Proving Archives - KK LEE MATHEMATICS

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Proving

Logical mathematical arguments used to show the truth of a mathematical statement. In a proof, we can use axioms or the existing theorems, that have themselves been proven. The result of a proof is often called a theorem. I use the existing theorem to calculate to prove that my result is correct.

STPM 2016 Term 3 Probability Booklet Permutation Solution

Jul 4 | KK LEE Booklet Solution

Sample solutions of STPM 2016 Term 3 Mathematics (T) Chapter 14 Probability Permutation and Combination Practice Page 6 to page 15

STPM 2017 MT MM Functions Booklet A Page 5 Problem

Jun 14 | KK LEE Booklet Solution

Sample solutions of STPM 2017 Term 1 Mathematics (T) and (M) Chapter 1 Functions A Problem Page 5

STPM 2016 MT Integration Booklet A Page 10 11 Problem 7 8 9

Feb 16 | KK LEE Booklet Solution

Solution for the Problem 7 8 9 from the Integration A booklet.

STPM 2016 MT Functions Booklet A Page 24 Question 5

Jul 1 | KK LEE Booklet Solution

Express $latex \frac{x^3+3x}{(x+1)(x^2+1)^2} $ as partial fractions.

STPM 2016 MT Functions Booklet A Page 5 Problem

Jun 18 | KK LEE Booklet Solution

Sample solutions of STPM 2016 Term 1 Mathematics Chapter 1 Functions A Problem Page 5

STPM 2015 MT Differentiation Booklet A Page 19 Problem 9 Question 12

Mar 3 | KK LEE Booklet Solution

STPM 2015 Term 2 Mathematics (T) Chapter 8 Booklet Differentiation A Page 19 Problem 9 Question 12 Solution

STPM 2015 MT Chapter 9 Booklet A Page 10 Problem 7 8 9

Feb 15 | KK LEE Booklet Solution

STPM 2015 Term 2 Mathematics (T) Chapter 9 Booklet integration A Page 10 Problem 7 Problem 8 Problem 9 Solution

Geometric Progression I

Feb 5 | Random Question

Geometric Progression I

STPM 2015 MT Chapter 8 Booklet B Page 35 Problem 17

Jan 30 | KK LEE Booklet Solution

June 2014/1

Pelangi Differentiation Exercise 2.15

Jan 20 | Textbook Solution

An inverted right circular cone of semi-vertical angle...

Polynomial Question from student I

Jan 14 | Random Question

Solve the equation $r^6-4.2r^4+3.2=0$ .

STPM 2015 MT Chapter 8 Booklet A Page 20 Problem 11 Question 2

Jan 4 | KK LEE Booklet Solution

Given that $y=\sqrt{\cos{x}}$ , show that $4y^3\frac{d^2y}{dx^2}+y^4+1=$ 0.

Integration question from student I

Dec 31 | Random Question

Random question which was asked by a lovely student.

STPM 2015 MT Chapter 8 Booklet A Page 20 Problem 11 Question 14

Dec 29 | KK LEE Booklet Solution

Given that $y=\sec^{-1}(e^x)$ , prove that $\frac{dy}{dx}=\frac{1}{\sqrt{e^{2x}-1}}$ .

2015 MT Chapter 8 Booklet A Page 20 Problem 11 Question 11

Dec 27 | KK LEE Booklet Solution

Given that $y=(\sin^{-1}x)^2$ , show that $(1-x^2)\frac{d^2y}{dx^2}-x\frac{dy}{dx}-2=$ 0.

2015 MT Chapter 8 Booklet A Page 20 Question 6

Dec 26 | KK LEE Booklet Solution

Given that $y=\ln(1+x)-x+\frac{1}{2}x^2$ show that $\frac{dy}{dx}>=0$ for all values of $x>-1$ .

2015 MT Chapter 8 Booklet A Page 20 Question 10

Dec 26 | KK LEE Booklet Solution

If $\sin y = 2 \sin x$ , show that (a) $(\frac{dy}{dx})^2=1+3\sec^2 y$ , (b) by differentiating (a) with respect to $x$ , show that $\frac{d^2y}{dx^2}=3\sec^2 y \tan y$ , and hence that $\cot y \frac{d^2y}{dx^2}-(\frac{dy}{dx})^2+1=$ $0$ .