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QuestionAnswer
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.
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