^2 + y^2 = 32 y = 1 + 3x

(c)
x^2 + y^2 = 100 y = 2x - 3
Solutions will be posted tomorrow - 03/03/2015



Spoiler:
Show

Solutions:

1. M is directly proportional to L^3
When L = 2, M = 160.
(a) Find the value of M when L = 3
(b) Find the value of L when M = 120.

M = K * L^3
160 = K * 2^3
160 = K * 8
K = 160 / 8 = 20

(a) M = K * L^3
If L = 3 and K = 20
M = 20 * 3^3
M = 20 * 27 = 540

(b) M = K * L^3
If M = 120 and K = 20
120 = 20 * L^3
L^3 = 120 / 20 = 6
L = \sqrt[3]{6} = 1.82 (3 s.f)

2. q is inversely proportional to the square of t.
When t = 4, q = 8.5
(a) Find a formula for q in terms of t.
(b) Caculate the value of q when t = 5.

(a) q = k / t^2
8.5 = k / 4^2
8.5 = k / 16
k = 16 * 8.5 = 136
q = \frac{136}{t^2}

(b) q = k / t^2
If k = 136 and t = 5
q = 136 / 5^2
q = 136 / 25 = 5.44

3. The time, T seconds, for a hot sphere to cool is proportional to the square root of the surface area, A m^2, of the sphere.
When A = 100, T = 40.
Find the value of T when A = 60.
Give your answers correct to 3 significant figures.

T = K * \sqrt{A} m^2
If A = 100 and T = 40
40 = K * \sqrt{100}
40 = K * 10
K = 40 / 10 = 4

T = K * \sqrt{A} m^2
If k = 4 and A = 60
T = 4 * \sqrt{60} m^2
T = 31.0 (3 s.f)

4. y is directly proportional to the square of x.
x is directly proportional to the square root of z.
(a) Find a formula for y in terms of z and a constant of proportionality.
u is directly proportional to the square of v.
v is inversely proportional to the square root of w.
(b) Show that the product of u and w is constant.

y = k * x^2
x = k * \sqrt{z}

(a) y = k * x^2, x^2 = k * z
y = k * z

u = k * v^2
v = \dfrac{l}{\sqrt{w}}

(b) v^2 = \dfrac{l^2}{w}
w = \dfrac{l^2}{v^2}

u * w = (k * v^2) * \dfrac{l^2}{v^2}

u * w = (k * l^2) = kl^2
kl^2 is a constant, and therefore the product of u * w is a constant!

Sorry, didn't know the solutions take 1 hour, first time using latex in detail.

1
reply
Chittesh14
Badges: 19
Rep:
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#2
Report Thread starter 7 years ago
#2
Well, I was wishing someone would actually post questions or ask for help on this thread -_-. Seems like no one has done so, therefore I will start it off. I will post questions & their solutions 1 day after.

Direct And Inverse Proportion

Question:

1. M is directly proportional to L^3
When L = 2, M = 160.
(a) Find the value of M when L = 3
(b) Find the value of L when M = 120.

2. q is inversely proportional to the square of t.
When t = 4, q = 8.5
(a) Find a formula for q in terms of t.
(b) Caculate the value of q when t = 5.

3. The time, T seconds, for a hot sphere to cool is proportional to the square root of the surface area, A m^2, of the sphere.
When A = 100, T = 40.
Find the value of T when A = 60.
Give your answers correct to 3 significant figures.

4. y is directly proportional to the square of x.
x is directly proportional to the square root of z.
(a) Find a formula for y in terms of z and a constant of proportionality.
u is directly proportional to the square of v.
v is inversely proportional to the square root of w.
(b) Show that the product of u and w is constant.

Solving simultaneous equations where one
is linear and the other is quadratic

4. Solve these simultaneous equations.

(a)
x^2 + y^2 = 13 y = x + 1

(b)
x^2 + y^2 = 20 y = 2 - x

(c)
x^2 + y^2 = 34 y = 1 + 2x

5. Solve these simultaneous equations. Give your answers correct to 3 significant figures.

(a)
x^2 + y^2 = 20 y = x + 4

(b)
x^2 + y^2 = 32 y = 1 + 3x

(c)
x^2 + y^2 = 100 y = 2x - 3
0
reply
Chittesh14
Badges: 19
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#3
Report Thread starter 7 years ago
#3
Solutions:

1. M is directly proportional to L^3
When L = 2, M = 160.
(a) Find the value of M when L = 3
(b) Find the value of L when M = 120.

M = K * L^3
160 = K * 2^3
160 = K * 8
K = 160 / 8 = 20

(a) M = K * L^3
If L = 3 and K = 20
M = 20 * 3^3
M = 20 * 27 = 540

(b) M = K * L^3
If M = 120 and K = 20
120 = 20 * L^3
L^3 = 120 / 20 = 6
L = \sqrt[3]{6} = 1.82 (3 s.f)

2. q is inversely proportional to the square of t.
When t = 4, q = 8.5
(a) Find a formula for q in terms of t.
(b) Caculate the value of q when t = 5.

(a) q = k / t^2
8.5 = k / 4^2
8.5 = k / 16
k = 16 * 8.5 = 136
q = \frac{136}{t^2}

(b) q = k / t^2
If k = 136 and t = 5
q = 136 / 5^2
q = 136 / 25 = 5.44

3. The time, T seconds, for a hot sphere to cool is proportional to the square root of the surface area, A m^2, of the sphere.
When A = 100, T = 40.
Find the value of T when A = 60.
Give your answers correct to 3 significant figures.

T = K * \sqrt{A} m^2
If A = 100 and T = 40
40 = K * \sqrt{100}
40 = K * 10
K = 40 / 10 = 4

T = K * \sqrt{A} m^2
If k = 4 and A = 60
T = 4 * \sqrt{60} m^2
T = 31.0 (3 s.f)

4. y is directly proportional to the square of x.
x is directly proportional to the square root of z.
(a) Find a formula for y in terms of z and a constant of proportionality.
u is directly proportional to the square of v.
v is inversely proportional to the square root of w.
(b) Show that the product of u and w is constant.

y = k * x^2
x = k * \sqrt{z}

(a) y = k * x^2, x^2 = k * z
y = k * z

u = k * v^2
v = \dfrac{l}{\sqrt{w}}

(b) v^2 = \dfrac{l^2}{w}
w = \dfrac{l^2}{v^2}

u * w = (k * v^2) * \dfrac{l^2}{v^2}

u * w = (k * l^2) = kl^2
kl^2 is a constant, and therefore the product of u * w is a constant!

Sorry, didn't know the solutions take 1 hour, first time using latex in detail.
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