Paper 1 Topics Flashcards
How to Answer a Separable Differentiation Question.
- Split up both sides to have x’s on one side and y’s on one side (remember if you are taking over something that is being multiplied, it goes underneath.
- Integrate both sides.
- Insert the values for x and y given at the beginning.
- Work out C by solving equation.
- rearrange the equation to have ‘y=’
How to Answer a Complex Roots Question.
- Work out other root. Just by switching sign of first root that was given (1)
- Multiply together (multiply first terms, add second terms in brackets, multiply brackets).
- Use algebraic long division to work out equation of third root.
- Solve the equation (may need to use quadratic formula).
How to Answer a Logarithmic Differentiation Question.
- Take log of both sides.
- Differentiate both sides.
- Bring Y over to have only dy/dx on one side.
- Substitute Y for whatever it was in the beginning.
- Multiply out.
How to Answer a Proof by induction Question.
- Sub n=1 into both sides to show that it is true.
- State ‘true for n=1’
- Work out aim, (sub k+1 into right hand side of original equation)
- Assume true for n=k (sub k for n into right side of original equation)
- Consider n = k+1 (sub k+1 for n into l left ide of original equation)
- Add n=k equation to the n=k+1 equation
- Tidy up to match the aim.
How to answer an Asymptotes Question from Stratch.
- Find X intercept/s by subbing in x=0 to original equation and solving.
- Find Y intercept/s by subbing y=0 and solving.
- Find vertical asymptote by making the denominator equal to zero. Find the behaviour by making a nature table and subbing in slightly lower and slightly higher numbers into the denominator equation.
- Find the non-vertical asymptote by using long division. Whatever is left on top of the division line is the non-vertical asymptote.
- Use the chain rule on the whole equation you just formed, including the end part (e.g remainer of long division/what you divided by) for stationary points.
- Solve the chain-ruled equation if possible.
- For stationary points sub x values from stage 6 back into original equation
How to answer a Volume of a Solid Using Integration.
- Draw a diagram.
- Calculate height of shape by subbing in x=0
- Work out equation (if there is pie, this can go on the outside of the rest of the equation, which is integrated since it is constant), subbing x for the radius or length, and dy for the height.
- rearrange original equation to find what x equals.
- integrate
- insert limits to calculate the final volume.
How to answer a Binomial Theorem Question.
1.
How to answer a Parametric Differentiation Question.
- Differentiate both equations.
2. multiply dx/dt and dy/dt together to get dy/dx.
How to answer a Partial Fractions With Integration Question.
- Separate.
- Cross multiply.
- Work out values.
- Rewrite in fraction.
- rewrite with integration sign.
- integrate.
- If there are limits, sub them in.
- tidy up. (You can take ln out as common factor and put any negatives underneath).
How to answer a Gaussian Elimination Question.
- Layout in table without any x’s, y’s. or Z’s (remember the answers to equations on the right.)
- Make the left terms in row 2 and 3 equal zero, by taking away row 1.
- Make the middle term in the bottom row equal 0 USING ROW 2.
- Work out the values of the A’s, B’s and C’s.
Arithmetic sequence/series.
Equation for the first term is: Un=a+(n-1)d
d=common difference
n=term number,
Get common difference by either;
just looking
or dividing the difference in terms by d (could be 2d)
For the sum of terms, use the equation Sn = 1/2n(2a+(n-1)d)
a=first term
Geometric sequence/series.
r is obtained by dividing two consecutive terms.
You can get the nth term by using the equation:
Un = ar^n-1
Partial Sum Formula = Sn = a(1-r^n)/1-r)
Infinite Geometric sequence.
S(infinity sign) = a/1-r.
How to answer a factorials Question.
(x) __n!__
(x) = r!(n-r)!
