Corbettmaths Flashcards

Holly Martin
Flashcards by Holly Martin, updated more than 1 year ago
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A level Maths (All Topics (brief)) Flashcards on Corbettmaths Flashcards, created by Holly Martin on 24/04/2018.
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Angles in parallel lines Alternate - interior 'Z' angles are equal Corresponding -interior 'F' angles are equal Cointerior - interior 'C' angles sum 180 Vertically opposite angles are equal
Angles in Polygons 1 Triangle - Angles sum 180 Quadrilateral - Angles sum 360 Pentagon - Angles sum 540 Hexagon - Angles sum 720 Heptagon - Angles sum 900 Octagon - Angles sum 1080 Sum of interior - 180(n-2)
Angles in Polygons 2 Sum of Exterior Angles = 360 Pentagon - 360/5 = 72 Interior + Exterior = 180 Pentagon = 180 - 72 = 108
Arc length Arc length = angle/360 x pi x d
Area of a Circle Area = pi x r^2 If asked to give terms of pi then leave it without multiplying by pi.
Area of a Sector Area = angle/360 x pi x r^2
Area of a Trapezium Area = 0.5(a+b) x h a and b are parallel lines h is height between them
Area of a triangle Area = 0.5abSinC a and b are two sides C is the enclosed angle
Bearings Bearings are a direction of travel Find the bearing of Nottingham from Dublin Join Dublin and Nottingham Draw a north kine at dublin Measure the angle clockwise from north All bearing should have 3 figures
Changing the Subject Make w the subject of c = 4w + h c - h = w (c - h)/4 = w Do the same on each side
Circle Theorems 1 The angle in a semi-circle is 90 The angle at the circumference is half the angle at the centre The angles in the same segment from a common chord are equal The opposite angles in a cyclic quadrilateral always add up to 180
Circle Theorems 2 The angle between a radius and a tangent is 90 The tangents to a circle from the same point will be equal length The radius through the midpoint of a chord will bisect the chord at 90
Alternate segment theorem The angle between the chord and the tangent is equal to opposite angle inside the triangle
Parts of a circle 1 Radius - half of the diameter Diameter - a line going halfway through the middle Circumference - the perimeter Chord - a line connecting two points
Parts of a circle 2 Arc - a small part of circumference Tangent - a line 90 degrees from the radius Sector - a 'pizza cut' of a circle Segment - the area between chord and circumference
Circumference Circumference = pi x diameter If only radius is given Circumference = pi x 2 x radius
Density Density = Mass/Volume Mass = Density x Volume Volume = Mass/Density
Pressure Pressure = Force/Area Force = Pressure x Area Area = Force/Pressure
Speed, Distance and Time Speed = Distance/Time Distance = Speed x Time Time = Distance/Speed
Congruent Triangles SSS - Side - Side - Side ASA - Angle - Side - Angle SAS - Side - Angle - Side RHS - Right angle - Hypotenuse - Side
Constructions Angle Bisector Perpendicular Bisector
Loci A tree is planted closer to the fence than the wall. The tree is no more than 1 meter from the well. Draw a circle around the well radius = 1 Angle bisector to find the wall:fence line
Cumulative Frequency Position of the median: 40/2 = 20 Draw across from 20 to the curve Draw straight down from the curve Read off the answer make sure you check the scale
Box Plots Interquartile Range = Upper quartile - Lower quartile Range = Highest value - lowest value
Recurring Decimals to Fractions Write 0.45 (0.454545.....) x = 0.45454545.... 100x = 45.45454545... 99x = 45 x = 45/99 x = 5/11
Equation of a Circle x^2 + y^2 = r^2 Centre = (0,0) radius = r
Forming and solving equations Find x on isosceles triangle with angle 1 being 2x and angle 2 and 3 being x + 20. 2x+x+20+x+20 = 180 4x + 40 = 180 x = 35
Expanding Two Brackets Expand: (x+3)(x-7) = X^2 - 7x + 3x - 21 = x^2 -4x -21
Factorising Quadratics place y at the front of both brackets The numbers will multiply to give (eg) -15 add to give (eg) 2 -3 + 5 = 2 (y - 3)(y + 5)
Solving Quadratics by Factorising Solve x^2 - 3x -10 = 0 (x - 5)(x + 2) = 0 x = 5 or x = -2 (to make the brackets equal 0)
Adding Fractions Work out 1/4 + 7/10 5/20 + 14/20 = 19/20
Dividing Fractions Work out 2/5 / 7/9 KFC = Keep Flip Change 2/5 x 9/7 = 18/35
Multiplying Fractions Work out 3/4 x 2/5 Multiply numerators together and denominators together = 6/20 =3/10
Composite Functions: fg(x) GIven f(x) = 2x +1 and g(x) = x^2 + 5 Substitute g(x) into f(x) fg(x) = 2(x^2 + 5) + 1 = 2x^2 + 10 + 1 = 2x^2 + 11
Composite Functions: gf(x) Given f(x) = 2x + 1 and g(x) = x^2 + 5 gf(x) = (2x + 1)^2 + 5 =(2x + 1)(2x + 1) + 5 = 4x^2 + 4x + 1 + 5 = 4x^2 + 4x + 6
Inverse Functions GIven f(x) = 3x + 2 find f-1(x) y = 3x + 2 make x subject (y - 2)/3 = x f-1(x) = (x -2)/3
Graphs of Exponential Functions y = 2^x x -2 -1 0 1 2 3 y 1/4 1/2 1 2 4 8
Graphs of Reciprocal Functions y = 1/x
Cubic Graphs y = ax^3 - bx - c
Transformations of Graphs 1 y = -f(x) is a reflection of y = f(x) in the x axis y = f(-x) is a reflection of y = f(x) in the y axis
Transformations of Graphs 2 y = f(x) + a moves y = f(x) a square upwards y = f(x+a) moves y + f(x) a square to the left
Graphs of trigonometric Functions y = sin x y = cos x y = tan x
Drawing Histograms Frequency Density = Frequency/Class Width
Reading HIstograms Frequency = Frequency Density x class width
Fractional Indices x^1/n = n root x x ^m/n = (n root x)^m 27 ^2/3 = 9
Laws of Indices m^3 x m^4 = m^7 (Add) m^8 / m^2 = m^6 (Subtract) (m^3)^2 = m^6 (Multiply
Negative Indices x ^-n = 1/x^n x^0 = 1
Limits of accuracy The height of a lighthouse is 48m to the nearest metre. Find the lower and upper bound. Lower = 47.5 Upper = 48.5
Drawing linear graphs Draw y = 2x - 1 x -2 -1 0 1 2 y -5 -3 -1 1 3
Equation of a line y = mx + c m = Gradient c = y - intercept Gradient = rise/run
Gradient Gradient = rise/run
Parallel Lines Parallel lines have the same gradient Equation has the same m value
Perpendicular lines Perpendicular lines cross at 90 If the gradient of one line is m The gradient of the other is -1/m (Negative reciprocal)
Equation of a tangent to a Cirlce Find gradient of OP (origin,point) Find the gradient of the perpendicular tangent Substitute into y = 1/2x + c
Estimated Mean (Frequency x Midpoint) / Frequency
Nth term fir Linear Sequences Find the difference between each number in sequence Multiply the original number by the difference Subtract this from the original number sequence
Nth term for Quadratic Sequences nth term = an^2 + bn + c Sequence = a + b + c First difference = 3a + b Second sequence = 2a
Percentage Change Percentage Change = Change/Original x 100
Compound intrest Initial x Multiplier^Time
Reverse Percentages Divide by Numerator Multiply by Denominator
Drawing Pie Charts Find the total frequency Divide 360 by total frequency To find the angle, multiply the frequency by the angle per person Draw and label the pie chart
Tree Diagrams Draw a line from a point for each possibility multiply each possibility by the probability
Product of Primes Write 60 as a product of primes Draw two lines out of 60 and a pair of factors Draw a circle around any primes and continue to write pairs until there are only primes.
LCM & HCF using product of primes The LCM is found by multiplying all the numbers in the Venn Diagram The HCF is found by multiplying the numbers in the middle of the venn diagram.
Direct Proportion C is directly proportional to the square of D When C = 200, D = 2. Find C when D = 5 C = k x D^2 200 = k x 4 K = 50 C = 1250
Inverse proportion P is inversely proportional to the cube of Q When P = 10, Q = 2. Find P when Q = 4 10 = k/8 k = 80 P = 80/64 P = 1.25
Pythagoras 1 a^2 + b^2 = c^2 a and b = length of shorter side c = length of hypotenuse
Pythagoras 2 a^2 + b^2 = c^2 If only short side and hypotenuse is given rearrange the equation
Quadratic Formula A quadratic equation in the form ax^2 + bx + c = 0 x = (-b +/- root(b^2 - 4ac)) / 2a
Quadratic Inequalities If the sign is 'less than' sketch it as '=' then only use values below the x-axis If the sign is 'greater than' sketch it as '=' then only use values above the x-axis
Ratio Find the total number of parts by adding the values in the ratio Divide the total amount of money by the total number of parts to find one part Multiply the amount of money in one part by the number of parts each person receives
Scatter Graphs For estimation, draw a line of best fit through the results. go along the x-axis to information required and draw a vertical line connection to the line of best fit. Draw another horizontal line from this point to the y-axis and read.
Correlation Positive - ascending from left to right Negative - ascending from right to left No Correlation - no pattern
Significant figures The first number that is not a zero is the first significant figure. The second is the second sf
Similar Shapes If the scale factor for the sides is n - the scale factor for the area is n^2 - the scale factor for the volume is n^3
Simultaneous Equations Multiply the equations to give a common multiple. If the operations are the same then subtract these two and solve the equation. If they are different then add. Then substitute this into A
Standard form Standard form is a really useful way of writing very large or very small numbers quickly and easily. a x 10^n A is between 0-10 n is a whole number
Surds root(a) x root(b) = root(ab) root(a) x root(a) = a root(a) / root(b) = root(a/b)
Rationalising the denominator To rationalise the denominator we multiply both the numerator and denominator of the fraction by the denominator
Enlargements If the scale factor is 2. Each point of the triangle will move twice as far away from the center of enlargement.
Enlargements with Negative Scale Factors If the scale factor is -3 Each point of the triangle will moves three times as far away from the center of enlargement in the opposite direction.
Reflections If the question was: Reflect shape A in the line x = 6 Draw a line at x = 6 and use this as a mirror to draw the reflection
Rotations Mark the center of rotation and trace triangle A onto the tracing paper Rotate 90 clockwise keeping the cross on the origin. Draw the triangle onto the grid.
Translations The top number is the horizontal movement The bottom number is the vertical movement
Trigonometry Sin(x) = Opposite /Hypotenuse Cos(x) = Adjacent / hypotenuse Tan(x) = opposite /adjacent
Cosine Rule a^2 = b^2 + c^2 - 2bc CosA
Exact Trig Values Angle sin cos tan 0 0 1 0 30 1/2 root(3)/2 root(3)/3 45 root(2)/2 root(2)/2 1 60 root(3)/2 1/2 root(3) 90 1 0 undefined
Sine Rule a/SinA = b/SinB = c/SinC
Vectors OAB is a triangle OA = a OB = b AB = AO + OB AB = -a + b AB = b - a
Venn Diagrams A = All in A section B = All in B section A' = everything but A B' = everything but B A U B = All of A and B sections A n B = anything A and B (the middle bit)
Volume of a Cone Volume = 1/3 pi r^2 h
Volume of a Prism Volume = Cross-Sectional Area x Length
Volume of a Sphere Volume = 4/3 pi r^3
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