Things to remember

Question 1

How do you find x% of y

Answer 1

Write % as a decimal/fraction Multiply by the no.

Question 2

How do you find the amount after a % increase/decrease

Answer 2

Calc the multiplier Multiply by the no.

Question 3

How do you express x as a %of y

Answer 3

Divide x by y Multiply by 100

Question 4

How do you find the percentage change

Answer 4

(Diff/OG)×100

Question 5

How do you find the original value

Answer 5

Write the amount in the question as a %of the original value Divide to find 1% Multiply to find 100%

Question 6

How do you find simple interest

Answer 6

Find the interest of one year Multiply by the no. of years

Question 7

What is the equation for compound interest?

Answer 7

N=No×(multiplier)^n N: Ans No: initial amount n: no. of days/weeks/years

Question 8

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?

Answer 8

% of males under 40: 100-35=65% 65%of 80%: 0.65×80= 52%

Question 9

The side length, x, of a cube is inc. by 10%. What is the %inc. in the vol. of the cube

Answer 9

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%

Question 10

How do you find a percentage of a percentage

Answer 10

Write the first percentage as a decimal, then multiply by the other percentage.

Question 11

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?

Answer 11

Rearrange to find the initial amount No=N/(m)^n No=7500/(1.3)^6 =1554

Question 12

What are the columns of a frequency table

Answer 12

Category frequency. Category×frequency

Question 13

For a frequency table how do you find the: Mode Range Median Mean

Answer 13

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.

Question 14

What are the columns in a grouped frequency table

Answer 14

Category. Frequency. Mid interval value. Frequency×mid interval value

Question 15

How do you find the: Mode median range mean from a grouped freq. table?

Answer 15

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

Question 16

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

Answer 16

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

Question 17

When do you use the sine or cosine rule

Answer 17

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

Question 18

What are the sine and cosine rules (+ for angles)

Answer 18

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

Question 19

Circle theorems

Answer 19

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.

Question 20

Polygon rules

Answer 20

For all: Sum of ext. = 360° Sum of int. = (N-2)×180 For regular polygons: Ext. Angle =360/n Int= 180°-ext.

Question 21

How do you solve inverse functions

Answer 21

Replace f(x) with x and x with y Rearrange to make y the subject Replace y with f^-1(x)