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SPM SEMINAR
2019
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PART 1
ADD MATHS
VIDEO PEMBELAJARAN LENGKAP DI
7/7/19
Quadratic Function
Completing the square | Quadratic Inequality.
Completing the Square
• Max/Min point | Sketch the graph | Find inverse function
! = #(% − '))++
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7/7/19
Quadratic Inequality
• !(#) > 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
7/7/19
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
7/7/19
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
7/7/19
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?
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7/7/19
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> 3@
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% $*#)% "9 9V .
8
7/7/19
Coordinate Geometry
Distance | Line Segment | Equation
Line Segment
Mid Point | Ratio
!" + !$ , '" + '$ = (!, ') +!" + ,!$ , +'" + ,'$ = (!, ')
2 2 + + , + + ,
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7/7/19
Distance & Area
Pythagoras Theorem | Area for polygon
c B
a A
b C
!" + $" = &" A B CA
' = 1 *+ *" *, *+
2 -+ -" -, -+
Forming an Equation
Gradient Form | Intercept Form | General Form
Gradient Form Intercept Form
! = #$ + & $ !
' + ( = 1 ! − !, = #($ − $,)
mc m
ab
General Form Perpendicular Gradient
'$ + (! + & = 0 #,×#0 = −1
Perpendicular Equation
! − !, = #0($ − $,)
Perpendicular Bisector Equation
! − !, = #0 $ − $, ,
234 56378 ($,, !,)
10
7/7/19
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
7/7/19
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
7/7/19
Questions
• Past Trial exam questions from different states - Year 2018
Terengganu 2018 - Paper 1 - Q19
Differentiation
Max/Min | Rate of change | Small change
13
7/7/19
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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7/7/19
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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7/7/19
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
7/7/19
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
7/7/19
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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7/7/19
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
7/7/19
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