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## Additional Mathematics spm seminar part1edit

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# Additional Mathematics spm seminar part1edit

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SPM SEMINAR
2019

#spmseminar 2019 #SPM2019 #BACFlix

PART 1

VIDEO PEMBELAJARAN LENGKAP DI

7/7/19

Completing the square | Quadratic Inequality.

Completing the Square

• Max/Min point | Sketch the graph | Find inverse function

! = #(% − '))++

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• !(#) > 0 | !(#) ≥ 0 | !(#) < 0 | !(#) ≤ 0

*#+ + -# + . < 0 *#+ + -# + . ≥ 0

#+3 #−5 <0 #+3 #−5 ≥0
−3 < # < 5 # ≤ −3 23 # ≥ 5

Questions

• Past Trial exam questions from different states - Year 2018

Terengganu 2018 - Paper 1 - Q15

4

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Questions

• Past Trial exam questions from different states - Year 2018

Kedah 2018 - Paper 1 – Q5

Questions

• Past Trial exam questions from different states - Year 2018
Negeri Sembilan 2018 - Paper 1 - Q15

5

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Questions

• Past Trial exam questions from different states - Year 2018

MRSM 2018 - Paper 1 - Q15

Log and Indices

Basic Law for Log and indices | Solving skill

6

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Basic Law for log and Indices
Log rules | Indices rules

Common mistake for log and Indices
Understanding the concept of log and Indices

!" + !\$ =? log ! + 7 =?

'( − '* =? log ! × log 7 =?

2 ' + 2 * = 2' + 4 * log '* = log ' *, -.//0-1?
-.//0-1?
!+7 = -
2 = 2 , correct? log ! + log 7 = log -
3 3 -.//0-1?

7

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Questions

• Past Trial exam questions from different states - Year 2018

Negeri Sembilan 2018 - Paper 1 – Q5 & Q6

5. !"#\$% &ℎ(& 5*+, − 5* = /000 . \$456\$77 % "% &\$687 9: 8.
12

6. !"#\$% &<ℎ9(=&,1<94=D> 5 = ? (%@ <9=A5 = B. ( 7"%=<\$ :6(F&"9%.
C456\$77 "% &\$687 9: ? (%@ B, (7

Kedah 2018 - Paper 1 – Q8

8. !"#\$% 8 = 2I (%@ % = 2J, \$456\$77 logN *OP in terms of r and/or t.
/,

Questions

• Past Trial exam questions from different states - Year 2018

Terengganu 2018 - Paper 1 – Q6,Q7&Q8
6. !"#\$% &ℎ% %()*&+",: 270×220 = 36.

7. !+78#+9:
log> 22 − log> [email protected]
log> 2 − log> 9

Kedah 2018 - Paper 2 – Q7

5. * C+\$%, &ℎ*& 20 = 3D = 18, %H8I%JJ ( +, &%I7 "9 H *,K :.
P
L M9 N = 1 + Q x and x = log25, 9+,K &ℎ% \$*#)% "9 9V .

8

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Coordinate Geometry

Distance | Line Segment | Equation

Line Segment

Mid Point | Ratio

!" + !\$ , '" + '\$ = (!, ') +!" + ,!\$ , +'" + ,'\$ = (!, ')
2 2 + + , + + ,

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Distance & Area

Pythagoras Theorem | Area for polygon

c B
a A

b C

!" + \$" = &" A B CA

' = 1 *+ *" *, *+
2 -+ -" -, -+

Forming an Equation

Gradient Form | Intercept Form | General Form

! = #\$ + & \$ !
' + ( = 1 ! − !, = #(\$ − \$,)
mc m
ab

'\$ + (! + & = 0 #,×#0 = −1

Perpendicular Equation
! − !, = #0(\$ − \$,)

Perpendicular Bisector Equation
! − !, = #0 \$ − \$, ,
234 56378 (\$,, !,)

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Equation of Locus

Distance | Perpendicular | Ratio into Fraction

General Equation: !"# + %&# + '" + (& + ) = 0

Twice the distance: AP=2BP
", − "# + (&, − &#) = 2 "1 − "# + (&1 − &#)

AP is perpendicular to BP AP:BP=1:3

&# − &, &1 − &, = −1 45 = 1
"# − ", "1 − ", 65 3

", − "# + &, − &# = 1
"1 − "# + (&1 − &# ) 3

Questions

• Past Trial exam questions from different states - Year 2018
Negeri Sembilan 2018 - Paper 1 - Q18

11

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Questions

• Past Trial exam questions from different states - Year 2018
Terengganu 2018 - Paper 1 - Q19

Questions

• Past Trial exam questions from different states - Year 2018

Terengganu 2018 - Paper 1 - Q19

12

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Questions

• Past Trial exam questions from different states - Year 2018

Terengganu 2018 - Paper 1 - Q19

Differentiation

Max/Min | Rate of change | Small change

13

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Differentiation

• First Derivative using product rule, quotient rule and chain rule.

Chain Rule (Composite Function) Product Rule
! = /01

! = #\$ + & ' (! = / 0 (1 + 1 0 (/
(\$ (\$ (\$

(! = ) #\$ + & '*+× ( (#\$ + &) Quotient Rule
(\$ (\$
! = /
1
(/ (1
(! = 1 0 (\$ − / 0 (\$
(\$ 13

Differentiation

• Equation of Tangent and Normal

Normal Steps to get equation of tangent:
Tangent !"
1. !#

2. Sub the x-value into !" to get \$%
!#
3. Forming the equation using

& − &( = \$%(+ − +()

Steps to get equation of Normal:
!"
1. !#

2. Sub the x-value into !" to get \$%
!#
(
3. \$- = − ./

4. Forming the equation using

& − &( = \$-(+ − +()

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Differentiation

• Max/Min and 2nd Derivative

Turning point or Stationary point Steps to get equation of tangent:

1. !"
!#
!"
2. Sub the x-value into !# to get \$%

3. Forming the equation using

& − &( = \$%(+ − +()

Steps to get equation of Normal:
!"
1. !#

2. Sub the x-value into !" to get \$%
!#
(
3. \$- = − ./

But how to determine it nature??? 4. Forming the equation using

& − &( = \$-(+ − +()

Differentiation

• Rate of Change | Small Change | Approximation

Rate of Change Small Change
(Chain Rule)
-" = !" ,
-% !%
!" !" !%
!# = !% × !# -% = %/01 − %34'
-" = "/01 − "34'
Key word:
'(
Rate of change of x = ')

Rate of change of volume = '* Approximation
') "/01 = "34' + -"
'+
Rate of change of Area = ')

Rate of change of radius = ',
')

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Questions

• Past Trial exam questions from different states - Year 2018

Terengganu 2018 - Paper 2 – Q5

Questions

• Past Trial exam questions from different states - Year 2018
Kedah 2018 - Paper 1 – Q11
Kedah 2018 - Paper 1 – Q12

16

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Questions

• Past Trial exam questions from different states - Year 2018

Terengganu 2018 - Paper 1 – Q2

Questions

• Past Trial exam questions from different states - Year 2018
MRSM 2018 - Paper 1 – Q11

17

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Questions

• Past Trial exam questions from different states - Year 2018

Practices Bestari 2018 - Paper 2 – Q10

Solution of Triangle

Sine Rule | Cosine rule | Area of Triangle

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Solution of Triangle

Sine Rule | Cosine Rule | Area of Triangle

Sine Rule

! = ' Cosine Rule
sin % sin ( !) = ') + +) − 2'+(cos %)

sin % = sin ( ') + +) − !)
! ' 2'+
cos % =

Area of Triangle

% = 1 !'(sin 3)
2

Solution of Triangle

Ambiguous Case of a Triangle

Ambiguous Case of a Triangle:
Forming two different type of triangle from the information given.

Example 1:
In a triangle ABC, ∡" = 43°, ( = 4)* (+, - = 7)*,
sketching two different type of triangle.

10cm A Example 2:
B 40°
Point C’ lies on BC such that AC’=AC.
(i) Sketch the triangle ABC’
C (ii) Calculate the area of triangle ABC’

19

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Questions

• Past Trial exam questions from different states - Year 2018

Kedah 2018 - Paper 2 – Q13

Questions

• Past Trial exam questions from different states - Year 2018
MRSM 2018 - Paper 2 – Q14

20