Secondary 3 Express Mathematics ST. GABRIEL’S SECONDARY SCHOOL

Discovering Mathematics 3 (by Star Publishing) Scheme of Work

Chapters 1 to 6 in Book 3A

Chapters 7 to 11 in Book 3B

TOPICS SPECIFIC INSTRUCTIONAL OBJECTIVES

1.1 – 1.2 Positive Indices and Laws of Indices, Zero and Negative Integral Indices

• state and apply the laws of indices

• state the definitions of zero and negative indices

• simplify expressions involving integral indices

1.3 Fractional Indices

• state the definitions of fractional indices

• simplify expressions involving fractional indices

Chapter 1

Indices

(Book 3A)

1.4 –1.5 Standard Form and Comparing Indices

• express numbers in standard form

• understand the prefixes in SI units for very large and very small numbers

• be aware of rounding and truncation errors in a calculator for very small and very large

numbers

• solve simple equations involving indices

2.1 – 2.2 Factorisation Method and Graphical Method

• solve quadratic equations by factorisation method and graphical method

2.3 – 2.4 Completing the Square Method and Quadratic Formula

• solve quadratic equations of the form x2 + bx + c = 0 by the completing the square method

• solve quadratic equations by using the quadratic formula

Chapter 2

More About

Quadratic

Equations

(Book 3A)

2.5 – 2.6 Fractional Equations and Problems Involving Quadratic Equations

• solve fractional equations that can be transformed to quadratic equations

• apply quadratic equations to solve everyday problems

5.1 Graph Sketching of Quadratic Functions

• sketch the graphs of quadratic functions of the forms:

y = ±(x – h)2 + k and

y = ±(x – p)(x – q)

5.2 Graphs of Power Functions

• draw the graph of the function y = axn for n = –2, –1, 0, 1, 2 and 3

Chapter 5

Functions and

Graphs

(Book 3A)

5.4 – 5.5 Graphs of Exponential Functions and Gradients of Curves • draw the graph of an exponential function y = ka

x, where a is a positive integer

• estimate the gradient of a curve by drawing a tangent to the curve

3.1 – 3.2 Basic Properties of Inequalities and Linear Inequalities in One Unknown

• understand the basic properties of inequalities

• solve linear inequalities in one unknown

• represent the solution of a linear inequality on the number line

Chapter 3

Linear

Inequalities

(Book 3A)

3.3 – 3.4 Simultaneous Linear Inequalities and Applications of Linear Inequalities

• solve simultaneous linear inequalities in one unknown

• apply linear inequalities to solve everyday problems

TOPICS SPECIFIC INSTRUCTIONAL OBJECTIVES

9.1 – 9.2 Length of a Line Segment and Gradient of a Straight Line

• find the length of a line segment on a coordinate plane

• find the gradient of a straight line given the coordinates of two points on it

Chapter 9

Coordinate

Geometry

(Book 3B)

9.3 Equation of a Straight Line

• interpret and find the equation of a straight line graph in the form y = mx + c

• solve geometric problems involving the use of coordinates

4.1 – 4.2 Congruent Triangles and Similar Triangles

• state the conditions for two triangles to be congruent

• identify congruent triangles

• state the conditions for two triangles to be similar

4.2 – 4.3 Similar Triangles, Ratio of Areas of Similar Plane Figures

• identify similar triangles

• determine whether two plane figures are similar

• state the relationship between the ratio of areas and the ratio of lengths of two similar plane

figures

Chapter 4

Conditions Of

Congruence And

Similarity

(Book 3A)

4.3 – 4.4 Ratio of Areas of Similar Plane Figures, Ratio of Volumes of Similar Solids

• apply the above property to solve problems

• determine whether two solids are similar

• state the relationship between the ratio of volumes and the ratio of lengths of two similar

solids

• apply the above property to solve problems

6.1 – 6.2 Chords of a Circle, Angles in a Circle

• recognise equal chords are equidistant from the centre

• recognise the perpendicular bisector of a chord passes through the centre of a circle

• apply the above properties to solve problems

• recognise the angle at the centre is twice the angle at the circumference

• recognise an angle in a semicircle is a right angle

• recognise the angles in the same segment are equal

6.2 – 6.3 Angles in a Circle, Angles in the Opposite Segments

• apply the above properties to solve problems

• state the properties of angles in opposite segments

Chapter 6

Properties Of

Circles

(Book 3A)

6.4 Tangents to a Circle

• draw a tangent to a circle

• understand that a tangent to a circle is perpendicular to the radius of the circle at the point of

contact

• apply the above properties to solve problems

• recognise tangents from an external point are equal in length

• recognise the line joining an external point to the centre of a circle bisects the angle between

the tangents from the external point

• apply the above properties to solve problems

Chapter 7

Trigonometry

7.1 Trigonometric Ratios of Acute Angles

• state the definitions of trigonometric ratios of sine, cosine and tangent for acute angles

TOPICS SPECIFIC INSTRUCTIONAL OBJECTIVES

• find a trigonometric ratio from a right-angled triangle

• obtain the values of trigonometric ratios from a calculator

• use the trigonometric ratios to calculate unknown sides and angles in a right-angled triangle

7.2 – 7.3 Trigonometric Ratios of Obtuse Angles and Formula for the Area of a Triangle

• state the definitions of sine and cosine functions for obtuse angles

• find the values of sine and cosine for obtuse angles

• find the area of a triangle using the formula:

Area = ½bc sin A

(Book 3B)

7.4 – 7.5 The Sine Rule and The Cosine Rule

• state the sine rule

• apply the sine rule to solve problems

• state the cosine rule

• apply the cosine rule to solve problems

8.1 – 8.2 Bearing Problems, Angles of Elevation and Depression

• solve problems involving bearings and navigation

• understand the idea of angles of elevation and depression

• solve problems involving angles of elevation and depression

Chapter 8

Applications Of

Trigonometry

(Book 3B)

8.3 Simple Three-Dimensional Problems

• apply trigonometry to solve simple 3-dimensional problems in our daily life

10.1 – 10.2 Arc Lengths, Sector Areas and Segment Areas

• understand the relationship between arc length and angle subtended by arc

• understand the relationship between sector area of a circle and angle subtended by arc

• calculate the arc length and sector area of a circle

• calculate the area of a segment

Chapter 10

Arc Lengths And

Sector Areas

(Book 3B)

10.3 – 10.4 Radian Measure, Formulae in Radian Measure • understand radian measure of angle

• convert between radians and degrees

• express arc length and sector area formulae using radian measure

• apply the formulae to solve problems

11.1 – 11.2 Cumulative Frequency Diagrams and Range, Quartiles, Interquartile Range and

Percentiles

• understand the term cumulative frequency

• recognise features of cumulative frequency curves

• interpret and analyse cumulative frequency curves

• understand the terms range, quartiles, interquartile range and percentiles

Chapter 11

Quartiles And

Percentiles

(Book 3B)

11.2 – 11.3 Range, Quartiles, Interquartile Range and Percentiles, and Box-and-Whisker Plots

• find the values of the above terms from a distribution

• recognise the features of a box-and-whisker plot

• interpret and analyse box-and-whisker plots