Search
Create
Log in
Sign up
Log in
Sign up
Core 1 & Core 2
STUDY
Flashcards
Learn
Write
Spell
Test
PLAY
Match
Gravity
Key facts useful to know for the Edexcel C1/C2 exams.
Terms in this set (104)
a^m x aⁿ =
What is a to the power of minus m?
Factorise x² - 49
(x - 7)(x + 7)
What is the quadratic formula?
where a is the coefficient of x², b is the coefficient of x and c is the constant.
How do you rationalise a denominator?
Multiply both numerator and denominator by the conjugate
What should you do when simplifying a surd?
Look for the largest square number that is a factor, then split it up.
What is a to the power of zero?
1
How do you find where a graph crosses the x-axis?
Let y=0
How do you find where a graph crosses the y-axis?
Let x=0
What shape is a x squared graph?
u (hand signal)
What shape is a minus x squared graph?
n (hand signal)
How do you complete the square?
1) Half the coefficient of x and put it in the bracket with x
2) subtract that number squared
3) put the constant on the end.
Complete the square for x² + 8x + 2
(x + 4)² - 16 + 2
(x + 4)² - 14
What is the discriminant?
b² - 4ac
When are there two unique real roots?
When b² - 4ac > 0
When are there no real roots?
When b² - 4ac < 0
When is there two equal roots?
When b² - 4ac = 0
What happens when you multiply/divide an inequality by a negative?
The sign switches
How do you find where a line and a curve meet?
If they are both in y= format, put them equal to each other.
If not, try substitution.
How do you solve a quadratic inequality?
Sketch the graph then shade in the region(s) of the curve that work.
Where does y=(x-2)(x-1)(x+3) cross the x-axis?
(2,0) (1,0) and (-3,0)
What shape is the graph y=x³+2x²+x+1
Hand gesture up, down and up
What does y = 1/x look like?
Where are the asymptotes for the y=1/x graph?
x=0 (y-axis)
y=0 (x-axis)
What does y=-1/x look like?
Same shape as y=1/x but in the other quadrants.
What effect does -f(x) have on a graph f(x)?
reflection in the x-axis
What effect does f(x) + 3 have on a graph f(x)?
Moves the graph up 3 squares (adds 3 to all the y-coordinates)
What effect does 2f(x) have on a graph f(x)?
Stretches the graph by scale factor 2 in the vertical direction. (Doubles all the y-coordinates)
What effect does f(-x) have on a graph f(x)?
Reflection in the y-axis
What effect does f(x+2) have on a graph f(x)?
Moves the graph 2 squares to the left. (Subtract 2 from all the x-coordinates)
What effect does f(2x) have on a graph f(x)?
Compresses it by scale factor 2 in the horizontal direction. (Halves all the x-coordinates)
What is the equation of a straight line?
y=mx + c, where m is the gradient and c is the y-intercept.
Or ax + by + c = 0 and a,b,c are all integers.
How do you find the gradient between two points?
rise over run
How do you find the equation of a line, if you know the gradient and a point it passes through?
Or
Use y=mx+c but substitute in the number for the gradient and the coordinate for x and y to work out the +c.
Two lines are parallel, so their gradients are....
the same
A line has gradient m and a line is perpendicular to it. It's gradient is?
How do you prove Sn for an arithmetic series?
1) Write out Sn as Sn = a + (a + d) + (a + 2d) ... etc
2) Reverse it.
3) Add the two lines together.
4) Make all the terms inside the bracket 2a + (n-1)d
5) Since there are n of them, write n(2a + (n-1)d)
6) Divide by 2.
What is Sn for an arithmetic series?
What is Un for an arithmetic series?
How do you differentiate?
Multiply by the power, then reduce it by 1
What do you get if you differentiate numbers?
zero.
What do you get if you differentiate x?
1
Differentiate 5x⁴
20x³
How do you find the equation of a tangent to a curve at a point (x,y)?
1) Differentiate the equation of the curve.
2) Sub in the x coordinate into dy/dx to find the gradient. This is the m in your y=mx+c
3) Sub in the coordinate into y=mx+c to find the c.
Done
How do you find the equation of a normal to a curve at a point (x,y)?
1) Differentiate the equation of the curve.
2) Sub in the x coordinate into dy/dx.
3) Take the negative reciprocal of this and this is the m in your y=mx+c
4) Sub in the coordinate into y=mx+c to find the c.
Done
How do you integrate?
Increase the power of x by 1, and divide by the new power.
What do you get if you integrate 4?
4x + c
What should you never forget when integrating?
+ c
Integrate 6x²
2x³ + c
You have been given dy/dx and a point on a curve. How do you find it's equation?
1) Integrate dy/dx
2) Sub in the coordinate to find c.
How do you show (x - a) is a factor of f(x)
Sub in a and show it equals 0.
THEN WRITE, THEREFORE IT IS A FACTOR.
How do you find the remainder when dividing by (x - a)?
Sub in a, and the numerical answer is the remainder.
What is factor theorem?
(x - a) is a factor of f(x), then f(a) = 0
What is remainder theorem?
If dividing f(x) by (x-a), then f(a) is the remainder.
What is the Sine rule?
What is the Cosine rule?
What is the area of a triangle?
or 1/2base x height
Write a^x = n as a logarithm
What is log (to base 4) of 16?
2
What is log (to base a) of a?
1
What is the log of 1?
0
How do you solve 6ⁿ = 11
Take logs of both sides and solve.
Log x + log y =
Log xy
Log xⁿ
nlogx
Log x - Log y =
Log x/y
How do you solve 6²ⁿ + 3(6ⁿ) - 10 = 0?
Rearrange to (6ⁿ)² + 3(6ⁿ) - 10 then treat as a quadratic.
How do you find the midpoint between two coordinates?
Add together then half.
How do you find the distance between two points?
Pythagoras
What is the equation of a circle?
Where (a,b) is the centre and r is the radius.
How do you find the equation of a tangent to a circle, at a given point?
1) Find the gradient of the radius.
2) Take the negative reciprocal
3) Write as y=mx + c
4) Sub in the coordinate to find c.
How do you calculate ⁶C₂?
Use your calculator (button above divide)
How do I use the binomial expansion on (a + bx)ⁿ?
1) Write (n0) then aⁿ
2) The next term is (n1)aⁿ⁻¹(bx)¹
3) The next term is (n2)aⁿ⁻²(bx)²
and so on...
What is π radians in degrees?
180
What is 360 degrees in radians?
2π
What is 90 degrees in radians?
π/2
What is 60 degrees in radians?
π/3
How do you convert from degrees to radians?
1) Divide by 180
2) Times by π
How do you convert from radians to degrees?
1) Divide by π
2) Times by 180
How do you work out the arc length?
l = rθ
That means times the radius by the size of the angle (in radians)
How do you find the area of a sector?
A = ½r²θ
Where r is the radius and θ is the angle.
How do you find the area of a triangle in radians?
It's still ½abSinC, but make sure you are in radians mode.
How do you find the common ratio of a geometric series?
Divide a term by the previous term.
or if you knew 5th and 3rd, you would do ar⁴÷ar² to find r² then square root.
What does a geometric sequence look like?
What is Un for a geometric series?
arⁿ⁻¹
What is Sn for a geometric series?
How do you prove Sn for a geometric series?
What is the sum to infinity for a geometric series?
When will a geometric series converge?
When -1<r<1
What does the CAST diagram look like?
What does the Sine Graph look like?
What does the Cosine Graph look like?
What does the Tangent Graph look like?
Asymptotes at x=90, x=270 etc
What does the y = 2^x graph look like?
How do you find a maximum/minimum/turning point/stationary point?
1) Differentiate the equation of the curve to find dy/dx
2) Put dy/dx = 0 and solve to find x.
3) Put the x value back into the equation of the curve.
How do you find d2y/dx2?
Differentiate y=.... once to find dy/dx and then differentiate again to find d2y/dx2
At a minimum, what will happen to the second derivative?
At a maximum, what will happen to the second derivative?
Tanθ =
State an identity linking sin²θ and cos²θ
sin²θ + cos²θ = 1
What are the steps in solving sinθ=0.5 between 0≤θ≤360
1) Find sin⁻¹0.5 .... 30°
2) Draw the CAST diagram
3) Since 0.5 was positive, it is in the A and S quadrants.
4) Start at 0 and go around anti-clockwise.
That will give 30 and 150.
What are the steps in solving 5sinx = -2 between 0 and 360.
Rearranging gives Sinx = -2/5
1) Find sin⁻¹(2/5) .... 23.6 (ignore -)
2) Draw the CAST diagram
3) Since it was -2/5, then we go for quadrants sin is negative in, C and T.
4) Start at 0 and go around anti-clockwise.
5) 203.6 and 336.4
How do you find the area under and curve, between x=a and x=b?
Integrate the curve between b and a.
That means integrate, sub in b and a and subtract.
What will happen if the area between the curve and x-axis is below the x-axis?
It will be a negative answer when integrated... just make positive.
What is the trapezium rule?
OTHER SETS BY THIS CREATOR
Higher Revision Cards
127 Terms
Corbettmaths
TEACHER
Foundation Revision Cards
190 Terms
Corbettmaths
TEACHER
Edexcel S1 Cards
78 Terms
Corbettmaths
TEACHER
THIS SET IS OFTEN IN FOLDERS WITH...
Edexcel Maths C1 key points
21 Terms
jbw63
Edexcel S2 Maths
21 Terms
stanton1-
Useful A Level Maths S1 Formulae
25 Terms
Livixbobbiex221b
Random core 2 stuff
5 Terms
ionascards