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US

4380393

Core 1

- Chapter 1 ~ Algebra and Functions
- Like terms
- Multiplying brackets
- Rules of Indices
- Factorising
- Surds
- √(ab)=√(a)x√(b)
- √(a/b)=√(a)/√(b)
- Rationalising
- Multiply top and bottom
by denominator with
opposite central sign

- Multiply top and bottom
by denominator with
opposite central sign

- √(ab)=√(a)x√(b)

- Like terms
- Chapter 2 ~ Quadratic Functions
- y = f(x) = ax^2 + bx +c
- Solve quadratic equations by factorisation
- Completing the square
- 1) Write formula >
y=x^2 + bx + c
- 2) Make a gap appear >
y=x^2 + bx ________________ + c
- 3) In the gap add on, then take off (0.5*b)^2 >
y=x^2 + bx + (0.5*b)^2 - (0.5*b)^2 + c
- 4) Add brackets > y=(x^2 + bx + (0.5*b)^2) - (0.5*b)^2 + c
- 5) Factorise large bracket and tidy up numbers at the end

- 5) Factorise large bracket and tidy up numbers at the end

- 4) Add brackets > y=(x^2 + bx + (0.5*b)^2) - (0.5*b)^2 + c

- 3) In the gap add on, then take off (0.5*b)^2 >
y=x^2 + bx + (0.5*b)^2 - (0.5*b)^2 + c

- 2) Make a gap appear >
y=x^2 + bx ________________ + c

- 1) Write formula >
y=x^2 + bx + c
- x = [-b±√((b^2)-4ac))]/2a
- Discriminant
- b^2>4ac and a>0
- Two different roots
- u shape crosses x-axis twice

- Two different roots
- b^2=4ac and a>0
- Two equal roots
- u shape sits on x-axis

- Two equal roots
- b^2<4ac and a>0
- No real roots
- u shape that doesn't touch x-axis

- No real roots
- b^2>4ac and a<0
- Two real roots
- n shape crosses x-axis twice

- Two real roots
- b^2=4ac and a<0
- Two equal roots
- n shape sits on x-axis

- Two equal roots
- b^2<4ac and a<0
- No real roots
- n shape that doesn't touch the x-axis

- No real roots

- b^2>4ac and a>0

- y = f(x) = ax^2 + bx +c
- Chapter 3 ~ Equations and Inequalities
- Solving simultaneous
linear equations
- Elimination
- Substitution

- Elimination
- Solving simultaneous
equations where one
quadratic and one
linear equation
- Substitution

- Substitution
- Inequalities
- Solve similar to equations
- Number lines
- Sketches

- Solve similar to equations

- Solving simultaneous
linear equations
- Chapter 4 ~ Sketching Curves
- Cubic Curves
- y = ax^3 + bx^2 + cx + d
- Use factors of equation to work out where the curve crosses the x-axis
- x-axis intersections are when x = 0
- eg (x-2) > intersection at (2,0). (x+5) > intersection at (-5,0)

- eg (x-2) > intersection at (2,0). (x+5) > intersection at (-5,0)

- x-axis intersections are when x = 0
- y = x^3
- Smooth curve through (0,0)

- Smooth curve through (0,0)

- y = ax^3 + bx^2 + cx + d
- Reciprocals
- y = k/x
- When k>0, curves appear in quadrants where
both values are either positive or negative
- When k<0, curves appear in quadrants where
one value is positive and the other is negative

- When k>0, curves appear in quadrants where
both values are either positive or negative
- The further away k is from
0, the further away the
curves are from the axes

- y = k/x
- Transformations
- f(x+a) > moves whole curve -a in the x-direction
- f(x)+a > moves whole curve +a in y-direction
- f(ax) > multiply x-coordinates by (1/a)
- af(x) > multiply y-coordinates by a

- f(x+a) > moves whole curve -a in the x-direction

- Cubic Curves
- Chapter 5 ~ Coordinate Geometry in the (x,y) Plane
- y = mx + c
- m is the gradient and c
is the y-intercept

- m is the gradient and c
is the y-intercept
- ax + by +c = 0
- a, b, and c are all integers

- a, b, and c are all integers
- Gradient between two
points = (y2 - y1)/(x2 - x1)
- Equation of a line using one point
and the gradient > y - y1 = m(x - x1)
- Equation of a line between two points
> (y - y1)/(y2 - y1) = (x-x1)/(x2 - x1)

- Equation of a line using one point
and the gradient > y - y1 = m(x - x1)
- Two lines
- Perpendicular
- Gradient = -1/m
- The product of two perpendicular lines is -1

- Gradient = -1/m
- Parallel
- Same gradient

- Same gradient

- Perpendicular

- y = mx + c
- Chapter 6 ~ Sequences and Series
- General term > nth term
- a + (n-1)d

- a + (n-1)d
- Un = 4n + 1
- C1 only has arithmetic sequences
- a > first term
- d > common difference

- a > first term
- Sum of an arithmetic sequence
- Sn = (n/2)[2a + (n - 1)d]
- sn = (n/2)(a + L)
- L is the last term

- L is the last term
- ∑_(r=1)^10(5+2r) =7+9+...+25

- Sn = (n/2)[2a + (n - 1)d]

- General term > nth term
- Chapter 7 ~ Differentiation
- Used to work out the gradient of a tangent
- f(x) = x^n
- f'(x) = nx^(n-1)
- To get f'(x), multiply power by
number in front of x, then reduce
power by 1 for each part separately

- f'(x) = nx^(n-1)
- (d^2y)/(dx^2) = f''(x)

- Used to work out the gradient of a tangent
- Chapter 8 ~ Intergration
- If dy/dx = x^n, the y = (1/(n+1))(x^(n+1)) + c
- ∫x^n dx= x^(n+1)/(n+1)+c
- Calculate c when given any point that the function of the curve passes through
- Reverse of differentiation

- If dy/dx = x^n, the y = (1/(n+1))(x^(n+1)) + c

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