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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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