## Math: A counting problem

Tutoring math 12 and some university courses, you get asked about counting. The tutor opens the discussion with a couple of examples. Questions that ask, “How many ways can people be lined up for a photograph” or “how many five-card …

## Physics: Impulse

Tutoring physics, you get asked about impulse now and again.  The tutor introduces the topic, explaining its connection with momentum. Impulse has many definitions.  Fundamentally, it means change in momentum.  Momentum is a vector quantity, which means it has a …

## Math: Systems of equations: a word problem

Tutoring math, you revisit this type of problem often.  The math tutor gives a quick reminder just ahead of exams. Here’s the problem: A saleswoman gets paid a base monthly salary plus commission.  One month she sells \$50 000 and …

## Math: a little more on factoring

Tutoring high school math, you might be in review mode now.  The math tutor brings up a couple of factoring instances. Instance 1:  Suppose you need to factor -2x^2 + 4x + 70.  How would you proceed? Solution: First, you …

## Physics: back emf

Tutoring physics 12, you encounter this concept.  The tutor offers the formula with an explanation. Induction refers to the creation of voltage in a wire that is not connected to a power source.  It’s the premise that enables generation of …

## Math: factoring difference of cubes

The math tutor continues with factoring cubes.  Tutoring calculus, this formula is another standby. Let’s turn to factoring x^3 – 64. Realizing that 64=4^3, you actually are facing x^3-4^3 You need the formula a^3 – b^3=(a-b)(a^2 + ab + b^2) …

## Math: factoring sum of cubes

Tutoring high school math, you rarely see this; it comes up often, however, in calculus.  The tutor offers a light treatment. How do you factor x^3 + 125? You need the following formula: a^3 + b^3 = (a + b)(a^2 …

## Math: How to handle multiple-stage fractions

Tutoring middle school or high school math, you come across these from time to time.  The math tutor explains how to unravel them. We sometimes might encounter a fraction such as (3/4)/8 How do you simplify such a fraction to …

## Biology: the female system, cont.

When you tutor Biology 12, which is needed for nursing, you cover the male and female reproductive systems.  Here is the continuation from the Dec 30 post. Previously I discussed the end of the monthly female cycle: if conception does …

## Math: an assessment style problem

Tutoring math, you work with people heading back to school who need to pass assessment tests.  The math tutor demonstrates a problem they often ask about. The problem is as follows: Joe and Bill are scene painters for a theatre …