Friday, November 15, 2013

EXCLUSIVELY FOR MY SPM 2013 MATHS STUDENTS

PREPARED BY CIKGU KUNG

For MARTIN PUDU, PERMAISURI AND PANDAN INDAH students.

Saya mendoakan anda mendapat gred cemerlang dalam Kertas 1441/2 kali ini.


 

Final Checklist b4 taking the 1449/1/2 paper – 98 ITEMS TO REVISE


 


 

Paper 1    You must remember :


 

Tick ( √ ) if u understand. Sekiranya anda tidak tahu atau sudah lupa sila rujuk kembali.


 

  1. Round off a number to 2 or 3 significant figures

    Be careful with the decimals like 0.006569 because 3 sf will make it as 0.00657 and not 0.01


     

  2. Express a number in standard form, A x 10 n


 

  1. express a standard form as a single number

    (Reminders 2 and 3 can use calculator).


     

  2. Solve linear equations in 1 variable eg 2x – 1/3 = 5x -2


 

  1. Express a base 5 number as a number in base 8

Remember the two steps, change to base 10 first, then to base 8.


 

  1. Add and subtract numbers in base 2 using calculator.


 

  1. Changing an expanded notation to a single number


 

  1. Express a base 10 number to base 8 using the division method.


 

  1. Sum of interior angles formula in polygons

    (Refer to my notes)


 

  1. Properties of rhombus, parallelogram, pentagon, hexagon, heptagon, octagon, nonagon and decagon.


 


 



 


 


 

  1. Sum of exterior angles in a convex polygon is 360º


 

  1. Number of sides in a regular polygon is 360º divide by 1 exterior angle


     

  2. Number of symmetries in a regular polygon is 360º divide by 1 exterior angle also


 

  1. When doing polygon questions, note every special characteristic or key words, like isosceles will mean 2 sides equal, equilateral will mean all equal sides and angles, regular will mean all sides equal….


     

  2. Know where is the angle between the tangent and a chord


 

  1. Know how to use the common tangent to solve problems on circles
  2. Translation must be defined by . Check which is the object before you proceed to find the image
  3. You must know how to find the centre of rotation and angle of rotation


 

  1. Reflection is the perpendicular line in the middle between the object and image


     

  2. Scale factor (k) is the length of the image ÷ length of the object.


 

  1. Recognize the graph of tangent, for tangent, cos and sine and the coordinates of the point of intersection between Sine and Cosine


 

  1. Pythagorean triples like 3,4 and 5 : 6, 8, and 10: etc


 

  1. Finding the value of tangent, cos or sine in a right angled triangle


 

  1. Where is the value of sin ө in the ordered pair of the unit circle


 

  1. Using "A S T C" to find the acute angles in the circle


 

  1. Naming the angle between a line and a plane in a cuboid


 

  1. Naming the angle between a plane and a plane in a pyramid/ prism


 

  1. Where mid points are given in the diagram, it must be used


 

  1. Angle of depression means from the top you look down


 

  1. Angle of elevation means from the bottom you look up


 

  1. Find the location of a place on the surface of the earth, ( latitude xoN/S , longitude yoE/W)


 

  1. Use ( ө x 60 ) to find the distance along the meridian/ longitude


 

  1. Use ( ө x 60 x cos latitude) to find the distance along the latitude


 

  1. Shortest distance is always along the North or South pole


 


 

  1. B is west of A means B is on the left


     

  2. In bearing, complete the isosceles or equilateral triangle if 3 points are given and draw up the north direction


 

  1. Use alternate angles and complete rotation to get the bearing from the point


 

  1. Bearing must be calculated starting from the North, clockwise and in 3 digits


 

  1. Be careful when the North is slanted. Draw properly.


 

  1. In algebraic formulae, the subject of the formula must always be positive value, single and preferably on the left. Skills like cross multiply, factorization and shifting must be used correctly.


 

  1. In algebraic expressions, know 4 types of factorization and expansion


 

  1. Addition and subtraction of algebraic fractions using LCM


 

  1. The 5 rules in Indices especially the bracket formula ( raising the formula)


 

  1. If you see the format of equation in Indices, make the base the same first in prime numbers


 

  1. In linear inequalities, the negative term on the right must always be changed to a positive term


 

  1. Mode is the most frequent data.


     

  2. Median is the middle value of an arranged data. Use (n+1) divide 2 to get the position of the median


     

  3. Mean is the average that is ( sum of mid points x frequency) divide by total frequency


 

  1. Calculate the sector angle in a pie chart


 

  1. Identify and draw any quadratic, reciprocal or cubic graph


 

  1. Know how to substitute a value into the given function


 

  1. In sets, list carefully the required elements before using union or intersection or prime to obtain the answer


 

  1. Unless bracket is given, solve the sets from left to right


 

  1. In the straight line, remember the 3 ways gradient is asked;
    1. From 2 points
    2. From the x and y intercepts
    3. From the parallel line


     

  2. Remember how to find the x intercept using y=mx + c or using –y intercept / x intercept


     

  3. The equation of the straight line besides y=mx+c can also be x=b or y=c


 

  1. Finding the probability of something means the answer must be in fraction or decimal


 

  1. Know how to find probabilities in card format and in table format


 

  1. In matrices, know how to add, subtract or multiply matrices


 

  1. No inverse means ad- bc =0


 

  1. In variations, varies directly as and varies inversely as sure to come out


 

  1. Be careful with cube or cube roots in Variations


 

  1. The constant value, k, must be obtained before any further calculations


 


 

Paper 2    You must remember :


 


 

  1. In shading the area represented by linear functions, know the correct area to shade- above the line means greater, below the line means lesser, on the right means greater, on the left means lesser, dashed line means not inclusive of the line


 

  1. In shading the area represented by sets, number every part first before you solve the question. Remember, union means all; intersection means only the same, prime means the complement and always solve the bracket first.


 

  1. Draw a Venn diagram to show the relationship between all the sets


 

  1. In solid geometry, volumes of shapes are given but for surface area the formula given may not necessarily be correctly used for example: total surface area of hemisphere is 3π² and not 2π²


 

  1. For composite (combined) solids, make sure you need to add or minus before you proceed.


 


  1. Naming the angle between a line and a plane

    The angle between the line AG and the plane ABCD is < GAC


     

  2. Naming the angle between a plane and a plane

    The angle between the plane EGCA and the plane EHDA is < GEH or < CAD


     


 



 


 

  1. Where mid points are given in the diagram, use them


 

  1. To calculate the angle, first write out the angle, example : ABC , then use trigonometry to calculate


 

  1. In mathematical reasoning, must know meaning of statement, converse, implication, conclusion, induction and deduction


 

  1. In simultaneous equations, make one coefficient the same first before you cancel it, and then substitute to find the answer. You can use elimination or substitution method


 

  1. In straight lines, parallel lines means same gradient, know how to find the equation with a gradient and a point, how to find the coordinate of the 4th vertex in a rhombus and the x intercept of an equation


 

  1. In quadratic equations, arrange to the order of before you solve for x.


     

  2. In matrices, a matrix with no inverse means ad-bc = 0, the determinant is ad-bc and the inverse means, where i is the inverse.


 

  1. In calculating sector area, get the radius correct, the angle and then see whether you need to add or minus


 

  1. In calculating perimeter, is it whole diagram or shaded area, follow the requirement


 

  1. In probability, must know how to calculate :


     

    1. one card taken at random and two cards taken at random : the meaning of " at least one card " and "both cards "
    2. list the possible outcomes
    3. meaning of 'and' and 'or'


 

  1. In distance time graph, in finding the distance, refer to the y axis and for time taken refer to x axis. Average speed , length of time and total distance calculations .


  2. In the speed time graph, area under the graph is the distance travelled.


 

Must know rate of change of speed, uniform speed and distance travelled.


 


 


 

  1. Translation must be defined by .
  2. Reflection along the line y = - x
  3. Rotation of an object
  4. Enlargement, scale factor ½ about centre O
  5. In functions remember how to draw a suitable straight line !


 

  1. Practice drawing a smooth curve as this may affect your answers


 

  1. Which one is the frequency polygon? And which one is the Histogram?


  1. Know how to draw an Ogive


 


 

  1. Know Upper quartile, median, lower quartile and interquartile range


 


 

  1. To draw plan and elevation, view like this
  2. Dashed lines ( dotted lines ) are hidden lines which must be drawn


 

  1. Location of a point on the Earth is written as ( latitude , longitude )


     

  2. Diameter of the Earth means the line must pass the centre of the Earth


     

  3. Diameter of the parallel of Latitude means just opposite along the same latitude


     


 

  1. Latitude is either x º N or x º S. Longitude is either y º W or y º E


 

  1. Distance along of the parallel of latitude is calculated by using


 

θ x 60 x cos of that latitude


 


  1. Distance along the meridian is calculated by using


 

θ x 60


 


 


 

35. Speed of an airplane is distance ÷ time


 


 


 


 

GOOD LUCK. MAY THE FORCE BE WITH YOU.

Saturday, October 5, 2013

Go! Go! Go!


final maths checklist 2013. GOOD LUCK!

CHAPTER 1 WHOLE NUMBERS
Identifying a number rounded off  to the nearest thousand 
Identifying a seven digit number in words, e.g. 3 634 001
Identifying  the digit value for a particular digit in the number
Solving combined operations of +,-,x ,÷  and brackets using BODMAS
CHAPTER 2  NUMBER PATTERNS AND SEQUENCES
Sequences of prime factors in ascending / descending order
Number Patterns
LCM and HCF
Common Multiples
CHAPTER 3  FRACTIONS
Solving combined operations of +,-,x ,÷  and brackets using BODMAS
Problem solving using the tree diagram
Ascending or descending order in a given set of fractions
CHAPTER 4 DECIMALS
Identifying a decimal on a number line
Solving combined operations of +,-,x ,÷  and brackets using BODMAS
CHAPTER 5 PERCENTAGES
Finding the value when a percentage of a number is given
Calculating bank interest with principal, time and rate.
CHAPTER 6 DIRECTED NUMBERS
Able to identify a number on the number line
Solving combined operations of +,-,x ,÷  and brackets using BODMAS
CHAPTER 7 ALGEBRAIC EXPRESSIONS
Factorise completely involving common factors and difference of two squares
Factorise completely perfect squares
Expressing as a single fraction in its lowest term
CHAPTER 8 BASIC MEASUREMENTS
Calculating remaining length in metres and cm after some is being used
Solving  using the 24 hr system
CHAPTER 9 LINES AND ANGLES
Identify corresponding angles, then interior angles.
CHAPTER 10 POLYGONS
Calculating  the value of x in a combination of isosceles triangle and quadrilateral
Number of sides in a regular polygon
Using (n-2) x 180º  to solve interior angles of a polygon
Focus on hexagon and octagon.
CHAPTER 11 PERIMETER AND AREA
Perimeter of the whole diagram involving rectangles and rhombus
Area of the shaded region involving triangles and rectangles
CHAPTER 12 SOLID GEOMETRY
Nets of  geometric solids like prism, cube and pyramid
Volumes of pyramid, sphere, hemisphere and cone 
CHAPTER 13 SQUARES, CUBES, SQUARE ROOTS AND CUBE ROOTS
Solving combined operations of cube and square roots  and brackets using BODMAS
Finding the values of the cube root of a decimal
CHAPTER 14 LINEAR EQUATIONS
Solving Simultaneous Linear Equations using Elimination or Substitution method
Solving Linear Equations using substitution method
CHAPTER 15 RATES, RATIOS AND PROPORTIONS
Solving ratios in 2 quantities
Finding the value of one quantity when the other is given
CHAPTER 16 PYTHAGORAS THEOREM
Using the 6 sets of Triples to solve length or area of rectangle or rhombus
CHAPTER 17 GEOMETRICAL CONSTRUCTIONS
Constructing a 45º followed by a 90º in a quadrilateral
Measuring the length of a perpendicular line after construction
CHAPTER 18 COORDINATES
Calculating the mid points of 2 pairs of coordinates.
Calculating the distance using distance formula or diagram
CHAPTER 19 LOCI IN 2 DIMENSIONS
stating a locus by using the letters , focus on arc/circle
Drawing the locus of an angle bisector.
remember what these lines look like ; horizontal line, vertical line, slant line, circle, arc, curve and ellipse.
CHAPTER 20 CIRCLES I,II
Calculate the length of arc of  a circle.
Calculate the perimeter of the whole diagram / shaded region
The 4 important theorems
CHAPTER 21 TRANSFORMATIONS
Describe / draw image under a  Translation in full
Describe / draw image under a Rotation in full
Describe / draw image under a  Reflection in full
Describe / draw image under an Enlargement in full and calculate the image area
CHAPTER 22 STATISTICS
Mode, the 6 types
Median, the two types
Mean, the two types
Bar chart
CHAPTER 23 INDICES
Calculate the value of x in an equation
Using the bracket formula to start solving the indices expression
CHAPTER 24 ALGEBRAIC FORMULAE
Expansion and cross multiplication technique
Solving with factorisation and shifting
CHAPTER 25 SCALE DRAWINGS
Drawing an image using a scale of 1: 3 or 1:1/2
Calculating the length in similar shapes.
CHAPTER 26 GRAPHS OF FUNCTIONS
Free hand drawing of a quadratic or reciprocal graph
Calculating values from a given table
Identifying the correct linear graph
CHAPTER 27 LINEAR INEQUALITIES
Solve a given inequality and list the integer values.
Solving Simultaneous linear inequalities
Identifying the correct number line 
CHAPTER 28 TRIGONOMETRY
Must apply triples and scale factor to triangles.
Remember Sine, Cosine and Tangent ratios
Finding the length of a side.

Tuesday, November 13, 2012

FORM 2 FIRST LESSON

PYTHAGORAS THEOREM
ANSWERS
1B
2B
3C
4B
5A
6C
7A
8A
9D
10B
11C
12B
13C
14C
15A
16B
17B
18C

Wednesday, November 7, 2012

GOOD LUCK!


spm 2012 reminders







Sunday, November 4, 2012

Working for SPM seminar 2012 (paper 1)