ADDITIONAL MATHEMATICS SCHEME OF WORK 2020 – 2022 FORM 4 TERM 1: Sept – Dec 2020

1. Statistics 2. Probability 3. Factorization

TERM 2: Jan – April 2021

1. Remainder & Factor Theorem 2. Quadratics 3. Simultaneous Equations 4. Inequalities

TERM 3: April – June 2021

1. Surds, Indices & Logarithms 2. Vectors 3. SBA work

FORM 5

TERM 1: Sept – Dec 2022

1. Coordinate Geometry

2. Sequences & Series 3. Trigonometry

TERM 2: Jan – April 2022

1. Differentiation

2. Integration

3. Kinematics

WEEKLY ADD MATHS SCHEME OF WORK: TERM 1

WEEK TOPIC LEARNING OBJECTIVES – Students should be able to: RESOURCES

1. STATISTICS

1. Appreciate and state the uses of statistics in various spheres of

everyday life. 2. Outline the process of statistics. 3. Distinguish between a sample and population 4. Collect data and recognize the difference between qualitative

and quantitative, discrete, and continuous data. 5. Calculate the measures of central tendency from raw data. 6. Interpret the measures of central tendency. Determine the

impact of an outlier. 7. Calculate the measures of central tendency from ungrouped

and grouped data.

MAIN RESOURCES: Textbook: Raymond Toolsie Mymaths software Khan Academy Youtube

▪ http://www.mymaths.co.uk /data

▪ https://www.khanacademy.org/math/ap-statistics/summarizing-quantitative-data-ap/measuring-center-quantitative/v/statistics-intro-mean-median-and-mode

▪ https://www.youtube.com/watch?v=vcbMinm_1Q8

▪ https://www.youtube.com/watch?v=VsdKEdua6nc

2 & 3

8. Calculate the measures of dispersion from raw data. ▪ Range ▪ Interquartile Range, ▪ Semi-IQR, ▪ Variance ▪ Standard Deviation

▪ https://www.youtube.com/watch?v=mk8tOD0t8M0&list=PLVfkYU9-iIctv_zr2YMzSwG6JpJ4HlvST&index=9&t=0s

▪ https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-data-statistics/cc-6th/v/calculating-interquartile-range-iqr

4. ASSESSMENT 1 Review Assessment

4 & 5

9. Calculate the measures of dispersion from ungrouped and grouped data.

(Range, Interquartile Range, Semi-IQR, Variance & Standard Deviation) 10. Interpret the measures of dispersion.

▪ https://app.mymaths.co.uk/821-lesson/standard-deviation-introduction

WEEK TOPIC LEARNING OBJECTIVES – Students should be able to: RESOURCES

6.

11. Represent numerical data diagrammatically. (Box and whisker plots & stem and leaf)

12. Outline the advantages and disadvantages of each diagram.

▪ https://www.khanacademy.org/math/probability/data-distributions-a1/box--whisker-plots-a1/v/constructing-a-box-and-whisker-plot

▪ https://app.mymaths.co.uk/510-lesson/box-and-whisker-plots

▪ https://app.mymaths.co.uk/370-lesson/stem-and-leaf-diagrams

7. ASSESSMENT 2 Review of Assessment

7 & 8

13. Calculate and interpret:

• Quartiles & percentiles from raw data, grouped data.

• Quartiles & percentiles from diagrams: ▪ Box & Whisker ▪ Stem & Leaf ▪ Cumulative Frequency curves

▪ https://www.youtube.com/watch?v=6D7aszsDJCg

▪ https://app.mymaths.co.uk/510-lesson/box-and-

whisker-plots

9. ASSESSMENT 3 Review of Assessment

9. PROBABILITY

1. Explain the concept of probability. 2. Distinguish between terms such as experiment, outcome,

sample space and event. 3. Calculate the probability of an event when all outcomes are

equally likely and has a finite sample space. 4. Calculate the relative frequency as an estimate of probability

▪ https://app.mymaths.co.uk/377-lesson/probability-intro

▪ https://app.mymaths.co.uk/378-lesson/simple-probability

WEEK TOPIC LEARNING OBJECTIVES – Students should be able to: RESOURCES

10. ASSESSMENT 4 Review of Assessment

10 &

11

5. Solve simple problems using the 3 basic laws of probability. 6. Identify and distinguish between mutually exclusive and

independent events. 7. Use the addition rule for 𝑃(𝐴 ∪ 𝐵) and product rule for

𝑃(𝐴 ∩ 𝐵), to calculate probabilities.

▪ https://www.youtube.com/watch?v=ynjHKBCiGXY ▪ https://www.youtube.com/watch?v=LS-_ihDKr2M ▪ https://www.youtube.com/watch?v=mnCHbsEwAC

w

12. 8. Calculate the conditional probability

𝑃(𝐴|𝐵) = 𝑃(𝐴∩𝐵)

𝑃(𝐵)

▪ https://www.youtube.com/watch?v=ibINrxJLvlM

13.

9. Construct and use:

• Possibility space diagrams

• Tree diagrams (2 branches)

• Venn diagrams (2 sets) to solve problems involving probability.

▪ https://www.youtube.com/watch?v=yWFPj47NLCc

▪ https://www.youtube.com/watch?v=gltPAZwepiY ▪ https://www.youtube.com/watch?v=gaEvsvHb4kk

ASSESSMENT 5 Revision Questions on the entire topic of Stats and Probability

WEEKLY ADD MATHS SCHEME OF WORK: TERM 2

WEEK TOPIC LEARNING OBJECTIVES – Students should be able to: RESOURCES

ALGEBRA

MAIN RESOURCES: Textbook: Raymond Toolsie Mymaths software Khan Academy Youtube

1.

1. Review on Simplifying expressions.

▪ Addition and Subtraction ▪ Multiplication and division of polynomials.

2. Review of Factorization:

▪ HCF ▪ Difference of 2 Squares ▪ Grouping ▪ Quadratics

3. Simplify rational expression (factorize)

▪ Page 3 Exercise 1.2 ▪ Page 4 Exercise 1.3

▪ https://www.youtube.com/watch?v=U6Fndtdg

pcA

▪ https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:rational/x2ec2f6f830c9fb89:cancel-common-factor/v/simplifying-rational-expressions-introduction

2.

4. Divide a Polynomial by a linear. Use this as an alternative method to factorize.

▪ Divide a polynomial by another polynomial. ▪ Factorize a cubic/ quartic polynomial into linear factors.

▪ https://www.khanacademy.org/math/algebra2/

x2ec2f6f830c9fb89:poly-div/x2ec2f6f830c9fb89:quad-div-by-linear/v/polynomial-division

▪ https://www.youtube.com/watch?v=-nlMXVrgtjw

▪ https://www.youtube.com/watch?v=hXXdCRsNYOU

WEEK TOPIC LEARNING OBJECTIVES – Students should be able to: RESOURCES

3.

5. Use the factor theorem to find factors. ▪ Find unknown coefficients. ▪ Find the remainder when a polynomial is divided by a linear. ▪ Evaluate unknown coefficients using Remainder Theorem.

▪ https://www.youtube.com/watch?v=F2V3Of8HuSM

▪ https://www.youtube.com/watch?v=4YMmBgNEelg

4. ASSESSMENT 1 Review of Assessment

4 & 5.

6. QUADRATICS

▪ Solve quadratic equations by: (1) Factorization (2) Quadratic Formula

▪ Express a quadratic in the form 𝑎(𝑥 + ℎ)2 + 𝑘

Where ℎ =𝑏

2𝑎 𝑎𝑛𝑑 𝑘 =

4𝑎𝑐−𝑏2

4𝑎

▪ https://www.youtube.com/watch?v=Sm0wvQSZf1g

▪ https://www.youtube.com/watch?v=k5XWHfTI

WkA

6.

▪ Use the completing the square method to: (1) Solve the quadratic (2) Determine the maximum/ minimum points (3) Range of the function (4) Find the intercepts on the axes. (5) Sketch the graph.

https://www.youtube.com/watch?v=5xp6-nqQXz8

ASSESSMENT 2 Review of Assessment

7.

Determine the nature of roots of a quadratic equation by calculating

the Discriminant = 𝒃𝟐 − 𝟒𝒂𝒄. ✓ 2 real and distinct roots ✓ Equal roots ✓ No real roots

▪ https://www.youtube.com/watch?v=VTQSGYnqw1Y

▪ https://www.youtube.com/watch?v=IJeZDVt_lY0

WEEK TOPIC LEARNING OBJECTIVES – Students should be able to: RESOURCES

▪ Determine the graphical representation of each type. ▪ Calculate missing coefficients given the nature of the roots.

8.

▪ Use the Vieta’s Root Theorem to determine the relationship

between the sum, α + β = - 𝒃

𝒂 and product, αβ =

𝒄

𝒂

of the roots of a quadratic. ▪ Form a quadratic equation given the sum and product. ▪ Apply the sum & product to roots involving (α + β) and/or αβ

in it. E.g. 𝟏

𝜶+

𝟏

𝜷

▪ https://www.youtube.com/watch?v=ho8blOkwLBk

▪ https://www.youtube.com/watch?v=LNrtAlOwJZc

▪ https://www.youtube.com/watch?v=0lG5xRRlJ8A

9. ▪ Solve equations involving disguised quadratics. (Quartic and surds)

▪ https://www.youtube.com/watch?v=iUltI8QKgSo

▪ https://www.youtube.com/watch?v=RaeHbqT1Zik

ASSESSMENT 3 Review of Assessment

10.

7. SIMULTANEOUS EQUATIONS ▪ Solve a pair of simultaneous equations with one linear and

one non-linear. ▪ Solve worded problems involving simultaneous equations.

Page 67 exercise 2.1

11.

8. INEQUALITIES ▪ Solve a quadratic inequality by identifying the critical values.

(for 𝑎𝑥2 + 𝑏𝑥 + 𝑐 < 𝟎,≤ 𝟎,> 𝟎,≥ 𝟎) ▪ Represent the solution:

- Graphically - Using set builder notation

▪ https://www.youtube.com/watch?v=ouTHUb7UVSI

WEEK TOPIC LEARNING OBJECTIVES – Students should be able to: RESOURCES

11.

▪ Solve rational inequalities with linear factors, identifying the

restriction for the denominator i.e. vertical asymptote

(for 𝑎𝑥+𝑏

𝑐𝑥+𝑑 < 𝟎,≤ 𝟎,> 𝟎,≥ 𝟎)

▪ Represent the solution: - Graphically - Using set builder notation

▪ https://www.youtube.com/watch?v=qAISKrifBq

g

▪ https://www.youtube.com/watch?v=SJecFvUbJOY

12. ASSESSMENT 4 Review of Assessment

WEEKLY ADD MATHS SCHEME OF WORK: TERM 3

WEEK TOPIC LEARNING OBJECTIVES – Students should be able to: RESOURCES

1. SURDS

1. Explain the concept of a surd as the root of a rational number.

2. Use the properties of surds: - √𝑥𝑦 = √𝑥 √𝑦

- √𝑥

𝑦=

√𝑥

√𝑦

3. Express a number in the simplest form k√𝑦 where k is a

constant from a perfect square.

4. Perform operations of Addition & Subtraction of surds.

Page 147 & 148 Exercise 5.1

2.

5. Perform operations of Multiplication of surds in the form of

squaring, difference of two squares, perfect squares and

distributive law.

6. Find the conjugate of a binomial which includes surds.

7. Understand the terms “rational” and “irrational”.

8. Convert a fraction with an irrational denominator with surds,

rational.

▪ https://www.youtube.com/watch?v=igXVhxk-IEM

▪ https://www.youtube.com/watch?v=QV8TfJSqsV8

▪ https://www.youtube.com/watch?v=ixClVENqZ6M

3. 9. Solve equations in x and surds that are reducible to quadratic

equation.

Eg: 𝑥 - 2√𝑥 + 1 = 0

Page 57 Exercise 2.8

ASSESSMENT 1

Review of Assessment

WEEK TOPIC LEARNING OBJECTIVES – Students should be able to: RESOURCES

4. VECTORS

1. Distinguish between a scalar and vector quantity.

2. Write a vector in the form (𝑥𝑦) 𝑎𝑛𝑑 𝑡ℎ𝑒 𝐶𝑎𝑟𝑡𝑒𝑠𝑖𝑎𝑛 𝑓𝑜𝑟𝑚

𝑥𝒊 + 𝑦𝒋

3. Understand and differentiate between the terms “position

vector” and “displacement vector”. Calculate a displacement

vector given the 2 position vectors.

4. Perform operations of addition (Triangle Law & Parallelogram

Law) to find the sum(resultant) of 2 displacement vectors.

5. Calculate the difference of 2 vectors.

6. Find the length/magnitude/modulus of a vector

|𝑂𝑃⃗⃗ ⃗⃗ ⃗| = √𝑥2 + 𝑦2

Page 268 Exercise 8.4 https://www.youtube.com/watch?v=9hMjkK1wghE https://www.youtube.com/watch?v=_mKUe0DJqzs Page 278 Exercise 8.8

5&6.

7. Calculate a unit vector in the direction of a = �̂� =𝑎

|𝑎|=

𝑥𝑖+𝑦𝑗

√𝑥2+𝑦2

8. Multiply a vector by a scalar quantity.

9. Find the scalar product of 2 vectors in terms of their

component.

(𝑥1

𝑦1) (

𝑥2

𝑦2) = 𝑥1𝑥2 + 𝑦1𝑦2

10. Find the scalar product of 2 vectors in terms of find the

angle between them. ( 𝑎. 𝑏 = |𝑎||𝑏|𝑐𝑜𝑠𝜃)

11. Use the calculation of the angle between two vectors to

prove that they are:

(i) Parallel (180°)

(ii) Perpendicular (90°)

▪ Page 274 Exercise 8.7

▪ https://www.youtube.com/watch?v=f5DHYCKyVRo

▪ https://www.youtube.com/watch?v=5qv8RmIpM_I

▪ Page 285 Exercise 8.9

ASSESSMENT 2

Review of Assessment

WEEK TOPIC LEARNING OBJECTIVES – Students should be able to: RESOURCES

7. INDICES

1. Use laws of indices to manipulate expressions with integral indices.

(v) (𝑥𝑦)𝑚 = 𝑥𝑚𝑦𝑚

(vi) (𝑥

𝑦)𝑚

=𝑥𝑚

𝑦𝑚

(vii) 𝑥𝑚

𝑛 = √𝑥𝑚𝑛

▪ Page 157 Exercise 5.4 ▪ Page 161 Exercise 5.5

8.

2. Use the laws of indices to solve exponential equations with

one unknown.

- Equations reducible to linear form

- Equations reducible to quadratic form.

Page 164 Exercise 5.6

ASSESSMENT 3

Review of Assessment

9. LOGARITHMS 1. Convert index form into logarithmic form and vice versa.

𝑎𝑐 = 𝑏 ↔ log𝑎 𝑏 = 𝑐

2. Simplify expressions (same base) using laws of logarithms:

https://www.youtube.com/watch?v=4UNkQcBrLaQ Page 168 Exercise 5.7

10. 3. Solve logarithmic equations (same base).

4. Solve logarithmic equations in the form ax = b

https://www.youtube.com/watch?v=rBnQiLa2TYo

11.

5. Transform non-linear equations into linear form:

𝑦 = 𝑎𝑏𝑥 & 𝑦 = 𝑎𝑥𝑛

by drawing a linear graph (log/ln), calculating the gradient

and y intercept.

Page 183 Exercise 5.11

ASSESSMENT 4

Review of Assessment