 # 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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