Matematik SPM/SMKTP/khtay

Mathematics ( SPM ) Paper 2 (2 hr 30 min )

Su mmary of p ap er

Section A (52%) : 11 questions . Answer allSection B (48%) : 5 questions . Choose any 4

Show all the important working

Section A : 11 questions

1. Quadratic equations ( F4) / 4m - Expand algebraic expression- Arrange as general form ( 2x2 + 3x – 5 = 0 )- Factorise : ( 2x - 3) ( x + 5) = 0- Find 2 values : x = 3, x = -2

2. Simultaneous equations (F3)/ 4m - 3 methods involved a) eliminationsb) substitution c) matrix

3. Graph of functions ( F5) / 3m - Shade region of inequalities- List inequalities of shaded region

or

Sets (F4) - Shading region (P U Q) , (P ∩ Q), ( P’ ∩ Q)- List of elements

4. Lines and Planes in 3 Dimensions (F4) / 4m - Find length of a side ( Pythagoras Theorem)- Name the angle between line and plane- Calculate angle between plane and plane

5. Straight line (F4) / 5m - find coordinates, x – intercept, y – intercept- find gradient, midpoint- find equation of a straight line ( y = mx + c)- find equation of parallel lines

6. Solid Geometry ( F3 ) / 4m - find volume- volume of cone, cylinder, pyramid, cuboid, sphere, hemisphere- volume of composite ( + or - )- usage of formulas and calculator- formulas given at 2nd / 3rd pages

7. Circle ( F2 ) / 6m - a) Perimeter of diagram ( length of arc = a n g le x 2π r )360

- b) Area of shaded / unshaded region ( area of sector = a n g le x π r 2 )360

Matematik SPM/SMKTP/khtay

8. Mathematical reasoning ( F4 ) / 5m - True / false- Implications (2) : If …….. then …..- Converse- Quantifier ( all / some )- “ and “ / “ or “- Complete premise

9. Probablity ( F4 & F5 ) / 5m - choosing 1 items randomly- choosing 2 items randomly

10. Gradient and area under graph ( F5) / 5m - graph ( distance – time )- graph ( speed – time )

11. Matrix ( F5 ) / 6m - matrix identity and multiplication of matrices- inverse matrix- solving matrix equation using inverse matrix

Section B : 5 questions. ( Choose any 4 )

12. Graph of function ( F5 ) / 12m - Complete table ( find 2 values for y )- Draw x- axis & y – axis according to scale- Plot points accurately- Draw a smooth curve graph- Find values from graph- Draw a suitable straight line , find point of

intersection- shade region of inequality

13. Transfomation ( F5 ) / 12m - Translation/ reflection/ enlargement/ rotation- Describe transformation- Double transformation- area of image = k2 x area of object

14. Statistics ( F4 ) / 12m - Calculate mean from table of class interval- frequency,midpoint, upper boundary, cumulative frequency- Draw ogive / histogram / frequency polygon- Find median, first quartile, third quartile, interquartile range,- state one information from graph

15. Plan and elevation ( F5 ) / 12m - Draw : Plan , front elevation , side elevation- extra line / missing one line = 0 marks- angle 90 accurate . measurement accurate- no extension/gap at corners

16. Earth ( F5) / 12m - Longitude / latitude- Location of point ( 40 N , 65 E )- Difference of angle : a) same lat/long , “ – “

b) different lat/long , “ + “

- Distance ( at equator/longitude ) = diff. of angle x 60’- Distance at latitude = diff. of angle x 60’ x cos lat- speed = distance time

Matematik SPM/SMKTP/khtay

Mathematics ( SPM) Paper 1 ( 1 hr 15 min)

40 objective questions. Answer all.

Summary of topics

1. Significant figure (F4) - 12. Standard Form ( F4) - 3 ( 2 involving + , - x , and 1 problem solving)3. Number bases ( F5) - 2 ( change of bases and +/- of base 2)4. Polygons (F3) - 2 (pentagon/hexagon involving angles/sides)5. Circle ( F3 & F4) - 1 ( find angle )6. Angles of elevation and depression (F4) - 17. Trigonometry (F4) - 2 ( graph sin/cos, quadrant, Pythagoras Theorem)8. Lines and planes with 3-D ( F4) - 1 ( name the angle between line and plane )9. Bearing ( F5) - 110. Earth ( F5) - 1 ( location of points/distance/long/lat)11. Transformation (F5) - 3 ( Translation/reflection/rotation/enlargement)12. Algebraic Expressions (F3) - 1 Expand/simplify13. Linear equation (F3) - 114. Algebraic fraction (F3) - 115. Algebraic Formulae ( F3) - 116. Indices (F3) - 2 ( involving number and alphabet)17. Linear inequality ( F3) - 218. Matrix ( F5) - 3 ( + , - and multiply)19. Graph of function (F5) - 120. Straight Lines ( F4) - 1 ( gradient, equation, intercept )21. Set ( F4) - 322. Variations (F5) - 2 ( direct , inverse and combined variation)23. Probablity ( F4 ) - 224. Statistics ( F3 & F4) - 1

Form 3 - 9 chapters

Form 4 - 9 chapters

Form 5 - 7 chapters