Mostly Definitions Flashcards
What is an integer?
An integer is another name for a whole number - either a positive or negative number, or zero.
Integers: -365, 0, 1, 785
Not integers: 0.5, 2/3, -102.3, 6.6,
multiplying decimals - where does the decimal go?
4.6 x 2.7 = 1242
-start by ignoring decimal points and do the multiplication using whole numbers
46 x 27 = 1242
-count the total number of digits after the decimal points in the original numbers
4.6 x 2.7 - there are 2 digits after the decimal
-make the answer have the same number of decimal places
4.6 x 2.7 = 12.42
Alternate Angles
A pair of equal angles found in a ‘Z’ shape within two parallel lines.
Angle Bisector
A straight line that cuts an angle exactly in half.
Approximation
A number that is not exact because it has been rounded or estimated.
Back-to-back Stem and Leaf Diagram
A stem and leaf diagram where two sets are plotted on the same stem.
Bar Chart
A chart where the height of the bars shows the frequency of each category.
Bar-line Chart
A chart where the height of the lines shows the frequency of each category.
When you have an exponent, what is the base?
In a power, this is the number or letter which is multiplied by itself.
Biased
Where something, e.g. a dice or a spinner, is more likely to land on one or more of its sides than others.
BODMAS
An acronym to describe the order that operations should be done in a calculation containing multiple operations. Brackets, Other, Division, Multiplication, Addition, Subtraction
What is an ‘average’ and name 3 types of average.
A measure of the most typical value in a set of data. Mean, median and mode are types of average.
Median
The median is the middle number in a set of data, when the data has been written in ascending size order.
To find the median, put all numbers into ascending order and work into the middle by crossing off numbers at each end.
-In an odd-numbered set, the median will be the number in the very middle of the list.
-In an even numbered set, there will be two numbers in the middle. The median is the number that is half way between these two numbers. (Take the two middle numbers of the even-numbered set, add the two numbers together, divide the total by 2)
Mean
The mean is the arithmetic average of a set of given numbers. Therefore, the mean in math is often referred to as simply the “average.”
-Add all the scores together.
-Divide the sum by the number of scores used.
Mode
The mode is the most frequently occurring score in a set of given numbers. Put another way, it is the score that appears the greatest number of times.
-Look at all the data scores
-Identify the data score that appears most often
Range
The range of a data set is the difference between the greatest value and lowest value within a collection of numbers.
Subtract the smallest from the greatest value in the set to find the range of given data points.
What is a Prime Number?
A whole number greater than 1 that cannot be exactly divided by any whole number other than itself and 1 (e.g. 2, 3, 5, 7, 11).
2 is the only even prime number.
What is the net of a cube?
A cube is a symmetrical three-dimensional shape which consists of six square faces, twelve edges, and eight vertices. A net of a cube is a two-dimensional shape that can be folded into a three-dimensional figure.
(Essentially it is a square box which has been unfolded.)
Equilateral Triangle
Has 3 equal sides.
Isosceles Triangle
Has 2 equal sides.
Scalene Triangle
Has no equal sides.
Acute Angle Triangle
Has 3 angles less than 90 degrees.
Right Angle Triangle
Has one angle = 90 degrees.
Obtuse Angle Triangle
Has one angle greater than 90 degrees.
What is an acute angle?
An angle which is measuring less than 90 degrees
What is an obtuse angle?
An angle that measures more than 90 degrees and less than 180 degrees.
Reflex Angle
A reflex angle is any angle that is more than 180 degrees (half circle) and less than 360 degrees (full circle). A reflex angle will always have either an obtuse or an acute angle on the other side of it.
Angles in a quadrilateral add up to how many degrees?
360 degrees
Angles in a triangle add up to how many degrees?
180 degrees
What do we know about alternate angles in parallel lines (Z angles)?
They are equal.
What do we know about corresponding angles in parallel lines (F angles)?
They are equal.
What do we know about interior angles in parallel lines (C angles)?
They add up to 180 degrees.
Can a square number be a prime number?
No, all square numbers have an odd number of factors. A prime number has 2 factors, 1 and itself. Therefore no square can be a prime and no prime can be a square.
Odd numbers
Numbers ending with 1, 3, 5, 7 and 9.
Can’t be evenly divided.
Even Numbers
Numbers ending with 0, 2, 4, 6 and 8.
Can be evenly divided.
Write 140,000,000 in standard form.
140,000,000
=1.4 x 10^8
Factorise x^2 + 7x + 10
x^2 + 7x + 10
=(X +2) (x + 5)
*remember you need to find 2 numbers that multiply to 10 and add to 7.
A cube has how many places of symmetry?
9
Volume of a box = ?
V of box = length x width x height
Adding with the same base and exponent.
a^n + a^n
The general form of adding exponents with the same base and exponents is a^n + a^n = 2a^n
Calculate variables with different exponents.
a) x^n + x^m
b) 4^2 + 4^3
To calculate variables with different exponents is x^n + x^m.
x^n + x^m
=x^n x m
b) 4^2 + 4^3
= 4^2 × 3
=4^6
= 4096
Multiplying with exponents when you have the same base
a) X^a x X^b
b) a^2 x a^ 6
c) 3p^2 x 5p^7
When multiplying with exponents, add them together. Only works if they have the same base.
a) X^a x X^b
=X^a+b
b) a^2 x a^ 6
=a^8
c) 3p^2 x 5p^7
=15p^9
Dividing exponents with the same base
3^7/3^3
When dividing exponents subtract the exponents on the bottom from the exponents on the top. Only works if they have the same base.
3^7/3^3
=3^4
What does a negative exponent do?
5^-3
We know that the positive exponent tells us how many times a number is multiplied by itself. Whereas, the negative exponent tells us how many times we have to divide the base number. In other words, the negative exponent describes how many times we have to multiply the reciprocal of the base.
5^-3
=1/5^3
=1/125
64^1/2
64^1/2 = √64 = (+ or -) 8^2
A number to the power of 1/2 is the same as square rooting the number.
(2x^2)^3
8x^6
How many grams in a kg?
1000g
How many kg in 6500g?
6.5kg
How many grams in 7.36kg?
7360g
How many mm in a cm?
10mm
How many cm in a metre?
100cm
How many metres in a kilometre?
1000m
How many cm in a km?
100,000cm
How many ml in a litre?
1000ml
How many litres in 6789ml?
6.789L
Factorise: 3p^2 + 5p^7.
3p^2 + 5p^7 (rearrange terms)
5p^7 + 3p^2. (find one factor)
p^2(5p^5 + 3)
Factorise: 24p^3 + 6p^8
24p^3 + 6p^8
6p^8 + 24p^3
6p^3(p^5 + 4)
What is a Trapezium?
Quadrilateral with one pair of opposite parallel sides.
Proper Fraction
5/12 *top integer is smaller than bottom integer
Improper Fraction
12/5 *top integer is bigger than bottom integer
Lines of symmetry
A line of symmetry divides the shape equally into two symmetrical pieces.
Rotational symmetry
Rotational Symmetry is the property a shape has when it looks the same after rotation as it did at its starting point.
An object’s degree of rotational symmetry is determined by the number of orientations in which it looks exactly the same as it did before rotation.
What is a sum?
The outcome of adding two or more numbers gives the sum.
What is a product?
The outcome of multiplying the two or more numbers gives the product.
What is the difference?
The outcome of subtracting the two numbers gives the difference.
What is the quotient?
The result of the division of one number by another is the quotient.
What is correlation?
Correlation is the relationship between 2 variables.
What does it mean to expand?
To expand is to multiply out brackets.
eg. 2(x + 3)
= 2x + 6
What is factorising?
Factorising is the reverse process of expanding brackets.
so factorising x^2 + 5x + 6
gives (x + 2) (x + 3)
What does tessellate mean?
Tassellate is to fit shapes together with no gaps.
How many rotations of symmetry does a kite have?
When a kite is rotated around its centre, it returns back to the original orientation without it fitting into itself again so the order of rotational symmetry for a kite is 1.
What is a hypotenuse?
The longest side of a triangle and always opposite the right angle.
How are bearings measured?
Clockwise from North.
What’s the difference between tally and frequency?
—————Tally Frequency
Digestives. III 3
Oreos. IIII 4
What is an outlier in a data set?
An outlier is an extreme value in a data set that is either much larger or much smaller than all the other values.
How to do long division with decimals?
51 ÷ 8.5
For long division eliminate the decimal point from the divisor then perform long division as usual.
51 ÷ 8.5
x10 x10
85√510
(I’ve used the square root symbol as there is no long division symbol)
Difference between congruent and similar shapes?
Congruent shapes are identical and have the same angle measures and the same side lengths. Similar shapes have the same shape, but not necessarily the same size.
Factors
A factor is an integer that divides exactly into a whole number. (eg factors of 12 are 1, 2, 3, 4, 6, 12)
Multiples
Multiples are the number you get when you multiply a number. (eg. multiples of 12 are 12, 24, 36, 48…)
What is a ratio?
A ratio compares values. A ratio says how much of one thing there is compared to another thing.
Eg. a drink with 3 shots of orange juice and 1 shot of vodka has a ratio of 3:1 (3 parts orange for every 1 part of vodka)
What is a bearing?
A bearing is the angle in degrees measured clockwise from north. Bearings are usually given as a three-figure bearing.
How many degrees do the angles of a triangle add up to?
180 degrees
How many degrees do the angles of a quadrilateral add up to?
360 degrees (2 triangles)
How many degrees do the angles of a pentagon add up to?
540 degrees (3 triangles)
What is y = x as a reflection line?
diagonal bottom left to top right
What is y = -x as a reflection line?
top left to bottom right
Venn diagram
SuE
What does the u mean?
it stands for union and includes everything within the circles (but not outside)
Venn diagram
P (SnE)
What do the P and the n stand for?
P = probability
n = intersection (overlap of circles)
Venn diagram
E’
What does the ‘ mean?
E’ means “not in” E
(+) x (+) = ?
(+) x (-) = ?
(-) x (-) = ?
(+) x (+) = (+)
(+) x (-) = (-)
(-) x (-) = (+)
6n+1
find the 60th term.
6 (60) + 1
=361
Solve 8x − (3x + 1) = 2
0.4
What is 2.1 hours in hours and minutes?
Since there are 60 minutes in an hour, you can multiply 2.1 hours by 60 to get the equivalent number of minutes:
2.1 hours × 60 minutes/hour = 126
minutes
2.1 hours×60 minutes/hour=126 minutes
So, 2.1 hours is equal to 126 minutes.
