GCSE Maths Revision

Chittesh14

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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

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

, 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)

(b)

(c)

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

(a)

(b)

(c)

Solutions will be posted tomorrow - 03/03/2015

Spoiler:

Show

Solutions:

1. M is directly proportional to

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 *

160 = K *

160 = K * 8
K = 160 / 8 = 20

(a) M = K *

If L = 3 and K = 20
M = 20 *

M = 20 * 27 = 540

(b) M = K *

If M = 120 and K = 20
120 = 20 *

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 /

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

(b) q = k /

If k = 136 and t = 5
q = 136 /

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

, 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 * $\sqrt{A}$

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

T = K * $\sqrt{A}$

If k = 4 and A = 60
T = 4 * $\sqrt{60}$

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 = k * $\sqrt{z}$

(a) y = k *

,

= k * z
y = k * z

u = k *

v = $\dfrac{l}{\sqrt{w}}$

(b)

= $\dfrac{l^2}{w}$
w = $\dfrac{l^2}{v^2}$

u * w =

* $\dfrac{l^2}{v^2}$

u * w =

=

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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Chittesh14

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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

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

, 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)

(b)

(c)

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

(a)

(b)

(c)

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Chittesh14

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Solutions:

1. M is directly proportional to

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 *

160 = K *

160 = K * 8
K = 160 / 8 = 20

(a) M = K *

If L = 3 and K = 20
M = 20 *

M = 20 * 27 = 540

(b) M = K *

If M = 120 and K = 20
120 = 20 *

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 /

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

(b) q = k /

If k = 136 and t = 5
q = 136 /

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

, 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 * $\sqrt{A}$

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

T = K * $\sqrt{A}$

If k = 4 and A = 60
T = 4 * $\sqrt{60}$

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 = k * $\sqrt{z}$

(a) y = k *

,

= k * z
y = k * z

u = k *

v = $\dfrac{l}{\sqrt{w}}$

(b)

= $\dfrac{l^2}{w}$
w = $\dfrac{l^2}{v^2}$

u * w =

* $\dfrac{l^2}{v^2}$

u * w =

=

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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