20 Quick Revision Topics

1
20 Quick Revision Topics!
2
To add two fractions, the bottom (denominator) of
the two fractions must be the same. 1/2 3/2
4/2 1/10 3/10 5/10 9/10 . If the
denominators are not the same, multiply or divide
the top and bottom of one of the fractions by a
number to make the denominator the same as the
other.Example5    2 5    4    9  
 36     3     6      6     6    2
3
The same is true when subtracting fractionsthe
bottom (denominator) of the two fractions must be
the same. 3/2 - 1/2 2/2 3/10 - 1/10 2/10
If the denominators are not the same, multiply
or divide the top and bottom of one of the
fractions by a number to make the denominator the
same as the other.Example5  -  4 10  -  4
   6    13     6     6      6     6  
 
4
Multiplying fractionsThis is simple, just
multiply the two numerators (top bits) together,
and the two denominators together2    5  
 10     53      8         24       12  
5
LCM and HCFThe lowest common multiple (LCM) of
two or more numbers is the smallest number into
which they evenly divide. For example, the LCM
of 2, 3, 4, 6 and 9 is 36. The highest common
factor (HCF) of two or more numbers is the
highest number which will divide into them both.
Therefore the HCF of 6 and 9 is 3.
6
BODMAS When simplifying an expression such as
3 4 5 - 4(3 2) remember to work it out in
the following order brackets, of, division,
multiplication, addition, subtraction. So do the
thing in the brackets first, then any division,
followed by multiplication and so on. The above
is 3 20 - 4 5 3 20 - 20 3. You
mustn't just work out the sum in the order that
it is written down.  
7
Related Angles
8
Lines AB and CD are parallel to one another
(hence the on the lines).a and d are
vertically opposite angles. Vertically opposite
angles are equal. (b and c, e and h, f and g are
also vertically opposite).g and c are
corresponding angles. Corresponding angles are
equal. (h and d, f and b, e and a are also
corresponding).d and e are alternate angles.
Alternate angles are equal. (c and f are also
alternate). Alternate angles form a 'Z' shape and
are sometimes called 'Z angles'.a and b are
adjacent angles. Adjacent angles add up to 180
degrees. (d and c, c and a, d and b, f and e, e
and g, h and g, h and f are also adjacent).d and
f are interior angles. These add up to 180
degrees (e and c are also interior).
Any two angles that add up to 180 degrees
are known as supplementary angles.The angles
around a point add up to 360 degrees.The angles
in a triangle add up to 180 degrees.The angles
in a quadrilateral add up to 360 degrees.The
angles in a polygon (a shape with n sides) add up
to 180(n - 2) degrees.The exterior angles of any
polygon add up to 360 degrees.   
9
Circle Theorems
10
Shapes
Parallelogram opposite sides are parallel,
opposite angles are equal, the diagonals bisect
one another.Rhombus (a parallelogram with all
four sides of equal length), diagonals bisect one
another at right angles.Trapezium One pair of
opposite sides are parallel.Square All sides
are equal, all angles are 90 degrees, diagonals
bisect one another at 90 degrees.Rectangle All
angles are 90 degrees, diagonals bisect one
another.
11
Transformations
12
Transformations
13
Area
14
Area
15
Expanding Brackets Brackets should be expanded
in the following ways For an expression of the
form a(b c), the expanded version is ab ac
i.e., multiply the term outside the bracket by
everything inside the bracket (e.g. 2x(x 3)
2x² 6x remember x x is x²) For an
expression of the form (a b)(c d), the
expanded version is ac ad bc bd, in other
words everything in the first bracket should be
multiplied by everything in the
second.ExampleExpand (2x 3)(x - 1)(2x
3)(x - 1) 2x² - 2x 3x - 3 2x² x 3
16
Pythagoras's Theorem In any right-angled
triangle, the square of the hypotenuse is equal
to the sum of the squares of the other two
sides.i.e. c² a² b² in the following
diagram
17
congruent
Basically, if two shapes are congruent, they are
the same (shape and size). It is often useful
to know whether two triangles are congruent.Two
triangles are congruent if any one of the
following is true -All three sides of one
triangle are the same length as all three sides
of the other triangle (i.e. a d, b f and c
e below) -Two of the angles and a side of one
triangle are equal to the corresponding two
angles and side of the other triangle (e.g. A
D, C E and a d) -An angle between two sides
of a triangle is equal to the corresponding angle
in the other triangle and the sides in question
are equal (e.g. C E, b f, a d) -Two right
angled triangles have the same hypotenuse and one
other equal side
18
(No Transcript)
19
Bearings A bearing is the angle, measured
clockwise from the north direction. Below, the
bearing of B from A is 025 degrees (note 3
figures are always given). The bearing of A from
B is 205 degrees.  
20
Finding the gradient of a straight-line
graph It is often useful or necessary to find
out what the gradient of a graph is. For a
straight-line graph, pick two points on the
graph. The gradient of the line (change in
y-coordinate)/(change in x-coordinate)  
21
Travel Graphs
22
Speed, Distance and Time The following is a
basic but important formula which applies when
speed is constant (in other words the speed
doesn't change) Speed distance               
time