2021 Learning Curve Senior Years Planner

2021 SENIOR LEARNING CURVE PLANNER www.learningcurve.com.au NAME.........................................................................................................................................................................................CLASS/HOUSE.........................................

Challenging Your Best Self

TO CREATE THE TYPE OF LIFE YOU WANT FOR YOURSELF To generate the motivation necessary to achieve this, you will need to be self-determined to challenge your best self.

about me This year my purpose is to:

Challenges I expect to face:

Choices that I will need to make to overcome challenges:

When having fun socialising with friends I will:

Character Strengths Weeks Every five weeks, challenge yourself to use the nominated character strength to build the wellbeing of your relationships in your life. The order of these weeks are: Gratitude, Teamwork, Curiosity, Kindness, Leadership, Hope, Zest, Perseverance, Love of Learning and Forgiveness.

Download these activity sheets from the Wellbeing Program/ Individual Resources/ Strengths for Relationships Weeks section of www.learningcurve.com.au

“What is necessary to change a person is to change their awareness of themselves.� Abraham Maslow 1

PERMAH+: Your Circle of Resilient Wellbeing THIS LESSON: The Wellbeing Learning Intention is for you to use PERMAH+ to build your wellbeing and self-determination. Wellbeing Reflection: what elements make up your wellbeing?

Your state of wellbeing and self-determination are reliant on how well you develop the following six equally important elements in yourself. It is a combination of all of them that indicates the health of your wellbeing and self-determination.

PPositive Emotions + gratitude Feeling good by giving and being kind

Creating positive emotions, handling negative emotions and being grateful for how these benefit your mental and physical wellbeing, respectful relationships and personal and academic growth.

What could you deliberately do to grow this element? .................................................................................................................................................................... ...................................................................................................................................................................

HHealth + strengths

EEngagement + mindfulness

Creating habits which enable your thriving mental and physical health, and using your strengths to support your learning progress and personal growth.

What could you deliberately do to grow this element?

Living your life with curiosity, zest and interest by having a focus on accomplishing your goals and involving yourself fully in your passions to grow your state of wellbeing.

What could you deliberately do to grow this element?

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Being determined to be healthy

Paying attention to what you need to

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AAccomplishment + optimism

PERMAH+

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is your Circle of Resilient Wellbeing

RRelationships + empathy

Being confident to achieve positively Having optimism and hope by setting, striving for and accomplishing personal goals, and deliberately practising to directly influence your own future.

What could you deliberately do to grow this element? ..............................................................................................................

Showing you value that other people matter Developing the social and emotional skills to build and maintain respectful and caring relationships with others, and having empathy for their needs and feelings.

What could you deliberately do to grow this element? ..............................................................................................................

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Meaning + purpose M

Having a meaningful purpose to strive for in your life Identifying and focusing on something larger than yourself, which gives you a sense of meaning, and a purpose to get out of bed every morning.

What could you deliberately do to grow this element? .................................................................................................................................................................... .................................................................................................................................................................... ..............................................................................................................................................................

Acknowledgement: P - Lyubomirsky, King & Diener, E - Hunter & Csikszentmihalyi, R - Norrish, Robinson & Williams, M – Cotton, Bronk & Damon, A – Hendren, Sheldon, H - Norrish, Robinson & Williams

“If you have a strong purpose in life, you don’t have to be pushed. Your passion will drive you there.” Roy T. Bennett 4

Continuum of Mindsets: your best self as a senior student

THIS LESSON: The Wellbeing Learning Intention is for you to explore how you can nudge your mindset more towards growth. Wellbeing Reflection: how can having the courage to welcome challenges assist you to become who you wish to become?

Your mindset comes from how self-determined you are to directly influence your own future. There are two extremes, Fixed and Growth, and most peoples’ mindsets lie somewhere in between them. Following are descriptors of these two mindsets.

GROWTH – the courage mindset because you are prepared to leave known safety to try more difficult things. You believe it is your choice to become the person you want to become. Tests don’t tell you anything about who you are, they only guide your learning.

The kings for you are courage to try, choice, process, challenging the status quo and commitment to deliberate practise.

WHICH STEP HAVE YOU REACHED TODAY?

FIXED – the fear mindset because you are fearful to leave known safety to try new things.

You believe that challenging yourself is an opportunity to fail, so you avoid this. Tests only show your limitations, not guiding your learning. The kings for you are fear to try, performance, maintaining the status quo and not having choices to change anything.

Mark where you think your mindset is in your current role as a senior student below.

Yes, I did it !

I WILL DO IT I CAN DO IT I’LL TRY TO DO IT HOW DO I DO IT? I WANT TO DO IT I CAN’T DO IT I WON’T DO IT

FIXED AND PERMANENT

GROWTH ORIENTATED

Nothing can change, so why try.

Set performance goals.

Change will happen through doing.

Set process goals.

Your brain is hard wired to perform at its best when you are positive, not negative. Setting goals to accomplish, provides you with a reason to look to the future with optimism and hope, which is an important skill of resilience. Goals connect you with yourself and are your anchors to self-determined progress. There are two main types of goals, performance and process, which are described below.

PERFORMANCE GOALS

PROCESS GOALS

» fixed mindset about proving you are not limited » aim for things which you can do with little effort » avoid tackling anything which will challenge you » only the outcome matters not how you get there » the only choice, only maintaining your known safety

» growth mindset about improving your abilities » aim for things which stretch your previous bests » see challenging yourself as the only way to grow » only the process you follow matters in learning » there are always choices to challenge your known safety

PROCESS GOAL Set one process goal for each of the following areas of your life:

EXERCISE and HEALTHY EATING .............................................................................................................................................................................................................................................................................................

ATTITUDES and OUTLOOKS .............................................................................................................................................................................................................................................................................................

LEARNING and THINKING .............................................................................................................................................................................................................................................................................................

WELLBEING and HAPPINESS .............................................................................................................................................................................................................................................................................................

FAMILY and FRIENDS .............................................................................................................................................................................................................................................................................................

Acknowledgement: Dweck, Ericsson, Anderson, Costa, Kellick

“I don’t divide the world into the weak and the strong, the successes and the failures. I divide the world into the learners and the non-learners.” Benjamin Barber 5

Engagement + mindfulness

PRIORITIES/DUE DATES 1

MONDAY

LIVING OR EXISTING? WHY?: by choosing to leave your comfort zone to try new more challenging things, which you could easily fail at, you will build both your self-awareness of possibilities and self-regulation to use grit to stick at them.

HOW: Oscar Wilde once said, “the rarest thing in the world is to

live, most people merely exist.” The happiest people are those who choose to live and make twice as many mistakes as others, to accomplish what they set out to do. To do this, pause, take notice, be curious and explore; avoid same old.

/mins

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TUESDAY

Acknowledgement: Kabat Zinn & Baer

DO: what is something that you really want to try which you will probably fail at first time? Give it a go! .......................................................................................................................................... .......................................................................................................................................... ..........................................................................................................................................

/mins

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WEDNESDAY

What is one courageous thing you could do to stop unconsciously doing the same old thing every day? .......................................................................................................................................... .......................................................................................................................................... ..........................................................................................................................................

How could the resilience skill, Thinking Flexibly, help you to do this? (page 118)

/mins

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THURSDAY

Gratitude Strengths Week It was once said, that “it is not happiness that brings us gratitude. It is gratitude that brings us happiness.” Who are three people that you are grateful for which make you happy?

/mins

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FRIDAY

1.........................................................................................................................................

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What went well this week?

1 2 3 12

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SATURDAY

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Study Tip

Have a margin on your page to jot down questions and ideas straight away.

ZZ

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February 2021

THINGS TO DO – WEEK: MONDAY

TUESDAY

WEDNESDAY

THURSDAY

FRIDAY

Communication/Comments

2 3 4 5

Feel in yourself?

2 3 4 5

Exercise daily?

2 3 4 5

Eat healthy?

1

For each of your Big Four, colour in how you did this week.

1

Weekly Big Four Check In

1

Parent/Guardian:

1

Teacher:

2 3 4 5

Sleep deeply?

13

Accomplishment + optimism

PRIORITIES/DUE DATES 5

MONDAY

GOALS AND ACADEMIC RIGOUR WHY?: by understanding that you need to begin by writing your goals down, you will move forward and avoid your dreams remaining just dreams.

HOW: this includes, setting time targets to achieve

along the way, creating strategies to complete each of these, and identifying obstacles you may need to overcome and what you need to learn. The Goals, Targets, Strategies, Plan (see page 33) is an effective tool to start converting dreams into goals and then into reality. Setting goals this way fills you with optimism and hope that you can shape your own future.

/mins

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TUESDAY

Acknowledgement: Sheldon, Gollwitzer & Adams Miller

DO: what is one goal you have, and identify possible obstacles you may need to overcome? .......................................................................................................................................... .......................................................................................................................................... ..........................................................................................................................................

/mins

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ZZ

WEDNESDAY

For one of your goals, complete the matrix. What things do you have to learn to accomplish it? .......................................................................................................................................... .......................................................................................................................................... ..........................................................................................................................................

How could the resilience skill, Optimism and Hope, help you to do this? (page 118)

/mins

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THURSDAY

Mindfulness Time Choose one of these resources to explore self-calming and minfulness activities.

/mins

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1 2 3 30

FRIDAY

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SATURDAY

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Study Tip

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Use a white board in your bedroom to write reminders and “stuff” to pump or relax you.

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What went well this week?

ZZ

April 2021

THINGS TO DO – WEEK: MONDAY

TUESDAY

WEDNESDAY

THURSDAY

FRIDAY

Communication/Comments

2 3 4 5

Feel in yourself?

2 3 4 5

Exercise daily?

2 3 4 5

Eat healthy?

1

For each of your Big Four, colour in how you did this week.

1

Weekly Big Four Check In

1

Parent/Guardian:

1

Teacher:

2 3 4 5

Sleep deeply?

31

Positive emotions + gratitude

PRIORITIES/DUE DATES 31

MONDAY

GRACEFUL NOTICING WHY?: by being aware that much advertising is distracting you from being grateful for what you have and creating feelings that you need more “stuff”, you will avoid your self-belief and wellbeing being threatened.

HOW: an effective coping strategy to contest this is to immediately, pause, start noticing the good things in your life and begin writing them down to fully appreciate them. Purely thinking about these things is not enough to self-generate positive emotions in yourself and increase your sense of autonomy, competence and connectedness. Be self-determined to show gratitude for what you currently have.

/mins

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TUESDAY

Acknowledgement: Ryan, Deci, Rievich & Shatte

DO: what is something that you really want, but really don’t need to make you feel happy? .......................................................................................................................................... ..........................................................................................................................................

/mins

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WEDNESDAY

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Do you feel that showing gratitude is a deliberate choice or something that comes naturally? .......................................................................................................................................... .......................................................................................................................................... ..........................................................................................................................................

How could the resilience skill, Self-belief, help you to do this? (page 119)

/mins

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ZZ

THURSDAY

Mindful Colouring In /mins

What went well this week?

1 2 3 48

FRIDAY

/mins

5

SATURDAY

6

SUNDAY

Study Tip

Start every morning with brisk exercise and a healthy breakfast; main meal of day.

ZZ

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ZZ

May / June 2021

THINGS TO DO – WEEK: MONDAY

TUESDAY

WEDNESDAY

THURSDAY

FRIDAY

Communication/Comments

2 3 4 5

Feel in yourself?

2 3 4 5

Exercise daily?

2 3 4 5

Eat healthy?

1

For each of your Big Four, colour in how you did this week.

1

Weekly Big Four Check In

1

Parent/Guardian:

1

Teacher:

2 3 4 5

Sleep deeply?

49

Strengths 360: your best self as a young adult

THIS LESSON: The Wellbeing Learning Intention is for you to notice when friends use particular strengths and when they notice you. Wellbeing Reflection: what strengths did you notice both yourself and your friends using?

Quite often in senior schooling it is easy to feel self-conscious of how others see you and how they feel you see them. Make this a positive learning experience by doing the following: At the beginning of a week, ask three friends to notice which character strengths that you tend to use most in your daily life and you do likewise for them. Then ask them to give examples of what you did to make them think this and you do so for them also. This is a fun and mindful activity to do with members of your family, teachers, coaches and others who know you well and you know them well.

Friends names

Your Strengths they noticed and what you did to make them think this.

1.

2.

3.

Friends names

Their Strengths you noticed and what they did to make you think this.

1.

2.

3.

Acknowledgement: Clifton, Seligman & Peterson

“Success is achieved by developing our strengths, not by eliminating our weaknesses.� Marilyn vos Savant 122

Self-Determination Word Search: your best self as a young adult

THIS LESSON: The Wellbeing Learning Intention is for you to practise using more accurate language. Wellbeing Reflection: what does each of these words mean to you?

Enjoy searching for the meaningful qualities, character strengths and essential ingredients to having a resilient state of wellbeing in the selfdetermination word search.

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ASSERTIVE

DOPAMINE

GROWTH

MINDFULNESS

RESPECTFUL

AUTONOMY

EMOTIONS

HABITS

MINDSET

SAVOURING

BELIEF

ENDORPHINS

HELP

NEURONS

SEROTONIN

CHALLENGES

ENGAGEMENT

HOPE

OXYTOCIN

SLEEP

COMPASSION

ETHICAL

JOMO

PERMAH

STRENGTHS

COMPETENCE

GENEROUS

JOY

PROCRASTINATION

TARGETS

CONNECTEDNESS

GOALS

KINDNESS

PURPOSE

TEAMWORK

COPING

GRATITUDE

LEADERSHIP

REALITY

WELLBEING

CORTISOL

GRIT

MEANING

RESILIENCE

“Why fit in when you were born to stand out?” Dr. Seuss 123

Regulating Emotions: your best self as a young adult

THIS LESSON: The Wellbeing Learning Intention is for you to learn to recognise when your emotions are intensifying and then to act immediately.

Wellbeing Reflection: what warning signals does your body send as your feelings rise?

While experiencing anxiety and stress can become more frequent in the senior years, the key is to act immediately to use coping strategies to self-calm and share your concerns with one of your champions. It will benefit you to be aware of your personal warning signals for being stressed.

Distress signals fall into three categories, which when combined affect your state of wellbeing: Physical: trembling, dizziness/headaches, skin disorders, pounding heart, breathlessness, tiredness.

Emotional: anxiety, anger, depression, ill temperament, panic, lack of interest/boredom.

Behavioural: disturbed sleeping patterns, frequent distraction, forgetfulness, abnormal eating habits.

Which distress signals do you feel most often. Rate them using Usually At Times Not Yet

Describe what kind of signals your body sends you when you are under pressure.

Also, write your distress signals on the different parts of your body outline drawn here.

Physical Usually At Times Not Yet

Emotional Usually At Times Not Yet

Behavioural Usually At Times Not Yet

Acknowledgement: Tal Ben Shahar, Karen Rievich, Andrew Shatte

“You never know how strong you are until being strong is the only choice you have.� Bob Marley 128

Your Best Self: your best self as a young adult

THIS LESSON: The Wellbeing Learning Intention is for you to design a personal plan to challenge your best self. Wellbeing Reflection: what does your best self value and act like, sound like, look like and feel like?

James Womack once said, “commitment unlocks the doors of imagination, allows vision, and gives us the right stuff to turn our dreams into reality.” To become the person who you want to become, will take self-determined commitment to use your strengths to make gritty choices.

Which quadrant currently best describes your commitment?

Lacking Commitment – going through the motions Content to not make the choice to …

No need to act with courage to …

Showing Commitment – being self-determined Making the choice to ….

Acting with courage to …

No Commitment – merely existing Refuse to make the choice to …

Unable to act with courage to …

Showing some Commitment – trying to be self-determined Unsure of how to make the choice to …

Unsure how to act with courage to …

Assessment of Your Commitment: Describe the reasons why you chose the quadrant that you feel you are currently in for commitment. ................................................................................................................................................................................................................................................................................................................................. ................................................................................................................................................................................................................................................................................................................................. ................................................................................................................................................................................................................................................................................................................................

Your Life Vision: Describe the life you want to create for yourself and the type of person who will be able to accomplish this. ................................................................................................................................................................................................................................................................................................................................. ................................................................................................................................................................................................................................................................................................................................. ................................................................................................................................................................................................................................................................................................................................

Anticipated Roadblocks: Describe challenges, obstacles, setbacks and difficult choices that you will be confronted with. ................................................................................................................................................................................................................................................................................................................................. ................................................................................................................................................................................................................................................................................................................................. ................................................................................................................................................................................................................................................................................................................................

Circle of Champions: Describe how each of your Champions can play roles to assist you on your journey. ................................................................................................................................................................................................................................................................................................................................. ................................................................................................................................................................................................................................................................................................................................. ................................................................................................................................................................................................................................................................................................................................

Assessment of Progress: Describe how you are progressing to become the person who you wish to become. ................................................................................................................................................................................................................................................................................................................................. ................................................................................................................................................................................................................................................................................................................................. ................................................................................................................................................................................................................................................................................................................................

Acknowledgement: Sonja Lyubormirsky

“If it doesn’t challenge you, it won’t change you.” Fred Devito 129

Exploring the World of Work: your best self as a young adult

THIS LESSON: : The Wellbeing Learning Intention is for you to show optimism for your future by exploring the world of work. Wellbeing Reflection: to create the type of life you want for yourself, what careers/jobs which interest you and what their entry requirements are.

Preparing yourself to thrive in your future life involves two main elements. Learning how to: » l ive a meaningful and fulfilling life using your strengths » e arn a living through a satisfying job or career by developing your skill sets » f ocusing on these equally will provide you with meaning and purpose, happiness and a sense of accomplishment.

Describe what you are currently doing to investigate careers.

Early engagement with the world of work through either work experience or part-time jobs has real benefits: » y our school Careers Counsellor, an expert on work options, is an important person for you to talk with.

Career decisions happen for different people at different times: » you are likely to retrain at least 8 times and change jobs 12 to 15 times » there is a difference between a job and a career » job: a specific activity » career: a number of jobs progressing through life.

Part-time jobs are positive opportunities to: » experience different types of careers and work » have timeout from study and meet new people » d evelop a savings plan to finance your needs and wants » feel a sense of independence.

Balance is the key: » no more than 10 hours weekly » avoid late night work as it can impact adversely on both your wellbeing and studies » achieving your goal of living the life you want to live.

Describe a part-time job you have had or would like.

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Look at www.myfuture.edu.au to: » reflect on your personality, skills, interests, needs, priorities and suitable levels of responsibility » complete the personal interest chart » match Jobs Chart with your personal characteristics and skills and level of education required.

Describe the careers you are interested in investigating. .......................................................................................................................................

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To investigate possible careers, you: » need to understand the connection between education and career opportunities » should plan careers as an extra subject.

Other websites which may assist you include: » www.jobsearch.gov.au » www.australianapprenticeships.gov.au » www.adecco.com.au » www.careersonline.com.au » www.self-directed-search.com » www.graduatecareers.com.au

“It wasn’t till quite late in life that I discovered how easy it is to say ‘I don’t know’.” W. Somerset Maugham 134

Exploring the World of Work: your best self as a young adult To learn about being employed on a full-time basis, ask someone in your chosen career area the following questions: » what do you do in a typical day? » what do you like and not like about your job? » what are your career highlights to date? » what education is required? » what education do you have? » what are your career ambitions? » what career advice could you give me?

Who did you talk to and what did you learn from them? ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... .......................................................................................................................................

Following are beneficial career planning activities: » display your skills to prospective employers on work experience » consider voluntary work experience » visit open days, careers expos and company websites » talk to career advisers, human resources staff, parents, friends, people in the jobs » contact the career association/union to ask if they have a student branch.

Action: What IS ONE THING I will start doing? ....................................................................................................................................... .......................................................................................................................................

Your resumé is a celebration of: » your skills, strengths and achievements and benefits you offer.

It provides potential employers an insight of your suitability for the position.

Research your target organisation to tailor your resumé to their needs: » they will be impressed you spent time to find out about them.

Be to the point: » three pages at most with relevant information » include a photo of yourself » introduce yourself via a covering letter emphasising specific parts of your resumé relevant to the position.

Use the headings: » Personal Particulars, including Qualifications and Training » Achievements, Skills, Strengths and Capabilities » names of three referees and ask each to focus on a specific area about you.

Highlight what you offer: » well developed communication skills, both oral and written » initiative and problem solving capabilities » ability to work to schedules and towards goals » achievements rather than responsibilities » work experience benefits » ensure the presentation of your resumé is stylish.

When choosing subjects to study, consider the following points: » are course prerequisites or those that keep your career options open » you enjoy, are capable of and that develop your individual talents » are your choices rather than those of family and friends.

Thanks for the contribution to this career planning guide from the “School of Hospitality, Tourism and Marketing” from Victoria University.

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“Attitude is a choice. Happiness is a choice. Optimism is a choice. Kindness is a choice. Giving is a choice. Respect is a choice. Whatever choice you make makes you. Choose wisely.” Roy T. Bennett 135

Maths Law and Formulae: your best self as a senior student SYMBOLS

Equality and Inequality Signs

..... is equal to

..... is not equal to

..... is less than

..... is greater than

..... is less than or equal to

..... is greater than or equal to

..... is not less than

..... is not greater than

..... is equivalent to

..... is approximately equal to

..... is congruent to

..... is proportional to

..... therefore

..... percentage

SET NOTATION

..... ..... ..... ..... ..... ..... ..... ..... ..... ..... .....

the set of such that is an element of is not an element of is a subset of is not a subset of the Universal set the null or empty set the intersection of the union of is equivalent to

SETS OF NUMBERS

N ..... the set of natural numbers J ..... the set of integers J-J+ ..... the sets of negative and positive integers Q ..... the set of rational numbers Q’ ..... the set of irrational numbers R ..... the set of real numbers R-R+ ..... the sets of negative and positive real numbers

..... pi, approximately 3.142 ..... angle

..... is parallel to

..... is perpendicular to

..... right angle

..... the co-ordinates of a point

..... the interval ST

..... the ray ST

..... the line ST

..... the length of interval ST or

..... the gradient of ST

..... the sum of

INDICES ..... .....

1st Law 2nd Law 3rd Law 4th Law 5th Law 6th Law

TYPES OF TRIANGLES

ax x ay = ax+y ax ÷ ay = ax-y ao = 1 (ax)y = axy (a x b)x = ax x bx

3 sides and angles add to 180° Scalene 3 sides different 3 angles different

7th Law

a x = ax b bx a-n = aIn

8th Law

ap/q = q ap = (q a)p

Isosceles 2 sides equal 2 angles equal Equilateral 3 sides equal 3 angles equal

LOG LAWS

log mn = log m + log n log m = log m – log n n log mp = p log m log I = 0 log ax = n x = an log 10x = n x = 10n In x = logex = n en = x

PARALLEL LINES are shown by arrows on the lines. The line that cuts the parallel lines is called the Transversal. a

b

d c f h g e

VERTICALLY OPPOSITE ANGLES a = c, b = d, e = g, h = f

ALTERNATE ANGLES c = e, d = f

CORRESPONDING ANGLES b = f, c = g, a = e, d = h

COINTERIOR ANGLES

c + f = 180˚ d + e = 180˚ These angles only apply to parallel lines.

GEOMETRY

INDEX LAWS

to the power ( )n square root

STANDARD FORM is given by (a number between 1 & 10) x (Power of 10) Ex. 456.7 = 4.567 x 102

STATISTICS

Measures of Central Tendency Mean, x, is the average.

Mode is the most common value.

Median is the middle value when the data is put in order.

Frequency is how often a value occurs.

Standard Deviation, SD is the spread around the Mean.

Range is the difference from the largest to the smallest value.

Boxplots and Interquartile Ranges show the spread of data around the Median.

Right-angled has a 90° angle

TYPES OF QUADRILATERALS 4 sides and angles add to 360° Irregular 4 sides different 4 angles different Kite 2 pairs of sides equal 1 pair of angles equal Rectangle 4 right angles 2 pairs of sides equal Rhombus 4 sides equal 2 pairs of sides equal Parallelogram Opposite sides equal and parallel 2 pairs of angles equal Square 4 right angles 4 sides equal Trapezium 1 pair of sides parallel

CO-ORDINATE GEOMETRY For two points (a,b) and (e,d) gradient = m = d – b = rise = tan e – a = run

distance between points = (e–a)2 + (d–b)2 = rise2 + run2 midpoint (a+e , b+d) 2 2

Gradient

Perpendicular lines m1 = – l m2

VECTORS

r = xi + yj + zk IrI = x2 + y2 + z2 r1 - r2 = r1r2 cos = r = x, x2 +y1 y2 +z1 z2

“There is only one good, knowledge and one evil, ignorance.” Socrates 140

y-intercept

equation of a straight line y = mx + c Parallel Lines m1= m2

Maths Law and Formulae: your best self as a senior student MENSURATION

QUADRATICS Solution of equation

Cone

Cylinder

Circle

Sphere

Surface area of cone = x r2 + rs Volume of a cone = r 2h 3

Surface area of cylinder = 2 rh + 2 r2 Volume of cylinder = r2h

Circumference of a circle = 2 r Area of a r circle = r2

Surface area of a sphere = 4 r2 Volume of a r sphere = 4 r3 3

s h r

h r

Rectangle

Box

Perimeter = 2(l+w) Area = l x w

Trapezium

Arc

h w

l

Parallelogram b

D

C

a h b

B

Area of ABCD = bh

a

B

a

A

w

l

Volume = l x w x h

c

r

h A

b

b

A

r L

D

Area of Trapezium ABCD = ½ h (a+b)

Arc length L = r Sector Area A = ½ r2

B

Area of bh ∆ ABC = 2

B

h B

h

Triangle C

CALCULUS

Pyramid

Volume of a pyramid = Bh 3 (B = area of base)

Area of ab ∆ABC = 2 a

c A

b

C

d dx d dx d dx d dx d dx d dx

(x n) = nx n-1 ∫x ndx = ( l ) x n+1 + c, n ≠ –1 n+1 ax ax ax (e ) = ae ∫e dx = ( l ) eax + c a l l (logex) = ∫( )dx = logex + c, for x >0 x x (sin ax) = a cos ax ∫sin ax dx = – l cos ax + c a (cos ax) = –a sin ax ∫cos ax dx = l sin ax + c a (tan ax) = +asec 2ax ∫sec 2 ax dx = l tan ax + c a d dv product rule: (uv) = u + v du

dx dx dx

quotient rule:

dv dv d ( u ) = v dx – u dx 2 dx v v

chain rule:

dy = dy du dx du dx

TRIGONOMETRY

PYTHAGORAS THEOREM

Sohcahtoa sin = opposite cos hypotenuse

c2 = a2 + b2 Cosine Rule: c2 = a2 + b2 – 2ab cos Sine Rule: a = b = c sinA sinB sinC Area of Triangle = ½ b.c.sin

tan

COMPLEX NUMBERS

= adjacent hypotenuse

= opposite = sin adjacent cos

cosec

z = x + iy = r (cos + isin ) = rcis lzl = x 2 + y 2 = r – < Arg z 1 1 z 1 z 2 = r 1 r 2 cis( 1 + 2) z = r cis ( 1 - 2) z2 r2 zn = rn cis n (de Moivre’s theorem)

=

1 sec = 1 cot = 1 sin cos tan

cos 2 + sin2 = 1, 1 + tan2 = sec 2 cot 2 + 1 = cosec 2 sin (a + b) = sin a cos b + sin b cos a sin (a – b) = sin a cos b – sin b cos a cos (a + b) = cos a cos b – sin a sin b cos (a – b) = cos a cos b + sin a sin b tan (a + b) = tan a + tan b 1 – tan a tan b

FACTORISING

a2 + 2ab + b2 = (a + b)2 a2 – 2ab + b2 = (a – b)2 a2 – b2 = (a + b) (a – b) a 3 + b 3 = (a + b) (a2 – ab + b2) a 3 – b 3 = (a – b) (a2 + ab + b2)

ALGEBRA – EXPANDING

ax 2 + bx + c = 0 is given by the formula x = –b± b2–4ac

2a If b2 – 4ac > 0, 2 solutions If b2 – 4ac = 0, 1 solution If b2 – 4ac < 0, no solutions b2 – 4ac is called the discriminant

( )

sin

cos

tan

0

0

1

0

6 (30°)

1 2

3 2

1 3

4 (45°)

1 2

1 2

1

3 (60°)

3 2

1 2

3

2 (90°)

1

0

undefined

tan (a – b) = tan a – tan b 1 + tan a tan b sin 2 = 2 sin

a (b + c) = ab + ac (a – b)2 = a2 – 2ab + b2 (a + b)2 = a2 + 2ab + b2 (a + b)(a – b) = a2 – b2 (difference of two squares) (a + b)3 = a 3 + 3a2b + 3ab2 + b 3 (a – b)3 = a 3 – 3a2b + 3ab2 – b 3 (x + a)n = xn + (n)xn-1a + (n)xn-2a2 + ... ( n )x 2an-2 = ( n )xan-1 + an 1 2 n-2 n-1

cos

tan 2

= 2 tan 1 – tan2

cos 2 = cos 2 – sin2 = 2 cos 2 – 1 = 1 – 2 sin2 sin a + sin b = 2 sin ½ (a + b) cos ½ (a – b) sin a – sin b = 2 cos ½ (a + b) sin ½ (a – b) cos a + cos b = 2 cos ½ (a + b) cos ½ (a – b) cos a – cos b = –2 sin ½ (a + b) sin ½ (a – b)

“Genius is I% inspiration and 99% perspiration.” Thomas Edison 141