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Description
Flashcards by Holly Martin, updated more than 1 year ago
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Created by Holly Martin
over 6 years ago
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| Question | Answer |
| 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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