Your SlideShare is downloading. ×
0
ANSWERING TECHNIQUES ADDITIONAL MATHEMATICS SPM  PAPER 1
<ul><li>CONTENTS OF THE SYLLABUS </li></ul><ul><li>FORMAT OF THE EXAMINATION PAPERS </li></ul><ul><li>EFFECTIVE TECHNIQUES...
CONTENTS OF THE SYLLABUS
CONTENTS CORE PACKAGE ELECTIVE PACKAGE
STATISTICS TRIGONOMETRY CALCULUS ALGEBRA GEOMETRY CORE  PACKAGE
<ul><li>Differentiation </li></ul><ul><li>Integration </li></ul>Calculus <ul><li>Coordinate Geometry </li></ul><ul><li>Vec...
<ul><li>Statistics </li></ul><ul><li>Permutation and Combination </li></ul><ul><li>Simple Probability </li></ul><ul><li>Pr...
ELECTIVE PACKAGE Applied Science And Technology Social Science Application Of Index Number Linear Programming Solutions of...
FORMAT OF PAPER 1  ADDITIONAL MATHEMATICS SPM
<ul><li>Type of instrument: Objective </li></ul><ul><li>Type of item: Graded objective </li></ul><ul><li>(Item requires ca...
Item of Knowledge and Understanding <ul><li>Does not involve complicated calculations </li></ul><ul><li>Measures the abili...
Item of Application  Skills <ul><li>Measures the ability of candidates to </li></ul><ul><ul><ul><li>carry out the calculat...
EXAMPLES OF ITEMS 3472/1
<ul><li>The first term of a geometric progression is 3  </li></ul><ul><li>and the common ratio of the geometric </li></ul>...
Diagram1 shows the graph of the quadratic function   y  = ( x  +  b )  2  +  c . State the values of  b  and  c .   [2 mar...
Application Skills <ul><li>Given  ,  find the value of  n. </li></ul><ul><li>  [3 marks] </li></ul><ul><li>Answer:…………………....
<ul><li>On the axes provided in the answer space, </li></ul><ul><li>sketch the graph of y =   sin2 x      </li></ul><ul>...
RANGE OF TOPICS IN PAPER 1
<ul><li>ALL the topics in the syllabus except  </li></ul><ul><ul><li>- topics from the AST and SS Packages </li></ul></ul>...
Marking Scheme <ul><li>Full marks are given to the correct answers. </li></ul><ul><li>However, if the answer is wrong, mar...
Example <ul><li>The quadratic equation x(x + 1) = px – 4  </li></ul><ul><li>has two distinct roots. </li></ul><ul><li>Find...
TECHNIQUES OF ANSWERING
<ul><li>Start by answering the easy questions first. </li></ul><ul><li>Answer according to the requirements of the questio...
<ul><li>1.  Given  and  , </li></ul><ul><li>find  in the form  </li></ul><ul><li>Answer: </li></ul><ul><li>or </li></ul>
<ul><li>2.  The quadratic  p x ² + q x  +1= 0 has two equal roots. Express p in terms of q. </li></ul><ul><li>q = 2√p </li...
<ul><li>Answer according to the instructions of the question.  </li></ul><ul><li>(This determines the method that must be ...
<ul><li>Understand the key words </li></ul>Given  , find   f´´(x)  Find the values of  m  and  n Example Find Determine Ca...
PRESENTATION OF  ANSWERS
<ul><li>READABLE  </li></ul><ul><li>AND  </li></ul><ul><li>NEAT </li></ul>HANDWRITING
<ul><li>Workings must be shown clearly </li></ul><ul><li>Common mistake: Answers without workings. </li></ul>
<ul><li>Answer : 7  [0 mark] </li></ul><ul><li>2 + 7 + 9 + 15 +  x  = 12 </li></ul><ul><li>5 </li></ul><ul><li>33 +  x  = ...
<ul><li>Final answer must be in simplified form. </li></ul><ul><li>Common mistakes: </li></ul><ul><li>;  2 x 2  – 4 x  + 6...
<ul><li>Solutions involving    ,answers can be given in terms of    , unless stated  </li></ul><ul><li> “ Using    = 3....
<ul><li>Precision  </li></ul><ul><li>Answers involving decimal numbers must be rounded off to 4 significant numbers. </li>...
<ul><li>Solve the equation 3cos 2 x  = 8sin x  – 5  for 0       x     360  </li></ul><ul><li>[3 marks] </li></ul><ul><...
<ul><li>Solve the equation 4 2x    1  = 7 x </li></ul><ul><li>[4 marks] </li></ul><ul><li>(2 x  - 1   )lg 4  =   x  lg 7 ...
<ul><li>Solve the equation 4 2x    1  = 7 x </li></ul><ul><li>[4 marks] </li></ul><ul><li>1.677 </li></ul><ul><li>B3 :  <...
More Common Mistakes
<ul><li>Graph of Trigonometric Function </li></ul><ul><li>On the axes provided in the answer space, sketch the graph of y ...
y 3  x 0 y 3  x 0
<ul><li>Progression </li></ul><ul><li>Find the ninth term of the arithmetic progression  </li></ul><ul><li>7,4,1,… </li></...
<ul><li>Functions </li></ul><ul><li>Defining functions. </li></ul>Condition for the function to exist must be written
<ul><li>Quadratic functions  </li></ul><ul><li>Quadratic inequalities </li></ul>
<ul><li>Quadratic Equations </li></ul><ul><li>Solving quadratic equations using the formula. </li></ul>Make sure ‘= 0’ is ...
IN THE  EXAMINATION HALL
<ul><li>The use of non-programmable scientific calculator is allowed. </li></ul><ul><li>Any valid method can be used to so...
<ul><li>Do not waste time  sketching  a graph. </li></ul><ul><li>Give only one answer in the answer space.   </li></ul><ul...
Example <ul><li>A badminton team consists of 7 players. The </li></ul><ul><li>team will be chosen from a group of 8 boys  ...
Upcoming SlideShare
Loading in...5
×

Pp smi add. maths paper 1

3,914

Published on

answering technique for paper 1 add maths

Published in: Education
0 Comments
3 Likes
Statistics
Notes
  • Be the first to comment

No Downloads
Views
Total Views
3,914
On Slideshare
0
From Embeds
0
Number of Embeds
1
Actions
Shares
0
Downloads
162
Comments
0
Likes
3
Embeds 0
No embeds

No notes for slide

Transcript of "Pp smi add. maths paper 1"

  1. 1. ANSWERING TECHNIQUES ADDITIONAL MATHEMATICS SPM PAPER 1
  2. 2. <ul><li>CONTENTS OF THE SYLLABUS </li></ul><ul><li>FORMAT OF THE EXAMINATION PAPERS </li></ul><ul><li>EFFECTIVE TECHNIQUES OF LEARNING </li></ul><ul><li>TECHNIQUES OF ANSWERING </li></ul>
  3. 3. CONTENTS OF THE SYLLABUS
  4. 4. CONTENTS CORE PACKAGE ELECTIVE PACKAGE
  5. 5. STATISTICS TRIGONOMETRY CALCULUS ALGEBRA GEOMETRY CORE PACKAGE
  6. 6. <ul><li>Differentiation </li></ul><ul><li>Integration </li></ul>Calculus <ul><li>Coordinate Geometry </li></ul><ul><li>Vector </li></ul>Geometry <ul><li>Functions </li></ul><ul><li>Quadratic Equations </li></ul><ul><li>Quadratic Functions </li></ul><ul><li>Simultaneous Equations </li></ul><ul><li>Indices and Logarithms </li></ul><ul><li>Progressions </li></ul><ul><li>Linear Law </li></ul>Algebra Topics Component
  7. 7. <ul><li>Statistics </li></ul><ul><li>Permutation and Combination </li></ul><ul><li>Simple Probability </li></ul><ul><li>Probability Distribution </li></ul>Statistics <ul><li>Circular Measures </li></ul><ul><li>Trigonometric Function </li></ul>Trigonometry Topics Component
  8. 8. ELECTIVE PACKAGE Applied Science And Technology Social Science Application Of Index Number Linear Programming Solutions of Triangle Motion In A Straight Line
  9. 9. FORMAT OF PAPER 1 ADDITIONAL MATHEMATICS SPM
  10. 10. <ul><li>Type of instrument: Objective </li></ul><ul><li>Type of item: Graded objective </li></ul><ul><li>(Item requires candidates to give responses with their own answers) </li></ul><ul><li>Number of question : 25 ( Answer all ) </li></ul><ul><li>Total marks : 80 </li></ul><ul><li>Duration : 2 jam </li></ul><ul><li>Construct : </li></ul><ul><li>Knowledge and Understanding: 20 % </li></ul><ul><li>Application skills: 80 % </li></ul><ul><li>Level of Difficulty : R : S : T = 6 : 3 : 1 </li></ul>
  11. 11. Item of Knowledge and Understanding <ul><li>Does not involve complicated calculations </li></ul><ul><li>Measures the ability of candidates to </li></ul><ul><ul><ul><li>Recall definitions, concepts, formulas and laws </li></ul></ul></ul><ul><ul><ul><li>Translate idea from one form to another. </li></ul></ul></ul><ul><ul><ul><li>Reason out a basic idea </li></ul></ul></ul><ul><li>Task Word : </li></ul><ul><li>State…, Name…, Write…. </li></ul>
  12. 12. Item of Application Skills <ul><li>Measures the ability of candidates to </li></ul><ul><ul><ul><li>carry out the calculation using the definitions, concepts, formulas and laws </li></ul></ul></ul><ul><ul><ul><li>sketch, draw and interpret graphs. </li></ul></ul></ul><ul><ul><ul><li>generate formulas or relation </li></ul></ul></ul><ul><li>Word task: </li></ul><ul><li>Find…, Calculate…,Solve…, Differentiate…, Integrate…, Evaluate…, Express… </li></ul>
  13. 13. EXAMPLES OF ITEMS 3472/1
  14. 14. <ul><li>The first term of a geometric progression is 3 </li></ul><ul><li>and the common ratio of the geometric </li></ul><ul><li>progression is −2. </li></ul><ul><li>List down the first four terms of the geometric </li></ul><ul><li>progression. [2 marks] </li></ul><ul><li>Answer:…………… </li></ul>Knowledge and Understanding
  15. 15. Diagram1 shows the graph of the quadratic function y = ( x + b ) 2 + c . State the values of b and c . [2 marks] Answer: b =…………… c=…...……….. y  (2,3) x 0 DIAGRAM 1
  16. 16. Application Skills <ul><li>Given , find the value of n. </li></ul><ul><li> [3 marks] </li></ul><ul><li>Answer:…………………. </li></ul>
  17. 17. <ul><li>On the axes provided in the answer space, </li></ul><ul><li>sketch the graph of y =  sin2 x  </li></ul><ul><li>for 0  x   </li></ul>Answer : y 0 x
  18. 18. RANGE OF TOPICS IN PAPER 1
  19. 19. <ul><li>ALL the topics in the syllabus except </li></ul><ul><ul><li>- topics from the AST and SS Packages </li></ul></ul><ul><ul><li>- Simultaneous Equations </li></ul></ul><ul><li>Questions involving proving will not be asked in </li></ul><ul><li>Paper 1 </li></ul>
  20. 20. Marking Scheme <ul><li>Full marks are given to the correct answers. </li></ul><ul><li>However, if the answer is wrong, marks will be given to the correct stage of the candidates’ working. </li></ul>
  21. 21. Example <ul><li>The quadratic equation x(x + 1) = px – 4 </li></ul><ul><li>has two distinct roots. </li></ul><ul><li>Find the range of values of p . </li></ul><ul><li>[3 marks] </li></ul><ul><li>Marking Scheme: </li></ul>p <  3 , p >5 B2: (p + 3)(p  5) > 0 B1: (1  p) 2  4(1)(4) > 0
  22. 22. TECHNIQUES OF ANSWERING
  23. 23. <ul><li>Start by answering the easy questions first. </li></ul><ul><li>Answer according to the requirements of the question. </li></ul><ul><li>(This determines how the answer must be written.) </li></ul><ul><li>Example : </li></ul><ul><li>Find  , in radians... </li></ul><ul><li>Give your answer correct to two decimal places... </li></ul>
  24. 24. <ul><li>1. Given and , </li></ul><ul><li>find in the form </li></ul><ul><li>Answer: </li></ul><ul><li>or </li></ul>
  25. 25. <ul><li>2. The quadratic p x ² + q x +1= 0 has two equal roots. Express p in terms of q. </li></ul><ul><li>q = 2√p </li></ul><ul><li>q² = 4p </li></ul><ul><li>p = q² </li></ul><ul><li>4 </li></ul>Answer:
  26. 26. <ul><li>Answer according to the instructions of the question. </li></ul><ul><li>(This determines the method that must be used when solving.) </li></ul><ul><li>Example: </li></ul><ul><li>Using , calculate… (Circular Measures) </li></ul><ul><li>Sketch the graph…(Quadratic Functions/ Trigonometric) </li></ul>
  27. 27. <ul><li>Understand the key words </li></ul>Given , find f´´(x) Find the values of m and n Example Find Determine Calculate Evaluate State Name Write Key Words Involves calculation and usually formulas are used. Answers can be obtained without calculation Action
  28. 28. PRESENTATION OF ANSWERS
  29. 29. <ul><li>READABLE </li></ul><ul><li>AND </li></ul><ul><li>NEAT </li></ul>HANDWRITING
  30. 30. <ul><li>Workings must be shown clearly </li></ul><ul><li>Common mistake: Answers without workings. </li></ul>
  31. 31. <ul><li>Answer : 7 [0 mark] </li></ul><ul><li>2 + 7 + 9 + 15 + x = 12 </li></ul><ul><li>5 </li></ul><ul><li>33 + x = 60 </li></ul><ul><li>x = 27 [1 mark] </li></ul><ul><li>Answer : 7 </li></ul>Given the mean of the numbers 2,7,9,15 and x is 12, find the value of x . [2 marks]
  32. 32. <ul><li>Final answer must be in simplified form. </li></ul><ul><li>Common mistakes: </li></ul><ul><li>; 2 x 2 – 4 x + 6 =0, </li></ul>
  33. 33. <ul><li>Solutions involving  ,answers can be given in terms of  , unless stated </li></ul><ul><li> “ Using  = 3.142 ” </li></ul><ul><li>Hence, this value of  must be used to obtain the answers. </li></ul>
  34. 34. <ul><li>Precision </li></ul><ul><li>Answers involving decimal numbers must be rounded off to 4 significant numbers. </li></ul><ul><li>Example: </li></ul><ul><li>tan  = 0.33 ,  = 180 ° 16’ [not precise] </li></ul><ul><li>tan  = 0.333,  = 180 ° 25’ [not precise] </li></ul><ul><li>tan  = 0.3333,  = 180 ° 26’ [precise ] </li></ul>
  35. 35. <ul><li>Solve the equation 3cos 2 x = 8sin x – 5 for 0   x  360  </li></ul><ul><li>[3 marks] </li></ul><ul><li>B1: 3(1 - 2sin 2 x ) = 8sin x – 5 </li></ul><ul><li>B2 : </li></ul><ul><ul><li>sin x = 0.67 </li></ul></ul><ul><ul><li> x = 42.06  </li></ul></ul><ul><ul><li>sin x = 0.6667 </li></ul></ul><ul><ul><li> x = 41.81  </li></ul></ul>not precise
  36. 36. <ul><li>Solve the equation 4 2x  1 = 7 x </li></ul><ul><li>[4 marks] </li></ul><ul><li>(2 x - 1 )lg 4 = x lg 7 </li></ul><ul><li>2 x (0.60) – x (0.85) = 0.60 </li></ul><ul><ul><li>x = 1.714 </li></ul></ul>
  37. 37. <ul><li>Solve the equation 4 2x  1 = 7 x </li></ul><ul><li>[4 marks] </li></ul><ul><li>1.677 </li></ul><ul><li>B3 : </li></ul><ul><li>B2 : 2 x lg 4 – x lg7=lg 4 </li></ul><ul><li>B1: (2 x - 1 )lg 4 = x lg 7 </li></ul>
  38. 38. More Common Mistakes
  39. 39. <ul><li>Graph of Trigonometric Function </li></ul><ul><li>On the axes provided in the answer space, sketch the graph of y = |3sin2 x | for 0  x   </li></ul><ul><li>Answer : </li></ul>y x
  40. 40. y 3  x 0 y 3  x 0
  41. 41. <ul><li>Progression </li></ul><ul><li>Find the ninth term of the arithmetic progression </li></ul><ul><li>7,4,1,… </li></ul><ul><ul><ul><ul><ul><li>T n =a+(n-1)d </li></ul></ul></ul></ul></ul><ul><li>T 9 =7+(9-1)-3 </li></ul><ul><li> =12 </li></ul><ul><li>T n =a+(n-1)d </li></ul><ul><li>T 9 =7+(9-1)(-3) </li></ul><ul><li> =-17 </li></ul>Make sure brackets is written to show multiplication
  42. 42. <ul><li>Functions </li></ul><ul><li>Defining functions. </li></ul>Condition for the function to exist must be written
  43. 43. <ul><li>Quadratic functions </li></ul><ul><li>Quadratic inequalities </li></ul>
  44. 44. <ul><li>Quadratic Equations </li></ul><ul><li>Solving quadratic equations using the formula. </li></ul>Make sure ‘= 0’ is written Show how the values of a , b and c are substituted into the formula
  45. 45. IN THE EXAMINATION HALL
  46. 46. <ul><li>The use of non-programmable scientific calculator is allowed. </li></ul><ul><li>Any valid method can be used to solve a problem. (paper 1) </li></ul>
  47. 47. <ul><li>Do not waste time sketching a graph. </li></ul><ul><li>Give only one answer in the answer space. </li></ul><ul><li>Do not cross out the solution that has been done; probably the first attempt is better than the second. </li></ul>
  48. 48. Example <ul><li>A badminton team consists of 7 players. The </li></ul><ul><li>team will be chosen from a group of 8 boys </li></ul><ul><li>and 5 girls. </li></ul><ul><li>Find the number of teams that can be formed </li></ul><ul><li>such that the team consists of 4 boys. </li></ul><ul><li>[2 marks] </li></ul><ul><li>Answer: 100800 </li></ul>
  1. A particular slide catching your eye?

    Clipping is a handy way to collect important slides you want to go back to later.

×