Singapore Mathematics Curriculum (Scope And Sequence) For 9th Grade and 10th Grade / Secondary 3 and Secondary 4 / GCE O LevelOur 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 10^{n} 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 12hour and 24hour 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 distancetime and speedtime graphs, acceleration and retardation
 calculate distance travelled as area under a linear speedtime graph
Graphs of functions  construct tables of values and draw graphs for functions of the form y = ax^{n} 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; a^{2}x^{2}  b^{2}y^{2}; a^{2} + 2ab + b^{2}; ax^{2} + 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 threefigure bearings measured clockwise from the north (i.e. 000^{o}360^{o})
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 semicircle
 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 rightangled 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 90^{o} and 180^{o}
 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, stemandleaf 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 (^{x}_{y}), AB or a; . add vectors and multiply a vector by a scalar
 calculate the magnitude of a vector (^{x}_{y}) as the square root of (x^{2}+y^{2}). (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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