Math Trick

Try solving this using algebra. :)
(Courtesy of Wenxin)

1. First of all, pick the number of times in a week that you would like to go out to eat. (a number more than 1 but less than 10)
2. Multiply this number by 2.
3. Add 5.
4. Multiply it by 50.
5. If you have already had your birthday this year add 1758. If you haven't, add 1757.
6. Now subtract the 4-digit year that you were born in. You should have a three digit number.

The first digit of this was your original number. (I.e., how many times you want to go out to eat in a week.)

The next two numbers are YOUR AGE !

THIS IS THE ONLY YEAR (2008) IT WILL EVER WORK!

U10: Volume

Key Learning Points:

• Volume = Length x Breadth x Height


• Sometimes, base area or area of one side of the container is given instead. Thus Volume = Area x Height


• A square box is a cube. There are 6 (square) sides and all the sides have the same length.


• 1 litre = 1000 ml or 1000 cm-cube

Do be familiar with your multiplication table:

• 1 x 1 x 1 = 1
• 2 x 2 x 2 = 8
• 3 x 3 x 3 = 27
• 4 x 4 x 4 = 64
• 5 x 5 x 5 = 125
• 6 x 6 x 6 = 216
• 7 x 7 x 7 = 343
• 8 x 8 x 8 = 512
• 9 x 9 x 9 = 729
• 10 x 10 x 10 = 1000
• 11 x 11 x 11 = 1331
• 12 x 12 x 12 = 1728

U9: Area and Perimeter

Key Learning Points:

• Perimeter = Add up all the exposed sides
  
• Area of Rectangle = Length x Breadth
  
• Area of a Square = Length x Length
  
• Area of a Triangle = 1/2 x Base x Perpendicular Height
  
• Area of a Circle = 'pi' x radius x radius
  
• Break up the irregular figure into shapes which you are familiar with.
  
• Fill up the missing dimensions.
  
• Apply the respective area formulae.
  
• Add up or subtract the areas (depending on the questions)

Do be familiar with your multiplication table:

• 1 x 1 = 1
• 2 x 2 = 4
• 3 x 3 = 9
• 4 x 4 =16
• 5 x 5 = 25
• 6 x 6 = 36
• 7 x 7 = 49
• 8 x 8 = 64
• 9 x 9 = 81
• 10 x 10 = 100
• 11 x 11 = 121
• 12 x 12 = 144

U8: Pie Charts

Key Learning Points:

• A complete pie chart represents one (1) whole of the data being measured.
  
• It can also mean 100% of the data which it is measuring on.
  
• Like a circle, the complete pie chart will have 360 deg angles in the centre.
  
• Thus the size of a pie chart slice can be measured by its angle. For example: A 90 degree angle of a slice of pie chart would mean 90/360 = 1/4 (1 quarter).
  
• Read the questions carefully. They may be asking for actual data figures, fractions, percentages or even ratios.

Circles and friends

The first person to give me the correct lyrics of this song shall earn 50 points for his/her group!

U7: Circles

Key Learning Points:

• The diameter of a circle is a straight line that starts from one point on the circle's perimeter, cutting through the centre of the circle and reaching the other point on the perimeter.
• The radius is a straight line drawn from the centre of the circle to the perimeter of the circle
• Thus 2 x radius = diameter
• Circumference is the perimeter of a circle
• Circumference = 'pi' x diameter or 'pi' x (2 x radius)
• 'pi' is generally taken to be 22/7 or 3.14 (questions will tell you which 'pi' to use)
• Area of a Circle = 'pi' x radius x radius

Generally, be careful with the units in this topic and if possible, try to use 'pi' as 22/7 as it is neater and does not contain decimals.

U6: Time & Speed

Key Learning Points:

(A) Time

• Time is like the name given to any moment. E.g. 4.45p.m., 9.45a.m. etc
• It is fixed at any one time
• It can be written in the 12 hour clock or 24 hour clock
• In the 24 hour clock, 0000 is midnight, that is, the start of a new day. Thus in the 24 hour clock format, the time starts from 0000 to 2359.
• Duration is a measurement of how much time an activity takes. E.g. 1h, 5h 30 min, 45s, 38min etc
• NEVER add or subtract time and duration together as they are 2 different things! E.g. 1.45pm + 15min = 2pm WRONG!!>
• When dealing with time and duration, always draw a timeline to represent your workings

(B) Speed

• This means how fast an object or person is travelling at any unit (1) time
• Distance = Speed x Time
  
• Before you apply the formula, always make sure that the units of each of the above parts are 'talking' to each other.
• Meaning to say, if speed is given as km/h, make sure that the distance must be in 'km' and time in 'h'. (Do the necessary conversions e.g. 1km = 1000m and 1h = 60min)
• After solving for the answer, double check that your answer has the same unit as what the question wants. E.g. if the question wants you to give time in hours, make sure you convert your time from minutes to hour.
• When finding Average Speed, find the total distance and divide it by the total time taken.

This topic is not that difficult as long as you are very careful and alert with the units and the way you present your workings. All speed questions must have these 3 parts (Distance, Speed, and Time). All you need to do is to find them, make sure the units 'talk' to each other and apply the formula and some common sense into it.

U5: Percentages

Key Learning Points:

• You can treat them as fractions that are out of a whole of 100 (that is, 58% means 58 out of 100 parts).
• This also mean that the denominator of the fraction is 100.
• If you see questions involving percentages, you can change them into fractions by removing the '%' sign, then add a denominator '100' (that is, 88% = '88/100').
• Thus if a question say 20% of 40 pupils, it will mean '20/100' of 40 pupils, or when simplified, it means '1/5' of 40 pupils.
• Alternatively, you can convert a fraction or a decimal to a percentage by multiplying it by 100%, with the '%' symbol in your working. Else the working will be marked wrong.

U4: Ratio

Key Learning Points:

(This is just to reinforce what that was learnt back in your P5 Math) Ratios are similar to fractions. The only difference lies in the comparison of parts to parts whilst in fractions, it is always parts to a whole.

• Always simplify your ratios (just like fractions).


• In your workings, give a heading to your ratios so that you know which parts you are comparing against with.


• When changing the ratios to equivalent ratios, make sure you either use the arrow sign or the equal sign.


• Do not write 2 ratios 'floating' in your working statements. You must show how they are related.

U3: Solids and Nets

Key Learning Points:

• Know the spellings of the various 3 dimensional solids.


• A cube has 6 faces and each face is a square. Thus all sides are of the same length.


• A cuboid has 6 rectangular faces. However, 2 of the sides can be squares.


• A prism can have a minimum of 5 sides. The 2 ends (either top or bottom) have the same shape and are parallel to each other.


• A pyramid can have a minimum of 4 sides. The base can be a triangle, square or rectangle. However the other faces on top must be triangles.


• A cylinder is similar to a prism but has 3 sides. The 2 parallel ends are circular in shape. The 3rd side is cylindrical / rounded in shape.


• Nets are figures that when folded, can form either one of the solids above.


• Given a Net or Solid, count the number of sides. Make sure that both numbers tally before matching them together.

U2: Angles in Geometric Figures

Key Learning Points:

The main properties are:

Simple straight lines

1. Sum of angles on a straight line is 180 deg.

2. Vertically Opposite Angles are equal (formed by 2 straight lines crossing each other like a big X).

3. Angles at a point adds up to 360 deg.

Triangles

4. Angles inside a triangle adds up to 180 deg.

5. Exterior angle is equal to the sum of the internal opposite angles.

6. Angles in an equilateral triangle are equal and each angle is 60 deg.

Parallelograms & Rhombuses

7. Internal opposite angles are equal.

8. Sum of the 2 angles bounded between 2 parallel lines adds up to 180 deg.

9. Sum of all angles inside a 4-sided figure (with at least a pair of parallel lines) is 360 deg.

Tips on solving questions:

• Highlight (on the diagram) the angles which you are required to find.
• Look out for the little square which indicates a 90 deg. Write down 90 deg above the square.
• Highlight all the straight lines (think about / spot rules 1 and 2).
• Highlight all the little straight lines on the triangles that indicates an isosceles or equilateral triangles (think about rules 5 and 6).
• Highlight all the arrows that indicate parallel lines (think about rules 7, 8 and 9).
• When dealing with rhombuses, think in terms of combining 2 isosceles triangles together.

U1: Algebra

Key Learning Points:

• Algebra is a method of solving Math problems. It uses alphabets to represent unknown numbers.
  


• Remember: they are still NUMBERS (it is just that they are unknown to you), so do still treat them the way you treat any number in your workings.
  


• For multiplication, 'marry' the numbers together and write the number in front of the alphabet. (E.g. 4 x y = 4y and not y4)
  


• For addition and subtraction involving known numbers, use brackets to 'group' them together if they are sharing the same unit. (E.g. w apples + 6 apples = (w+6)apples)



• When 0 multiplies any number (including algebraic numbers), answer will always be 0 (E.g. 0 x m = 0 and not 0m; similarly 4h - 4h = 0 and not 0h)