mathspm keynotes

8/9/2019 MathSPM Keynotes

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Sekolah Menengah Kebangsaan Cherang RukuPasir Puteh

Kelantan

Keynote & Check List

For Mathematics SPM(Paper 1 and 2)

Disediakan Oleh

Abd Laziz Bin Ghani

Tarikh : 25 29 Julai 2010


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FORMAT INSTRUMEN PENTAKSIRAN BAGI MATA PELAJARAN

MATEMATIK SPM

Wajaran Kontruk Pengetahuan - 45%Kemahiran - 55%

Pengetahuan - 25%Kemahiran - 70%

Nilai 05%

Aras kesukaran

Rendah - RSederhana - STinggi - T

R : S : T = 5 : 3 : 2 R : S : T = 5 : 3 : 2

PERKIRAAN MARKAH

SIMBOL PERMARKAHAN (SKIMA)

Question Mark scheme Sub Mark Total Mark

PKN

Simbol Keterangan

P Diberi untuk respon/jawapan calon dengan Pengetahuan yang

ditaksirkan

K Diberi untuk kerja calon, sesuai dengan Kemahiran yang ditaksirkan

N Diberi untuk kerja calon, sesuai dengan Nilai yang ditaksirkan

K Menandakan ikut terus kerjanya yang betul selepas suatu kesilapan

BC Been cancelled-menandakan kerja/jawapan dibatalkan oleh calon.

SOS See other solution-menandakan ada penyelesaian lain lebih baik telahdiambil.

BOD Benefit of Doubt-menendakan kes kurang pasti tetapi markah diberi

kepada calon.

Kk Menendakan jawapan betul tetapi jalan kerja tidak ditunjukkandengan sempurna.

%100140

21

+KK= %


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SOME REMINDERS

q Round off only at the last answer.

q All steps must be clearly shown.

q Read the instructions and question very carefully.

q The answer must be in the lowest form, to 4 significant figures and to 2 decimal places.

q Calculate , find , solve

all steps are clearly shown.q Describe in full ...

all the propertiesq Master the scientific calculator.

q State - give only the answerq Labeling Vertex , point or measurement must be labeled correctly

SOME REMINDERS

(Jawapan Akhir)

1. Dalam bentuk teringkas

a)2

3

2

3-

-b) 3

1

3

c)2

1

4

2 d)

4

43

4

310 =

2. Betul kepada dua tempat perpuluhan atau empat angka bererti

i) ).2(33.213

121 pt= tetapi ).1(3.21

3

121 pt=

ii) 213.19 = 213.2( 4 a.b) tetapi 213.19 213 (3 a.b)

3. Jawapan dalam derjah dan minit

i) 21.670 = 21.70 (1 t.p)

ii) 210 31.3 = 210 31

Format Soalan dan Jangkaan Soalan

1. Kertas 1 mengikut format/tajuk asal2. Kertas 2, bahagian A (Graf Fungsi dengan Set)

bahagian B (Format Kebarangkalian)


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IMPORTANT CHECK LIST ON SPM MATHEMATICS PAPER 2

No HIGHLIGHTED NOTES FOR THE STUDENTS

1 SETSShade the region

Intersection = Union = Compliment of A = A'

Teorem Set

(P Q ) = P Q

(P Q ) = P QP (Q R) = (PQ) (PR)P (QR) = (P Q ) (P R)

n(P Q ) = n(P) + n(Q) n(PR)

2 GRAPHS OF FUNCTIONSShade the region that satisfies the inequalitiesKnow how to DRAW a straight line : e.g.x = 2 is a vertical line andy = 3 is a horizontal line

Understand the inequality sign : < or > is represented by a broken line ( ): or is represented by a full line ( )

Make sure you have three inequlities line,from the (2 question is given) and make one line.3 VOLUME / SURFACE AREA OF A SOLIDDetermine the two solids involvedChoose the Mathematical operation : addition or

subtractionUse the correct given formulae

Substitute with the correct values ofr, d, h, land w.

Formula is given in page 2 .

SPM question paper

4 LINES AND PLANES IN 3DSketch the right-angled triangleIdentify the angle and name it

Calculate the angle using trigonometry, e.g. tan q=

b

a

- line between plane

- plane between planeOperation the teorem pithygoras can be used

BASIC CONCEPT MUST

BE USING THE TRIANGLE

righ-angle triangle

a

5 MATHEMATICAL REASONINGA statement or Not a statement : Answers such as YES , NO only are not accepted

Use of AND , OR , ALL , SOME

Sentence : if and only if : write down two implicationsImplication : If .., then . : e.g. : Ifx is greater than zero, thenx is a positive number.

Converse implication : e.g. Ifx is a positive number, thenx is greater than zero.

Arguments : e.g. 1 :Premise 1: All hexagons have six sides.Premise2 :

Conclusion : PQRSTU has six sides.

PQRSTU is a hexagon

b


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e.g. 2 : Premise 1 : Ifx is greater than zero, thenx is a positive number.Premise 2 :

Conclusion : 6 is a positive number.

e.g. 3 : Premise 1 : If 4x = 16 , thenx = 4.Premise 2 :

Conclusion : 164 x All the answers can be derived from the question itself. Dots must be at least three.Make conclusion using the:

1. Induction making general conclusion to specificEg: 7,16,21, n term = 9n -2, where n=1,2,3,

2. Deduction- making specific conclusion to general

6 SIMULTANEOUS LINEAR EQUATIONSi) When there is a fraction , multiply every term of the equation by the denominator to createa new equation

Solve by elimination or substitutionii) Use inverse matrix to solve

use a calculator to check the answers

7 STRAIGHT LINE

Gradient , ;erceptx

erceptym

int

int

-

--=

Equation of a straight line :y = mx + c

Parallel lines , same gradientx-intercept ,y = 0y-intercept = c , whenx = 0

x-intercept = 12 , Do not write x = 12 or ( 12 , 0 )- state the coordinate

- Write the equation-Find the x or y intercept

From equestion

y= mx + c

8 QUADRATIC EQUATION

Rearrange to general form of quadratic equation , 02 =++ cbxax Involved with factorise and expandFactorise , ( ) ( ) = 0 . Equation must be written in this form.

e.g. : ( )( ) 0243 =-+ xx

( ) 023

4=-

+ xx cannot be accepted

State the values ofx.

Check by calculator.example slide

6 is greater than zero

4

21

21

xx

yym

-

-=

Gradient y-intercept

x-intercept


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9 MATRICESMake suru understand the concept of AA

-1=A

-1A = I

and AI = AWhen the matrix has no inverse , ad bc = 0

Convert simultaneous equations into the matrix form

e.g. : 2x 3y = 14x + 3y = 13

Formula of the inverse matrix write the inverse matrix before.e.g. :

Give the value ofx and the value ofy (not in matrix form)

10 CIRCLES III

Use the correct given formulae ,2

2 randr pp

Stress on : rarclength pq

2360

= and 2360

sec rtorofarea pq

=

Substitute with the correct values of r and d.

Answers can be in fractions or 4 significant figures or 2 decimal placese.g. 3028.32

11 PROBABILITY II

Must know when to use)(

)()(

Sn

AnAP = and )(1)( ' APAP -=

For the combination using the tree diagram

Involved two events( return or not)12 GRADIENT AND AREA UNDER THE GRAPHDuration or length of time is the total time taken

Area of trapezium = hba )(2

1+

Distance-time graph, gradient = speed (the rate of change of distance)- graph shows a horizontal line vehicle is at rest

Speed-time graph , gradient = acceleration ( the rate of change of speed)- graph shows a horizontal line uniform speed/constant speed

-=

-

-

13

14

31

32

y

x

inverse matrixon the left

-

=

13

14

21

33

3

1

y

x

-=

-

-

1314

3132

y

x

distance

speed

time time

uniform speedUniform acceleration

vehicle is at restuniform speed/constant speed


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13 GRAPHS OF FUNCTIONSEmphasise on the use of the calculator to calculate the unknowns

Draw the graph : emphasise on :

- The Scale and the range of x given

- Plot the points accurately using a cross symbol

- Can use flexible curve- The curve must be smooth, passing through every point.

Marks deducted when :

the scale is wrong x is not in the given range

The scale is not uniform the curve/line is double

line

thickness of curve is not

uniform (bold + thin lines)

crooked curve is drawn

The curve does not pass

through all the points

ruler is used to join the

points

Draw the straight line required- eliminate variables that have indices to get equation of straight line- if there are 3 intersections , give 3 answers for the values of x.

All answers are obtained from the graph. Calculated values not accepted.

14 TRANSFORMATIONS IIICombined transformation RS means transformation S followed by transformation R.Please use the right terminology.

Always start the answer with the transformation first.Spelling of the transformation.

Describe in full the transformation.

Translation

by

yx

Reflection

Rotation oq (90o, 180

o, 270

o, 60

o)

centre (x,y )

direction clockwise/anticlockwise

Enlargementcentre (x,y )

scale factor = k

15 STATISTICSModal class

Mean

- the use of formulaeFrequency Polygon- table must have column for midpoint

- labeling at thex-axis must use midpoint- the graph must be closed at both ends

- All lines must be drawn by using ruler.Histogram

- table must have columns for midpoint or upper boundary


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- labeling at thex-axis can be midpoint, upper boundary and class interval- there should be a gap between they-axis and the first bar

Ogive- table must have column for cumulative frequency and upper boundary

- extra one class before the first given class interval with cumulative frequency = 0

- labeling at thex-axis must be upper boundary- the graph must intersect at thex-axis- median

- quartiles and interquartile rangeInformation of the graph :

Median is quartile is

Interquartile range is Statement : 45 students have a height of 155 cm

16 PLANS AND ELEVATIONSCorrect shapeSatisfies conditions given

Measurement must be accurate.

Hidden line dashed lineMust use the geometrical instruments to draw. e.g. : ruler , compasses, set squareDO NOT SKETCH... MUST DRAW full scale

Less marks will be given if

a line is a double line gaps in the

drawing of thelines

thickness of line is notuniform (bold + thin lines)

an extension isseen

reflected image is drawn it is not a rightangle

bigger size / smaller size isdrawn

it is not a straightline

17 EARTH AS A SPHERESketch the earth and the anglesi. Fine the location and distance

- Location (Latitude U0/S

0, Longitude W

0/N

0)

-Distance between two ponit:

a) along agreat circle (longitude)(1 at the centre of the earth = 1 natical miles on the surface of the earth)

b) shortest distance : Distence measured along a great circec) distance between AB = (difference angle in longitude x 60 ) nm

distance along the parallel latitude = (difference in longitude in degrees) x 60 xcosine angle of latitude)

ii. the formula of average speed,)(

)(tan)(

hourtime

mileceDisknotSpeed =

iii. knot= nautical miles per hour

iv. latitude small circle


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