2F Math Blog 2009

Below are the solutions for 2007 Paper 1

If you are not sure, please come and see me as soon as possible.

Important things to note:-

Ex 5.3, 5.4, 5.5 Feedback

1. Some of you did not define the unknowns x and y. E.g. Let x be number of apples. Let y be number of lemons.
2. Quite a number of you did not label your equations. Please label them. E.g. x + y = 7 ……(1), x – y = 3 ……(2)
3. Always show clearly what you are doing. E.g. (1) + (2) means equation 1 add to equation 2. Do not make the teacher hunt or guess what you are trying to do. Be POLITE, write CLEARLY.
4. Do not include UNITS in your equations. E.g. x + y = $2. Instead write x + y = 2.
5. Finally write down the final answer. Does the question require values of x and y only? Or are they looking for a certain answer? READ the question. The question is not over until you have answered all the required parts.
6. IF you are kiasu or quite careless, take the time to LOOK through all the answers, verify that they are correct. This is the topic where you can check your own answers.

Ex 6.2 Feedback

1. Quadratic curves are parabolas, they are symmetrical. ) or ( …Never \_/… I would like to know who sabotaged your friends’ answers. This is math. Not geography. All your curves must have peaks, no plateaus!! Remember the happy face (: and the sad face ): No straight face |:
2. Invest in a curve ruler, most of you cannot draw smooth curves. When they are smooth, they are not symmetrical. So please get a curve ruler. IF you do not know how to use, please ASK! If you dislike curve rulers, you can ask me for an alternative called the french curve.
3. For graphs, always display
   • table of values
   • name of equation e.g. y = x + 1
   • curve must pass through all the points
   • curve must look symmetrical
   • line of symmetry is always x = c, where c is some number
   • a quadratic curve may have 0, 1 or 2 x-intercepts: write them down as x = a, x = b unless you are asked for the coordinates.
   • y-intercept must be written down as y = c unless you are asked for the coordinates.
   • use a 2B pencil and keep an eraser
4. When asked to answer graph questions, always READ from the graph. Use dotted lines on your graph to show that you know how to find the answer. So far, nobody has done this. I am sad ):

Step 0: Know thy enemy. Topics to be tested are from Chapter 1 to Chapter 6.2 (inclusive).

Step 1: Do all your corrections. This way you know where you have gone wrong.

Step 2: Do the 2007 and 2008 papers if you have not done so. Do not wait until the last minute. Time waits for no one. You manage your own time.

Step 3: Stay healthy. Get enough rest. Do not do funny things that will result in injuries. If you are bored, do more math! You can do the review exercises, the workbook questions etc. Need to check answers? Find me (:

Step 4: Check your pencil case on the day before the exam. For math you need:-

• Approved electronic calculator. If you using a calculator other than the one purchased in the school bookshop, please come and check with me.
• 2B pencil, preferably mechanical pencil. If not, please keep a sharpener as well.
• Soft eraser. You do not want to tear your script do you?
• 15 cm clear plastic ruler. Kiddy rulers with fancy designs are strictly not allowed. This is not to discourage your creativity but to improve your accuracy.
• Curve ruler or french ruler. Make sure you know how to use either one of these instruments. When in doubt, ASK!
• Dark blue/black pen. Preferably ball point. Smudges make things complicated.

Step 5: Take note of the following…

• Always answer in pencil for questions on graph paper.
• Answer all questions in Section A and choose only 1 from Section B.
• Be neat and clear. (Tanyakorn I hope you are reading this!)
• Leave 15 minutes to check the entire paper.

Step 6: Spread this news to everyone. And goodluck. May the force be with you! F = MA <— no force without acceleration! (;

I will put up the solutions for a limited time only. I will also put them up only after I’ve gone through them in class.

39 passes, 1 failure, 2 unknown

Date of release: To be confirmed

General comments: Quite well done

Here’s something to entertain you. It’s a problem. Try to solve it. Your answer must be simple enough to explain to a 10 year old kid. I’m sure you would have no problem with that. Once you’ve solved this problem, try relating it to coordinate geometry. That’s the catch. You can work in groups or in pairs, even individually. Approach me personally to check your answers.

The problem is outlined as follows:

Given a bathtub of water and unmarked 7 litre and 11 litre bottles, how can 2 litres of water be measured into the smaller bottle?

This problem is dedicated to Jazin. Be curious people, be very curious

Here’s something that you will find useful. Trust me. And it’s not only for maths. Humans solve problems on a daily basis. And we come across problems every other second. Some we know the answer to. Some requires a little bit of thinking and some are just mind boggling. Happy reading!

George Polya (1887 – 1985) was one of the most famous mathematics educators of the 20th century (so famous that you probably never even heard of him). Dr. Polya strongly believed that the skill of problem solving could and should be taught – it is not something that you are born with. He identifies four principles that form the basis for any serious attempt at problem solving:

1. Understand the problem
2. Devise a plan
3. Carry out the plan
4. Look back (reflect)

1. Understand the problem

• What are you asked to find out or show?
• Can you draw a picture or diagram to help you understand the problem?
• Can you restate the problem in your own words?
• Can you work out some numerical examples that would help make the problem more clear?

2. Devise a plan

A partial list of Problem Solving Strategies include:

• Guess and check
• Solve a simpler problem
• Make an organized list
• Experiment
• Draw a picture or diagram
• Act it out
• Look for a pattern
• Work backwards
• Make a table
• Use deduction
• Use a variable
• Change your point of view

3. Carry out the plan

• Carrying out the plan is usually easier than devising the plan
• Be patient – most problems are not solved quickly nor on the first attempt
• If a plan does not work immediately, be persistent
• Do not let yourself get discouraged
• If one strategy isn’t working, try a different one

4. Look back (reflect)

• Does your answer make sense? Did you answer all of the questions?
• What did you learn by doing this?
• Could you have done this problem another way – maybe even an easier way?

One of your classmates requested for answer keys to the past year papers that I’ve distributed for practice. Thank you for suggesting it. I am uploading the 2008 answer key first. Coming up is the 2007 answer key. Don’t have it with me right now so please wait a few more days. Patience is a virtue. Mathematicians need to be patient. Think calmly and you’ll be able to solve the problem.

2008 Paper 1 Answer key Click me!

2008 Paper 2 Answer key Click me!

320 km and 305 km is for the distance

Speed for Car X should be 76 km/h

Speed for Car Y should be 61 km/h

I’m really sorry to be missing lessons. My face is still swollen and the medicine is making me drowsy all the time. I hope you guys can be independent and check your answers here. The test will be going on as usual tomorrow. Another teacher would be coming in to administer the test. Answers are on the following word document:

Latest update: Download answers here

I missed out question 5 and 6. Fixed question 4 answers.