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# Km

Question | Answer | |||||
---|---|---|---|---|---|---|

Which 2 numbers can prime numbers not be divided by to get an integer? | 3 and 7. | |||||

What is the formula for the nth term for triangle numbers? | O.5n^2 + 0.5n | |||||

Prime numbers only divide by | 1 and themselves. | |||||

Breaking down a number into a string of prime numbers is known as..? | prime factor decomposition. | |||||

The numerator is divided by the denominator when converting........? | fractions to decimals. | |||||

The first significant figure is simply the first digit which isn't | 0. | |||||

Area of triangle= | (base x vertical height) divided by 2. | |||||

Area of trapezium= | 0.5(a+b) x h a= length of top side. b=length of buttom side. This formula can be be remembered easier with the poem: | half the sum of the parallel lines, times the length between them, this is how we calculate the area of a trapezium. | ||||

Area of circle= | pi x (radius squared). | |||||

Circumference of circle= | diameter times pi. | |||||

The radius of a circle is half of its | diameter. | |||||

The perimeter of a circle is the same as its | circumference. | |||||

Negative number + Negative number→ | further from 0. | |||||

Negative number + positive number→ | Closer to a million+. | |||||

Negative number x positive number= | negative number. | |||||

Negative number x negative number= | positive number. | |||||

What is an integer? | A whole number that's positive or negative. | |||||

0.2 ÷ 0.1= | 0.2 x 10. | |||||

0.2 ÷ 0.4 | 0.2 x 2.5. | |||||

0.2 ÷0.8 | 0.2 x 1.25. | |||||

Bodmas; | Brackets, other, division, multiplication, addition, subtraction. | |||||

1 millilitre is equivalent to 1 | cm cubed. | |||||

1 gallon in litres is approximately | 4.5. | |||||

1 metric ton is approximate to 1 | imperial tonne. | |||||

1 inch in cm is | 2.54. | |||||

1 pound in kg is approximately | 0.453592 and one kilogram in pounds is approximately | 2.20462. | ||||

When multiplying fractions: | Multiply top and buttom seperately. | |||||

When dividing fractions; | turn the second fraction upside down and then multiply. | |||||

When adding fractions when the denominators are different; | multiply the denominators so they're the same, multiply the numerator of each fraction by the same amount as the denominator, then add the numerators. | |||||

When subtracting fractions when the denominators are different; | multiply the denominators so they're the same, multiply the numerator of each fraction by the same amount as the denominator, then subtract the numerators. | |||||

Standard form is the same as | standard index form. | |||||

The formula for standard index form is | a * 10^n. | |||||

In standard index form (a x 10^n), 'a' is between [] and [] inclusive. | 1 and 10 inclusive. | |||||

10^-3 means that the decimal point moves | 3 places left (making it smaller). | |||||

Exp and EE are the calculator buttons for | standard index form. | |||||

On a calculator for 5.74 x 10^9, the buttons that would be pressed are | 5.74, (EXP/EE), 9 and the display would be | 5.74e9 or 5.74e^9. | ||||

To enter 1 2/3 into a calculator, the buttons that would be pressed are | 1(A b/c)2(A b/c)3. | |||||

To enter 2/3 into a calculator, the buttons that would be pressed are | 2(A b/c)3. | |||||

When expressing something as a percentage of another, one method to use is | f.d.p (fractions, decimal, percentage). | |||||

To reduce a ratio to the form 1:n or n:1: | divide both by the smallest number. | |||||

When multiplying 2 numbers which have indices, | add the indices. | |||||

When dividing two numbers which have indices, | subtract the indices. | |||||

When raising one indices to another, | multiply the indices. | |||||

'N' to the power of 1 | is itself. | |||||

'N' to the power of 0 | is 1. | |||||

A number is put to the power of 1/2 is its | square root. | |||||

When a number is put to the power of 1/3 is | its cubed root | |||||

When there is a common difference, Nth term= | dn + (a-d) | |||||

6 types of number patterns are: | common difference, increasing difference, decreasing difference, common multiplying difference, common dividing difference, Fibonacci sequence. | |||||

In the Fibonacci sequence | two consecutive numbers add together to make the next. | |||||

In quadratic sequences, after finding the difference of the differences, the formula for finding a (the buttom one) is | 2a=x | |||||

In quadratic sequences, after finding the difference of the differences, the formula for finding b (the middle one) is | 3a + b=x | |||||

In quadratic sequences, after finding the difference of the differences, the formula for finding c (the top one) is | a+b+c=x. | |||||

When trying to find the nth term of quadratic sequences, the found values of a,b and c are substituted into the formula | an^2 + bn + c. | |||||

In a formula triangle, the 2 numbers that are multiplied by each other go | at the buttom and the other one goes at the top | |||||

In x, y, z coordinates x and y show 2d coordinates, but when z is used | they show 3d coordinates. | |||||

The order to write x, y and z coordinates in is | x, y, z. | |||||

The 'y' axis is also the line x= | 0. | |||||

The 'x' axis is also the line y= | 0. | |||||

In graphs the line for when x=a goes straight UP through | 'a' on the 'x' axis. | |||||

The line for when y=a goes straight ACROSS through | a on the y axis. | |||||

On a graph, on the line Y=x, the 'y' and 'x' coordinate | are always the same. | |||||

On a graph, on the line Y=-x, the 'y' and 'x' coordinate | are the same except when 'y' is positive, 'x' is negative and vice versa. | |||||

In Y=ax and Y=-ax, a/-a is | the gradient of the line. | |||||

The method for finding gradients is to find 2 clear, accurate | points that are reasonably | far apart, use the lines to make a | right-angled triangle, find change in both | 'y' and 'x', to get the gradient divide | the change in 'y' by change in 'x'(remembering to put a minus sign in front of it if it's negative). | |

After finding the gradient on a graph, the letter usually added to the end is | x because | the gradient or slope is what 'x' is multiplied by. | ||||

In graphs where y=ax+c, the lines are | straight. | |||||

In graphs where y=ax+c, c is the | y intercept. | |||||

In graphs the 'y' intercept is the value of 'y' when | a line crosses the 'y' axis | |||||

'Y' is always on its own in the graph equation | Y=ax+c | |||||

The line in x^2 graphs (eg: y=x^2, f=2g^2) have to an extent the shape of a letter | U (at times possible with an extended or compressed | top end). | ||||

The line in all -x^2 graphs (eg: y=-x^2,f=-2g^2) have to an extent the shape of an upside-down letter | U (at times possible with an extended or compressed | bottom end). | ||||

The line in x^3 graphs (eg: y=x^3,f=2g^3) have to an extent: the shape of a sometimes tilted (with straight leg missing) reversed | 'h', going up from the | buttom left. | ||||

The line in -x^3 graphs (eg: y=-x^3,f=-2g^3) have the shape of a sometimes tilted | 'h', going up from the | buttom right. | ||||

The line in all Y=a/x graphs, where 'a' is a number, in the higher right quadrant, have roughly the shape of the letter | l, and are reflected onto the other side of the line: | y=-x as it reoccurs in the quadrant that's in the | lower left. The graph does not take into account the value of 'x' as | 0. | ||

If b as well as c are in inverse proportion if b doubles, | c halves. | |||||

When plotting straight line graphs: | Y=ax+c, chose 3 values of | x, for each value of x work out the value of | y , plot the | coordinates and | draw the line. | |

To solve simultaneous equations using graphs;do a | table of three values for both equations, draw the | two lines, then find the values of | x and y where the | lines cross. | ||

To solve simultaneous inequations with inequalities using graphs: | convert each inequality symbol to an | equals sign, do a table of three values for | each equation and then on the graph; | draw the lines, before shading the | enclosed section which is the area sought. | |

All the sides are the same in a regular | polygon. | |||||

In regular polygons the sum of all exterior angles is | 360°. | |||||

In regular polygons the formula for finding the amount of degrees in one exterior angle is | 360° ÷ number of sides. | |||||

In regular polygons the formula for finding the sum of degrees of all interior angles is | (n-2) x 180°. Where n is | the number of sides in the shape. | ||||

In regular polygons the formula for finding the amount of degrees in one interior angle is | (n-2)x180°)÷n. | |||||

Instead of lines of symmetry, 3d objects have | planes of symmetry. | |||||

Rotational symmetry is where a shape looks exactly the same when | rotated. | |||||

A triangle that has two equal sides is called | an isosceles triangle. | |||||

A triangle that has no equal sides is called | a scalene triangle. | |||||

The formula for finding the area of a parallelogram is | base x vertical height. | |||||

A tangent is a straight line that just touches | the outside of the circle. | |||||

Any line drawn across the inside of a circle is | a chord. | |||||

An arc is | part of the circumference of a circle. | |||||

Volume of prism= | area of cross section x length. | |||||

The angles on a straight line add up to | 180°. | |||||

When a line goes across 2 parallel lines, the 2 bunches of angles | are the same. | |||||

In a 'z' shape, the 2 inside angles are | the same and they're called and their angles are | alternate angles. | ||||

In a 'c' shape, the 2 inside angles add up to | 180° and are called | supplementary angles. | ||||

In an 'U' shape, the 2 inside angles add up to | 180° and are called | supplementary angles. | ||||

In a 'f' shape, the first and third inside angles are | the same and are called | corresponding angles. | ||||

When a tangent and radius meet at the same point they make an angle of | 90°. | |||||

Isosceles triangles are formed in a circle by the meeting of | 2 radii. | |||||

When using letters to specify angles, the middle letter is | where the angle is and the other 2 letters tell you | which 2 lines enclose the angle. | ||||

If two things are the same size and the same shape then they're | congruent. | |||||

In graphs where y=ax+c, a is the | gradient. | |||||

In a translation vector, the number at the top indicates | how far it moves along, while the one at the buttom indicates how far | it goes up or down. | ||||

The basic formula for Pythagoras' theorem is | a^2 + b^2=c^2. Where 'c' is | the hypotenuse. | ||||

A bearing is the direction travelled | clockwise from the | north line written as an | angle, often in | degrees, using | three numbers. | |

For Pythagoras' theorem to be used on a triangle the triangle needs to be | a right-angled triangle. | |||||

In a right angled triangle, the longest side is called a | hypotenuse, which is also the side opposite the | right-angle. | ||||

In a triangle the adjacent side is the side | next to the angle being used. | |||||

In a triangle the opposite side is the side opposite | the angle being used. | |||||

The angle of elevation is the angle | upwards from the horizontal. | |||||

The angle of depression is the angle | downwards from the | horizontal. | ||||

The angle of elevation is equal to | the angle of depression. | |||||

Probabilities of 0 means | it will never happen, while a probability of 1 means | it will surely happen. | ||||

The way to write probability (when 'e' is the event and 'n' is the probability) is | P(e)=n. | |||||

In the notation for probability: P(e)=n, 'P' stands for | probability, 'e' is | the event and 'n' is | the probability of | e. | ||

Probabilities can be written in | fractions, percentages and decimals. | |||||

The probability of multiple possible outcomes for an event adds up to | 1. | |||||

Sample spaces are | all possible outcomes. | |||||

A line graph is also known as a frequency | polygon. | |||||

The middle value in a class is called the | mid interval value. | |||||

The 'total so far' is | the cumulative frequency. | |||||

If using a formula triangle to find how to calculate something, | cover it up and the calculation for it is what's left. | |||||

The only type of triangles that trigonometry works on are | right-angled triangles. | |||||

The method for trigonometry is 1) Label the side: | 'o', 'a' and 'h'. 2)decide which sides are involved, before choosing | 'soh', 'cah' or 'toa'. 3)Get the right formula triangle with the middle letter being at | the top of the formula triangle. 4)Cover up what you want to find, translate into | numbers and | calculate. | |

Press Inverse(inv) before 'sin', 'cos' or 'tan', when trying to find | an angle. | |||||

The locus of points equidistant from a given point is | a circle. | |||||

The locus of points equidistant from a given fixed line(not a line segment) are the | two lines parallel to it. The locus of points equidistant from a given line segment is an | oval or (a 'running-track' or 'capsule' shape). | ||||

The locus of points which are equidistant from two intersecting lines are the | angle bisectors. | |||||

The locus of points which are equidistant from 2 given points is | the perpendicular bisector of the line connecting the two points. | |||||

When trying to draw the locus of points n away from a square the edges of the outer one may be | curved. | |||||

To construct a perpendicular line from a point on a line: move the compass to the | point on the line. On the line, on either sides of the point, draw an | arc, widen the compasses and to both arcs make | arcs that | intersect then | draw a line through the intersection. With the exception of when the compass should be widened, before the drawing of another pair of arcs: between use the width of the compass should remain (to some extent(a high one)) | the same. |

The formula to find the expected number of occurences may be; expected number of occurrences= | estimated probability x number of tries. | |||||

If 2 triangles are similar: they have the same set of | angles. | |||||

When triangles have the same set of angles and their sides are equal: then the triangles are | equal. | |||||

The loci of points equidistant to two parallel lines is a line that is also | parallel, but from both: is an | equal distant. | ||||

If 2 things are the same shape and different sizes, then they are | similar. The corresponding sides are in a fixed | ratio. | ||||

To rearrange formulae to find the value of 'x', undo the | operations around | 'x' while doing the same thing on the | other side of the | '=' in the order of | bodmas backwards. |

Created by:
Toluo