Basic revision Flashcards
(a + b)²
a² + 2ab + b²
a² - b²
(a - b)(a + b)
fraction
a measure of how something is to be divided up or shared out
numerator
the top number in a fraction
denominator
the bottom number in a fraction
proper fraction
a fraction in which the numerator is smaller than the denominator
equivalent fractions
are two or more fractions that have the same value but are different in form eg
3/4, 6/8, 63/84, 75%, 0.75
all look different but they all have the same value
product
the product is the result given by the operation of multiplication
quotient
the quotient is the result given by the operation of division
32 divided by 8 is 4
the quotient is 4
divisor
the number in a division sum that does the dividing
18 divided by 9 is 2
the divisor is 9
test for dividing by 3
if the digits in the number add up to a multiple of 3
3597 is divisible by 3 since
3+5+9+7 = 24
square – (as a verb)
to square a number means to multiply it by itself
isosceles triangle
a triangle which has two sides with the same length
there will be two angles of the same size as well
equilateral triangle
a triangle in which all three sides have the same length
therefore the angles in an equilateral triangle are the same
each is 60º
negative times negative
positive
4
- even
- square
3, 4, ?
5 – 3, 4, 5 is a pythagorean triple ie when these 3 numbers are considered as lengths of the sides of a triangle the angle opposite the longest side will necessarily be a right angle
5, 12, ?
13 – 5, 12, 13 is a pythagorean triple
9
- odd
- square
{1, 8, 27, 64, 125}
the set of the first 5 cube numbers
16
- even
- square
- 2 to the power of 4
25
- odd
- square
{2, 3, 5, 7, 11, 13, 17, 19, 23}
the set of the first 9 prime numbers
how to divide by a fraction?
- “kiss and flip”
- eg 8 divided by ½ is the same as 8 times 2
mixed number
an improper fraction written as a whole number followed by a proper fraction
eg 2¾ = 11/4
cancel – as a verb
to express a fraction in its simplest or lowest terms
eg 6/8 = 3/4 – we have cancelled the factor of 2 on the left hand side of the ‘=’ sign by dividing top and bottom of the fraction by 2 to get the fraction in its lowest terms (3 and 4 do not have any common factors)
surd
a number that cannot be expressed as fraction, or ratio of whole numbers, hence it is sometimes called an irrational number
the square root of 2
the cube root of 5
3 + sqrt(2)
negative divided by a negative
positive
