SCZ Math&Add Math

Summary of Form 4 Chapter 2 Type 1: Completing the Square (CTS) https://t.me/SCZaddmath/48?single Type 2: α, β roots https://t.me/SCZaddmath/51?single Type 3: b²-4ac https://t.me/SCZaddmath/56?single Type 4: Sketching (Quadratic) https://t.me/SCZaddmath/58?single Type 5: Proving (Quadratic formula and α, β roots) https://t.me/SCZaddmath/61?single Type 6: KBAT https://t.me/SCZaddmath/64?single

F4C2 Type 6: KBAT Skills needed: i) Mastering: Type 1: Completing the Square https://t.me/SCZaddmath/48?single Type 2: α, β roots https://t.me/SCZaddmath/51?single Type 3: b²-4ac https://t.me/SCZaddmath/56?single Type 4: Sketching (Quadratic) https://t.me/SCZaddmath/58?single Question from: SPM 2020 paper 2 no. 2

F4C2 Type 5: Proving (Quadratic formula and α β roots) Skills needed: i) Knowing the first step to start the proving (Example: For quadratic formula, starting from ax²+bx+c=0 and use CTS to prove Resources from: Koleksi Pembuktian: Matematik Tambahan SPM

F4C2 Type 4: Sketching (Quadratic) Skills needed: i) Sketching quadratic graph Conclusion of sketching: If y=ax²+bx+c, p≤x≤q Step 1: Construct a table for y=ax²+bx+c which is consist of: i) p and corresponding value of y ii) q and corresponding value of y iii) x-intercept and y=0 ❗️Find b²-4ac to determine the x-intercept exist or not) iv) y-intercept and x=0 ❗️Make sure the y-intercept does not out of domain v) Min/max point (Use CTS to find it) Step 2: Sketch the graph (a＞0, ∪-shaped a＜0, ∩-shaped) Additional note: i) If f(x) is reflected about x-axis to form g(x), g(x) = -f(x) ii) If f(x) is reflected about y-axis to form g(x), g(x) = f(-x) Question from: SPM 2016 paper 2 no. 2(b)

Very useful table to identify b²-4ac👆

F4C2 Type 3: b²-4ac Skills needed: i) Knowing the keyword to identify discriminant (b²-4ac) Questions from: SPM 2016 paper 1 no. 18 SPM 2018 paper 1 no. 20

Famous types of roots in spm👆

F4C2 Type 2: α, β Roots Skills needed: i) Knowing if y=ax²+bx+c, sum of roots=-b/a product of roots=c/a Questions from: SPM 2016 paper 1 no. 17 SPM 2018 paper 1 no. 21

F4C2 Type 1: Completing the square(CTS) Skills needed: i) Converting general form, y=ax²+bx+c into vertex form, y=a(x-h)²+k ii) Determining max/min point from vertex form iii) Knowing axis of symmetry=-b/(2a) Conclusion of CTS: If y=ax²+bx+c Step 1 (a=1 no need do this step): Factorizing a from ax²+bx+c Step 2: Adding and subtracting [(coefficient of x)/2]² Step 3 (a=1 no need do this step): Multipling a to get vertex form Step 4 (if question needed): Determining max/min point from vertex form If y=a(x-h)²+k, min/max point(h, k) Question from: SPM 2021 paper 2 no. 4(b ii)

Form 4 Chapter 2 Quadratic Functions Difficulty in spm: ⭐️⭐️ Similar with Chapter 1, spm seldom come out kbat/application, basic question like i) Completing the square ii) α,β roots iii) b²-4ac iv) sketching are some famous types in spm.

For those who want to buy this very useful addmath google drive(just RM 5)👆,can pm me @scz2004 (Additional updating: I am compiling a new file which is including every content in this channel)

Summary of Form 4 Chapter 1 Type 1a: Basic arrow diagram https://t.me/SCZaddmath/29?single Type 1b: Advanced arrow diagram https://t.me/SCZaddmath/30?single Type 2: "Express" question https://t.me/SCZaddmath/33?single Type 3: Comparison https://t.me/SCZaddmath/35?single Type 4: Sketching (linear) https://t.me/SCZaddmath/37?single Type 5: Line test https://t.me/SCZaddmath/38?single Type 6: f ²(x), f ³(x)...f ⁿ(x) https://t.me/SCZaddmath/41?single Type 7: KBAT https://t.me/SCZaddmath/43?single (These types maybe will continue update)

F4C1 Type 7: KBAT Skills needed: i) Mastering: Type 1b: Advanced arrow diagram https://t.me/SCZaddmath/30?single Type 2: "Express" question https://t.me/SCZaddmath/33?single Type 3: Comparison https://t.me/SCZaddmath/35?single Question from: SPM 2020 paper 1 no. 3

F4C1 Type 6: f ²(x), f ³(x)...f ⁿ(x) Skills needed: i) identify the general rule of f(x) Question from: SPM 2021 paper 2 no. 3(b ii)

F4C1 Type 5: Line test Skills needed: i) Knowing horizontal line test and vertical line test Vertical line test: i) Is function The line intersects only 1 point ii) Not function The line intersects more than 1 point Horizontal line test: i) Have inverse function The line intersects only 1 point ii) Not have inverse function The line intersects more than 1 point Question from: SPM 2021 paper 1 no. 13(c ii)

F4C1 Type 4: Sketching (linear) Skills needed: i) Sketching linear graph (mostly have modulus) ii) Can form a composite function from 2 functions iii) Knowing how to find domain and range based on the graph Conclusion of sketching: If y=｜f(x)｜+k, a≤x≤b such that f(x) is linear Step 1: Construct a table for y=｜f(x)｜ which is consist of: i) a and corresponding value of y ii) b and corresponding value of y iii) x-intercept and y=0 iv) y-intercept and x=0 Step 2: Sketching the graph based on the table ❗️Make sure the graph is touch or above x-axis Step 3 (k=0 no need do this step): If k＞0, move the whole graph upward by k units If k＜0， move the whole graph downward by k units Question from: SPM 2018 paper 2 no. 2(b)

F4C1 Type 3: Comparison Skills needed: i) Knowing how to compare coefficient ii) Can form a composite function from 2 functions For anyone who don't know the meaning of coefficient , click form 1 math textbook (page 110-111)👇🏻 https://online.anyflip.com/fznx/sdlu/mobile/index.html Question from: SPM 2016 paper 1 no. 12

F4C1 Type 2: "Express" question Skills needed: i) Knowing what is the meaning of "Express () in terms of ()" ii) Can form a composite function from 2 functions For anyone who is still very weak in solving "Express () in terms of ()", click form 2 math textbook(page 50-61)👇🏻 https://online.anyflip.com/fznx/htkw/mobile/ Question from: SPM 2015 paper 1 no. 2

F4C1 Type 1(b): Advanced arrow diagram Skills needed : i) Identify functions based on the diagram ii) Knowing the steps to form inverse function and composite function iii) Determining a function when one composite function and one of the functions are given Questions from: SPM 2014 paper 2 no. 3

F4C1 Type 1(a): Basic arrow diagram Skills needed: i) Identify object and image based on the diagram and hence figure out the corresponding function. ii) Knowing what is function notation. Questions from: SPM 2015 paper 1 no. 1 SPM 2020 paper 1 no. 2