This would be a multiple series posts aimed at teaching the students about the various SAT maths concepts so as to foster greater understanding of the subjects amongst them. This is the time when most of the high school students, seniors and juniors, prepare for their SAT exam and appear for it before October so as to be able to use their SAT scores for the early action admission rounds as well as regular action admission rounds.

In the previous post, we learnt about the basics of number system, the real numbers, the integers and the odd numbers. Continuing further, let us take a quick look at the prime numbers, composite numbers, co-primes, factors and multiples of a number. Before beginning with these, understand that the integers consist of negative, zero and positively signed numbers which can be represented on a number line as given below:

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For all the developers exploring new resources W3C has announced the third version of its standards for the inclusion of mathematical expressions in Web pages- MathML. This Mathematical Markup Language is aimed to make math on the Web more accessible and more international.

(Mathematical Markup Language) is designed to make math on the Web more easily reachable and more international. While the basic markup remains the same, this version brings to it some improvements for assistive technology, as well as for formulas in languages that are written from right to left.

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SAT Maths: What is Direct Variation?

Let the cost of 1 pen be $12. By unitary method, we can find the cost of any number of pens. Clearly, the cost of 2 pens is $ 24; the cost of 3 such pens is $ 36; the cost of 5 such pens is $ 60; the cost of 8 such pens is $ 96 and so on…

Number of pens (a)              Cost in Dollars(b)

1                                                  12

2                                                  24

3                                                  36

5                                                  60

8                                                 96

We find that:

The more the number of pens, the greater the cost;

Lesser the number of pens, lesser the cost.

Also, the ratio a/b = Number of pens/cost in dollars = 1/12 (constant)

We say that the number of pens varies directly as the cost in dollars.

We may also notice that the ratio of the number of pens is equal to the ratio of their costs.

1:2=12:24, 2:3= 24:36, 3:8= 36:96 etc.

Direct Variation: Two quantities a and b are said to vary directly if the ratio a/b remains constant.

The ratio a/b is called the constant of variation. In the above example, the constant of variation is 1/12.

Important Rule of Direct Variation:

If two quantities a, b are in direct variation, the ratio of any two values of ‘a’ is equal to the ratio of the corresponding values of ‘b’.

Example 1: Read more…