Introduction to equations - Introduction
This section looks at different types of equations, and some methods for solving them.
This Revision Bite covers:
Wednesday, March 10, 2010
junior cert transformations
Introduction to transformations - Introduction
If a shape is transformed, its appearance is changed. This can be done in a number of ways, including translation, rotation, reflection and enlargement.
This Revision Bite covers:
Tuesday, March 9, 2010
Junior Cert Scientific notation
Exponents: Scientific Notation (page 3 of 5) Sections: Basics, Negative exponents, Scientific notation, Engineering notation, Fractional exponents By using exponents, we can reformat numbers. For very large or very small numbers, it is sometimes simpler to use "scientific notation" (so called, because scientists often deal with very large and very small numbers). The format for writing a number in scientific notation is fairly simple: (first digit of the number) followed by (the decimal point) and then (all the rest of the digits of the number), times (10 to an appropriate power). The conversion is fairly simple.
This is not a very large number, but it will work nicely for an example. To convert this to scientific notation, I first write "1.24". This is not the same number, but (1.24)(100) = 124 is, and 100 = 102. Then, in scientific notation, 124 is written as 1.24 × 102. Actually, converting between "regular" notation and scientific notation is even simpler than I just showed, because all you really need to do is count decimal places.
Since the exponent on 10 is positive, I know they are looking for a LARGE number, so I'll need to move the decimal point to the right, in order to make the number LARGER. Since the exponent on 10 is "12", I'll need to move the decimal point twelve places over. First, I'll move the decimal point twelve places over. I make little loops when I count off the places, to keep track:
Then I fill in the loops with zeroes: Copyright © Elizabeth Stapel 1999-2009 All Rights Reserved
In other words, the number is 3,600,000,000,000, or 3.6 trillion Idiomatic note: "Trillion" means a thousand billion — that is, a thousand thousand million — in American parlance; the British-English term for the American "billion" would be "a milliard", so the American "trillion" (above) would be a British "thousand milliard".
In scientific notation, the number part (as opposed to the ten-to-a-power part) will be "4.36". So I will count how many places the decimal point has to move to get from where it is now to where it needs to be:
Then the power on 10 has to be –11: "eleven", because that's how many places the decimal point needs to be moved, and "negative", because I'm dealing with a SMALL number. So, in scientific notation, the number is written as 4.36 × 10–11
Since the exponent on 10 is negative, I am looking for a small number. Since the exponent is a seven, I will be moving the decimal point seven places. Since I need to move the point to get asmall number, I'll be moving it to the left. The answer is 0.000 000 42
This is a small number, so the exponent on 10 will be negative. The first "interesting" digit in this number is the 5, so that's where the decimal point will need to go. To get from where it is to right after the 5, the decimal point will need to move nine places to the right. Then the power on 10will be a negative 9, and the answer is 5.78 × 10–9
This is a large number, so the exponent on 10 will be positive. The first "interesting" digit in this number is the leading 9, so that's where the decimal point will need to go. To get from where it is to right after the 9, the decimal point will need to move seven places to the left. Then the power on 10 will be a positive 7, and the answer is 9.3 × 107 Just remember: However many spaces you moved the decimal, that's the power on 10. If you have a small number (smaller than 1, in absolute value), then the power is negative; if it's a large number (bigger than 1, in absolute value), then the exponent is positive. Warning: A negative on an exponent and a negative on a number mean two very different things! For instance: –0.00036 = –3.6 × 10–4 Don't confuse these! You might be asked to multiply and divide numbers in scientific notation. I've never really seen the point of this, since, in "real life", you'd be dealing with these messy numbers by using a calculator, but here's the process.
Since I'm multiplying, I can move things around and simplify some of this stuff easily: (2.6 × 105) (9.2 × 10–13) Now I have to deal with the 2.6 times 9.2, remembering to convert to scientific notation: 2.6 × 9.2 = 23.92 = 2.392 × 10 = 2.392 × 101 Putting it all together, I have: (2.6 × 105) (9.2 × 10–13) Then (2.6 × 105) (9.2 × 10–13) = 2.392 × 10–7 Dividing numbers in scientific notation works about the same way.
First, I'll deal with the exponents: (1.247 × 10–3) ÷ (2.9 × 10–2) Now I'll deal with the division: 1.247 ÷ 2.9 = 0.43 = 4.3 × 10–1 Putting it all together, I get: (1.247 × 10–3) ÷ (2.9 × 10–2) So the answer is: (1.247 × 10–3) ÷ (2.9 × 10–2) = 4.3 × 10–2 If you are required to do problems like these, remember that you can always check your answers in your calculator. For instance, entering "1.247 EE –3 / 2.9 EE –2" on my calculator returns "0.043", which equals 4.3 × 10–2 in scientific notation. If you have to do a lot of these problems, you may find it useful to set your calculator to display all values in scientific notation. Check your owner's manual for instructions. |
more venn diagrams
Venn Diagram - Word Problems
1) Stephen asked 100 coffee drinkers whether they like cream or sugar in their coffee. According to the Venn diagram below, how many like
a) Cream?
b) Sugar?
c) Sugar but not cream?
d) Cream but not sugar?
e) Cream and sugar?
d) Cream but not sugar?
e) Cream and sugar?
f) Cream or sugar?
Solution:
a) 16 + 20 = 36
b) 20 + 35 = 55
c) 35
d) 16
e) 20
f) 16 + 20 + 35 = 71
Practice Questions:
2) Eon asked 60 students whether they listen to two popular radio stations, WROK and WRAP. He found that 23 listen to WROK, 18 listen to WRAP, and 8 listen to both. How many students in Robert's survey listen toa) WROK but not WRAP
b) WRAP but not WROK
c) neither WROK nor WRAP
3)Oshkosh did a study of the colors used in African national flags. He found that 38 flags have red, 20 have blue, 13 have both red and blue, and 8 have neither red nor blue. How many flags
a. have red but not blue?
b. have blue but not red?
c. were inclulded in the study?
4) Kroner asked 100 adults whether they had studied French, Spanish or Japanese in school. According to the Venn diagram below, how many had studied
a. Spanish?
b. Spanish but not French?
c. Japanese but not French?
d. French and Spanish?
e. French or Spanish?
f. French and Spanish but not Japanese?
5. Coach Krutch offered to buy hot dogs for players on his team. Of the 44 players, 28 wanted ketchup, 20 wanted mustard, 14 wanted relish, 10 wanted ketchup and mustard, 11 wanted ketchup and relish, 8 wanted mustard and relish and 6 wanted all three condiments. How many players wanted
a. Ketchup only?
b. Mustard but not relish?
c. Relish but not mustard?
d. Ketchup and mustard but not relish?
e. Relish and mustard but not ketchup?
f. None of the three condiments?
Monday, March 1, 2010
trigonometry Leaving Cert
rigonometry Questions for Leaving Cert Honours Level Maths
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