 Singapore Additional Mathematics Curriculum (Scope And Sequence) For 9th Grade And 10th Grade / Secondary 3 And Secondary 4 / GCE O Level

Our Singapore Additional Math books for 9th Grade / Secondary 3 and Singapore Additional Math books for 10th Grade / Secondary 4 are written in English and based on the Singapore Additional Math curriculum for 9th Grade And 10th Grade / Secondary 3 And Secondary 4, which covers the following topics.

If your child uses our Singapore Additional Math books for 9th Grade / Secondary 3 and Singapore Additional Math books for 10th Grade / Secondary 4, he will be able to:

(Some of the following symbols may not display properly.)

Set language and notation

• use set language and notation, and Venn diagrams to describe sets and represent relationships between sets as follows:
• A = {x: x is a natural number}
• B = {(x, y): y = mx + c}
• C = {x: a < x < b }
• D = {a, b, c,. . . }
• understand and use the notation for the following :
• Union of A and B
• Intersection of A and B
• Number of elements in set A
• ". . . is an element of . . ."
• ". . . is not an element of . . ."
• Complement of set A
• The empty set
• Universal set
• A is a subset of B
• A is a proper subset of B
• A is not a subset of B
• A is not a proper subset of B

Functions

• understand the terms function, domain, range (image set), one-one function, inverse function and composition of functions
• use the notation f(x) = sin x, f: x --> lg x, (x > 0), f -1(x) and f2 (x) [=f(f(x))]
• understand the relationship between y = f(x) and y = | f(x) |, where f(x) may be linear, quadratic or trigonometric
• explain in words why a given function is a function or why it does not have an inverse
• find the inverse of a one-one function and form composite functions
• use sketch graphs to show the relationship between a function and its inverse

• find the maximum or minimum value of the quadratic function f : x --> ax2 + bx + c by any method
• use the maximum or minimum value of f(x) to sketch the graph or determine the range for a given domain
• know the conditions for f(x) = 0 to have (i) two real roots, (ii) two equal roots, (iii) no real roots; and the related conditions for a given line to (i) intersect a given curve, (ii) be a tangent to a given curve, (iii) not intersect a given curve
• solve quadratic equations for real roots and find the solution set for quadratic inequalities

Indices and surds

• perform simple operations with indices and with surds, including rationalising the denominator

Factors of polynomials

• know and use the remainder and factor theorems
• find factors of polynomials
• solve cubic equations

Simultaneous equations

• solve simultaneous equations in two unknowns with at least one linear equation

Logarithmic and exponential functions

• know simple properties and graphs of the logarithmic and exponential functions including lnx and ex (series expansions are not required)
• know and use the laws of logarithms (including change of base of logarithms)
• solve equations of the form ax= b

Straight line graphs

• interpret the equation of a straight line graph in the form y = m x + c
• transform given relationships, including y = axn and y = Abx, to straight line form and hence determine unknown constants by calculating the gradient or intercept of the transformed graph
• solve questions involving mid-point and length of line
• know and use the condition for two lines to be parallel or perpendicular

Circular measure

• solve problems involving the arc length and sector area of a circle, including knowledge and use of radian measure

Trigonometry

• know the six trigonometric functions of angles of any magnitude (sine, cosine, tangent, secant, cosecant, cotangent)
• understand amplitude and periodicity and the relationship between graphs of e.g. sin x and sin 2x
• draw and use the graphs of y = a sin(bx) + c, y = a cos(bx) + c, y = a tan(bx) + c, where a, b are positive integers and c is an integer
• use the relationships sin A / cos A = tan A, cos A / sin A = cot A, sin2 A + cos2 A = 1, sec2 A = 1 + tan2 A, cosec2 A = 1 + cot2 A, and solve simple trigonometric equations involving the six trigonometric functions and the above relationships (not including general solution of trigonometric equations)
• prove simple trigonometric identities

Permutations and combinations

• recognise and distinguish between a permutation case and a combination case
• know and use the notation n!, (with 0! = 1), and the expressions for permutations and combinations of n items taken r at a time
• answer simple problems on arrangement and selection (cases with repetition of objects, or with objects arranged in a circle or involving both permutations and combinations, are excluded)

Binomial expansions

• use the Binomial Theorem for expansion of (a + b)n for positive integral n
• use the general term (nr)an - r br, 0 < r < n (knowledge of the greatest term and properties of the coefficients is not required)

Vectors in 2 dimensions

• use vectors in any form, e.g. (ab), p, ai - bj
• know and use position vectors and unit vectors
• find the magnitude of a vector. Add and subtract vectors and multiply vectors by scalars
• compose and resolve velocities
• use relative velocity including solving problems on interception (but not closest approach)

Matrices

• display information in the form of a matrix of any order and interpret the data in a given matrix
• solve problems involving the calculation of the sum and product (where appropriate) of two matrices and interpret the results
• calculate the product of a scalar quantity and a matrix
• use the algebra of 2 x 2 matrices (including the zero and identity matrix)
• calculate the determinant and inverse of a non-singular 2 x 2 matrix and solve simultaneous line equations

Differentiation and integration

• understand the idea of a derived function
• use the notations f '(x), f "(x), dy/dx, d2y/dx2 [=d/dx(dy/dx)]
• use the derivatives of the standard functions xn (for any rational n), sin x, cos x, tan x, ex, lnx, together with constant multiples, sums and composite functions of these
• differentiate products and quotients of functions
• apply differentiation to gradients, tangents and normals, stationary points, connected rates of change, small increments and approximations and practical maxima and minima problems
• discriminate between maxima and minima by any method
• understand integration as the reverse process of differentiation
• integrate sums of terms in powers of x excluding 1/x
• integrate functions of the form (ax + b)n (excluding n = -1), eax+b, sin (ax + b), cos (ax + b)
• evaluate definite integrals and apply integration to the evaluation of plane areas
• apply differentiation and integration to kinematics problems that involve displacement, velocity and acceleration of a particle moving in a straight line with variable or constant acceleration, and the use of x-t and v-t graphs

Please enter a number in the Qty box next to the products that you want to order, and then click on the Add to cart button.

You Save1

Qty

S34SGBOXAMSGBox Singapore Additional Math Curriculum For 9th Grade And 10th Grade / Secondary 3 And Secondary 4Editor’s PickUSD97.88USD0.10 (0%) S3SGBOXMSGBox Singapore Math Curriculum For Ninth Grade / Grade 9 / Secondary 3Rave customer testimonials , Editor’s PickUSD301.88USD12.04 (4%) 1 This is the total amount that you save compared to ordering the equivalent number of items in each pack separately (a la carte).

Recommended complementary products

Qty

DIS3MABDiscounted Math Achiever Book B For Ninth Grade / Grade 9 / Secondary 3 (1st page before preface missing)USD27.99 DIS3NSMDiscounted New Syllabus Mathematics For Ninth Grade / Grade 9 / Secondary 3 Package (7th edition,1st page before preface missing)USD47.99 GCEOLAMSMTGCE O Level Additional Mathematics Past Years' Questions And Solutions Manual (Topical)USD29.99 GCEOLAMSMYGCE O Level Additional Mathematics Past Years' Questions And Solutions Manual (Yearly)USD29.99 OLEMC1GCE O Level Elementary Maths Companion 1USD29.99 OLEMC2GCE O Level Elementary Maths Companion 2USD29.99 GCEOLMSMYGCE O Level Mathematics Past Years' Questions And Solutions Manual (Yearly)USD29.99 OLMPGCE O Level Maths PapersUSD29.99 S3MAAMath Achiever Book A For Ninth Grade / Grade 9 / Secondary 3USD29.99 S3MABMath Achiever Book B For Ninth Grade / Grade 9 / Secondary 3USD29.99 S3MLTEMath Learning Through Examples For Ninth Grade / Grade 9 / Secondary 3USD27.99 S3MTA1Math Tutor For Ninth Grade / Grade 9 / Secondary 3 Book 3A Part 1USD27.99 S3MTA2Math Tutor For Ninth Grade / Grade 9 / Secondary 3 Book 3A Part 2USD27.99 S3MTBMath Tutor For Ninth Grade / Grade 9 / Secondary 3 Book 3BUSD29.99 S34NSAMNew Syllabus Additional Mathematics For 9th Grade And 10th Grade / Secondary 3 And Secondary 4 Package (10th Edition)BestsellerUSD67.99 S3NSMNew Syllabus Mathematics For Ninth Grade / Grade 9 / Secondary 3 Package (7th Edition)Rave customer testimonialsUSD49.99 S3NSMTB New Syllabus Mathematics For Ninth Grade / Grade 9 / Secondary 3 Textbook USD43.60 S3NSMWB New Syllabus Mathematics For Ninth Grade / Grade 9 / Secondary 3 Workbook USD16.40 S3NSMWSMNew Syllabus Mathematics For Ninth Grade / Grade 9 / Secondary 3 Workbook Solutions Manual (7th Edition)USD89.99 You Save1

Qty

S34SGBOXAMSGBox Singapore Additional Math Curriculum For 9th Grade And 10th Grade / Secondary 3 And Secondary 4Rave customer testimonials , Editor’s PickUSD97.88USD0.10 (0%) S4SGBOXMSGBox Singapore Math Curriculum For Tenth Grade / Grade 10 / Secondary 4Editor’s PickUSD273.88USD42.04 (13%) 1 This is the total amount that you save compared to ordering the equivalent number of items in each pack separately (a la carte).

Recommended complementary products

Qty

S34AAPTB All About Physics For 9th Grade And 10th Grade / Secondary 3 And Secondary 4 Textbook USD56.00 DIS4NSMDiscounted New Syllabus Mathematics For Tenth Grade / Grade 10 / Secondary 4 Package (7th edition,1st page before preface missing)USD47.99 DIS4NSMWSMDiscounted New Syllabus Mathematics For Tenth Grade / Grade 10 / Secondary 4 Workbook Solutions Manual (7th Edition, 1st page before preface missing)USD87.99 GCEOLAMSMTGCE O Level Additional Mathematics Past Years' Questions And Solutions Manual (Topical)USD29.99 GCEOLAMSMYGCE O Level Additional Mathematics Past Years' Questions And Solutions Manual (Yearly)USD29.99 OLEMC1GCE O Level Elementary Maths Companion 1USD29.99 OLEMC2GCE O Level Elementary Maths Companion 2USD29.99 GCEOLMSMYGCE O Level Mathematics Past Years' Questions And Solutions Manual (Yearly)USD29.99 OLMPGCE O Level Maths PapersUSD29.99  S4MTAMath Tutor For Tenth Grade / Grade 10 / Secondary 4 Book 4AUSD29.99 S4MTB1Math Tutor For Tenth Grade / Grade 10 / Secondary 4 Book 4B Part 1USD27.99 S4MTB2Math Tutor For Tenth Grade / Grade 10 / Secondary 4 Book 4B Part 2USD27.99 S34NSAMNew Syllabus Additional Mathematics For 9th Grade And 10th Grade / Secondary 3 And Secondary 4 Package (10th Edition)BestsellerUSD67.99 S4NSMNew Syllabus Mathematics For Tenth Grade / Grade 10 / Secondary 4 Package (7th Edition)Rave customer testimonialsUSD49.99 S4NSMTB New Syllabus Mathematics For Tenth Grade / Grade 10 / Secondary 4 Textbook USD43.60 S4NSMWB New Syllabus Mathematics For Tenth Grade / Grade 10 / Secondary 4 Workbook USD16.40 S4NSMWSMNew Syllabus Mathematics For Tenth Grade / Grade 10 / Secondary 4 Workbook Solutions Manual (7th Edition)USD89.99 SPS4DMSpecial Order Discovering Mathematics For Tenth Grade / Grade 10 / Secondary 4 Package (2nd Edition)USD49.99       follow us  