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Kerry Latter
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About me
My name is Kerry Latter. I am a student at New Rickstones Academy and I am 14 years old. I play an acoustic guitar.
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New Rickstones Academy
MyMaths
Multiplication.com
Homework
Graphs
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Quadractic Graphs
The line on a quadratic graph is always a 'U' shape. It has to be drawn free hand, no ruler. y = kx2 (The larger the value of k, the steeper the graph) For example, a graph with y=3x2 will be steeper than a graph with y=2x2
Cubic Graphs
y = kx3 (k=number) Once the graph is plotted, the line will go diagonaly across the graph in the shape of a snake.
Straight Line Graphs
The equation of a straight-line graph can contain; an x term, a y term, and a number. Although some equations for straight lines might have only two of those, like an x term and a number, eg x=5.
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Estimation
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Examples
10.1 would be rounded to 10 34.56 would be rounded to 34.6 or 35 1658 would be rounded too 1700 or 2000
Example Question
How to work out; Estimate 2376 x 1890 First, you would round 2376 to 2000 as it is below 2500. Next, round 1890 to 2000 because it is over 1500. Finally, type the rounded sum into a calculator (Or work it out in your head) and you have your answer
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Simple And Compound Interest
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Simple Interest
When you have a certain percent of money you gain on any loan or invinvestment. This will not change.
Histograms
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Facts
It is A/A* work They are NOT bar charts Each bar has a different width The area represents the frequency, not the height. It's incorrect to label the vertical axis 'frequency' The label should be 'frequency density'
Formulas
Frequency (Area) = Frequency Density x Class Width Frequency Density = Frequency (Area) ÷ Class Width
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Simultaneous Equations
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Quadratic Simultaneous Equations
Solving simultaneous equations using quadratics uses a graph. We can use it to solve: x2 - 9x + 20 = 0 The answers are along the x axis where the graph reaches y = 0 (where it crosses the x axis). Using the graph the answers are x = 4 and x = 5. We can also solve this equation by factorising: y = x2 - 9x + 20 y = (x - 4) (x - 5) This shows that the solutions are x = 4 and x = 5 which matches the answers in the graph above.
Simultaneous Equations
Solve these simultaneous equations and find the values of x and y. Equation 1: 2x + y = 7 Equation 2: 3x - y = 8 Add the two equations to eliminate the y's: 2x + y = 7 3x - y = 8 ------------ 5x = 15 x = 3 Substitute the x in one of the questions (doesn't matter which one) for 3. We work out that 2 x 3 is 6, then we have to see what +'s together with 6 to get 7, this is 1. Therefor, y is 1. Therefor, y= 1
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Circle Theorem
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Facts
The angle at the center of the shape is always double the angle substended from the circumference. Radius meets tangent at 90 degrees. Angles in a triangle add up to 180 degrees. Angles on a straight line add to 180 degrees.
Quadratic Expressions
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Examples
1) (x+2)(x-4) 2) (x+6)(x+4) 3) (x-3)(x-2) x times x = x2 x times x = x2 x times x = x2 x times -4 = -4x x times 4 = 4x x times -2 = -2x 2 times x = 2x 6 times x = 6x -3 times x = -3x 2 times -4 = -8 6 times 4 = 24 -3 times -2 = 6 x2 - 4x + 2x - 8 x2 + 4x + 6x + 24 x2 - 2x - 3x + 6 x2 - 2x - 8 x2 + 10x + 24 x2 -5x + 6
Next
x2 + 7x + 10x You have to find what adds to +7 and also times together to get +10 The answer is 5 and 2 (5+2=7) (5 x 2=10)
Pythagoras
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Facts
It is true for all triangles which are right-angled.
Pythagoras 2D
If you add the areas of the smallest two sides get the area of the largest side In any right-angled triangle, the square of the longest side is the sum of the squares of the other two sides. This can be written in the formula: a2 + b2 = c2
Pythagoras 3D tips
Remember to use all decimal places at each stage in your calculation - working on a calculator makes this easier to do. When giving your final answer, always round according to what the question is asking for, eg to 2 decimal places.
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Vectors
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When making your journey, if you go against the arrows it will be negative and if you go the same way as them it'll be postive.
Direct proportion
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Rules
x= 12 y= 6 x ~ y x = ky 12= 6k 12 divided by 6 is 2 k = 2
Example
x=10 y=5 x=25 y=5 x ~ y x ~ y x = ky x = ky 10 = 5k 25 = 5k k = 2 k = 5
Area of a sector
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Steps
First, work out the fractor of the sector Then, times the fraction by the area of the whole circle. Now you have to area of that specific sector. Area of a whole circle - π x r²
Example
The fraction of this sector is 45/360 because it is 45 degrees out of the 360 degrees (360 degrees = full circle) Area of circle = π x r² π x 20² π x 400 1256 cm Tmes the fraction by the area of the whole circle - 45/360 x 1256cm² = 50 cm²
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Length of an arc
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Steps
First, work out the fractor of the sector. Then, times the fraction by the circumference of the whole circle. Now you have to area of that arc. Circumference of a whole circle = 2 x π x r
Example
The fraction of this sector is 90/360 because the angle is 90 degrees out of a possible 360. Circumference of a circle - 2 x π x r 2 x π x 3 6π 18.84 cm Times the fraction by the circumference of thw whole circle: 90/360 x 18.84 = 4.71 cm
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Indices
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Laws
Multiplication law: Multiplication law: a to the power of m times a to the power of n equals a to the power of m plus n. Division law: a to the power of m divided by a to the power of n equals m to the power of m minus n.
Example
Use the multiplication law. This tells you to add the indices. y to the power of seven times y to the power of 3 times y to the power of 5 equals y to the power of 7 plus 3 plus 5 equals y to the power of 15
Area of a triangle
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Formula
1/2 ab Sin C
How to
Sustitute... 1/2 x a x b x Sin C 1/2 x 5.2 x 7.1 x Sin 42 = 12.4 cm squared (1 D.P) Use calculator
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