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What should I not do ?

Do not just read through your Maths text book or the Credit Revision Notes. If you do, you will just convince
yourself you are revising, but it will be ineffective.

How should I revise ?

With paper and pencil.

By all means look at the text book, or the Credit Revision Note. You should read the relevant sections and then
Make Notes, to summarise the essential points. You should also Try the Examples, to make sure you
understand what is going on.

Practice using Past Papers - When you have finished them - do them again.
The more times you go over them, the more readily you will recognise the type of question.

If you need more practice in a certain area - use the Past Paper Questions by Topic booklet.
Watch out for the remaining solutions being posted on this site for download.

If you are not sure how to do a question, look at the solution. Copy it out carefully, trying to understand the
processes involved. Then immediately, try and do it again yourself, without the solution. You may wish to look
up the relevant topic in the Credit Revision Notes booklet or your Maths text book.

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What topics should I concentrate on ?

Whilst it is not advisable to try to second guess the SQA as regards what questions are likely to be on this
year's paper, from looking at past papers it is fairly clear on which topics the SQA tend to favour questions.

Below is a list of topics together with brief description giving a suggested order for revision. If you work down this
list and make sure that you feel confident at both Recognising the Question and also being able to do it,
you will be well on your way.

The topics towards the end of the list are generally more difficult, but in many cases this is where the bulk of
the RE marks come from.

Topics near the beginning of the list are the easier KU questions, which you should already be confident with.

This list shows all the topics that have come up previously, and whilst every topic will obviously not come up this
year, these will no doubt form the bulk of the paper.

For pupils who find the work difficult, start at the top and make sure you are comfortable with each topic as
you work your way down, they are in general graded by level of difficulty. The further down the list you can get to,
the more marks are available to you. You may feel that you have to leave a particular topic if you cannot really
get to grips with it.

Do not spend an excessive amount of time on any one topic, if you really cannot understand it, then put your
efforts into an area where you can make progress.

To achieve a good grade at credit level, you should be able to cope with most of the topics below. If you
need help, use the email link provided.

Good Luck !


1.   Decimals, Fractions, Percentages:

Decimal
Calculations
  

BODMAS
     Knowing the order of calculatons, multiply and divide before add or subtract

Using a calculator
     
know how to use powers, roots, brackets.

Addition, subtraction, multiplication, division

Simple powers and roots

Being able to use brackets to aid calculations.

 
Fractions

Adding and subtracting
        Using the common denominator

Multiplication
        Do any cancelling, then multiply numerators (top), multiply denominators (bottom)

Division
        invert second fraction and change to multiply

Remember 'of' means multiply.

Changing mixed numbers to improper (top heavy) fractions

Changing improper fractions to mixed numbers

 
Percentages

Find percentage of a quantity without a calculator.
     Find 10% and 5%, then combine. e.g. 35% = 3 x 10% + 1 x 5%

Find percentage of a quantity using a calculator.
      Change percentage to a decimal and multiply. 7% =  fraction

Using percentage multipliers for increasing and decreasing a value.
      e.g. increase of 15% multiply by 1.15; decrease of 12% multiply by 0.88

Calculating appreciation and depreciation.

 
Reversing
the change

Finding the price without VAT.    p x 1.175 = price with VAT
     Divide inclusive price by 1.175

Finding an original price when you know how much it has reduced in value.
     e.g. new price of £72 is 40% less than the original price.
            original price = £p,   then    p x
0.6 = 72.     Thus     p = 72/0.6   = £120

Finding an original price when you know how much it has increased in value.
     e.g. new price of £104 is 30% more than the original price.
            original price = £p,   then    p x
1.3 = 104     Thus     p = 104/1.3   = £80

 
Standard
Form


Writing a large or small number in standard form
     e.g. example

Calculations involving standard form - usually multiplying or dividing.

      e.g. a container of rock weighs example gm,
what would 18 containers weigh?   
                              
                                                                                               answer

Calculations may involve distance, speed or time.
      e.g. Light travels at  example  km/sec and Neptune is  example  km from the sun,
            How long does it take light from the sun to reach Neptune
            Give your answer to the nearest hour.
                                  [ Ans.   4 hours  ]

Calculations can also involve circumference of circles
      e.g. Neptune is 
example  from the sun, assuming Neptune travels in a circular orbit,
            What is the length of Neptunes orbit.

answer



2.   Algebra
Evaluation of
an expression
Substituting given values into an expression
and evaluating it.

     e.g. if u = 5,  v = -3  and w = -1, evaluate  example         [ Ans.   16 ]
 
Simplify
expressions
with brackets

Multiply out any brackets and group like terms.

      e.g.   Simplify:   example                               [Ans.  26x - 20 ]

 
Difference of
2 squares

Recognise difference of two squares and be able to factorise

     e.g.     basic type              example

                with multipliers        example

                with common factor   example

 
Common
factors

Factorising using common factors.

     e.g.   factorise  example      

               factorise    example

 
Factorisation
of a trinomial
(quadratic)

Putting a trinomial (quadratic expression) into two brackets

     e.g.   factorise   example

              factorise   example

 
Solve linear
equations

Solving simple linear equations with one unknown.

     e.g.     2(x + 3) - 5 = 3(1 - 2x)                                    [ Ans.   x = 1/4 ]

 
Functions

Evaluating functions

      e.g. Given   example  evaluate  f(-2)
              (Replace the x with -2 and evaluate)                                       [ Ans.  13 ]

Evaluating by using the function in reverse

      e.g. Given  example     Find a
             Replace the x with a and replace f(a) with -7                       [ Ans.  a = -2 ]

 
Solve
quadratic
equations

Factorise using a common factor
     e.g.  example                     [ Ans.  x = 0 or x = 2 ]

Factorise a trinomial - into two brackets
     e.g.   
example             [ Ans.  x = -3 or x = -2 ]

Use the formula   quadratic formula
     e.g.     example      a = 2,  b = -5,  c=1         [ Ans.  x =2.3 or x = 0.2 ]
     
The formula type can be identified by the question asking you to solve it
correct to 1 decimal place
or 2 significant figures etc. (an approximation)

 
Solving
inequalities

Treat these exactly the same as equations, but use the inequality signs.

If you multiply or divide by a negative number, you MUST change the
direction of the inequality sign.

e.g.   Solve    example

e.g.   Solve   example

          Note the change in the direction of the sign as a result of divding by  -7

 
Changing the
subject of the
formula

These formulae may involve brackets, fractions, roots and powers.

  • Get rid of any fractions first.
  • Multiply out any brackets
  • Put the required subject on the left hand side of the equation
  • Use standard rules of algebra - do the same to each side of the equation.

Example:     If   example   change the subject of the formula to V

                 example

 
Algebraic
Fractions

Find a common denominator
Put each fraction over this
Combine the fractions and simplify

Example:   example

          example

 
Algebraic
Fraction
Equations

Find a common denominator

Multiply throughout by the common denominator

Make sure you multiply EACH term.

Straight line form, re-arrange, solve.

Example:       Solve         example

               Common denominator is 6, so multiply throughout by 6 (or cross multiply)

example

 
Simultaneous
Equations


Form two equations to model a problem.

Multiply one or both equations by a suitable number to make one of the
unknown variables have the same number in front of it (coefficient).

Add or subtract the equations to reduce to a simple equation with one
unknown.

Solve this equation.

Substitute into either of the original equations to find the other unknown.


 
Indices This will be added later when it is dealt with in the course
 
Surds This will be added later when it is dealt with in the course
 
Algebra is a very important section - make sure you are confident on it.
3.   Data Handling

Simple Probability

Everyday situations.

Common sense approach will work with these questions.

Write down the basic fraction and then SIMPLIFY it

 
Probability
from
Relative Frequency

Using a table of data

Description often involves AND / OR

Common sense approach will work with these questions.

Watch your arithmetic

 

Boxplots,
5 figure
Summary


Stem and Leaf
diagrams

Pie Charts

These are a new addition to the SQA syllabus only appearing from 2001.

Any or all of these are likely to come up.

Again, mainly a common sense approach providing you know your quartiles,
and can calculate angles for a pie chart.

 
Standard
Deviation

Make sure you know how to draw up the table.

You can probably get away with just knowing how to use the simple formula
.

However, both formulae will be given on your formula sheet.

standard deviation formulae

Watch your arithmetic, when you have finished, check it again.

You m ay be asked to make comparison with other data.

 
Comparisons

When asked to compare two distributions, the examiner is looking for
comments about the consistency or variability of the data as well as
comparing the mean or median.

How spread out are the two data sets.

 
4.   Area and Volume
Cylinder

A cylinder is a circular prism

Volume of a cylinder      cylinder

Curved surface area of a cylinder    formula

 
Prisms

Volume = Area of cross section x length

The cross section will often be a composite shape made up of:

Rectangles, triangles, trapezium, semi-circle

 
Applications

Sometimes you are asked to work out the height (or length) of a prism from
the volume and cross-sectional area.

Often this may be related to a cylinder and a cuboid having the same volume.

 
5.   Similar Shapes and Similar Triangles
Using
Area and Volume
scale factors

Area scale factor = linear scale factor squared.

Volume scale factor = linear scale factor cubed.

Make sure you get the scale factor the right way round.

Enlargement   > 1          Reduction  < 1

The final size goes on the top of the fraction.

 



Similar
Triangles


Finding
sides
in triangles.

Buildings

Roofs

Roads


Showing two triangles are similar
Triangles are equiangular - triangles are similar.

Ratios of corresponding sides are equal.

Put the side you are trying to find on TOP of the fraction.
Cross multiply and solve the simple equation.

Parallel lines in triangles

Finding part of a side where you need to find the whole side first

Example:

Triangles ADE and ABC are similar. Find DE.

            eqwuation

                           equation 2

diagram

Example:

Triangles ADE and ABC are similar. Find DB.

equation

equation

Thus: DB = AB - 5 = 4

diagram

Example:

Triangles ADE and ABC are similar. Find AD.

Let AD =  x

equation

equation

So AD = 3

diagram
 
6.   Pythagoras in the circle

Milk and Oil
tanks

Bridges

Sheep
Shelters

Barns

Look for the right angled triangle.

Chords, symmetry, isosceles triangles

Look for lengths equal to the radius.

Draw your triangle and fill in lengths of sides.

Form an expression for Pythagoras.

 
7.   The Circle

Length of
an arc

Area of
a sector

Perimeters of
tables

Angle Properties of the circle
Angle in a semi-circle, tangents at 90° to radius, Chords, symmetry, isosceles triangles,
SOH-CAH-TOA

Finding fractions of a circle

360° degrees in a circle

Proportion of circumference or area

 
8.   Trigonometry   SOH-CAH-TOA

Right angled
triangles

Trees

Telegraph
poles

Ramps

Buildings

Finding sides and angles

Often need to find another side or angle, before you can complete
the question.

 
9.   Trigonometry   Non-Right angled triangles

Ships and
bearings

Heights of
satellites

Aeroplanes

Balloons

Areas of fields

Sine Rule sine rule
Cosine Rule formula
Area of a triangle Area  =  formula

Sometimes need to find the height of an aeroplane, satellite, balloon.
Use sine or cosine rule and then SOH-CAH-TOA

In some cases you have to find another side or angle before you can find
the one you want.

Could be given the area of a triangle and you need to find the angle.

 
10.   Simultaneous Equations

Tiles

Tickets

Bricks

Hotels

Form two equations to model a situation.

Solve them simultaneously, by elimination

Sometimes use your solution in a final part of the question

 
11.   Ratio & Proportion

Ratios of:

People

Components

Ingredients

Use proportion to answer a question

May be a ratio between 2 or 3 quantities.

 
12.   Variation & Proportion

Direct

and

Inverse
Proportion

often science
based

Using a proportionality statement to make an equation.

Finding the constant.

Using the equation to calculate a quantity.

OR

Using a proportionality statement to make an equation.

Halving or doubling variables to deduce what happens to the subject of the
formula.

Joint Variation - proportionality with more than one variable.

 
13.   Gradients and Straight Line Modelling

Finding
gradient

Finding
equation

Line of
best fit

Using
equation

Interpretation
of model

Using gradient = Rise over Run or gradient formula.

Using   y = mx + c
      
Where m is the gradient and c is the y-intercept

Finding where line cuts the axes (when x = 0, or  y = 0)

A point which lies on a line, satisfies the equation of the line.

Using line of best fit to predict a mark or value

 
14.   Making and using formulae

Reading
information
from a table

Deducing a
rule to
calculate a
quantity not
in a table

Making formula to model a situation.

Using a formula.

Having to change the subject.

Solving equations - quadratic or linear

 
15.   Functions and the Parabola

Properties of
the Parabola

Using the
Parabola
as a model

Finding where the parabola crosses the x and y axes.
(Crosses x axis when y = 0 and  crosses y axis when x = 0)

Finding the roots of the equation.
Put into two brackets - or use common factor

Maximum and minimum points.
Look for symmetry - line of symmetry lies half way between the two roots.

A point which lies on a curve, satisfies the equation of the curve.

Making a model with a quadratic equation (parabola)

Solving the equation and interpreting the solution.

Negative coefficient of x squared                   Positive coefficient of x squared

           graph                                                graph

 
16.   Trigonometry - Graphs and Equations

Graphs of
Trig functions

 

Solving Trig
equations

Finding constants a and b   in   y = a sin bx + c   and   y = a cos bx + c
a = amplitude:   distance from centre line to top (or bottom) of wave.
b = frequency:   number of complete waves in 360 degress.
c = centre:        location of the centre line of the wave.

Maximum and minimum of a trigonometric function and Applications

Solving simple Trig equations
Using All Sinners Take Care to deduce which quadrants the solutions are in

 
17.   Sequences

Sequences of:

Squares
Cubes

Odd numbers

Even numbers

Writing down terms in the sequence

Writig down the sum of a number of terms

Forming an expression for the nth term

Forming the expression for a sum

Proving an expression is always odd/even etc.

 

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