# Year 10 Maths Descriptions

 The symbol Tn is used to represent a term in a number sequence. T = the term and n = the distinct term in a number sequence. E.g. T55 A term is any distinct quantity, fraction or proportion in a sequence or series. In exercise 1, find the value of the term indicated in ( ). To do this, use the formula given for each problem. Every number sequence has its own unique formula for finding the term. Example: If Tn = 9n - 7 then find T 78 T78 = (9 x 78) - 7        = 702 - 7        = 695

 A.P. is an abbreviation for "Arithmetic Progression"; an A.P. is a number sequence. In this exercise the variables a and d have the following meaning... a = 'the first term' (this is the very first term in an arithmetic progression) d = 'the common difference' (common difference is the difference between the first term and the second term) We use the formula: Tn = a + (n - 1)d to find the value of any term in a number sequence (A.P.)To solve the problems in exercise 2, find the value of a and d, then use the formula Tn = a + (n - 1)d   to work out the answer. Example: Find the 20th term of the sequence 2, 7, 12, 17,... Tn ...= a + (n - 1)d          a = 2  (2 is the very first term in the number sequence above) T20= 2 + 19(5)             d = 5  (5 is the common difference between 2 and 7, 7and 12, 12 and 17, etc.)        = 97

 To find the sum of n Terms, find a and d as in the example above, apply the formula l = a + (n - 1)d After finding the product, use the formula Sn = to find the answer. This method is very useful, when finding the sum of many terms. S = the sum of n = number of terms Example: Find the sum of the following A.P. S10       a = 1, d = 1 l = a + (n - 1)d l = 1 + (10 - 1)1 l = 1 + 9 = 10 l = 10 Sn = = = 55 Answer = 55

## To find the volume of any cylinder,

use the formula. V = π x r2x h

V = Volume
π = pi (3.14)
h = height
Example: A can shaped like a cylinder has a height of 4 cm and a radius of 1.5 cm.
Find the volume of the can.

V = 3.14 x 1.52 x 4
= 3.14 x 2.25 x 4
= 7.065 x 4
= 28.26

## Square root

When working out the square root of a number it is sometimes necessary to check your answer for accuracy by multiplying the answer by itself. This should come close to the number that was originally calculated.

E.g. the square root of 9 is 3, because 3 x 3= 9, the square root of 25 is 5, because 5 x 5 = 25

To find the square root of any number, follow the steps below...

We will use an example to explain the steps, the rules apply for all numbers.

Place the decimal point behind the number (27) Place an amount of zeros in pairs behind the decimal point. Remember the more pairs of zeros, the more accurate the answer.

Calculate a number, when multiplied by itself comes close or equal to the number (27) to be calculated. (In this case 5)  Place the  number (5) before the decimal point on top of the square root sign and the result of that number  (which is 25) underneath the number being calculated (27) and subtract it (25) from the number being calculated.(27)

5 x 5 = 25 Bring down the first two zeros and place them behind the result of the subtraction, (which is 2). Double the number (5)    and place it near the next number down (200). See example...
5 + 5 = 10 Determine the biggest number placing it behind the number (in this case 10) multiply the total of that number (101) by the number placed behind (10) (in this case 1) remember it must give a result less than or equal to the number being matched (200 in this case). The number you wrote next to the (10) (1), you also write above the last zero which you brought down. Repeat the above steps until you have completed the problem. See example below.

1 x 101 = 101, 9 x 1029 = 9261, 6 x 10386 = 62316 The side opposite the square of any right angle triangle is called the hypotenuse. To find the hypotenuse, use the formula , where c = the hypotenuse, a = the base of the triangle and b = the height of the triangle. The square is the 90 deg angle in the triangle. Example: A right angle triangle has a height of 5 cm and a base of 3 cm, find the hypotenuse.  (note: this answer is rounded to the nearest hundredth)