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Singapore Mathematics Curriculum (Scope And Sequence) For 9th Grade
and 10th Grade / Secondary 3 and Secondary 4 / GCE O Level
Our Singapore Math books for 9th Grade /
Secondary 3 and Singapore Math books for 10th
Grade / Secondary 4 are written in English and based on the Singapore
Maths curriculum for 9th Grade and 10th Grade / Secondary 3 and
Secondary 4 / GCE O Level, which covers the following topics.
If your child uses our Singapore Math books for 9th Grade / Secondary 3
and Singapore Math books for 10th Grade / Secondary 4, he will be able to:
(Some of the following symbols may not display properly.)
Numbers
- use natural numbers, integers (positive, negative and zero), prime
numbers, common factors and common multiples, rational and irrational
numbers, real numbers
- continue given number sequences, recognise patterns within and
across different sequences and generalise to simple algebraic
statements (including expressions for the nth term ) relating to such
sequences
Squares, square roots, cubes and cube roots
- calculate squares, square roots, cubes and cube roots of numbers
Vulgar and decimal fractions and percentages
- use the language and notation of simple vulgar and decimal fractions
and percentages in appropriate contexts
- recognise equivalence and convert between these forms
Ordering
- order quantities by magnitude and demonstrate familiarity with the
symbols =, (not equal)‚, >, <, (greater than or equal to
symbol), (smaller than or equal to symbol)
Standard form
- use the standard form A x 10n where n is a positive or
negative integer, and 1 (less than or equal to symbol) A <10
The four operations
- use the four operations for calculations with whole numbers, decimal
fractions and vulgar (and mixed) fractions, including correct ordering
of operations and use of brackets
Estimation
- make estimates of numbers, quantities and lengths
- give approximations to specified numbers of significant figures and
decimal places
- round off answers to reasonable accuracy in the context of a given
problem
Ratio, proportion, rate
- demonstrate an understanding of the elementary ideas and notation of
ratio, direct and inverse proportion and common measures of rate
- divide a quantity in a given ratio
- use scales in practical situations
- calculate average speed
- express direct and inverse variation in algebraic terms and use this
form of expression to find unknown quantities
Percentages
- calculate a given percentage of a quantity
- express one quantity as a percentage of another
- calculate percentage increase or decrease
- carry out calculations involving reverse percentages, e.g. finding
the cost price given the selling price and the percentage profit
Use of a scientific calculator
- use a scientific calculator efficiently
- apply appropriate checks of accuracy
Everyday mathematics
- use directed numbers in practical situations (e.g. temperature
change, tide levels)
- use current units of mass, length, area, volume, capacity and time
in practical situations (including expressing quantities in terms of
larger or smaller units)
- calculate times in terms of the 12-hour and 24-hour clock (including
reading of clocks, dials and timetables)
- solve problems involving money and convert from one currency to
another
- use given data to solve problems on personal and household finance
involving earnings, simple interest, compound interest (without the
use of formula), discount, profit and loss
- extract data from tables and charts
Graphs in practical situations
- interpret and use graphs in practical situations including travel
graphs and conversion graphs
- draw graphs from given data
- apply the idea of rate of change to easy kinematics involving
distance-time and speed-time graphs, acceleration and retardation
- calculate distance travelled as area under a linear speed-time graph
Graphs of functions
- construct tables of values and draw graphs for functions of the form
y = axn where n = -2, -1, 0, 1, 2, 3, and simple sums of
not more than three of these and for functions of the form y = kax
where a is a positive integer
- interpret graphs of linear, quadratic, reciprocal and exponential
functions
- find the gradient of a straight line graph
- solve equations approximately by graphical methods
- estimate gradients of curves by drawing tangents
Coordinate geometry
- demonstrate familiarity with cartesian coordinates in two dimensions
- calculate the gradient of a straight line from the coordinates of
two points on it
- interpret and obtain the equation of a straight line graph in the
form y = mx + c
- calculate the length and the coordinates of the midpoint of a line
segment from the coordinates of its end points
Algebraic representation and formulae
- use letters to express generalised numbers and express basic
arithmetic processes algebraically
- substitute numbers for words and letters in formulae
- transform simple and more complicated formulae
- construct equations from given situations
Algebraic manipulation
- manipulate directed numbers
- use brackets and extract common factors
- expand products of algebraic expressions
- factorise expressions of the form ax + ay; ax + bx + kay + kby; a2x2
- b2y2; a2 + 2ab + b2; ax2
+ bx + c
- manipulate simple algebraic fractions
Indices
- use and interpret positive, negative, zero and fractional indices
Solutions of equations and inequalities
- solve simple linear equations in one unknown
- solve fractional equations with numerical and linear algebraic
denominators
- solve simultaneous linear equations in two unknowns
- solve quadratic equations by factorisation and either by use of the
formula or by completing the square
- solve simple linear inequalities
Geometrical terms and relationships
- use and interpret the geometrical terms: point, line plane,
parallel, perpendicular, right angle, acute, obtuse and reflex angles,
interior and exterior angles, regular and irregular polygons,
pentagons, hexagons, octagons, decagons
- use and interpret vocabulary of triangles, circles, special
quadrilaterals
- solve problems (including problems leading to some notion of proof)
involving similarity and congruence
- use and interpret vocabulary of simple solid figures: cube, cuboid,
prism, cylinder, pyramid, cone, sphere
- use the relationships between areas of similar triangles, with
corresponding results for similar figures and extension to volumes of
similar solids
Geometrical constructions
- measure lines and angles
- construct simple geometrical figures from given data using
protractors or set squares as necessary
- construct angle bisectors and perpendicular bisectors using straight
edges and compasses only
- read and make scale drawings. (Where it is necessary to construct a
triangle given the three sides, ruler and compasses only must be
used.)
Bearings
- interpret and use three-figure bearings measured clockwise from the
north (i.e. 000o-360o)
Symmetry
- recognise line and rotational symmetry (including order of
rotational symmetry) in two dimensions, and properties of triangles,
quadrilaterals and circles directly related to their symmetries
- recognise symmetry properties of the prism (including cylinder) and
the pyramid (including cone)
- use the following symmetry properties of circles:
- equal chords are equidistant from the centre
- the perpendicular bisector of a chord passes through the centre
- tangents from an external point are equal in length
Angle
- calculate unknown angles and solve problems (including problems
leading to some notion of proof) using the following geometrical
properties:
- angles on a straight line
- angles at a point
- vertically opposite angles
- angles formed by parallel lines
- angle properties of triangles and quadrilaterals
- angle properties of polygons including angle sum
- angle in a semi-circle
- angle between tangent and radius of a circle
- angle at the centre of a circle is twice the angle at the
circumference
- angles in the same segment are equal
- angles in opposite segments are supplementary
Locus
- use the following loci and the method of intersecting loci:
- set of points in two dimensions
- which are at a given distance from a given point
- which are at a given distance from a given straight line
- which are equidistant from two given points
- sets of points in two dimensions which are equidistant from two
given intersecting straight lines
Mensuration
- solve problems involving:
- the perimeter and area of a rectangle and a triangle
- the circumference and area of a circle
- the area of a parallelogram and a trapezium
- the surface area and volume of a cuboid, cylinder, prism,
sphere, pyramid and cone. (Formulae will be given for the sphere,
pyramid and cone.)
- arc length and sector area as fractions of the circumference and
area of a circle
Trigonometry
- apply Pythagoras theorem and the sine, cosine and tangent ratios for
acute angles to the calculation of a side or of an angle of a
right-angled triangle (angles will be quoted in, and answers required
in, degrees and decimals of a degree to one decimal place)
- solve trigonometrical problems in two dimensions including those
involving angles of elevation and depression and bearings
- extend sine and cosine functions to angles between 90o
and 180o
- solve problems using the sine and cosine rules for any triangle and
the formula 1/2 ab sinC for the area of a triangle
- solve simple trigonometrical problems in three dimensions.
(Calculations of the angle between two planes or of the angle between
a straight line and a plane will not be required.)
Statistics
- collect, classify and tabulate statistical data
- read, interpret and draw simple inferences from tables and
statistical diagrams
- construct and use bar charts, pie charts, pictograms, dot diagrams,
stem-and-leaf diagrams, simple frequency distributions and frequency
polygons
- use frequency density to construct and read histograms with equal
and unequal intervals
- calculate the mean, median and mode for individual data and
distinguish between the purposes for which they are used
- construct and use cumulative frequency diagrams
- estimate the median, percentiles, quartiles and interquartile range
from the cumulative frequency diagrams
- calculate the mean for grouped data
- identify the modal class from a grouped frequency distribution
Probability
- calculate the probability of a single event as either a fraction or
a decimal (not a ratio)
- calculate the probability of simple combined events, using
possibility diagrams and tree diagrams where appropriate (in
possibility diagrams outcomes will be represented by points on a grid
and in tree diagrams outcomes will be written at the end of branches
and probabilities by the side of the branches)
Transformations
- use the following transformations of the plane: reflection (M),
rotation (R), translation (T), enlargement (E), shear (H), stretch (S)
and their combinations (if M(a)=b and R(b)=c the notation RM(a)=c will
be used; invariants under these transformations may be assumed)
- identify and give precise descriptions of transformations connecting
given figures
Vectors in two dimensions
- describe a translation by using a vector represented by (xy),
AB or a; . add vectors
and multiply a vector by a scalar
- calculate the magnitude of a vector (xy) as
the square root of (x2+y2). (Vectors will be
printed as AB or
a and their magnitudes denoted by modulus signs, e.g. |AB|
or |a|. In their answers to questions candidates are expected to
indicate a in some definite way, e.g. by an arrow or by underlining,
thus AB or a)
- represent vectors by directed line segments
- use the sum and difference of two vectors to express given vectors
in terms of two coplanar vectors
- use position vectors
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