# You Want To See Rapidly-Improved Results

### We Have Singapore’s Largest Team Of Effective Private Tuition Teachers*

### Latest MOE Syllabus

##### *Based On Feedback And Reviews By Parents & Students Every Year

## Within 4 Lessons:

- Learn how to prevent the common mistakes and wrong habits that will lead you to writing imprecise answers
- Avoid “mental blocks”, cope with exam stress, prevent any tendency to make careless mistakes
- We will show you crucial analytical steps that lead you to the right answers, no matter how “tricky” the Math questions are
- Difficult questions will not surprise you any more, because you would be familiar with the skills you need in order to correctly answer what is required
- Pace yourself, so that you have enough time to answer every Math exam question, as well as to check your answers at least once before you hand in your work
- Start on a systematic approach to strengthen the answering skills that require you to compare, contrast and use critical/creative thinking techniques

#### Singapore Tuition Is Single-Minded In Helping You Boost Your Scores

## Starting Today

Our tuition coordinators are former MOE teachers from good schools.

We are very familiar with how to properly shortlist and interview the correct home tutors before we show you between 4 to 10 profiles of qualified tutors.

Each of these private tutors have proven experience in dependably helping their students’ grades quickly improve by at least 10 to 20 marks – as shown in the good feedback that parents had given to us.

Our accomplished tutors each have between 2 to over 30 years of teaching and tutoring experience in primary/secondary school, junior college home tuition.

We have a strong team of tuition teachers who specialize in preparing students for the important PSLE, GCE O and A Level exams.

Every year since 2006, we have helped satisfied clients hire their perfect tutors.

Our team of 31,000 experienced tutors comprise MOE teachers, PhD-tutors, graduated/post-graduate/undergraduate tutors.

There are Math tests and exams in school every few weeks. Once any student does not pay strict attention in class for 1 to 2 weeks, it is close to impossible to catch up.

Being wrongly-prepared for your school and national exams will impact your prospects of being admitted to the class, school and university of your choice.

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## Hire The Best Tuition Teacher From Our Large Database - And Have Peace Of Mind

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## You Can Be On Your Way To An Easy Distinction

### Dependable & Qualified Private Tutors

Latest MOE Syllabus

**Prepare well. Put yourself ahead of those who are competing with you to get into a good class, school or university. And have a successful career**

## Improve By 10 to 25 Marks Within 1 Semester

#### Reliable Professional Tutors

Latest Exam Requirements

Trusted By Parents & Students Annually

### Math And Science

## Featured Professional Tutors

Mr BH has 7 years of Math tuition experience. He is NIE-trained, and taught at MOE schools for 9 years. Mr BH has a Bachelor’s in Applied Mathematics from NUS (Honours). Mr BH’s private 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 RTW 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 RTW’s home tuition students attended Palm View Primary School, Rosyth School, Temasek Primary School, Deyi Secondary School, Fuchun Secondary School, and Dunman High School Integrated Programme.

Ms CN has 14 years of Math tuition experience. She has a Bachelor’s in Applied Mathematics from NUS (First Class Honours). Ms CN was the Head of Mathematics at the group of tuition centres where she taught for 8 years. Ms CN’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.

Ms DH has 6 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 DH’s home 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 ST has 3 years of Math tuition experience. He has a Bachelor’s in Computer Science & Applied Mathematics from NUS (Honours). His private tuition students attended Oasis Primary School, Jing Shan Primary School, Cedar Girls’ Secondary School, Bowen Secondary School, Catholic Junior College, and Nanyang Junior College.

Ms LPC has 7 years of Math tuition experience. She has a Master’s in Applied Mathematics from Princeton University. Ms LPC’s Bachelor’s in Mathematical Sciences was from NTU (First Class Honours). Ms LPC’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.

## Learn From An Expert - Score an A

#### Committed Responsible Math Tutors

Many Successful Students

## Profiles Of Popular Math Tutors

Mr MZB has 16 years of Math tuition experience. He is NIE-trained, and taught at MOE schools for 11 years. Mr MZB has a Bachelor’s in Quantitative Finance from NUS (2nd Upper Class Honours). Mr MZB’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.

Ms GF has 4 years of Math tuition experience. She has a Bachelor’s in Mathematical Sciences from NTU. Ms GF taught at a tuition centre for 3 years. Her 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 PSH has 11 years of Math tuition experience. She has a Master’s in Statistics from the University of Michigan. Ms PSH’s Bachelor’s in Mathematics was from NUS (First Class Honours). Ms PSH taught at a leading tuition centre for 7 years. Her 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 RK has 3 years of Math tuition experience. He has a Bachelor’s Mathematical and Computer Sciences from NTU. Mr RK taught at a tuition centre for 2 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 DS has 9 years of Math tuition experience. She was the Head of Mathematics at a group of tuition centres where she taught for 8 years. Ms DS has a Master’s in Applied Mathematics from Oxford University. Her Bachelor’s in Mathematical Sciences was from NTU (First Class Honours). Ms DS’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.

Ms PFB has 3 years of Math tuition experience. She is NIE-trained, and taught at leading MOE schools for 12 years. Ms PFB has a Bachelor’s in Data Science and Artificial Intelligence from NTU (Honours). Her home 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.

Mr TN has 9 years of Math tuition experience. He has a Bachelor’s in Mathematical and Computer Sciences (Double Major) from NTU (Honours). Mr TN was an MOE contract teacher for 2 years and had taught at tuition centres for 4 years. Mr TN’s home 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 YWG has 7 years of Math tuition experience. She has a PhD in Financial Mathematics from the University of California, Berkeley. Her Bachelor’s in Applied Mathematics was from NUS (First Class Honours). Ms YWG’s 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.

Ms AL has 3 years of Math tuition experience. She has a Bachelor’s in Mathematics from NUS. Ms AL was an MOE contract teacher for 2 years. Her 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.

Mr NKW has 8 years of Math tuition experience. He has a PhD in Mathematics from the University of Cambridge. Mr NKW’s Bachelor’s in Mathematics was from NUS (First Class Honours). Mr NKW was an MOE contract teacher for 2 years. His private 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 HG has 12 years of Math tuition experience. He is NIE-trained and taught at MOE schools for 9 years. Mr HG 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.

Ms SP has 5 years of Math tuition experience. She has a Bachelor’s in Mathematical Sciences and Economics (Double Major) from NTU. Ms SP was an MOE contract teacher for 2 years. Her 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 CL has 14 years of Math tuition experience. She has a Bachelor’s in Mathematical Sciences from NTU (Honours). Ms CL taught at a tuition centre for 5 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 BH 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 BH was a contract teacher at one of Singapore’s top junior colleges for 2 years. His home tuition students attended Nanyang Junior College, Victoria Junior College, Raffles Institution, Eunoia Junior College, Anderson Serangoon Junior College, and Anglo-Chinese Junior College.

Ms WPS has 2 years of Math tuition experience. She has a Bachelor’s in Mathematics from NUS (2nd Upper Class Honours). Ms WPS was a contract teacher at one of Singapore’s top schools for 1 year. Her 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 HN has 12 years of Math tuition experience. She is NIE-trained and taught at MOE schools for 7 years. Ms HN has Bachelor’s in Mathematical Sciences with Minor in Finance from NTU. Ms HN’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 WTA has 15 years of Math tuition experience. He has a Master’s in Applied Mathematics from Yale University and a Bachelor’s in Mathematical Sciences from NTU (First Class Honours). Mr WTA 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. Mr WTA’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 YP has 13 years of Math tuition experience. She is NIE-trained, and taught at MOE schools for 8 years. Ms NP has a Bachelor’s in Quantitative Finance from NUS (Honours). Ms NP’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.

Ms GK has 4 years of Math tuition experience. She has a Bachelor’s in Mathematics from NUS (Honours). Ms GK was an MOE contract teacher for 1 year and she taught at tuition centres for 3 years. Ms GK’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 SLM has 13 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 SLM’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 HT has 7 years of Math tuition experience. He is NIE-trained, and taught at MOE schools for 9 years. He has a Bachelor’s in Quantitative Finance from NUS (2nd Upper Class Honours). Mr HT’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 RN has 2 years of Math tuition experience. She has a Bachelor’s in Mathematical Sciences from NTU. Ms RN’s home 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 ACY has 15 years of Math tuition experience. She has a Bachelor’s in Mathematical Sciences and Economics (Double Major) from NTU (2nd Upper Class Honours). Ms ACY’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.

Ms BL has 4 years of Math tuition experience. She has a Bachelor’s in Mathematics from NUS (First Class Honours). Ms BL was a contract teacher at a top MOE school for 2 years. Her private 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 TNP has 6 years of Math tuition experience. He is NIE-trained, and taught at top junior colleges for 9 years. Mr TNP has a Bachelor’s in Data Science & Analytics (2nd Upper Class Honours) from NUS. His private 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 CY has 4 years of Math tuition experience. He has a Bachelor’s in Mathematics from NUS. Mr CY taught at a tuition centre for 3 years. His home 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 MW has 8 years of Math tuition experience. She has a Bachelor’s in Physics and Mathematical Sciences (Double Major) from NTU. Ms MW 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.

Mr KJG has 2 years of Math tuition experience. He has a Bachelor’s in Mathematics from NUS. Mr KJG 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.

Mr CSM has 8 years of Math tuition experience. He has a Bachelor’s in Mathematics from NUS (First Class Honours). Mr CSM wrote the Math curriculum for primary and secondary school levels at a leading group of tuition centres. Mr CSM’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 YH has 11 years of Math tuition experience. He has a Bachelor’s in Mathematics from NUS (2nd Upper Class Honours). Mr YH’s home 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 GCM has 6 years of Math tuition experience. She has a Bachelor’s in Mathematical and Computer Sciences (Double Major) from NTU. Ms GCM was an MOE contract teacher for 1 year. Her home 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 RK has 2 years of Math tuition experience. He has a Bachelor’s in Mathematics from NUS. Mr RK’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.

Ms CLH has 2 years of Math tuition experience. She is NIE-trained and taught at MOE schools for 11 years. Ms CLH has a Bachelor’s in Mathematical Sciences from NTU (Honours). Her private 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 AT has 9 years of Math tutoring experience. She has a Bachelor’s in Engineering Mathematics from NTU (2nd Upper Class Honours). Ms AT taught at Singapore’s leading tuition centres for 5 years. Her private tuition students attended Methodist Girls’ School (Primary), Red Swastika School, Dunman High School Integrated Programme, St Andrew’s Secondary School, Anglo-Chinese Junior College, and Catholic Junior College.

Mr MC has 16 years of Math tuition experience. He has a Master’s in Applied Mathematics from Yale University and a Bachelor’s in Mathematical Sciences from NTU (First Class Honours). Mr MC 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. Mr MC’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 GJN has 11 years of Math tuition experience. She has a Bachelor’s in Mathematics from NUS and was an MOE contract teacher for 3 years. Ms GJN’s home tuition students attended Raffles Girls’ Primary School, Ai Tong School, CHIJ Secondary (Toa Payoh), Hai Sing Catholic School, Jurong Pioneer Junior College, and Raffles Institution

Ms LW has 6 years of Math tuition experience. She is NIE-trained and taught at MOE schools for 8 years.

## You Can Be On Your Way To An Easy Distinction

### Improve By 10 to 25 Marks This Semester

Experienced Qualified Math Tutors

Learn Important Exam Skills

##### 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 Qualified 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