# GCSE Maths Revision Cards - Higher Tier

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Z Angle
Alternate Angles
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F Angle
Corresponding Angles
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C Angle
Co-Interior Angles
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X Angle
Vertically Opposite Angles
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Angles in a triangle add up to..
180 Degrees
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360 Degrees
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Angles in a pentagon add up to..
540 Degrees
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Angles in a hexagon add up to..
720 Degrees
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Angles in a heptagon add up to..
900 Degrees
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Angles in an octagon add up to..
1080 Degrees
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Sum of Interior Angles
(n-2) x 180 Where n is the number of sides
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Sum of Exterior Angles
360 divided by n Where n is the number of sides
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Arc Length
θ divided by 360 x π x d Where d is the diameter
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Area & Circumference of a circle
C=π x d A=π x r^2 Where r is the radius
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Area of a Sector
θ divided by 360 x π x r^2 θ is the greek letter Theta. It represents the angle
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Area of a trapezium
1/2(a+b) x h Replace a, b and h using the values from the trapezium
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Area of a triangle
1/2 x a x b x Sin C
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Bearings
1. Join the two places 2. Draw a north line on the asked place 3. Measure the angle 90 Degrees from north 4. All bearings should have 3 figures
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Circle Theorems 1-7
I'm literally the worst at this lmao. It also doesnt help with this website not letting you use pictures so now it's going to be very hard to describe them all ahaha; good luck figuring it out!
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Triangle at diameter touching circumferance
The angle in a semi-circle is 90 Degrees
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The angle at the centre is twice the angle at the circumference
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Bow Tie
The angles in the same segment are equal
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Opposite angles in a cyclic quadrilateral sum to 180 Degrees
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The angle between a radius and a tangent is 90 Degrees
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triangle & a tangent
Alternate Segment Theorem
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two tangents
Tangents which meet at the same point are equal in the lengthy
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Iteration
X^n+1= 3/5 - Xn^3 divided by 5
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Congruent Triangles *name all 4*
SSS=Side Side Side ASA=Angle Side Angle SAS=Side Angle Side RHS=Right-Angle Hypotenuse Side
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Equation of a circle
x^2+y^2=r^2
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Graphs of Exponential Functions (terrible explanation but err just memorize the equation lmao)
y=2^x Should look like a descending curve and should remain in positive y
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Graphs of Reciprocal Functions (also a terrible explanation but again just memorize the equation)
y=1/x Should look like two curves: one in positive xy and one in negative xy
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Cubic Graphs
y=x^3 - 3x - 1 Basically looks like two curves connected at the y axis *lmao like a worm*
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Transformation of Graphs 1-4
lol lets see how well i do on describing these graphs now
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Y=-f(x)
a reflection of y=f(x) in the x-axis
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y=f(-x)
a reflection of y=f(x) in the y-axis
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y=f(x)+a or y=f(x)-a
+a moves y=f(x) a squares up or -a moves y=f(x) a squares down
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y=f(x+a) or y=f(x-a)
+a moves y=f(x) a squares to the left or -a moves y=f(x) a squares to the right
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Graphs of Trigonometric Functions 1-3
These coordinates are good to know like if you're doing a non-calc or actually.. with a calc as well because my calculator is actually ******
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y=sin x
*S Shape* (0,0) (90,1) (180,0) (270,-1) (360,0)
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y=cos x
*U Shape* (0,1) (90,0) (180,-1) (270,0) (360,1)
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y=tan x *This one is so ******* confusing*
*3 curves* (0,0) to (90,1) (90,-1) to (180,0) (180,0) to (270,1) (270,-1) to (360,0)
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Equation for Frequency Density (histograms)
Frequency divided by Class Width For example if the class width was 15<l≤25 the class width would be 10
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Equation for Frequency (histograms)
Frequency Density x Class Width
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nth term=an^2+bn+c Sequence=a+b+c First differences=3a+b Second differences=2a
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Percentage Change
Change divided by Original x 100
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Compound Interest
initial x multiplier^time
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Direct Proportion
C=k x D^2
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Inverse Proportion
P=k divided by Q^3
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Pythagoras
a^2+b^2=c^2
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x=-b±√b^2-4 x a x c / 2 x a
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Trigonometry
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Sine rule
a/sin A=b/sin B=c/sin C
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Venn Diagrams 1-6
iiiiiii dont even know anymore
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A
everything in A
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B
everything in B
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A'
Everything but A
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B'
everything but B
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A U B
Everything in A & B
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A n B
Just the centre of A & B
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Volume of a cone
1/3 x π x r^2 x h
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Volume of a prism
Cross sectional area x length
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Volume of a sphere
4/3 x π x r^3
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## Other cards in this set

### Card 2

#### Front

Corresponding Angles

F Angle

### Card 3

#### Front

Co-Interior Angles

### Card 4

#### Front

Vertically Opposite Angles

180 Degrees