## Recommended Algebra Books

Description from Amazon:

If you think algebra has to be boring, confusing and unrelated to anything in the real world, think again! Written in a humorous, conversational style, this book gently nudges students toward success in pre-algebra and Algebra I. With its engaging question/answer format and helpful practice problems, glossary and index, it is ideal for homeschoolers, tutors and students striving for classroom excellence. It features funky icons and lively cartoons by award-winning Santa Fe artist Sally Blakemore, an Emergency Fact Sheet tear-out poster, and even an “Algebra Wilderness” board game guaranteed to help students steer clear of “Negatvieland”–and have fun.The Algebra Survival Guide is the winner of a Paretns’ Choice award, and it meets the Standards 2000 of the National Council of Teachers of Mathematics. Its 12 content chapters tackle all the trickiest topics: Properties, Sets of Numbers, Order of Operations, Absolute Value, Exponents, Radicals, Factoring, Cancelling, Solving Equations, the Coordinate Plane and yes even those dreaded word problems. The Guide is loaded with practice problems and answers, and its 288 pages give students the boost they need in a style they’ll enjoy to master the skills of algebra.

Also, check out the workbook:

## Maths Challenge

Hi, do feel free to try out our Maths Challenge (Secondary 4 / age 16 difficulty):

Source: Anderson E Maths Prelim 2011

If you have solved the problem, please email your solution to mathtuition88@gmail.com .

(Include your name and school if you wish to be listed in the hall of fame below.)

Students who answer correctly (with workings) will be listed in the hall of fame. 🙂

# Hall of Fame (Correct Solutions):

1) Ex Moe Sec Sch Maths teacher Mr Paul Siew

2) Queenstown Secondary School, Maths teacher Mr Desmond Tay

3) Tay Yong Qiang (Waiting to enter University)

# Why Additional Maths (A Maths) is important for entering Medicine:

Pathway: A Maths (O Level) –> H2 Maths (A Level) –> NUS Medicine

Quote: While NUS and NTU Medicine does not (officially) require H2 Maths (ie. ‘A’ level Maths), some other (overseas) Medical schools might. And not having H2 Maths might (unofficially) disadvantage your chances, even for NUS and NTU.

Therefore (assuming you intend to fight all the way for your ambition), your safest bet would be to (fight for the opportunity) to take both H2 Bio and H2 Math. The ideal Singapore JC subject combination for applying to Medicine (in any University) is :

H2 Chemistry, H2 Biology, H2 Mathematics

Quote: pre-requisites for nus medicine will be H2 Chem and H2 bio or physics.

as for what’s best,
H2 math is almost a must since without it you’ll be ruling out a lot of ‘back-up courses’

## Maths tutoring adds up for students: OECD study (Singapore PISA tuition effect)

Many of the world’s most mathematically gifted teenagers come from countries with the most lucrative tutoring industries.

Figures released this week show tutoring in Asia’s powerhouses is widespread, with participation rates more than double those  in Australia, though the extent to which their success is a result of a punishing study schedule is unclear.

In test results released by the OECD, 15-year-olds from Shanghai  topped the mathematics rankings, performing at a level equivalent to three years ahead of students in Australia.

## Bukit Panjang 2010 P1 Q3a Logarithm Question Solution (A Maths Tuition)

Question:
Solve the following equation:

(a) $5^{2x}-7^x-35(5^{2x})+36(7^x)=0$

Solution:

$-34(5^{2x})+35(7^x)=0$

$35(7^x)=34(5^{2x})$

Ln both sides, we get

$\ln 35 + x\ln 7=\ln 34+2x\ln 5$

$\ln 35-\ln 34=x(2\ln 5-\ln 7)$

$\displaystyle \boxed{x=\frac{\ln 35-\ln 34}{2\ln 5-\ln 7}=0.0228}$

## Xinmin Secondary 2010 Prelim Paper I Q24 Solution (Challenging/Difficult Probability O Level Question)

A bag A contains 9 black balls, 6 white balls and 3 red balls. A bag B contains 6 black balls, 2 white balls and 4 green balls. Ali takes out 1 ball from each bag randomly. When Ali takes out 1 ball from one bag, he will put it into the other bag and then takes out one ball from that bag. Find the probability that

(a) the ball is black from bag A, followed by white from bag B,
(b) both the balls are white in colour,
(c) the ball is black or white from bag B, followed by red from bag A,
(d) both the balls are of different colours,
(e) both the balls are not black or white in colours.

Solution:

(a) $\displaystyle\frac{9}{18}\times\frac{2}{13}=\frac{1}{13}$

(b) Probability of white ball from bag A, followed by white ball from bag B=$\displaystyle=\frac{1}{2}\times\frac{6}{18}\times\frac{3}{13}=\frac{1}{26}$

Probability of white from B, followed by white from A=$\displaystyle=\frac{1}{2}\times\frac{2}{12}\times\frac{7}{19}=\frac{7}{228}$

Total prob=$\displaystyle\frac{205}{2964}$

(c) Prob. of ball is black or white from bag B=$\displaystyle\frac{6}{12}+\frac{2}{12}=\frac{8}{12}$

$\displaystyle\frac{8}{12}\times\frac{3}{19}=\frac{2}{19}$

(d) Prob of both red = P(red from A, followed by red from B)=$\displaystyle\frac{1}{2}\times\frac{3}{18}\times\frac{1}{13}=\frac{1}{156}$

P(both green)=P(green from B, followed by green from A)=$\displaystyle\frac{1}{2}\times\frac{4}{12}\times\frac{1}{19}=\frac{1}{114}$

P(both black)=P(black from A, followed by black from B)+P(black from B, followed by black from A)=$\displaystyle\frac{1}{2}\times\frac{9}{18}\times\frac{7}{13}+\frac{1}{2}\times\frac{6}{12}\times\frac{10}{19}=\frac{263}{988}$

P(both white)=$\displaystyle\frac{205}{2964}$ (from part b)

$\displaystyle 1-\frac{1}{156}-\frac{1}{114}-\frac{263}{988}-\frac{205}{2964}=\frac{1925}{2964}$

(e)

P(neither black nor white from A, followed by neither black nor white from B)=$\displaystyle\frac{1}{2}\times\frac{3}{18}\times\frac{5}{13}=\frac{5}{156}$

P(neither black nor white from B, followed by neither black nor white from A)=$\displaystyle\frac{1}{2}\times\frac{4}{12}\times\frac{4}{19}=\frac{2}{57}$

$\displaystyle\frac{5}{156}+\frac{2}{57}=\frac{199}{2964}$