The webpage includes four worked examples and a short list of common errors to avoid when drawing Cumulative Frequency Curves.
Thanks to the UK’s Training and Development Agency for providing this resource. Visit Cumulative Frequency.
Sunday, August 8, 2010
1st and 2nd years,copy and paste this link to your browser to get algebra movies
http://deimos3.apple.com/WebObjects/Core.woa/Browse/inFlorida.edu.2637105050.02637105056
leaving cert higher maths 2010 paper 2
Saturday, April 3, 2010
Friday, April 2, 2010
pie charts
Pie charts
A pie chart is a way of illustrating information by using sectors of a circle to represent parts of the whole.
Example
A newly qualified teacher (NQT) was given the following information about the ethnic origins of the pupils in a class.
| Ethnic origin | No. of pupils |
|---|---|
| White | 12 |
| Indian | 7 |
| Black African | 2 |
| Pakistani | 3 |
| Bangladeshi | 6 |
| TOTAL | 30 |
The 30 pupils in the class are classified into five different ethnic origins. The whole pie chart represents the class of 30 pupils, and the five sectors represent 12, 7, 2, 3 and 6 pupils, as shown in the table.
The pie chart has a legend (key) indicating what it represents.
Worked examples
The pie chart below summarises the amount of time spent on various areas of the key stage 2 curriculum in a primary school.
Example one
The total time spent each week on the various areas of the curriculum is 26 hours. How much time is spent on history, geography and music?
The pie chart represents 26 hours.
Look at the pie chart and note that the total time spent on history, geography and music is 25%.
25% is 
so 25% of the total time is 26 ÷ 4 = 6.5 hours. 6.5 hours = 6 hours and 30 minutes.
So 6 hours and 30 minutes is spent on history, geography and music each week.
Example two
The total time spent each week on the various areas of the curriculum is 26 hours. How much time is spent each week on English, mathematics, science and ICT together?
The pie chart represents 26 hours.
Look at the pie chart and note that 58% of the total time was spent on English, mathematics, science and ICT.
58% can be converted to a decimal.
58% = 58 ÷ 100 = 0.58
Using a calculator, 0.58 x 26 = 15.08
To find how many minutes the 0.08 represents in the answer, 15.08 hours, you can calculate:
0.08 x 60 minutes = 4.8 minutes
So to the nearest minute, 15 hours and 5 minutes are spent each week on English, mathematics, science and ICT together.
Using pie charts to compare data
Pie charts are often used to show comparisons between two sets of data.
Worked example
The following pie charts show an analysis of the destinations of pupils leaving a sixth form college.
Which of the following statements are true?
- More pupils went into higher education in 1994 than in 2003
- 136 pupils went into employment in 2003
- More pupils decided on a gap year in 2003 than in 1994.
Statement one
In 1994, 50% of pupils went into higher education and in 2003 only 40%, but the number of pupils is different.
50% of 520 = 1/2 x 520 = 260 pupils
40% of 680 = 40/ 100 x 680 = 272 pupils
There were more pupils in 2003, so statement 1 is false.
Statement two
In 2003, 20% of pupils went into employment.
20% of 680 = 20 ÷ 100 x 680 = 136 pupils
Statement two is true.
Statement three
In 1994, 10% of pupils decided on a gap year.
x 520 = 52 pupils
In 2003, 15% of pupils decided on a gap year.
x 680 = 102 pupils
Statement three is true.
Wednesday, March 10, 2010
1st year equations
Introduction to equations - Introduction
This section looks at different types of equations, and some methods for solving them.
This Revision Bite covers:
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. |
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