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PENINGKATAN PRESTASI

MATEMATIK TAMBAHAN

Mengenalpasti kelemahan dan kesilapan lazim

pelajar dan cadangan cara mengatasinya Mengikut kategori pelajar:

Pelajar Lemah (Markah 0 29)

Pelajar ederhana (Markah !0 "0)

Pelajar #arget $ (Markah "% &9)

Pelajar 'emerlang (Markah 0 %00)

GENERAL COMMENTS

For Very Weak Students :

Organise a class where teacher emphasises on how to get at least one mark for every

question (sub questions either in !aper " or !aper #$

For %ntermediate students:

&mphasise on topics where questions are certain to come out$

For &'cellent Students

o a lot of papers in S!) format to reduce careless mistakes$

&mphasise on the steps * details required to get full marks+ especially in

paper # such as round off errors$

PAPER 1

Topic Weakness / Common Mistakes Rectification / Reminder

Functions Weak Students (0 !"

(a ,nable to determine the type of

function especially when the relation

is not given as arrow diagram$

(b ,nable to distinguish between ob-ect

and image eg: (* . /

Suggestion

(a 0sk student to convert to arrow diagram$

(b &mphasised on ob-ect and image$

raw an arrow diagram

"


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(c )ake mistakes when question asks to

find the ob-ect if the image is given$

A#era$e Students (%0 &0"

(d ,nable to find inverse function$

E'ceent Students ()0 100"

(e id not write the condition for(*

involving fractions$

+ronto,ject -ack image

(d Suggestion:

&'plained inverse function as the inverse of the operation for simple function as a*1 b $

(* . * a*1 ,

2hus

3"(*.a

bx *

(e For functions involving fractions+ the

condition for(* ),S2 be written:

for (* .

x

+ * 4

*uadratic

E+uations

Weak Students (0 !"

(a ifficulty in converting to general

form$

,nable to identify the constants a+ b

and c when the equation is not

written in general form$

&'ample : 5*#6 k*1 #k. " 6 7*

Suggestion:

i$ )ake the 89S . 4 5*#6 k*1 #k6 " 1 7*. 4

ii$ raw 5 bo'es for each constant as such:

*# 1 * 1 . 4

Fill in any Fill in any Fill in any

constants constants constants

with*# with* without*or*#

a ; b ; c ;

*uadratic

Functions

Tar$eted A Students (&1 ,!"

(a could not relate the information

given in equation of completing thesquare form with the graph given$

(b !roblems in inequalities ,nable

to determine the range$

(a o more e'ercise on sketching$


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2

"

.


(a !roblem in finding c+ e'ample+

5

#7

7"=

=

=m

Students tend to do: > . m? 1 c

*y . 5*#1 c

su,st/ (2 ") to * and y/(#(7 . 5(## 1c

Write down: > . m? 1 c

Find mand c@&FO8& substituting theyand

the *3a'is given from the graph$

R

,se calculator to find the y3intercept and the

gradient$

Pro$ression Tar$eted A Students (&1 ,!"

(a Weak in finding+ e'ample+

(i S56 A(ii 2nwhen Snis given$

uggestion

(a &'plain using diagram : e'ample

(i 1 2 3 4 5 6 7 S3 7= S7 S2 (Sa b= Sb Sa-1)

(ii 1 2 3 4 5 T5= S5 S4(Tn= Sn Sn-1)

(b ,se only # data to show it is a

(b 8emind students that they must use at least 5 datato show whether itBs a

Circuar

Measures

Weak Students (0 !"

(a ,nable to change degree to radian

and vice versa$

(b ,se angle in degree in the formula$


(c When finding usings1ror

$.r# students tend to multiply the

value of with"C4

as if to change it to

rad$

(d ifficulty finding the area of

segment

formula not given$

(a &mphasise on the use of calculator to change

radian to degree$

(c &mphasise that is in radian$

(d 8emind students of the formulae not given$

DD For 0rea of segment . r#( 3 sin

(since is in radian+ to get sin use calculator

to mark it as rad+ thus+ no need to change to degree

*ample: %f r. 5 and

. "$#7 radian

4$7 5 *# ( "$#7 3 sin "$#7 shift 0ns # .

On screen 4$7'5#("$#7 6 sin "$#7r

2ectors Weak Students (0 !"

(a ,nable to write unit vector correctly

(b for parallel vectors : ais parallel to ,

(a &mphasise on phythagoras theorem to find the

magnitude$

Show the formula and how to substitute$

uggestion

(b ,se the ratio of each vector$

5

(#+ 7

(7+ "=

*y

*

Mode

AC

Reg LinEnter points

2 5 M+

5 14

S3ift 2 Press rightarrow twice A =

,

, M+

y-intercept

S3ift 2 Press rightarrow twice B = gradient


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students tend to take a. ,$ *ample: 3 p. 5i1 =4and 4. mi1 C4are

parallel find m$

olutions:C

=5=

m similar

triangle;

5ifferentiation Weak Students (0 !"

(a Eo attempt to answer


(b onfuse between rate of change and

small changes$

(a 2each how to get at least one mark$

Suggestion

(b Observe the unit given ms3"rate of change

Gist out questions involving the subtopics and

ask students to identify the e'act subtopic$

Trio$onometric

Functions


(a o not give all the values of

especially involving 4$

Suggestion

(a(i ,se the 8 H 8 0 steps$

3


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8 Tar$eted A Students(%0 ,!"

(b Forget to find the other unknown

(c

(a 9istogram: 3 raw with incorrect a'is

3 Forget how to get the mode

3 ,nable to read the value$

(b ,nable to use the formula for median

correctly wrong median class$

use the F from the median class

(a rilling

(b rilling

Coordinate

-eometr.


(a Find 0rea+ forget+

i$ to close the points: 0 @ 0

ii$ the constant included in the formula$

(b !roblems to find the equations of line$

(b rill students with finding equations of

parallel line and perpendicular lines$

3 use formula y . m' 1 c

7


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(c ,nable to find the equation of locus$


8 Tar$eted A Students (&1 ,!"

(d Gocus: )ake mistake when giving the ratio

of the distance$(e Gocus: When solving+ it is required to

square both sides to get rid of the square

rootsstudents forget to square the

constants too$

or y 6 y". m(' 6 '"

(c 8emind students to apply the distance

formula whenever the word MlocusB is seen$

(d onvert the ratio into fraction+ eg+

$-:$' . # : 7 7

#=

$'

$-

or 7$-. #$'

6orma

5istri7ution

E'ceent Students ()0 100"

(a ifficulty solving problems when the

probability is given$ &'ample!(I N k . 4$A+ find k$

Suggestion:

(a (i sketch the graph

(ii remember these shortcuts$

%ntegrations A#era$e Students (%0 &0"

(a When given the gradient function :

Students make mistake such as:

(i use equation of the straight line to find

the equation of the curve$

(ii differentiate the gradient function toget the gradient of tangent$

(a &mphasise on

(i the term gradient function

(ii y

d*d*dy

d*

dy

Ginear Gaw Weak Students (0 !"

(a o not show tables for the new a'es$

(b @est3fit line does not touch the y3a'is$


8 Tar$eted A Students (&1 ,!"

(c )istakes when finding the value of ' giveny or v$v$do not use the a'es given$

(d Values in tables are not given to at least #

decimal places$

(e o not use points on the graph to find the

gradientstudents tend to take any #

points from the table without checking

whether the points are on the line or not$

When doing revision+ emphasise on where

the marks are given$

For weaker students+ make sure that they

are able to do part(a of the questions$

2rigonometric

Functions

Tar$eted A Students(&1 ,!"

(a ,nable to get the equation of the required

straight line to solve the equation given$

(a


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trigo e'pression$

Ginear

!rogramming

Weak Students (0 !"

(a ,nable to interpret the problem given into

mathematical inequality$

(b Weak in drawingy. m*$


(c ,nable to get the correct shaded region

&'ample for ' N #y students shade the

upper region$

(a &mphasise on the terms: at least+ at most+

not more than+ not less than+ e'ceeds by+twice+ three times+ P

(b 8emind students to read from the

direction of positivey$

*N #y can be written as #y*

8ead from positive3y+ thus+ it is the lower

region$

DD 2wo ways to find the ma' * min value

%t is recommended to use the points of thecorners of 8+ and substitute into the

optimum equation$

The End

A

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