simsenghuat, May 20, 2017

This Geogebra book is being compiled with an aim to enhance teaching and learning for teachers and students in Singapore taking the GCE Syllabus examination. It leverages on the collective efforts of all who create teaching and learning resources using the Geogebra tools and align the topics according to SEAB GCE Mathematics Syllabus published on their website.

• primes and prime factorisation • finding highest common factor (HCF) and lowest common multiple (LCM), squares, cubes, square roots and cube roots by prime factorisation • negative numbers, integers, rational numbers, real numbers, and their four operations • calculations with calculator • representation and ordering of numbers on the number line • use of the symbols I, K, Y, [ • approximation and estimation (including rounding off numbers to a required number of decimal places or significant figures and estimating the results of computation) • use of standard form A × 10n , where n is an integer, and 1 Y A I 10 • positive, negative, zero and fractional indices • laws of indices

• 1. Copy of IM Grade 6: Unit 7 - Rational Numbers
• 2. Check if Number is Prime
• 3. Prime Factorization
• 4. HCF & LCM of Two Numbers by Short Division
• 5. What is a square root?
• 6. Estimate the percent shaded in
• 7. Approximation: Decimal Places VS Significant Figures
• 8. addition and subtraction of directed numbers
• 9. Meaning of Indices
• 10. Index laws - multiplication
• 11. Index laws - division
• 12. Power of Powers
• 13. Scientific Notation

• ratios involving rational numbers • writing a ratio in its simplest form • map scales (distance and area) • direct and inverse proportion

• 1. Copy of IM Grade 7: Unit 2 - Introducing Proportional Relationships
• 2. Continued Ratio 連比
• 3. Simplifying ratios
• 4. Map Scales [ Area ]

• expressing one quantity as a percentage of another • comparing two quantities by percentage • percentages greater than 100% • increasing/decreasing a quantity by a given percentage • reverse percentages

• 1. Copy of IM Grade 7: Unit 4 - Proportional Relationships and Percentages
• 2. Fractions & Percentages 分數和百分數
• 3. Percentage Increase/Decrease Bar Model
• 4. Percentage Changes

• average rate and average speed • conversion of units (e.g. km/h to m/s)

• 1. Speed Distance Time Calculations

using letters to represent numbers • interpreting notations: • evaluation of algebraic expressions and formulae • translation of simple real-world situations into algebraic expressions • recognising and representing patterns/relationships by finding an algebraic expression for the nth term • addition and subtraction of linear expressions • simplification of linear expressions such as: • use brackets and extract common factors • factorisation of linear expressions of the form ax + bx + kay + kby • expansion of the product of algebraic expressions • changing the subject of a formula • finding the value of an unknown quantity in a given formula • factorisation of quadratic expressions ax • multiplication and division of simple algebraic fractions such • addition and subtraction of algebraic fractions with linear or quadratic denominator

• 1. Subtracting two expressions
• 2. Adding algebraic expressions
• 3. Completing the square for Quadratic Expressions
• 4. Practice: Addition and Substraction of Algebraic Fractions Ex1
• 5. Verbal to Algebraic!

Cartesian coordinates in two dimensions • graph of a set of ordered pairs as a representation of a relationship between two variables • linear functions (y = ax + b) and quadratic functions (y = ax 2 + bx + c) • graphs of linear functions • the gradient of a linear graph as the ratio of the vertical change to the horizontal change (positive and negative gradients) • graphs of quadratic functions and their properties: ∗ positive or negative coefficient of x 2 ∗ maximum and minimum points ∗ symmetry • sketching the graphs of quadratic functions given in the form: ∗ y = – (x − p) 2 + q ∗ y = − (x − p) 2 + q ∗ y = – (x − a)(x − b) ∗ y = − (x − a)(x − b) • graphs of power functions of the form y = axn, where n = −2, −1, 0, 1, 2, 3, and simple sums of not more than three of these • graphs of exponential functions y = kax, where a is a positive integer • estimation of the gradient of a curve by drawing a tangent

• 1. straight line y = mx + c
• 2. Quadratic Function
• 3. maximum and minimum points ∗ symmetry
• 4. Graphs of power function
• 5. Exponential Functions: Graphs
• 6. Gradient of Curve

• solving linear equations in one variable • solving simple fractional equations that can be reduced to linear equations such as: 3 4 2 3 = − + x x 6 2 3 = x − • solving simultaneous linear equations in two variables by ∗ substitution and elimination methods ∗ graphical method • solving quadratic equations in one unknown by ∗ factorisation ∗ use of formula ∗ completing the square for y = x + px + q 2 ∗ graphical methods • solving fractional equations that can be reduced to quadratic equations such as: 3 4 6 = + + x x 5 3 2 2 1 = − + x − x • formulating equations to solve problems • solving linear inequalities in one variable, and representing the solution on the number line

• 1. Quadratic factorisation
• 2. Solve Simple Linear Equations
• 3. Lineair equations with fractions
• 4. Solving simultaneous equation
• 5. Simultaneous Equations:Substitution
• 6. Simultaneous Equations:Elimination
• 7. Solving Quadratic Equations using Quadratic Formula
• 8. Completing the Square for Quadratic Equation (II) : Solving the Equation
• 9. Solving Quadratic Equations
• 10. Solve linear inequality

• use of set language and the following notation: Union of A and B A ∪ B Intersection of A and B A ∩ B ‘… is an element of …’ ∈ ‘… is not an element of …’ ∉ Complement of set A A′ The empty set ∅ Universal set A is a (proper) subset of B A ⊂ B A is not a (proper) subset of B A ⊄ B • union and intersection of two sets • Venn diagrams

• 1. Venn diagram calculator
• 2. Venn diagram
• 3. Venn Diagram for set theory
• 4. Set Notation & Venn Diagrams

• display of information in the form of a matrix of any order • interpreting the data in a given matrix • product of a scalar quantity and a matrix • problems involving the calculation of the sum and product (where appropriate) of two matrices

• 1. Multiplying two matrices

right, acute, obtuse and reflex angles • vertically opposite angles, angles on a straight line and angles at a point • angles formed by two parallel lines and a transversal: corresponding angles, alternate angles, interior angles • properties of triangles, special quadrilaterals and regular polygons (pentagon, hexagon, octagon and decagon), including symmetry properties • classifying special quadrilaterals on the basis of their properties • angle sum of interior and exterior angles of any convex polygon • properties of perpendicular bisectors of line segments and angle bisectors • construction of simple geometrical figures from given data (including perpendicular bisectors and angle bisectors) using compasses, ruler, set squares and protractors, where appropriate

• 1. Angle Properties
• 2. Angles at a point
• 3. Parallel Lines and Alternate and Corresponding Angles
• 4. Angle Properties of Polygons
• 5. Regular Polygons symmetry lines relations to rotational sym

• congruent figures and similar figures • properties of similar triangles and polygons: ∗ corresponding angles are equal ∗ corresponding sides are proportional • enlargement and reduction of a plane figure • scale drawings • determining whether two triangles are ∗ congruent ∗ similar • ratio of areas of similar plane figures • ratio of volumes of similar solids • solving simple problems involving similarity and congruence

• 1. Triangle Congruence
• 2. Similar Triangles
• 3. Side, Perimeter, and Area of Similar Figures.
• 4. Ratio of area and Ratio of Volume videos
• 5. Enlargement with scale factor
• 6. 09.5A Enlargement and Reduction(放大及縮小)

• 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 ∗ the line joining an external point to the centre of the circle bisects the angle between the tangents • angle properties of circles: ∗ angle in a semicircle is a right angle ∗ angle between tangent and radius of a circle is a right angle ∗ angle at the centre is twice the angle at the circumference ∗ angles in the same segment are equal ∗ angles in opposite segments are supplementary

• 1. Perpendicular Lines to Chords of Circles
• 2. Angle Properties of Tangents To Circles
• 3. Angle properties of circle
• 4. tangent chord angles
• 5. tangent-chord angle

use of Pythagoras’ theorem • determining whether a triangle is right-angled given the lengths of three sides • use of trigonometric ratios (sine, cosine and tangent) of acute angles to calculate unknown sides and angles in right-angled triangles • extending sine and cosine to obtuse angles • use of the formula 2 1 ab sin C for the area of a triangle • use of sine rule and cosine rule for any triangle • problems in two and three dimensions including those involving angles of elevation and depression and bearings

• 1. Pythagoras Theorem
• 2. Pythagorean theorem
• 3. Copy of Introducing Trig functions
• 4. Explore Trigonometric Ratios (SOH CAH TOA)
• 5. Right Triangle Trigonometry: Intro
• 6. Introducing Trig functions
• 7. Sine and Cosine Components
• 8. Sine and cosine to obtuse angle
• 9. Proofs of sine rule, cosine rule, area of a triangle
• 10. Introduction to Bearings
• 11. Bearings
• 12. Angle of elevation and depression
• 13. 3D Trigonometry problem
• 14. 3D : trigo
• 15. Application of Trigonometry

area of parallelogram and trapezium • problems involving perimeter and area of composite plane figures • volume and surface area of cube, cuboid, prism, cylinder, pyramid, cone and sphere • conversion between cm2 and m2 , and between cm3 and m3 • problems involving volume and surface area of composite solids • arc length, sector area and area of a segment of a circle • use of radian measure of angle (including conversion between radians and degrees

• 1. area of a parallelogram
• 2. Area of a Trapezium
• 3. Area of Trapezium Demonstration
• 4. Area of a composite shape
• 5. 1.4 Surface Area and Volume of Prisms and Cylinders
• 6. Net of a Cylinder
• 7. Cylinder - Volume and Surface Area
• 8. Total Surface Area & Volume of Cylinder (with net shown)
• 9. Trisecting the Cube into 3 Pyramids
• 10. Copy of Volume of pyramid is 1/3 volume of cube
• 11. Rectangular Pyramid
• 12. Volume and Surface Area of Cone
• 13. Volume of a Cylinder vs Cone
• 14. volume of sphere
• 15. Volume of Sphere Proof
• 16. Self Review Mensuration of Composite Cylinder & Hemisphere
• 17. Self Review Mensuration of Composite Hemisphere & Cone
• 18. Illustration of surface area of a sphere
• 19. Surface area of Sphere
• 20. Find Arc Lengths and Areas of Sectors of Circles
• 21. Arc length and area of sector(Degree)
• 22. Arc length and area of sector (Radian)
• 23. Area of a Circle Exploration

• finding the gradient of a straight line given the coordinates of two points on it • finding the length of a line segment given the coordinates of its end points • interpreting and finding the equation of a straight line graph in the form y = mx + c • geometric problems involving the use of coordinates

• 1. Straight Line - gradient
• 2. S3E 9.1 Length of a Line Segment
• 3. y=mx+c

• use of notations: • representing a vector as a directed line segment • translation by a vector • position vectors • magnitude of a vector • use of sum and difference of two vectors to express given vectors in terms of two coplanar vectors • multiplication of a vector by a scalar • geometric problems involving the use of vectors

• 1. Magnitude of a Vector
• 2. Vector Addition
• 3. Vector Subtraction
• 4. Scalar Multiplication of a Vector
• 5. Scaling Vectors

• analysis and interpretation of: ∗ tables ∗ bar graphs ∗ pictograms ∗ line graphs ∗ pie charts ∗ dot diagrams ∗ histograms with equal class intervals ∗ stem-and-leaf diagrams ∗ cumulative frequency diagrams ∗ box-and-whisker plots • purposes and uses, advantages and disadvantages of the different forms of statistical representations • explaining why a given statistical diagram leads to misinterpretation of data • mean, mode and median as measures of central tendency for a set of data • purposes and use of mean, mode and median • calculation of the mean for grouped data • quartiles and percentiles • range, interquartile range and standard deviation as measures of spread for a set of data • calculation of the standard deviation for a set of data (grouped and ungrouped) • using the mean and standard deviation to compare two sets of data

• 1. Bar Chart
• 2. Pie Chart
• 3. Dot Plot Tool
• 4. Histogram Worksheet
• 5. Stem and Leaf
• 6. 05.2B Cumulative Frequency Polygon
• 7. Box-and-Whisker Plot Generator
• 8. AQR Section 17: Creating a Box and Whisker Plot
• 9. dotplot
• 10. Standard Deviation Formulae
• 11. Mean, Median, and Standard Deviation
• 12. Visual Demo of Standard Deviation
• 13. Cum Freq, Box plot
• 14. Median and Interquartile Range
• 15. Center and Spread Variation Exploration
• 16. Calculate Inter quartile range
• 17. Bar Charts and Pie Charts
• 18. AQR Section 16: Creating a Pie Chart From a Dot Plot