Singapore Additional Mathematics Curriculum (Scope And Sequence) For 9th Grade And 10th Grade / Secondary 3 And Secondary 4 / GCE O LevelOur 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), oneone function, inverse function and composition of functions
 use the notation f(x) = sin x, f: x > lg x, (x > 0), f^{ 1}(x) and f^{2} (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 oneone function and form composite functions
 use sketch graphs to show the relationship between a function and its inverse
Quadratic functions  find the maximum or minimum value of the quadratic function f : x > ax^{2} + 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 e^{x} (series expansions are not required)
 know and use the laws of logarithms (including change of base of logarithms)
 solve equations of the form a^{x}= b
Straight line graphs  interpret the equation of a straight line graph in the form y = m x + c
 transform given relationships, including y = ax^{n} and y = Ab^{x}, to straight line form and hence determine unknown constants by calculating the gradient or intercept of the transformed graph
 solve questions involving midpoint 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, sin^{2} A + cos^{2} A = 1, sec^{2} A = 1 + tan^{2} A, cosec^{2} A = 1 + cot^{2} 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 (^{n}_{r})a^{n  r} b^{r}, 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. (^{a}_{b}), 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 nonsingular 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, d^{2}y/dx^{2} [=d/dx(dy/dx)]
 use the derivatives of the standard functions x^{n} (for any rational n), sin x, cos x, tan x, e^{x}, 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), e^{ax+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 xt and vt graphs
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