core Flashcards
What are the 3 ways used to factorise quadratic equations?
What is the MOST COMMON MISTAKE made according to mark schemes ?
Disguised quadratics
Checking solutions
Find the difference between
what 3 things must you do when checking answers?
- check the orginal power of x and make sure that you have that many solutions
- check all lines of working for ” =0 “
- test to discard solutions, especially when the original euqation has a root or a fractional power
what are some other uses of the completed square form?
- to find the minimum/ maximum point of equation (turning point)
- can find the line of symetry of the parabola
- identifying stransformations
how do you find the line of symetry?
the x axis of the turning point
what knowns are needed to sketch a graph?
- shape of parabola
- y intercept
- roots
derive the quadratic formula
What is the discriminant?
What are the discriminant uses ?
What are the 2 ways to solve simultaneous equations?
What is the rule when solving inequalities?
Flip the sign when multiplying or divining by negative numbers
How would you show that 3 points are co linear?
Derive
What are the gradients of two parallel lines and two perpendicular lines?
Parallel: have the same gradients , different y intercept
Perpendicular: gradients are the negative reciprocal of each other
How would you show that a shape is a trapezium?
What is the shortest distance from a point to a line.
The perpendicular distance from the point to the line
What is the equation of circles with centre at the origin, with centre not at the origin?
How can you determine the centre of the circle from two points on the circle?
Which of the circle theroms are applicable in Co -ordinate geometry?
How can you determine how many intersections lines have with circles?
Derive the exact trig values
Draw a unit square and equilateral triangle
What is sin (θ) and cos(θ) and tan (θ)?
sin (θ) = y
cos(θ) = x
tan(θ) = y/x
Derive the trig identity: sin ^2 (θ) + cos ^2 (θ) = 1
Draw the tan, cos and sin graph
What are the trig angle laws?
sin (θ) = sin (180 - θ)
cos (θ) = cos (360- θ)
tan (θ) = tan (180 + θ)
sin (θ) = cos (90- θ)
What are odd functions?
What are even functions?
How would you know when sin θ, cos θ, tan θ are negative/positive values ?
Solving for intervals
Solving for intervals 2
What is the order of a polynomial?
The value of the highest power of x
Sketching cubics
Sketching more cubics
What is the general shape of quartics?
Sketching Quartics
What does the reciprocal graph look like and it’s equation?
What is the difference between these two reciprocal graphs?
What is the difference between these two reciprocal graphs?
What is the difference between these two graphs?
1/x squared has a larger width to origin than 1/x
What is an asymptote?
A line which the graph approaches but never reaches
Divisor: thing that is getting divided
Dividend: the part which is doing the division (2nd number)
Do
What is the Factor Theorem?
How would you allocate the signs
- Look at the left hand statement, if it is true does the right hand statement also become true if so then (=>)
- Look at the right hand statements, if it is true does the left hand statement also become true (<=)
If both then <=>
What is some of the mathematical language used in implications?
What is the converse of a therom?
The opposite of a theorem
Therom = A implies B
Converse of Theorem = Does B imply A ?
what are the different types of proof?
- deuction: show the logical steps- normally iincolves algebra
- counter argument : show 1 example that does not follow the conjecture
- exhaution: trying out all the possibilities
Proof by deduction
Proof by deduction
Exam Tip
ALWAYS write a conclusion at the end (therefore ….repeat the question)
Why are some sketching tips for graphs?
Order (shape)
Direction (sign of leading coefficient )
Intersections with axis
Leading co-efficient (stretches of compressions)
Draw g(x) and f(x) on the same axis
How does the leading co efficient affect the shape of the graph?
Because the larger the value, the more faster it increases
The transformation y=f(x) + a
The transformation y= (fx +a)
Transformation y=af(x)
Transformation y=f(ax)
Transformation y= -f(x)
Transformation y= f(-x)
What is the general rule of transformations?
If inside the bracket —> x axis and opposite
If outside the bracket —> y axis and does that
How does f(2x) and 2f(x) affect the asymptotes?
How would you describe the transformation from the parent graph?
Transformations with Trig
Sin (x +30)
Proof question
