October 2019

The odds of finding the
perfect man are easy......just
take the square root of
negative one!
Taking the square root of negatives
Image result for cartoon math
Divide by Zero
Image result for unforgivable sin funny

The two unforgivable sins of math (before Algebra 2 introduction of i and the limit concept when evaluating intermediate forms like 0/0).

Math Equation? Math question? or is it just simplify this expression?

The New York Times (https://www.nytimes.com/2019/08/02/science/math-equation-pedmas-bemdas-bedmas.html?utm_source=pocket-newtab) ran a story about it.

The author (Prof. Steven Strogatz) state: ” The question above has a clear and definite answer, provided we all agree to play by the same rules governing “the order of operations.” When, as in this case, we are faced with several mathematical operations to perform ”

This is clearly in-line with Math4Teens approach to math. This is a second language. Like any language, without agreeing on the punctuation and grammar, it will be extremely hard to express ourselves without ambiguity. An article worth reading even if you are not interested in math.

Summer 2019

This has been a busy summer. We moved to Aspen Hill and will open our center at the start of the school year. Most tutoring will continue to take place at the students home or preferred library. The center will be an additional option for those who find the conditions at home to be less than ideal (little siblings, noise, distractions,etc.) or on days the libraries are closed.

Transition to the redesigned SAT – first PSAT in the new format

Below is the link to an article which was in the New York Times regarding the new SAT. I think students and parents will find it very helpful!



SAT Question of the Day transition from email to app.

Well, it seems the makers of the SAT do not want to send us emails any more.

If you have an Apple phone or tablet there is an App for you. For the rest of us with Android based machines the College board seems to think we will run and buy one?

I would expect the College board to be more mature and design the transition better.

Hopefully someone there will realize they need to provide a platform for all users.

I will visit the SAT official website and continue to post the SAT question of the day.

Good luck.


SAT Question of the Day August 11th 2013

If Kelly buys t pens priced at 2 dollars each and u pens priced at 4 dollars each, which of the following expresses, in terms of t and u, the average (arithmetic mean) price, in dollars, of these pens?

A.     (3 times t) + (3 times u) over (t + u)

B.     (3 times t) + (3 times u) over (t imes u)

C.     (3 times t times u) over (t + u)

D.     ((2 times t) + (4 times u)) over (t + u)

E.     ((2 times t) + (4 times u)) over (t times u)

Very similar to the question discussed in the previous post, we have a word to equation problem.

One way (not recommended) is plug in and see that you obtain the number you expect to get.

The better way, in my opinion, is to try and translate the problem.

Lets say Kelly buys 4 pens, each for $2. She will pay for them $8. If she buys the other kind, lets say 5 of them, she will pay for each $4 and for these $4 pens she’ll pay $20.

She bought 9 pens for a total of $28.

Each pen, on average, will cost $28/9 which is a little less than $3.5

This is the way to calculate a weighted average (where we care about the amount we have of each ingredient).

If we follow the steps we just took using the letters t and u instead of the actual numbers it is clear we should mark D.

68% got it right.

SAT Question of the Day August 8th 2013

For every 10 dollars Ken earns mowing lawns, he gives 3 dollars to his younger brother, Tim, who helps him. Which of the following gives the relationship between d, the number of dollars Ken earns, and t, the number of dollars he gives to Tim?

A.     d equals (3 times t) over 10

B.     d equals (10 times t) over 3

C.     d equals 3 over (10 times t)

D.     d equals 10 over (3 times t)

E.     d equals (3 times t) minus 10

Yet another reading and understanding question.

We don’t need to do any calculations – just write down an equation.

We have two brothers (Ken and Tim). They earn d dollars mowing the lawn.

For every 10 dollars they earn Tim gets 3 . If Tim got T dollars how can we calculate d?

Well, if Tim got 3 dollars d must be $10. if Tim got 6, d must be $20 and so on.

That means we need to divide the t dollars tim gets by 3 and multiply it by 10 to obtain the d dollars they earned all together.

Answer b should do the trick.

Another way is to plug in 6 as the number of dollars tim earns and see that we get 20 as the d dollars they earn together.

46% of 170,000 got it right !

SAT Question of the Day August 05 2013




The graph above shows the distribution of the number of days spent on business trips in 2010 by a group of employees of Company W. Based on the graph, what is the median number of days spent on business trips in 2010 for these employees?


A.     22

B.     22.5

C.     22.75

D.     23

E.     23.5

This is a typical reading comprehension question – the fact that it is in the math section indicates we need to be familiar with key concepts of graph reading and in this case with the definition of the median.

The median is a statistic (a number that represents a group that can be ordered and ranked) which has half the group members above it and half below it. In case we have an even number of group members it will be the average of the two members that are closest to the middle.

As we discussed in previous posts, we first want to be able to read the data in the graph. Choosing randomly the third bar from the left we make sure we read it as: “5 employees spent 22 days  on business trips in 2010”.

Now, the median will be the number of days spent on business trips in 2010 that half the employees traveled less than and half traveled more than.

How many employees do we have presented in the graph?


That mean we are looking for the number of days the 16th worker traveled (15 employees or half traveled less or the same and 15 employees – or the other half traveled more).

Counting from the left 5+6+5=16.

The 16th employee traveled then 22 days.

34% out of 218,000 got it right.


SAT Question of the Day August 2nd 2013

A 25-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on concrete 7 feet from the base of the building. If the top of the ladder slips down 4 feet, then the bottom of the ladder will slide out

A.     4 feet

B.     5 feet

C.     6 feet

D.     7 feet

E.     8 feet

One of the hardest SAT questions of the day I’ve seen so far.

It requires knowledge of the pythagorean theorem and for most students, a use of a calculator.

Lets draw a diagram that will help us understand what is going on.

We have a 25 foot ladder (constant length) leaning against a wall. This creates a right triangle with the floor. The base is 7 feet from the wall. Using pythagorean theorem (the sum of the squares of the lengths of a right triangle equals the square of the length of it’s hypotenuse).


Using this theorem we conclude the ladder’s top is 24 feet from the ground.





Now the ladder slips down 4 feet – that means we now have a different right triangle. The length of the ladder did not change (25 feet) but the distance from the top of the ladder to the ground and from the bottom part of the ladder to the wall both do. Now we look for our b





The ladder then slides from it’s initial location, 7 feet from the wall, to a new location 15 feet from the wall. It was displaced 8 feet.

39% out of 151,000 got it right.

SAT Question of the Day July 30th 2013

All numbers divisible by both 4 and 15 are also divisible by which of the following?

A.     6

B.     8

C.     18

D.     24

E.     45

This is a number set property question asking us about the divisibility of a set of numbers that are divisible by both 4 and 15.

If a number is divisible by 4 it is also divisible by 2 (1, 2, 4, and the number itself). If this number is also divisible by 15 it is divisible by 3 and 5 (1, 3, 5, 15, and the number itself).

If it is divisible by both it is divisible by any combination of 4 and 15 prime divisors (1, 2, 2, 3, and 5).

The only number that does NOT have any additional prime divisors is 6. 8 (1, 2, 2, 2) has another 2 as its prime divisors. 18 has an additional 3 (1, 2, 3, 3). 24 has an additional 2 (1, 2, 2, 2, 3) and 45 has an additional 3 (1, 3, 3, 5).

56% of 192,000 got it right.