# Math Tuition

## We Are Famous For Our Responsible & Qualified Tutors

# Our Clients Know About Us From Their Child's School, Parent Forums/Chat Groups, And Referrals

Since 2005, our only goal is to help our students’ grades improve.

This means that no matter how many tutors apply to join our team, we keep only a steady core of less than 30,000 active and qualified tutors.

These professional tuition teachers are in our database because parents and students had given good and highly positive feedback about how these qualified tutors were able to help their students’ grades improve quickly.

**Latest MOE Syllabus And Exam Requirements**

## Gain 10 to 20 Marks Within 3 Months

## Private Math Tuition That 100% Matches Your Requirements

#### Accomplished Home Tutors For All MOE Subjects

## Whatsapp Us

## +65 9448 9800

### Hire Math Tuition Teachers Who Deliver Results. Fast.

###### Rapid And Sustained Improvement Of Grades And Content Mastery

## Better Grades = Greater Chance To Enter The School/Junior College/University Of Your Choice

## Choose A Committed And Dependable Tutor Who Accurately Customizes Lessons That You Can Quickly Understand

**Select from 29,000 professional and qualified tutors****We have Singapore’s largest effective team of MOE teachers, PhD-tutors, Bachelor’s/Master’s/Undergraduate tuition teachers****Each experienced 1 to 1 home tutor has between 2 to over 30 years of established track records in helping their students’ grades improve. FAST****We will show you profiles of between 4 to 10 reliable tutors within 24 hours after you tell us your requirements****We have many suitable Math tuition teachers. Whatever your learning pace & style, your achievement goals, and your budget****Once you hire a dedicated and competent teacher who carefully tailors the Math lesson plan according to your own unique learning style, you can easily score much better grades within the FIRST month of private tuition****In school, you are not allowed to choose the teachers of any of your subjects.****Because of this, many of our clients tell us that no matter how hard they try, they still cannot catch up with the Math syllabus****Once you have chosen responsible and qualified tutors, your private academic mentor will accelerate your understanding of the important concepts, and teach you valuable exam skills (all our tutors scored A’s in the subjects they teach). Using the latest MOE syllabus and Math exam marking scheme**

## Grades Are Always Important

No Matter What Anyone Else Says

## Study Effectively And Confidently

- Exam Preparation
- Homework Guidance
- Patient & Clear Explanations
- Exam Skills, How To Answer Difficult Application Questions

- Intensive Revision
- Project Assistance
- Experts At The Subjects They Teach
- Study Ahead Of The Syllabus

## Secure Your Future By Scoring Solid Math Grades. Starting Now

## Ensure That You Get The Good Grades That You Want And Need

## Qualified Tutors With Proven Track Records To Help Their Students Score A's

###### Rapid And Sustained Improvement Of Grades And Content Mastery

## Better Grades = Greater Chance To Enter The School/Junior College/University Of Your Choice

## Profiles Of Featured Math Tuition Teachers

Ms GL has 9 years of Math tuition experience. She has a Bachelor’s in Mathematical and Computer Sciences (Double Major) from NTU (Honours). Ms GL was an MOE contract teacher for 3 years and had taught at tuition centres for 6 years. Ms GL’s private tuition students attended Raffles Girls’ Primary School, Sembawang Primary School, Northland Secondary School, Hai Sing Catholic School, Jurong Pioneer Junior College, and Hwa Chong Institution.

Ms THK has 7 years of Math tuition experience. She has a PhD in Statistics from Stanford University. Her Bachelor’s in Applied Mathematics was from NUS (First Class Honours). Ms THK’s private tuition students attended Anglo-Chinese School (Independent), CHIJ St Nicholas Girls’ School Integrated Programme, NUS High School of Mathematics and Science, Victoria Junior College, Hwa Chong Institution, and National Junior College.

Mr MS has 3 years of Math tuition experience. He has a Bachelor’s in Computer Science & Applied Mathematics from NUS (Honours). His home tuition students attended Oasis Primary School, Jing Shan Primary School, Cedar Girls’ Secondary School, Bowen Secondary School, Catholic Junior College, and Nanyang Junior College.

Mr HCL has 8 years of Math tuition experience. He is NIE-trained, and taught at MOE schools for 7 years. He has a Bachelor’s in Quantitative Finance from NUS (2nd Upper Class Honours). Mr HCL’s home tuition students attended Corporation Primary School, CHIJ Our Lady of Good Counsel Primary, Hong Wen School, Methodist Girls’ School (Primary), Singapore Chinese Girls’ Primary School, and St Gabriel’s Primary School

Ms NFN has 8 years of Math tuition experience. She has a Bachelor’s in Mathematics from NUS (First Class Honours). Ms NFN wrote the Math curriculum for primary and secondary school levels at a leading group of tuition centres. Ms NFN’s private tuition students attended White Sands Primary School, St Andrew’s Junior School, St Stephen’s School, Chua Chu Kang Secondary School, Methodist Girls’ School (Secondary), and St Andrew’s Secondary School.

Mr BH has 5 years of Math tuition experience. He has a Master’s in Data Science and Machine Learning from NUS. His Bachelor’s in Mathematics was from NUS (2nd Upper Class Honours). Mr BH’s private tuition students attended Palm View Primary School, Rosyth School, Temasek Primary School, Deyi Secondary School, Fuchun Secondary School, and Dunman High School Integrated Programme.

## Private Tuition That Is Tailored To Your Requirements

## Accomplished & Qualified Tutors For All MOE Subjects

## Profiles Of Featured Math Tutors

Ms SS has 16 years of Math tuition experience. She is NIE-trained, and taught at MOE schools for 11 years. Ms SS has a Bachelor’s in Quantitative Finance from NUS (2nd Upper Class Honours). Ms SS’s private tuition students attended CHIJ St Joseph’s Convent, Anglo-Chinese School (Barker Road), Jurong West Secondary School, Changkat Changi Secondary School, Boon Lay Secondary School, and Hwa Chong Institution Integrated Programme.

Mr LKH has 4 years of Math tuition experience. He has a Bachelor’s in Mathematical Sciences from NTU. Mr LKH taught at a tuition centre for 2 years. His home tuition students attended Waterway Primary School, CHIJ Primary (Toa Payoh) Primary, Queenstown Secondary School, Presbyterian High School, Jurong Pioneer Junior College, and Victoria Junior College.

Ms WXC has 6 years of Math tuition experience. She has a Bachelor’s in Mathematical and Computer Sciences (Double Major) from NTU. Ms WXC was an MOE contract teacher for 2 years. Her private tuition students attended Paya Lebar Methodist Girls’ School (Primary), St Andrew’s Junior School, Hillgrove Secondary School, Meridian Secondary School, Anglo-Chinese Junior College, River Valley High School.

Mr BN has 12 years of Math tuition experience. He has a Bachelor’s in Applied Mathematics from NUS (First Class Honours). Mr BN was the Head of Mathematics at the group of tuition centres where he taught for 7 years. Mr BN’s private tuition students attended Nanyang Primary School, Methodist Girls’ School (Primary), St Andrew’s Secondary School, Singapore Chinese Girls’ Secondary School, Temasek Junior College, and Raffles Institution.

Mr KFS has 8 years of Math tuition experience. He has a Master’s in Applied Mathematics from Cornell University. His Bachelor’s in Computer Science & Mathematics was from NUS (First Class Honours). Mr KFS was a contract teacher at one of Singapore’s top junior colleges for 2 years. His private tuition students attended Nanyang Junior College, Victoria Junior College, Raffles Institution, Eunoia Junior College, Anderson Serangoon Junior College, and Anglo-Chinese Junior College.

Ms TC has 6 years of Math tuition experience. She has a PhD in Mathematics from the University of Cambridge. Ms TC’s Bachelor’s in Mathematics was from NUS (First Class Honours). Ms TC was an MOE contract teacher for 2 years. Her home tuition students attended Pei Chun Public School, Maha Bodhi School, Catholic High School Integrated Programme, CHIJ Secondary (Toa Payoh), Eunoia Junior College, and Anglo-Chinese Junior College.

Mr NGH has 9 years of Math tuition experience. He is NIE-trained and taught at MOE schools for 11 years. Mr NGH has a Bachelor’s in Applied Mathematics from NUS (Honours). His home tuition students attended Cedar Primary School, Fuhua Primary School, Nanyang Primary School, Ai Tong School, De La Salle School, and St Anthony’s Canossian Primary School.

Mr BC has 2 years of Math tuition experience. He has a Bachelor’s in Mathematics from NUS. Mr BC taught at a tuition centre for 1 year. His private tuition students attended Nanyang Primary School, Keng Cheng School, Bukit Panjang Govt. High School, Bartley Secondary School, Catholic Junior College, and Raffles Institution.

Ms RH has 15 years of Math tuition experience. She has a Master’s in Applied Mathematics from Yale University and a Bachelor’s in Mathematical Sciences from NTU (First Class Honours). Ms RH wrote the Math syllabus content for primary, secondary school and junior college levels for a leading group of tuition centres where she taught for 9 years. Ms RH’s private tuition students attended Tao Nan School, Marymount Convent School, Anglo-Chinese School (Barker Road), CHIJ St Nicholas Girls’ School, Hwa Chong Institution Integrated Programme, and Singapore Chinese Girls’ Secondary School Integrated Programme.

Ms GPY has 2 years of Math tuition experience. She has a Bachelor’s in Mathematical Sciences from NTU. Ms GPY’s private tuition students attended Lianhua Primary School, Innova Primary School, River Valley Primary School, Yuan Ching Secondary School, CHIJ St Theresa’s Convent, and St Hilda’s Secondary School.

Ms SK has 11 years of Math tuition experience. She is NIE-trained and taught at MOE schools for 5 years. Ms SK has Bachelor’s in Mathematical Sciences with Minor in Finance from NTU. Ms SK’s home tuition students attended Greenridge Secondary School, Montfort Secondary School, Admiralty Secondary School, Xinmin Secondary School, CHIJ St Joseph’s Convent, and St Andrew’s Secondary School.

Mr BH has 4 years of Math tuition experience. He has a Bachelor’s Mathematical and Computer Sciences from NTU. Mr BH taught at a tuition centre for 3 years. His private tuition students attended Dazhong Primary School, Henry Park Primary School, Jurongville Secondary School, Anglican High School, Jurong Pioneer Junior College, and River Valley High School.

Ms EGL has 9 years of Math tuition experience. She has a Bachelor’s in Mathematical Sciences from NTU (Honours). Ms EGL taught at a tuition centre for 3 years. Her private tuition students attended Yishun Primary School, Fairfield Methodist School (Primary), Bukit Merah Secondary School, Commonwealth Secondary School, Hwa Chong Institution, and Raffles Institution.

Mr FN has 7 years of Math tuition experience. He is NIE-trained, and taught at MOE schools for 9 years. Mr FN has a Bachelor’s in Applied Mathematics from NUS (Honours). Mr FN’s home tuition students attended St Joseph’s Institution, Holy Innocents’ High School, Geylang Methodist School (Secondary), Yusof Ishak Secondary School, Woodlands Ring Secondary School, and Kuo Chuan Presbyterian Secondary School

Mr TY has 3 years of Math tuition experience. He has a Bachelor’s in Mathematics from NUS (2nd Upper Class Honours). Mr TY was a contract teacher at one of Singapore’s top schools for 2 years. His private tuition students attended Raffles Girls’ Primary School, Keming Primary School, Hua Yi Secondary School, Maris Stella High School, Jurong Pioneer Junior College, and National Junior College.

Ms CHH has 7 years of Math tuition experience. She was the Head of Mathematics at a group of tuition centres where she taught for 7 years. Ms CHH has a Master’s in Applied Mathematics at Oxford University. Her Bachelor’s in Mathematical Sciences was from NTU (First Class Honours). Ms CHH’s private tuition students attended Beacon Primary School, Maha Bodhi School, Tanglin Secondary School, Dunman High School Integrated Programme, Anderson Serangoon Junior College, and Eunoia Junior College.

Mr NG has 11 years of Math tuition experience. He has a PhD in Financial Mathematics from the University of California, Berkeley. His Bachelor’s in Applied Mathematics was from NUS (First Class Honours). His private tuition students Victoria School Integrated Programme, NUS High School of Mathematics and Science, Nanyang Girls’ High School Integrated Programme, Methodist Girls’ School (Secondary) IB programme, CHIJ St Nicholas Girls’ School Integrated Programme, and Hwa Chong Institution.

Mr BCL has 5 years of Math tuition experience. He has a Bachelor’s in Mathematics from NUS. Mr BCL taught at a tuition centre for 4 years. His private tuition students attended Northoaks Primary School, Pei Tong Primary School, Bendemeer Secondary School, Crescent Girls’ School, National Junior College, and Yishun Innova Junior College.

Ms ST has 7 years of Math tuition experience. She has a Bachelor’s in Physics and Mathematical Sciences (Double Major) from NTU. Ms ST taught at a leading tuition centre for 5 years. Her private tuition students attended Raffles Girls’ School (Secondary) Integrated Programme, NUS High School of Mathematics and Science, CHIJ St Nicholas Girls’ School Integrated Programme, Hwa Chong Institution, St Andrew’s Junior College, and Eunoia Junior College.

Ms HPG has 2 years of Math tuition experience. She is NIE-trained, and taught at leading MOE schools for 11 years. Ms HPG has a Bachelor’s in Data Science and Artificial Intelligence from NTU (Honours). Her private tuition students attended Cedar Girls’ Secondary School Integrated Programme, Loyang View Secondary School, Anglo-Chinese School (Independent), Punggol Secondary School, Teck Whye Secondary School, and Victoria School.

Ms PBM has 4 years of Math tuition experience. She has a Bachelor’s in Mathematics from NUS. Ms PBM’s private tuition students attended Anglo-Chinese School (Primary), Red Swastika School, St Margaret’s Primary School, Beatty Secondary School, Jurong West Secondary School, and Tanjong Katong Girls’ School.

Mr JS has 11 years of Math tuition experience. He has a Bachelor’s in Mathematics from NUS (2nd Upper Class Honours). He was an MOE contract teacher for 2 years, and taught at a leading tuition centre for 5 years. Mr JS’s private tuition students attended Hougang Secondary School, East Spring Secondary School, Nanyang Girls’ High School Integrated Programme, Jurong Pioneer Junior College, Temasek Junior College, and Dunman High School.

Mr DH has 7 years of Math tuition experience. He has a Master’s in Applied Mathematics from Princeton University. Mr DH’s Bachelor’s in Mathematical Sciences was from NTU (First Class Honours). Mr DH’s private tuition students attended St Anthony’s Canossian Secondary School, Nan Chiau High School, Dunman High School, Anderson Serangoon Junior College, Hwa Chong Institution, and River Valley High School.

Ms GYK has 2 years of Math tuition experience. She is NIE-trained and taught at MOE schools for 6 years. Ms GYK has a Bachelor’s in Mathematical Sciences from NTU (Honours). Her home tuition students attended Gan Eng Seng Primary School, Xinghua Primary School, Anglo-Chinese School (Primary), Kong Hwa School, Ngee Ann Primary School, and St Joseph’s Institution Junior.

Ms FN has 5 years of Math tuition experience. She has a Bachelor’s in Mathematics from NUS (First Class Honours). Ms FN was a contract teacher at a top MOE school for 2 years. Her home tuition students attended Zhangde Primary School, Catholic High School – Primary, Teck Whye Secondary School, Maris Stella High School, Nanyang Junior College, and St Joseph’s Institution.

Mr RC has 11 years of Math tuition experience. He has a Bachelor’s in Mathematics from NUS (2nd Upper Class Honours). Mr RC’s private tuition students attended Si Ling Primary School, Raffles Girls’ Primary School, Northland Secondary School, Catholic High School Integrated Programme, Anglo-Chinese Junior College, and Raffles Institution.

Ms EGH has 13 years of Math tuition experience. She has a Bachelor’s in Mathematical Sciences and Economics (Double Major) from NTU (2nd Upper Class Honours). Ms EGH’s private tuition students attended Singapore Chinese Girls’ Secondary School Integrated Programme, Raffles Girls’ School (Secondary) Integrated Programme, St Patrick’s School, Bowen Secondary School, Eunoia Junior College, and River Valley High School.

Mr WS has 9 years of Math tuition experience. He has a Master’s in Statistics from the University of Michigan. Mr WS’s Bachelor’s in Mathematics was from NUS (First Class Honours). Mr WS taught at a leading tuition centre for 6 years. His private tuition students attended Singapore Chinese Girls’ Primary School, Red Swastika School, River Valley High School Integrated Programme, Catholic High School Integrated Programme, St Andrew’s Junior College, and Raffles Institution.

Mr ML has 4 years of Math tuition experience. He has a Bachelor’s in Mathematical Sciences and Economics (Double Major) from NTU. Mr ML was an MOE contract teacher for 1 year. His private tuition students attended Canossa Catholic Primary School, Anglo-Chinese School (Junior), Yusof Ishak Secondary School, Fairfield Methodist School (Secondary), Nanyang Junior College, and Temasek Junior College.

Ms PTH has 12 years of Math tuition experience. She is NIE-trained, and taught at MOE schools for 7 years. Ms PTH has a Bachelor’s in Quantitative Finance from NUS (Honours). Ms PTH’s private tuition students attended Methodist Girls’ School (Primary), Tampines North Primary School, Telok Kurau Primary School, Dunearn Secondary School, Greenridge Secondary School, and Naval Base Secondary School.

Mr JF has 5 years of Math tuition experience. He has a Bachelor’s in Mathematics from NUS (Honours). Mr JF was an MOE contract teacher for 1 year and he taught at tuition centres for 4 years. Mr JF’s private tuition students attended West Spring Primary School, Haig Girls’ School, Guangyang Secondary School, Nan Hua High School, Jurong Pioneer Junior College, and Yishun Innova Junior College.

Mr SBW has 3 years of Math tuition experience. He has a Bachelor’s in Mathematics from NUS. Mr SBW was an MOE contract teacher for 2 years. His private tuition students attended North View Primary School, Pei Tong Primary School, Qifa Primary School, Bartley Secondary School, Kent Ridge Secondary School, and Nan Hua High School.

Ms HC has 6 years of Math tuition experience. She is NIE-trained, and taught at top junior colleges for 10 years. Ms HC has a Bachelor’s in Data Science & Analytics (2nd Upper Class Honours) from NUS. Her home tuition students attended St Andrew’s Junior College, Hwa Chong Institution, Anderson Serangoon Junior College, Dunman High School, Catholic Junior College, and River Valley High School.

Mr RC has 11 years of Math tuition experience. He has a Bachelor’s in Mathematics from NUS (2nd Upper Class Honours). Mr RC’s private tuition students attended Si Ling Primary School, Raffles Girls’ Primary School, Northland Secondary School, Catholic High School Integrated Programme, Anglo-Chinese Junior College, and Raffles Institution.

Ms TS has 8 years of Math tuition experience. She is NIE-trained and taught at MOE schools for 7 years. Ms TS has a Bachelor’s from NTU, majoring in Mathematics (2nd Upper Class Honours). Her Math tuition students attended Ai Tong School, Kong Hwa School, Fairfield Methodist School (Secondary), NUS High School of Mathematics and Science, Catholic Junior College, Temasek Junior College.

Ms WKL has 15 years of Math tuition experience. She has a Bachelor’s in Mathematics from NUS (Honours). Ms WKL was an MOE contract teacher for 3 years and taught at tuition centres for 8 years. Ms WKL’s private tuiton students attended Meridian Primary School, Marymount Convent School, Naval Base Secondary School, Anglo-Chinese School (Barker Road), Temasek Junior College, and National Junior College.

## Grades Are Always Important

No Matter What Anyone Else Says

## Study Effectively And Confidently

## The MOE states that students must be familiar with:

- Numbers and their operations
- Primes and prime factorisation
- Highest common factor (HCF) and lowest common multiple (LCM),
- squares, cubes, square roots and cube roots by prime factorisation
- Negative numbers, integers, rational numbers, real numbers, and their four
- operations
- Approximation and estimation
- Positive, negative, zero and fractional indices

#### Your Math tuition teacher will clearly explain to you:

- Ratio and proportion
- Ratios involving rational numbers
- Writing a ratio in its simplest form
- Map scales (distance and area)
- Direct and inverse proportion
- Expressing one quantity as a percentage of another
- Comparing two quantities by percentage
- Percentages greater than 100%

- Increasing/decreasing a quantity by a given percentage
- Reverse percentages
- Average rate and average speed
- Conversion of units (e.g. km/h to m/s)
- Using letters to represent numbers
- Interpreting notations
- Evaluation of algebraic expressions and formulae
- Translation of simple real-world situations into algebraic expressions

- Recognising and representing patterns/relationships by finding an algebraic
- expression for the nth term
- Addition and subtraction of linear expressions
- Simplification of linear expressions
- Extract common factors
- Factorisation of linear expressions
- Expansion of the product of algebraic expressions
- Changing the subject of a formula

- Finding the value of an unknown quantity in a given formula Factorisation of quadratic expressions
- Multiplication and division of simple algebraic fractions
- Addition and subtraction of algebraic fractions with linear or quadratic
- denominator
- Cartesian coordinates in two dimensions
- Graph of a set of ordered pairs as a representation of a relationship between two variables

- Linear functions and quadratic functions
- Graphs of linear functions
- The gradient of a linear graph as the ratio of the vertical change to the
- horizontal change (positive and negative gradients)
- Graphs of quadratic functions and their properties:
- Positive or negative coefficient of x2

- Maximum and minimum points
- Symmetry
- Sketching the graphs of quadratic functions
- Positive integers
- Estimation of the gradient of a curve by drawing a tangent
- Solving linear equations in one variable
- Solving simple fractional equations that can be reduced to linear equations
- Substitution and elimination methods

- Problems involving the calculation of the sum and product (where
- appropriate) of two matrices
- Interpreting and analysing data from tables and graphs, including distance–
- time and speed–time graphs
- Interpreting the solution in the context of the problem
- Properties of triangles, special quadrilaterals and regular polygons
- (pentagon, hexagon, octagon and decagon), including symmetry properties
- Classifying special quadrilaterals on the basis of their properties

- Pythagoras’ theorem
- Determining whether a triangle is right-angled given the lengths of three
- sides
- Use of trigonometric ratios (sine, cosine and tangent) of acute angles to
- calculate unknown sides and angles in right-angled triangles
- Extending sine and cosine to obtuse angles
- Problems in two and three dimensions including those involving angles of
- elevation and depression and bearings

- Area of parallelogram and trapezium
- Perimeter and area of composite plane figures
- Volume and surface area of cube, cuboid, prism, cylinder, pyramid, cone
- and sphere
- Volume and surface area of composite solids
- Arc length, sector area and area of a segment of a circle
- Radian measure of angle (including conversion between radians and
- degrees)

- Position vectors, displacement vectors and direction vectors
- Magnitude of a vector
- Collinearity
- Ratio theorem in geometrical applications
- Scalar and vector products in vectors
- Calculation of the magnitude of a vector and the angle between two vectors
- Vector and cartesian equations of lines and planes
- Foot of the perpendicular and distance from a point to a line or to a plane

- Extension of the number system from real numbers to complex numbers
- Complex roots of quadratic equations
- Conjugate of a complex number
- Conjugate roots of a polynomial equation with real coefficients
- Representation of complex numbers in the Argand diagram
- Calculation of modulus (r) and argument (θ) of a complex number
- Multiplication and division of two complex numbers expressed in polar form
- Differentiation of simple functions defined implicitly or parametrically

- Determining the nature of the stationary points (local maximum and minimum points and points of inflexion) analytically, in simple cases, using
- the first derivative test or the second derivative test
- Locating maximum and minimum points using a graphing calculator
- Equations of tangents and normals to curves, including cases where the curve is defined implicitly or parametrically
- Local maxima and minima problems
- Connected rates of change problems
- Derivation of the first few terms of the Maclaurin series
- Repeated differentiation
- Repeated implicit differentiation
- Definite integral as a limit of sum
- Definite integral as the area under a curve
- Area of a region bounded by a curve and lines parallel to the coordinate axes, between a curve and a line, or between two curves
- Area under a curve defined parametrically

- Addition and multiplication principles for counting
- Concepts of permutation and combination
- Addition and multiplication of probabilities
- Use of tables of outcomes, Venn diagrams, tree diagrams, and permutations and combinations techniques to calculate probabilities
- Calculation of conditional probabilities in simple cases

- Discrete random variables, probability distributions, expectations and variances
- Binomial distribution B(n, p) as an example of a discrete probability distribution and use of B(n, p) as a probability model, including
- conditions under which the binomial distribution is a suitable model
- Mean and variance of binomial distribution (without proof)
- Normal distribution as an example of a continuous probability model and its mean and variance

- Probability model
- Standard normal distribution
- Symmetry of the normal curve and its properties
- Population, random and non-random samples
- Sample mean X as a random variable
- Distribution of sample means from a normal population
- Central Limit Theorem to treat sample means as having normal distribution when the sample size is sufficiently large