Online Algebra Math Tutor

Online Algebra Math Tutor

Online Algebra Math Tutor Pakistan USA Canada, +92332-3343253, Skype id:ascc576.

Al-Saudia Virtual Academy, Pakistan First and the Largest online Academy, based in Karachi, providing world best algebra tutor and online tutor of math, physics, chemistry, biology, statistics, economics, accounting, sociology, psychology, business studies, English literature and linguistics, over a period of 5 years.

Algebra is now no more a headache for you, We provide world best and expert online math algebra tutor from Pakistan. Our expert online teachers are well versed and fully equipped with modern methods of teaching online, they use different interactive method which can ease to understand the hardest topics of algebra with ease.

•  Linear Relations and Functions
• Equations and Inequalities
• Matrices and Determinants
• System of Equations and Inequalities
• Quadratic Functions and Graphs
• Polynomials Functions
• Complex Numbers
• General Functions
• Conic Sections
• Radical Functions and Rational Exponents
• Rational Expressions
• Sequences and Series
• Exponential and Logarithmic Functions
• Trigonometry Ratios and Functions
• Trigonometric Graphs, Identities and Equations
• Probability and Statistics.

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Methods of Differentiation

Methods of Differentiation 

Methods of Differentiation – Derivatives Techniques – Question of Differentiation.

Online Math Tutor Karachi Pakistan, Online Math Tuition Pakistan

Methods of Differentiation – Derivatives Techniques

Online Tutor Pakistan: Al-Saudia Virtual Academy, Pakistan first and the largest online tutoring services, online tuition Pakistan, started free help to the students online, free worksheets on calculus, algebra 1 and algebra 2, geometry, infinite geometry, these worksheets are the actual lectures online by Professor Masood Amir, describe the simple methods and approach to different topics.

Professor Masood Amir is a well experienced highly qualified and dedicated math tutor, having and experience of over 28 years of teaching mathematics and statistics, he is well versed in different branches of math and stats. You can contact us for the best online math tutor Pakistan, Professor Masood Amir.

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Free Online Math Past Papers

Free Online Math Past Papers

Past Papers from Karachi Board: XI Mathematics

1992.Q.1.(a) (i) IF A={2,3}, B={3,4} AND C={4,5}, Prove that

Ax(BΠC) =(AxB)Π(AxC)

1992.Q.1(a)  Let U = {0,1,2,3}, A={0,1), B={1,2}, C={2,3), then prove that

Ax(BUC) = (AxB)U(AxC)

1993. Q.1 (b) Let S={A,B,C,D}, where A={1}, B={1,2}, C={1,2,3} and D=φ

Construct the multiplication tables to show that U and Π are binary operations on S.

1994. Q.1. (a) IF U={1,2,3,4,5,6}, A={1,2,3}, B={1,3,5} and C={2,4,6}, Find A-C, and verify

That A Π B is a subset of A and A is a subset of AUB

1995. Q,1. (c) State De Morgan’s Law and verify it when A={3,4}, B={3,5} & U={1,2,3,4,5}

1996. Q.1. (d) Let A={0,1,2,4} Define a*b=a Ѵ a,b є A. Construct table for * in A

1997 Q.1. (a) Verify the property Ax(BUC)=(AxB)U(AxC) in the following sets   A={a,b}, B={b,c}, C={c,d}

1998 Q.1. (a) Let A={0,2,4}, B={1,2} and C={3,4} then prove that            Ax(BUC)=(AxB)U(AxC)

1999 Q.1. (a) Let U={1,2,3,4,5,6}, A={1,2,3,4}, B={1,3,4,5}

                                        show that (A Π B)’ = A’ U B’

2000 Q.1. (a) Let U={2,3,4,5,6}, A={2,1}, B={3,4}, C={4,5}

                                                Show that (B-C)’ = B’

2003 Q.1. (a) If A={2,3}, B={3,4}, C={c,f} and U={2,3,4,c,f} find (AxB)U(AxC) and B’-A’.

2004 Q.1. (a) If A={1,2,4}, B={2,3,4}, U={1,2,3,4,5} find (AUB)’ and

                                                      (A Π A’)’

2005 Q.1. (a) If A and B are the subsets of the universal set. Then prove that

                              AUB = AU(A’nB)

2006 Q.1. (a) If A and B are the subsets of the universal set. Then prove that

                              AUB = AU(A’nB)

2007 Q.1. (a) If U={a,b,c,d,e}, A={a,b,c}, B={b,c,d}, find (AnB)

2008 Q.1. (a) If A={2,3}, B={3,4}, C={4,5}, find Ax(BUC)

Cont……………………..d

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Complex Numbers Past Papers Math Worksheet

Complex Numbers Past Papers Math Worksheet

Online Math Tutor Pakistan

COMPLEX NUMBERS

COMPLEX NUMBERS PAST PAPERS KARACHI BOARD (XI)

By Professor Masood Amir

Real Complex Numbers

2008.

Q.1. (a) (ii). Express X2 + y2=9 in terms of conjugate co-ordinates

(iii) If Z1= 1 +I and Z2=3+2i, evaluate |Z1 – 4Z2|.

(b) (i): Find the real and imaginary parts of i(3+2i).

(ii) Find the multiplicative inverse of the complex no, (3,5)

2007.            

Q.1 (a)(ii) If Z1= 1 +I and Z2=3+2i, evaluate |5Z1 – 4Z2|

(iii) Solve the complex equations (x,y).(2,3)=(-4,7)

(b) Separate the following into real and imaginary parts

                                                (1+2i)/(3-4i) + 2/5

2006.

Q.1. (b) Show that (a,b).(a/a2+b2, -b/a2+b2) = (1,0)

Q.1. ( c ) If z=(x,y), then show that Z.Z’ =|Z|2

2005.

Q.1. (a) (ii). Solve the complex equation, (x + 2yi)2 = xi

2004.

Q.1. (a) (ii) If Z1 and Z2  are complex numbers, verify that | Z1. Z2|=| Z1|| Z2|

(iii) Solve the complex equations (x,y).(2,3)=(-5,8)

2003.

Q.1. (a)(ii). If Z1= 1 +I and Z2=3+2i, evaluate |5Z1 – 4Z2|

(iii) Separate (7-5i)/(4+3i) into real and imaginary parts.

(iv) Find the additive and multiplicative inverse of (3,-4)

2002.

Q.1. (a) (ii) Find the multiplicative inverse of (√3+i)/( √3-i), separating the real and imaginary parts.

(iii) Solve the complex equations (x,y).(2,3)=(5,8)

2001.

Q.1. (a) (ii) Define modulus and the conjugate of complex numbers Z= x – iy

(iii) If Z= (1+i)/(1-i), then show that Z.Z’=|Z|2 verify that

(1+3i)/(3-5i) + -4/17 = -4/17 + 7i/17

2000.

Q.1. (a) (ii) Separate into real and imaginary parts (1+2i)/(2-i) and hence find |(1+2i)/(2-i)|.

(iii) By using the definition of multiplicative inverse of two ordered pairs, find the multiplicative inverse of (5,2) and solve the equation (2,3).(x,y)=(-4,7)

1999.

Q.1.(a)(ii) Divide 4+I by 3-4i.

(iii)Prove that (3/25, -4/25) is a multiplicative inverse of (3,4)

(iv) Multiply (-3,5) by (2,1)

1998.

 Q.1.(a)(ii) Solve the complex equation (x + 2yi)2 = xi

(iii) Find the additive and multiplicative inverse of (2-3i).

(iv) Is there a complex number whose additive and multiplicative inverse are equal?

1997.

Q.1.(a)(ii) If Z1 and Z2  are complex numbers, verify that | Z1. Z2|=| Z1|| Z2|

1996.

Q.1. (b)(iv). The multiplicative identity in C is ___________.

Q.1. © What is the imaginary part of [(2+7i)’]2.

1995.

 Q.1.(a) Show that (1-i)4 is a real number.

Q.1. (b) Find the additive and multiplicative inverse of (1,-3)

1994.

Q.1.(b) If Z1 = 1-I and Z2=3+2i evaluate (i) [(Z1)’]2 (ii) Z1/Z2

1993.

Q.1.(a) If Z1 and Z2  are complex numbers, verify that | Z1. Z2|=| Z1|| Z2|

1992.

Q.1. (a) (ii) Simplify (x,3y).(2x-y)

Q.1. (a) (iii) show that Z = 1±i, satisfies the equation Z2-2Z+2=0

1991.

Q.1.(a) (ii)  Express X2+Y2=9 in terms of conjugate co-ordinates

Q.1. (b)(i) Solve the complex equation (X + 3i)2 = 2yi

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Online Math Tutor Pakistan

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Online Math Tutor Pakistan – Differentiation Worksheets- Free Online Math Worksheets, Calculus Worksheets, derivatives worksheets, differentiation worksheets.

first principle

derivative first formula y= x^n

derivative 2nd formula y=(a + bx)^n

product rule of differentiation y=UV

quotient rule of differentiation y=u/v

chain rule of differentiation

implicit functions

logarithmic functions

exponential functions

trigonometric functions

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Online Skype Tuition Pakistan

Online Skype Tuition Pakistan

Online Skype Tuition Pakistan +92332-3343253, Skype id: ascc576, Al-Saudia Virtual Academy, Pioneer and the largest online tuition Pakistan, provides Pakistan best online tutors for math, physics, chemistry, biology, statistics, economics and accounts.

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