Formulas


Area
Area of circle:   A = PI × r2 Area of parallelogram:   A = b × h
Area of rectangle:   A = l × w Area of triangle:   A = ½ × b × h
Surface Area
Surface area of sphere:   As = 4 × PI × r2 Surface area of cylinder:   As = 2 × PI × r × (h + r)
Circumference of a circle
C = 2 × PI × r
Volume
Volume of a cone:   V =  1/3 × PI × r2 × h Volume of a cylinder:   V = PI × r2 × h
Volume of a pyramid:   V = 1/3 × l × w × h Volume of a rectangular prism:   V = l × w × h
Volume of a sphere:   V = 4/3 × PI × r3 Volume of a triangular prism:   V = ½ × b × h × l

Year 8-9 Maths help

GCF

The Greatest Common Factor of two numbers is the greatest whole number that can be divided evenly by both numbers. E.g. GCF of 12 and 14 is 2

To find the GCF of two numbers, find the greatest number which can be divided evenly into both numbers.

Example:

Find the GCF of 18 and 27

18 ÷ 9 = 2  and  27 ÷ 9 = 3

No number greater than 9 can be divided evenly into 18 and 27, so the GCF of 18 and 27 = 9

LCM

The Lowest Common Multiple of two numbers is the smallest whole number that both numbers can be divided into. E.g. LCM of 6 and 14 = 42.   (42 is the lowest number that 6 and 14 can be divided into equally.)

Example 1:

14 ÷ 6 = 2R2    2x14=28

28 ÷ 6 = 4R4   3x14=42

42 ÷ 6 = 7R0   Because there are no remainders, 42 is the LCM.
                           Multiply 14 by 1, 2, 3, etc until you get the number that 6 can be divided into equally.

To find the LCM of two numbers, multiply the second number by 1, 2, 3, 4, etc, and divide by the first number until you get an equal quotient.

Note: the dividend is the number to be divided and the quotient is the final result of any division.

Example 2:

Find the LCM of 8 and 22

22 ÷ 8 = 2R6    2x22=44

44 ÷ 8 = 5R4    3x22=66

66 ÷ 8 = 8R4    4x22=88

88 ÷ 8 = 11R0   Because there are no remainders, 88 is the LCM.
                            Multiply 22 by 1, 2, 3, etc until you get the number that 8 can be divided into equally.

To find the LCM of two numbers, multiply the second number by 1, 2, 3, 4, etc, and divide by the first number until you get an equal quotient.

Note: the dividend is the number to be divided and the quotient is the final result of any division.

Square root

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

Percentage

Calculating a percentage of a number, convert the percent into a decimal, remember that a percentage is a part of a whole amount. The whole amount can be any quantity but we understand the whole amount as being one (1). A percentage is a part of one, the reason we convert the percentage into a decimal is so we can subtract the percentage from the whole amount. Refer to example below.

Example:

Calculate 32½% of $56.70

32½% = 32.5 ÷ 100 = 0.325

0.325 × $56.70 = $18.43 rounded to the nearest cent.

Answer: $18.43


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