Flashcards
C3 Modulus, Numerical Methods and Transformations
Flashcards do conjunto (27)
- 1modulus on graphs? e.g. y = |x|anything below x axis on normal graph will be reflected to make positive
- 2how would you you explain this in an exam?EXACTLY - this graph is obtained by reflecting any parts of the graph below the x-axis in the x-axis, and leaving any parts above the x-axis the same
- 3|2x-1| = 4?square both sides, bring to one side and solve quadratic
- 4|4x-1| = |2-x| ?square both sides, bring to one side and solve quadratic
- 5|f(x)| < k?-k < f(x) < k
- 6|f(x)| > k?-k > f(x) or f(x) > k
- 7modulus on both sides? e.g. |x+2| > |2x-5|square both sides, bring to one side on inequality making other side 0, solve quadratic/cubic then from that get critical values, draw graph for inequality, then give the values either [a < x < b] or [xb]
- 8Simpsons Rule?x values, corresponding y values,
1/3h[first + last +4(odds) +2(evens)]
h = what x values are going up in - 9graphical location of roots?draw graphs and show clearly whether they do/don't intersect
- 10change in sign?if a graph is continuous and crosses axis between x=a and x=b, may be a sign change
- 11how to show equation has root between a and b?- rearrange to f(x) = 0
- work out f(a) and f(b) USING RADIANS IF TRIG IS INVOLVED
- if there is a sign change AND THE GRAPH IS CONTINUOUS, there is a root between a and b - 12how would you word the answer?change of sign between __ and __. Since f(x) is continous between __ and __, there is a root
- 13how would you do an iteration question?- rearrange so there's an x on both sides (may already do this in Q)
- pick starting value of x, usually given, call this X0
-generate sequence :
-put X0 into calc. and press '='
-then put in equation w/ 'Ans' where x should be
-keep pressing '=' until the right amount of decimal places
-KEEP RECORD OF EVERY ANSWER
- stop after the number of decimal places + 1 stops changing - 14f(-x)?reflection in y-axis
- 15-f(x)?reflection in x-axis
- 16af(x)?stretch sf a in y-axis
- 17f(ax)?stretch sf 1/a in x-axis
- 18composite transformations?if the transformations are in the same axis it DOES MATTER. Think about it like an equation, would the transformation affect the other bits already in the 'equation'?
- 19graph of y =x^n ? where n is positive and even
- 20graph of y =x^n ? where n is positive and odd
- 21graph of y =1/x^n where n is positive and even
- 22graph of y =1/x^n ? where n is positive and odd
- 23graph of y =root x ?
- 24graph of y =a^x ? where a>1
- 25graph of y =a^x ? where 0 < a < 1
- 26graph of y = |x| ?
- 27REMEMBER...when curve sketching, draw asymptotes to help and use a pencil!
Informações
- Descrição
- A level Maths (C3) FlashCards sobre C3 Modulus, Numerical Methods and Transformations, criado por Maisie Carroll em 26-02-2017.
- Criado por
- Maisie Carroll
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