The document provides information about answering techniques for the Additional Mathematics SPM Paper 1 exam in Malaysia, including: 1) It outlines the format of Paper 1 which is an objective test consisting of 25 multiple choice questions testing knowledge and application skills. 2) It discusses effective techniques for answering questions such as starting with easier questions, showing working, and presenting neat and precise answers. 3) It provides examples of different types of questions and mistakes to avoid when answering questions involving topics like functions, quadratic equations, graphs and progressions.

1. ANSWERING TECHNIQUES ADDITIONAL MATHEMATICS SPM PAPER 1

2. CONTENTS OF THE SYLLABUS FORMAT OF THE EXAMINATION PAPERS EFFECTIVE TECHNIQUES OF LEARNING TECHNIQUES OF ANSWERING

3. CONTENTS OF THE SYLLABUS

4. CONTENTS CORE PACKAGE ELECTIVE PACKAGE

5. STATISTICS TRIGONOMETRY CALCULUS ALGEBRA GEOMETRY CORE PACKAGE

6. Component Topics Algebra Functions Quadratic Equations Quadratic Functions Simultaneous Equations Indices and Logarithms Progressions Linear Law Geometry Coordinate Geometry Vector Calculus Differentiation Integration

7. Component Topics Trigonometry Circular Measures Trigonometric Function Statistics Statistics Permutation and Combination Simple Probability Probability Distribution

8. ELECTIVE PACKAGE Applied Science And Technology Social Science Application Of Index Number Linear Programming Solutions of Triangle Motion In A Straight Line

9. FORMAT OF PAPER 1 ADDITIONAL MATHEMATICS SPM

10. Type of instrument: Objective Type of item: Graded objective (Item requires candidates to give responses with their own answers) Number of question : 25 ( Answer all ) Total marks : 80 Duration : 2 jam Construct : Knowledge and Understanding: 20 % Application skills: 80 % Level of Difficulty : R : S : T = 6 : 3 : 1

11. Item of Knowledge and Understanding Does not involve complicated calculations Measures the ability of candidates to Recall definitions, concepts, formulas and laws Translate idea from one form to another. Reason out a basic idea Task Word : State…, Name…, Write….

12. Item of Application Skills Measures the ability of candidates to carry out the calculation using the definitions, concepts, formulas and laws sketch, draw and interpret graphs. generate formulas or relation Word task: Find…, Calculate…,Solve…, Differentiate…, Integrate…, Evaluate…, Express…

13. EXAMPLES OF ITEMS 3472/1

14. The first term of a geometric progression is 3 and the common ratio of the geometric progression is −2. List down the first four terms of the geometric progression. [2 marks] Answer:…………… Knowledge and Understanding

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. Application Skills Given , find the value of n. [3 marks] Answer:………………….

17. On the axes provided in the answer space, sketch the graph of y =  sin2 x  for 0  x   Answer : y 0 x

18. RANGE OF TOPICS IN PAPER 1

19. ALL the topics in the syllabus except - topics from the AST and SS Packages - Simultaneous Equations Questions involving proving will not be asked in Paper 1

20. Marking Scheme Full marks are given to the correct answers. However, if the answer is wrong, marks will be given to the correct stage of the candidates’ working.

21. Example The quadratic equation x(x + 1) = px – 4 has two distinct roots. Find the range of values of p . [3 marks] Marking Scheme: p <  3 , p >5 B2: (p + 3)(p  5) > 0 B1: (1  p) 2  4(1)(4) > 0

22. TECHNIQUES OF ANSWERING

23. Start by answering the easy questions first. Answer according to the requirements of the question. (This determines how the answer must be written.) Example : Find  , in radians... Give your answer correct to two decimal places...

24. 1. Given and , find in the form Answer: or

25. 2. The quadratic p x ² + q x +1= 0 has two equal roots. Express p in terms of q. q = 2√p q² = 4p p = q² 4 Answer:

26. Answer according to the instructions of the question. (This determines the method that must be used when solving.) Example: Using , calculate… (Circular Measures) Sketch the graph…(Quadratic Functions/ Trigonometric)

27. Understand the key words Key Words Action Example State Name Write Answers can be obtained without calculation Find the values of m and n Find Determine Calculate Evaluate Involves calculation and usually formulas are used. Given , find f´´(x)

28. PRESENTATION OF ANSWERS

29. READABLE AND NEAT HANDWRITING

30. Workings must be shown clearly Common mistake: Answers without workings.

31. Answer : 7 [0 mark] 2 + 7 + 9 + 15 + x = 12 5 33 + x = 60 x = 27 [1 mark] Answer : 7 Given the mean of the numbers 2,7,9,15 and x is 12, find the value of x . [2 marks]

32. Final answer must be in simplified form. Common mistakes: ; 2 x 2 – 4 x + 6 =0,

33. Solutions involving  ,answers can be given in terms of  , unless stated “ Using  = 3.142 ” Hence, this value of  must be used to obtain the answers.

34. Precision Answers involving decimal numbers must be rounded off to 4 significant numbers. Example: tan  = 0.33 ,  = 180 ° 16’ [not precise] tan  = 0.333,  = 180 ° 25’ [not precise] tan  = 0.3333,  = 180 ° 26’ [precise ]

35. Solve the equation 3cos 2 x = 8sin x – 5 for 0   x  360  [3 marks] B1: 3(1 - 2sin 2 x ) = 8sin x – 5 B2 : sin x = 0.67 x = 42.06  sin x = 0.6667 x = 41.81  not precise

36. Solve the equation 4 2x  1 = 7 x [4 marks] (2 x - 1 )lg 4 = x lg 7 2 x (0.60) – x (0.85) = 0.60 x = 1.714

37. Solve the equation 4 2x  1 = 7 x [4 marks] 1.677 B3 : B2 : 2 x lg 4 – x lg7=lg 4 B1: (2 x - 1 )lg 4 = x lg 7

38. More Common Mistakes

39. Graph of Trigonometric Function On the axes provided in the answer space, sketch the graph of y = |3sin2 x | for 0  x   Answer : y x

40. y 3  x 0 y 3  x 0

41. Progression Find the ninth term of the arithmetic progression 7,4,1,… T n =a+(n-1)d T 9 =7+(9-1)-3 =12 T n =a+(n-1)d T 9 =7+(9-1)(-3) =-17 Make sure brackets is written to show multiplication

42. Functions Defining functions. Condition for the function to exist must be written

43. Quadratic functions Quadratic inequalities

44. Quadratic Equations Solving quadratic equations using the formula. Make sure ‘= 0’ is written Show how the values of a , b and c are substituted into the formula

45. IN THE EXAMINATION HALL

46. The use of non-programmable scientific calculator is allowed. Any valid method can be used to solve a problem. (paper 1)

47. Do not waste time sketching a graph. Give only one answer in the answer space. Do not cross out the solution that has been done; probably the first attempt is better than the second.

48. Example A badminton team consists of 7 players. The team will be chosen from a group of 8 boys and 5 girls. Find the number of teams that can be formed such that the team consists of 4 boys. [2 marks] Answer: 100800