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1. To go from y =x to x =y, plot a graph of x against y, then rotate 90°anti clockwise then reflect in Y axis (draw arrows on the original x and y axis to help. Then between first and end step with the co ordinates of any points from the x=y graph
2. Know that for a -x^2 the Turing point (a, b) in equation -(x -a)^2 +b
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Remember the constraints that logs apply, it can never be negative
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For a number to be an integer it cannot have any negative powers (as this would create a fraction)
One of the power laws is that the power can be distributed to the factors of the base.
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Good triangle splitting fraction technique
ALSO PLEASE REMEMBER IT IS R^2 NOT R
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Check your solutions and be careful when substituting the hidden quadratic equations
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Just know that you can switch the integral sign
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Know that log functions are strictly always increasing.
Know how to maximise / minimise equations
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“Closest to origin” means smallest distance
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Different method for completing the square with -1 as coefficient of x sqaured
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Using logs in inequalities and approximating “in between “ of logs
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Watch the algebra
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The reflected points and reflection line are perpendicular to one another
Don’t stop and keep going after finding intersection points
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Logic?
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Substituting logs and see how many digits a number to the power of 10 has (one less)
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Binomial expansion
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Know that the square root of a number less than 1 (0.7) is greater than the number itself. Just like how squaring a number less than one gives a smaller number
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Using matrices in simultaneous
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Trapezium rule
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Minimum point
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Don’t forget the 10s (those numbers ending in digit 0)
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Really hard trigonometry question considering extreme values of sin and cos
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Draw a quadratic and a quartic together:
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KNOW that sin^2(°) and cos ^2 (°) can never both be =0 , as this is true for no value of sin^2 + cos^2 =1
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What are the characteristics of a positive quartic , “with 4 real solutions “?
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charactertistics of a quartic
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“Intersects “ means the discriminant is greater than or equal to zero (could be one or two solutions )
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Acknowledge the 2n hinting towards two separate series in one
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Diving through by cos ^2 to create a tan. BUT checking that cos (x) != 0 for this to happen
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Characteristics of the sin^2 graph include: no negative y values, maxima and minima always occur at 0 and 1. Also manipulating sin to find the roots of sin (root x) to find that the roots are not evenly spaced
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Just keep on subbing in values and trying to
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Fundamental Therom of calculus
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Plotting log/ exponential graphs with inequalities
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Approach all “must be trues” with an initial guinea pig.
Know that a square is also a rectangle
Know that the cube /square of decimals is so small
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“Largest value” for which previous term is greater than next term is minimum value -1
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Knowing sin values and working in radians really well. Drawing a clear graph and understanding the question
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Sine rule and diagram manipulation
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When you get to the sin^2 cos^2 phase sub in the 1=c^2 +s^2
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Integrating as a function properly using equations
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Cancelling out logs in powers
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Sequences question
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What are translational sin formula?
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Integrating and substituting, integrating with constant
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How does the trapezium rule work?
Please remember to draw in trapeziums from the last point NOT TRIANGLES
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Consider what goes on between the integer functions
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Always check solutions esp if logs or square roots are involved
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What is the general shape of x2, x3, x4, x5, x6 on one graph
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Square all terms
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Look carefully at question before diving in
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Sometimes just look at options and substitute values
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What are the angle formula for a circle in radians?
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Sin (180 - °) = °
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Square rooting a square and quartic
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Check the leading coefficients rather than just looking at the power, because they can cancel each other out
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Get used to quickly differentiating to find the turning point of a graph to plot an overall shape. Look at the answers in the multiple choice to help you decide where you are heading
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Know this other equation used to represent a circle. In co ordinate geometry questions, look for things like if it is on the line y=x
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Using the cases of tending to infinity and tending to zero
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Sometimes minimum values can become maximum
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Multi nominal expansion and grouping
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More multi nominal expansion
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Looking at patterns of sums
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Dummy variable and integrating each component of equation separately to get desired result
TMUA
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