2012 s3 math sow parents - sst school · chapter 7 (am) coordinate ... describe simple interest and...

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SST MATH PROGRAMME

S e c o n d a r y 3

SCHEME OF WORK (PARENTS)

f o r

M A T H E M A T I C S

A C A D E M I C Y E A R 2 0 1 2



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Textbook: Discovery Mathematics Book 1A, 1B & 2A by Chow Wai Keung Publisher: Star Publishing Pte Ltd References: 1. Discovering Mathematics TextBook 3A, 3B, 4A, 4B Star Publishing Pte Ltd

2. Panpac Additional Mathematics, EPB Pan Pacific

Time Topics

Content

T1

W1 D3 – D5

W2

D1 – D5

Chapter 4 (AM) Polynomials and Partial Fractions

1. Add, subtract and multiply polynomials 2. Find the unknown constants in polynomial identities. 3. Divide a polynomial by another polynomial. 4. Apply the Remainder Theorem: (a) to find the remainder when a polynomial is divided by a linear divisor. (b) to form and solve equations to find unknown(s). 5. Apply the Factor Theorem. 6. Solve cubic equations by factorization. 7. Express a rational expression in partial fractions.

T1

W3

D1 – D3

Chapter 2 (AM) Indices, Surds

1. Simplify surds using a × b = ab ,

ba =

ba

2. Use conjugate surds to rationalize the surd denominator of a fraction. 3. Solve simple equations involving surds. 4. Apply the rules of indices to simple problems.

T1

W3 D4

Chapter 2 (AM) Indices, Logarithms

5. Solve exponential equations of the form a

x = b where b = a

n

6. Solve exponential equations using substitutions. 7. Use the definition



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Time Topics

Content

W4

D3 – D5

W6 D1 – D3

y = ax ⇔ x = logay to convert an expression from index form to logarithmic form and vice

versa. 8. State that a logarithm logay is defined when (i) y > 0, (ii) a > 0, a ≠ 1. 9. Apply the results loga 1 = 0 and loga a = 1. 10. Evaluate common and natural logarithms using a calculator. 11. Apply the following laws of logarithms: logax

r = r logax

logaxy = logax + logay loga

xy

!

" # $

% & = logax – logay

logab = log c blog c a

, where the logarithms are defined.

12. Evaluate a logarithm to any base by first converting it to base 10 or base e 13. Apply the result

logaM = logaN ⇔ M = N or the result in 11 to solve logarithmic equations. 14. Solve equations of the form a

x = b using logarithms.

15. Apply the rules of indices and laws of logarithms to solve practical problems

T1

W6 D4 – D5

W7

D1 – D5

Chapter 3 (AM) Quadratic Equations and Inequalities

1. State and apply the sum and product of roots of a quadratic equation. 2. Apply the above relations to evaluate expression involving these roots. 3. Form an equation whose roots are related to the roots of another quadratic equation. 4. Identify the nature of the roots of a quadratic equation by considering the discriminant. 5. Apply the relation between the discriminant and the nature of the roots to find the unknown in

the quadratic equation. 6. State and apply the conditions for ax2 + bx + c to be always positive or always negative



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Content

7. Apply the relation between discriminant and the nature of roots of a quadratic equation to determine whether a line intersects a curve at two distinct points, one point (tangent) or none at all

8. Solve a quadratic inequality using the corresponding quadratic curve

T1

W8 D1

TB 3A Chapter 5 (EM) Functions And Graphs 5.1 Graph Sketching of Quadratic Functions

1. Sketch the graphs of quadratic functions of the forms: y= a (x – h)2 + k where a ≠1

y = ± (x – h)2 + k and y = ± (x – p)(x – q)

T1

W8 D2 – D3

5.2 Graphs of Power Functions

2. Draw the graph of the function y = axn for n = -2, -1, 0, 1, 2 and 3

T1

W8 D4 – D5

5.3 Graphs of Sums of Power Functions

3. Draw the graph of the sum of not more than 3 functions of the form y = axn for n = -2, -1, 0, 1, 2 and 3

T1

5.4 – 5.5 Graphs of Exponential Functions and

4. Draw the graph of an exponential function y = kax, where a is a positive integer 5. Estimate the gradient of a curve by drawing a tangent to the curve



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Time Topics

Content

W9 D1 – D2

Gradients of Curves

T1 W9

D3 – D5

Chapter 5 (AM) The Modulus Function

1. Evaluate or simplify expressions involving absolute values. 2. Solve simple equations involving modulus. 3. Sketch graphs of modulus functions.

T1

W10 D1

TB 3B Chapter 9 (EM) Coordinate Geometry 9.1 – 9.2 Length of a Line Segment and Gradient of a Straight Line

6. Find the length of a line segment on a coordinate plane 7. Find the gradient of a straight line given the coordinates of two points on it

T1 W10 D1

9.3 Equation of a Straight Line

8. Interpret and find the equation of a straight line graph in the form y = mx + c

9. Solve geometric problems involving the use of coordinates

T1

W10 D1 – D5

Chapter 7 (AM) Coordinate Geometry

1. Find the midpoint and the length of a line segment. 2. Find the area of a rectilinear figure from its vertices. 3. Find the equation of the straight line passing through A(x1, y1) and B(x2, y2) using

y – y1 = m(x – x1) where m = y2 – y1x2 – x1

4. Apply the result:



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l1 and l2 are parallel ⇔ m1 = m2. 5. Find the point of intersection of two non-parallel lines. 6. State the result: Two non-vertical lines with gradients m1 and m2 are perpendicular ⇔ m1m2 =

–1. 7. Find the equation of a straight line perpendicular to a given line. 8. Find the

(a) coordinates of the foot of a perpendicular (b) perpendicular distance from a point to a straight line. 9. Find the distance between two parallel lines. 10. Find the equation of the perpendicular bisector of two given points A and B using the following

method: Step 1:Find (x1, y1), the midpoint of A and B. Step 2: Find the gradient of the perpendicular bisector mʹ′ = – 1

m where m = gradient of AB.

Step 3: Equation of the perpendicular bisector is y – y1 = mʹ′ (x – x1).

T2 W1

D1 – D3

(EM) TB 4B Chapter 5 Mathematics In Practical Situations

1. Explain the terms involving profit and loss 2. Calculate profit and loss as a percentage of the cost price 3. Describe simple interest and compound interest and draw a comparison between them 4. Calculate simple interest and compound interest in daily life 5. Calculate interest in hire-purchase plans 6. Solve problems involving utility bills 7. Solve problems involving money exchange among different currencies 8. Understand and solve problems involving calculation of income tax and property tax.

T2 W1

(EM) TB 4B Chapter 6 Graphs In Practical Situations

1. Interpret and draw distance-time graphs and speed-time graphs



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Content

D4 – D5 2. Apply the idea of rate of change to easy kinematics involving distance-time and speed-time graphs, acceleration and retardation

3. Calculate distance travelled as area under a linear speed-time graph

T2 W2

D1 – D5 Chapter 8 (AM) Linear Law

1. Express a relationship in the linear form Y = mX + c

2. Find the relationship between two variables given a straight line graph of Y against X. 3. Plot an appropriate straight line from given experimental data. 4. Find the values of m (gradient) and c (y-intercept) from the plotted graph of the Linear Law, Y = mX + c and obtain estimates of unknown constants in the equation in x and y.

T2 W3

D1 – D2

TB 3A Chapter 6 (EM) Properties Of Circles 6.1 – 6.2 Chords of a Circle, Angles in a Circle

1. Recognise equal chords are equidistant from the centre 2. Recognise the perpendicular bisector of a chord passes through the centre of a circle 3. Apply the above properties to solve problems 4. Recognise the angle at the centre is twice the angle at the circumference 5. Recognise an angle in a semicircle is a right angle 6. Recognise the angles in the same segments are equal

T2 W3

D3 – D4

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

7. apply the above properties to solve problems 8. state the properties of angles in opposite segments

T2 W4

D1 – D2

6.4 Tangents to a Circle

9. draw a tangent to a circle 10. understand that a tangent to a circle is perpendicular to the radius of the circle at the point of contact 11. apply the above properties to solve problems 12. recognise tangents from an external point are equal in length 13. recognise the line joining an external point to the centre of a circle bisects the angle between the



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tangents from the external point 14. apply the above properties to solve problems

T2 W4 D3

TB 3B Chapter 4 Conditions Of Congruence And Similarity 4.1 – 4.2 Congruent Triangles and Similar Triangles

1. state the conditions for two triangles to be congruent 2. identify congruent triangles 3. state the conditions for two triangles to be similar

T2 W4 D3

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

4. identify similar triangles 5. determine whether two plane figures are similar 6. state the relationship between the ratio of areas and the ratio of lengths of two similar plane figures

T2 W4

D4 – D5

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

7. apply the above property to solve problems 8. determine whether two solids are similar 9. state the relationship between the ratio of volumes and the ratio of lengths of two similar solids 10. apply the above property to solve problems

T2 W5

D1 – D5

Chapter 10 (AM) Plane Geometry

1. State and apply the properties of similar triangle 2. State the Midpoint Theorem and Intercept Theorem and apply them to prove geometrical results 3. Prove geometrical results using the angle properties of a circle 4. State and apply the Tangent-Chord Theorem, Intersecting Chords Theorem and the Tangent-

Secant Theorem T2 W6 D1

TB 3B Chapter 7 (EM) Trigonometry 7.1 Trigonometric Ratios of Acute Angles

1. State the definitions of trigonometric ratios of sine, cosine and tangent for acute angles 2. Find a trigonometric ratio from a right-angled triangle 3. Obtain the values of trigonometric ratios from a calculator 4. Use the trigonometric ratios to calculate unknown sides and angles in a right-angled triangle



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Time Topics

Content

T2 W6

D2 – D4

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

5. State the definition of sine and cosine functions for obtuse angles 6. Find the values of sine and cosine for obtuse angles 7. Find the area of a triangle using the formula Area = ½ bc sin A

T2 W6 D5 W7

D1 – D2

7.4 – 7.5 The Sine Rule and The Cosine Rule

8. State the sine rule 9. Apply the sine rule to solve problems 10. State the cosine rule 11. Apply the cosine rule to solve problems

T2 W7

D3 – D4

TB 3B Chapter 8 (EM) Applications Of Trigonometry 8.1 – 8.2 Bearing Problems, Angles of Elevation and Depression

1. Solve problems involving bearings and navigation 2. Understand the idea of angles of elevation and depression 3. Solve problems involving angles of elevation and depression

T2 W8

D1 – D4

8.3 Simple Three-Dimensional Problems

4. Apply trigonometry to solve simple 3-dimensional problems in our daily life

T2 W9

D1 – D2

TB 3B Chapter 10 (EM) Arc Lengths And Sector Areas 10.1 – 10.2 Arc Lengths, Sector Areas and Segment Areas

1. Understand the relationship between arc length and angle subtended by arc 2. Understand the relationship between sector area of a circle and angle subtended by arc 3. Calculate the arc length and sector area of a circle 4. Calculate the area of a segment



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Time Topics

Content

T2 W9

D3 – D5

10.3 – 10.4 Radian Measure, Formulae in Radian Measure

5. Understand radian measure of angle 6. Convert between radians and degrees 7. Express arc length and sector area formulae using radian measure 8. Apply the formulae to solve problems

T2 W10

REVISION

T3 W1 D1

Chapter 11 (AM) Trigonometric Functions

1. Find the sine, cosine and tangent of an acute angle. 2. Find the sine, cosine and tangent of 30°, 45° and 60° 3. Apply the results: sin ( 90° – θ ) = cos θ cos ( 90° – θ ) = sin θ tan ( 90° – θ ) = 1

tan! , tan θ ≠ 0

4. Determine the quadrant of a given angle. 5. Find the basic angle of a given angle. 6. Find angles in a specified interval from its basic angle.

T3 W1

D2 - D3


7. Define sin θ = yr , cos θ = x

r and tan θ = y

x , x ≠ 0.

8. Use the ‘CAST’ diagram to determine the sign of a trigonometric ratio of an angle in any quadrant.

9. Use the ‘CAST’ diagram to express the trigonometric ratio of any angle as the signed ratio of its basic angle.

10. State the results for negative angles: cos (–α ) = cos α sin (–α ) = –sin α tan (–α ) = –tan α



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Content

11. Solve basic trigonometric equations of the forms sin θ = k, cos θ = k and tan θ = k for angles in a specified interval.

T3 W1

D4 – D5 W2

D1 – D4


12. Sketch the graphs of y = sin θ , y = cos θ and y = tan θ . 13. State and apply the following basic properties of the three trigonometric functions: (a) axis of the graph, amplitude (for sine and cosine) and the period (b) –1 ! sin θ ! 1 and –1 ! cos θ ! 1. (c) The values of θ for which (i) sin θ = 0, 1 or –1 (ii) cos θ = 0, 1 or –1 (iii) tan θ = 0, 1 or –1 (d) Symmetries of the curves (e) Principal values of sin−

1y, cos−1y and tan−

1y. 14. Sketch the graphs of y = a sin bx + c, y = a cos bx + c, sin xy a c

b⎛ ⎞= +⎜ ⎟⎝ ⎠

, cos xy a cb⎛ ⎞= +⎜ ⎟⎝ ⎠

and

y = a tan bx, where a, b ∈ Z+ and c ∈ Z,

by considering the axis of the curve, its amplitude (where appropriate) and its period. 15. Find the number of solutions of f(x) = g(x) from the points of intersection of the curves y = f(x)

and y = g(x). T3 W3

D1 – D5

W4 D1 – D5

Chapter 12 (AM) Simple Trigonometric Identities and Equations

1. Apply the fundamental identities:

secθ = θcos1

cosec θ = θsin1

cot θ = θtan1



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Time Topics

Content

tan θ = sin!cos!

, cos θ ≠ 0

cot θ = cos!sin!

, sin θ ≠ 0

sin2 θ + cos

2 θ = 1

1 + tan2 θ = sec

2 θ

1 + cot2 θ = cosec

2θ

2. Prove simple trigonometric identities using the fundamental identities in 1. 3. Solve simple trigonometric equations reducible to the form T(x) = k. 4. Solve simple trigonometric equations which can be factorised. 5. Solve simple trigonometric equations of the form T(ax + b) = k.

T3

W5

D1 – D5

W6 D1 – D5

Chapter 13 (AM) Further Trigonometric Identities

1. Apply the Addition Formulae 2. Apply the Double-angle Formulae 3. Apply the R-formulae 4. Apply the Factor formulae

T3

W7 D1 – D2

TB 3B Chapter 11 (EM) Quartiles And Percentiles 11.1 – 11.2 Cumulative Frequency Diagrams and Range, Quartiles, Interquartile Range and Percentiles

1. understand the term cumulative frequency 2. recognise features of cumulative frequency curves

3. interpret and analyse cumulative frequency curves 4. understand the terms range, quartiles, interquartile range and percentiles

T3 11.2 – 11.3 Range, Quartiles, 5. find the values of the above terms from a distribution



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Time Topics

Content

W8

D1 – D3

Interquartile Range and Percentiles, and Box-and-Whisker Plots

6. recognise the features of a box-and-whisker plot 7. interpret and analyse box-and-whisker plots

T3

W8 D4 – D5

TB 4A Chapter 1 Standard Deviation (EM)

1. State the drawbacks of range and interquartile range as measures of spread and able to define standard deviation

2. State the definition of standard deviation for ungrouped data and perform its calculation. 3. State the definition of standard deviation for grouped data and perform its calculation 4. Calculate mean and standard deviation using a calculator 5. Use of standard deviation to discuss and compare the spread or variability of two data sets

T3

W9 D1 – D4

W10

D1 – D2

Chapter 6 (AM) Binomial Theorem

At the end of the chapter, students should be able to: 1. Construct the Pascal’s triangle and use it to expand (1 + b)

n , especially for smaller values of

n. 2. Use the Binomial Theorem to expand (1 + b)

n to any number of terms.

3. Identify and find a particular term in the expansion of (1 + b)n using the result Tr + 1 = r

n! " #

$

% & b

r.

4. Use the Binomial Theorem to expand (a + b)

n to any number of terms.

5. Use the result Tr + 1 = rn!

" #

$

% & a

n – rb

r to find a particular term in the expansion of (a + b)

n

T3

W10 D3 – D4

REVISION

T4

Chapter 9 (AM) Curves and Circles

1. Recognise the graphs of y = axn and y2 =kx and their properties.



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Time Topics

Content

W1 D1 – D5

2. Find the intersection of a curve and a straight line. 3. Recognise the equation of a circle and find its centre and radius. 4. Find the intersection of a circle and a straight line.

T4

W2 D1 – D5

W3

D1 – D5

TB 4A Chapter 4 (EM) Vectors In Two-Dimensions

1. Represent a vector by a directed line segment and its magnitude using correct notations 2. Find the magnitude and direction of a vector 3. Perform addition and subtraction of two vectors 4. Express given vectors in terms of two coplanar vectors 5. Multiply a vector by a scalar 6. Understand position vectors 7. Perform addition and subtraction and scalar multiplication with respect to position vectors 8. Represent a vector on the Cartesian coordinate plane using column vector notation 9. Find the magnitude and direction of a column vector 10. Use vectors to solve some geometric problems

T4 W4 –W5

END-OF-YEAR EXAMINATIONS

T4 W6

REVIEW OF END-OF-YEAR EXAMINATIONS

T4 W7 –W9

FORMAL LESSONS CONTINUE

T4 W10

SCHOOL CLOSES



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correct as of 27 Dec 2011, any updates will be communicated to students through the subject teachers. Curriculum may extend beyond the GCE O-Level syllabus in terms of knowledge and skills to better prepare students for their next level of study, either in a junior college or a polytechnic. School will make responsive changes if necessary in the interest of students’ learning. SST MATHEMATICS ASSESSMENT SCHEDULE

SUGGESTED BREAKDOWN OF WEIGHTAGE

• CONTINUED ASSESSMENT 1 (20%) CONTINUED ASSESSMENT 2 (20%) SEMESTER

ASSESSMENT (40%)

→ Level Test 1 (5%) @ T1W07 Level Test 3 (5%) @ T3W05 EOY Exams (40%)

@ T4W05

→ Level Test 2 (5%) @ T2W03 Level Test 4 (5%) @ T3W09

→ Alternative Assessment (10%) Performance Task (10%) (T2W08 – T3W04)

• COMMON TEST (20%) @ T2W07

• American Mathematics Competition 10B @ T1W08

• SMO Mathematics Senior Competition @ 29 May 2012 (Tentative)

2012 s3 math sow parents - sst school · chapter 7 (am) coordinate ... describe simple interest and...

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