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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
Quadratic functions
- 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
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