Things to remember Flashcards
How do you find x% of y
Write % as a decimal/fraction Multiply by the no.
How do you find the amount after a % increase/decrease
Calc the multiplier Multiply by the no.
How do you express x as a %of y
Divide x by y Multiply by 100
How do you find the percentage change
(Diff/OG)×100
How do you find the original value
Write the amount in the question as a %of the original value Divide to find 1% Multiply to find 100%
How do you find simple interest
Find the interest of one year Multiply by the no. of years
What is the equation for compound interest?
N=No×(multiplier)^n N: Ans No: initial amount n: no. of days/weeks/years
Working with percentages Q: 80% of the members at a gym are male. 35% of the male members are aged 40 and over. What is the %of males under 40 years old?
% of males under 40: 100-35=65% 65%of 80%: 0.65×80= 52%
The side length, x, of a cube is inc. by 10%. What is the %inc. in the vol. of the cube
The side length,x, of a cube is inc. by 10%. What is the increase in vol. of the cube?( Express x as a % of y)
OG vol. : x3
10% Inc: 1+0.1=1.1 Inc. side length: 1.1x
Inc. vol. :(1.1x)3=1.331x3
1.331x3-x3 (Treat the x as a 1)=0.331x3
%inc: Inc/OG×100 (0.331x3/ x3)×100= 33.1%
How do you find a percentage of a percentage
Write the first percentage as a decimal, then multiply by the other percentage.
Compound interest: The no. of bacteria in a sample increases at a rate of 30% each day. After 6 days the no. of bacteria is 7500. How many bacteria were there in the original sample?
Rearrange to find the initial amount No=N/(m)^n No=7500/(1.3)^6 =1554
What are the columns of a frequency table
Category frequency. Category×frequency
For a frequency table how do you find the: Mode Range Median Mean
Mode : category with the most entries Range: Difference between the highest and lowest. (Don’t include categories with no frequency) Median: (the total frequency+1)/2 Find the position of the median Mean:. (total freq×category)/total freq.
What are the columns in a grouped frequency table
Category. Frequency. Mid interval value. Frequency×mid interval value
How do you find the: Mode median range mean from a grouped freq. table?
Mode: the one with the highest frequency Median: (total frequency+1)/2, find the position of the median by counting through the frequency column Range: the difference between the highest and lowest class boundaries Mean: total of the mid interval value×freq ÷ total frequency
What two measures of spread do box plots show Is the range or the IQR a more reliable measure of spread. What %of the overall box plot do the LQ, UQ and median show What doesn’t a box plot show
1) a box plot shows range and the IQR 2)The IQR is only based on the middle 50%of the data values , so it isn’t affected by outliers=more reliable 3)LQ:25% UQ:75% M:50% 4) The box plot shows the minimum and maximum values in a data sets and the values of the quartiles. But it doesn’t show the individual data values
When do you use the sine or cosine rule
Sine: Two angles plus any given side Two sides plus an angle not enclosed between them Cosine: Two sides plus angle enclosed All three sides but no angles
What are the sine and cosine rules (+ for angles)
Sine: a/sinA sinA/a b/sinB. SinB/b c/sinC. SinC/c Cosine: a^2= b^2+c^2-2bcCosA CosA= b^2+c^2 -a^2/2bc
Circle theorems
The tangent meets the radius at 90° Two radii form an isosceles triangle The perpendicular bisector of a chord passes through the centre of the circle The angle subtended at the centre of the circle is twice the angle at the circumference. The angle in a semi circle is 90° Angles in the same segment are equal Opposite angles in a cyclic quadrilateral add up to 180° Tangents from the same point are the same length and form two congruent right angles The alternate segment theorem: The angle formed between the tangent and the chord is equal in the opposite segment.
Polygon rules
For all: Sum of ext. = 360° Sum of int. = (N-2)×180 For regular polygons: Ext. Angle =360/n Int= 180°-ext.
How do you solve inverse functions
Replace f(x) with x and x with y Rearrange to make y the subject Replace y with f^-1(x)
