Math info

If one vector is a multiple of another vector....

They are parallel Eg: AB=8a+20b and CD=2a+5b AB is parallel to CD because AB=4CD

how is UQ and LQ calculated from a cf graph?

UQ= 3/4 of the total LQ=1/4 of total frequency

Where is cumulative frequency shown on the graph?

Vertical axis

Ratio of X to y is : 2:3. What is X in correlation to y?

X=2/3 of y

The size of an animal population on an islands increases exponentially. Rate of increase was 25% per year and try size of a particular animal population at the start of 2015 was 4500. Work out the size of the population at the start of 2010?

Y=a^x a= population 2015-2010 is 5 years a x 1.2^5=4500 a=4500/1.25^5 =1475 animals

If given an unknown quantity but another quantity is given and you need to find the best value what can you do

YOU CAN ASSUME A QUANTITY SUCH AS $1 JUST TO MAKE YOUR POINT

What do you do when you find a medium of a stem and leaf diagram and are given two numbers?

You find the mean of two numbers

What do you get when you add an odd and even number?

Odd number

What happens when you multiply an odd number by an odd number?

Odd number

When the velocity time graph is a curve how is the acceleration calculated?

Draw a tangent at the point mentioned in the question and then calculate the gradient of the tangent line.

How do you draw a line equidistant from A and B?

Draw an imaginary line between A and B and then bisect it. Then

What is consecutive? How can two consecutive odd numbers be represented?

Eg : 2,3,4,5, Consecutive odd numbers would be 3,5 2n+1 and 2n+3 are two consecutive odd numbers

When you have completed the square, how do you find the coordinates of the turning point of the curve?

Eg: (x+5)^2-10 The coordinates are: X coordinate is the inverse of the value inside the brackets so instead of +5, the X coordinate is -5. The y coordinate is simply -10.

What does is mean If two shapes are similar?

One shape is an enlargement of the other. scale factor is involved

Circle theorems; cyclic quadrilaterial

Opposite angles of a cyclic quadrilateral add up to 180 degrees-all four points need to touch the circumferance

What happens when you add 1 to an odd number or subtract 1?

Even number

circle theorem= prove angles in same segment are equal

Extra= - the left 32 degree angle is labelled point B - right 32 angle is labelled D - Botton left angle is labelled A - Bottom right angle is labelled C - O is the centre 1. draw a radius from OA and OC 2. Angle AOC [below angle AOC] is twice the angle of B and D [subtended at centre circle theorem] 3. So angle ABC= ADC as they are both equal to X

For all values of X, F(X)=x^2-3 and G(x)=5+x.... Find fg(2):

F(g(2))=f(5+2) =f(7) =7^2-3 =49-3 =46

For all values of X, F(x)=x^2+2x and G(x)=x-2......show that fg(X)=x^2-2x

F(g(X))=f(X-2) =(X-2)^2 +2(X-2) =x^2-4x+4x+4+2x-4 =x^2-2x

What is f(x) equal to?

F(x)=y

To prove that 3 points lie on a straight line...

You need to make 2 vectors out of them and show that these are parallel. You also need to state that they share a common point EG: AB=2a-b and BC=6a-3b Point b is common and they are parallel as BC is a multiple of AB so the three points lie on a straight line

How do you calculate the average speed for a curved velocity time graph?

Finding the distance travelled by drawing trapeziums under the curved graph as close to the graph as possible and then finding the area of these trapeziums and triangles. Then divide the distance by the overall time

In the internal where X is between 0 and 360 degrees, find the value of X for which sin X = -0.5243, give your answer to the nearest degree:

First find the inverse of sin and multiple it by -0.5243, therefore giving you a negative number. Then use the rule and subtract this number from 180 to give you 212. Then add 360 to this negative number to get you 328

Write the geometric progression sequence equation for 3, 6, 12, 24, 48, 96

First term or a= 3 Common ratio or r=2 a, ar, ar^2, ar^3 Nth term= ar^(n-1)

How do yo find the values of p and q in the equation y=pq^x?

You put in 0 into X coordinate so that q is 1, and can be ignored to leave p, which is equal to the y coordinate when X is 0. Therefore p has been found out. Then find out q to the power of 1 by finding the y coordinate so that q is by itself with the value of p. Then divide the p value by the q value (when the y coordinate is in relation with an X coordinate of 1). Then you have the q value Eg: Y=pq^x =px1 1/2=p Y=1/2 q^x Y=1/2 x q^1 2=1/2 q q=4

What is the equation for frequency?

Frequency= frequency density X class width

What does exponentially mean?

Getting bigger increasingly quickly

When are two triangle congruent?

If they are identical in size and shape

The first term of a geometric progression is 4 and the common ratio is 5. A) write down the first 4 terms of the progression: B) what is the 10th term?

a) 4, 20, 100, 500 b) ar^(n-1) 4x 5^(10-1)=7812500

What is the general nth term of arithmetic series?

a+ (n-1)d Where a is the first term and d is the common difference

What is the nth term of a geometric progression?

ar^(n-1)

Cubic function?

ax^3 +bx^2 +cx + d =0

Area scale factor=

(Linear scale factor)^2

For a box plot, when your given a series of numbers put into a box plot, yet the amount of numbers is even, meaning unequal numbers on either side of median, what do you do?

(N+1)/2

Stratified sampling equation?

(Sample size/population) X stratum size

What is the sum of the roots of the quadratic equation given by?

-(b/a)

Volume of pyramid

b=base area h=height

circle theorm; semi circle

diameter is a straight line so angles add up to 180 at centre. 180 / 2 = 90 angle at centre is twice angle at circumferance. so the angle in a semi circle is a right angle.

How do you find f^-1(x) where f(x)=2x+5? Then find f^-1(17):

1. Equate 2x+5 to y instead of f(x): Y=2x+5 2. Make X the subject: Y-2x=5 X=(5-y)/-2 3. change X for y and y for X: Y=-(5-x)/2 F^-1(x)=x-5/2 F^-1(17)=17-5/2 =6

WHAT ELSE CAN X/2 BE WRITTEN AS?

1/2 x X DONT FORGET!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!'nbnclufirirodotor

1/f = 1/u plus 1/v find f, when u = 3.5 cm and v= -4

1/f = 1/3.5 plus 1/-4 1/f = 2/7 - 1/4 = 8/ 28 - 7/28 =1/28 f=28

To draw a cumulative frequency graph, where are the x coordinates found in the intervals table? E.g where in 0<t<10

10 would be the x coordinate in the example. The x coordinate is the end point of the graphs

Walken Reds is a basketball team. At the end of 11 games, their mean score was 33 points per game. At the end of 10 games, their mean score was 2 points higher. Jordan says, Reds must have scored 13 points in their 11th game. Is he right

11 x 33 = 363 10 x 35 = 350 363 - 350 = 13 yes he's right

In a class : 11 students play football and cricket 9 don't play football or cricket 17 play football 13 play cricket Find probability that student chosen at random plays football or cricket or both:

19/28

In a quadratic sequence what equations are used to find out a, b and c in the equation an^2+bn +c?

2a=2nd difference 3a+b=2nd term - 1st term a+b+c=1st term

1 length of edging = 1.75 meters. How would you find out the number of lengths of edging when the meters are 9.3898

9.3898 / 1.75 = 5.3656 YOU NEED TO ROUND UP TO 6. so its 6 lenghts and NOT 5.4656 lengths

In a velocity time graph, where is the acceleration represented and the distance?

Acceleration= gradient Distance = area under graph

What is the equation for percentage decrease?

Actual decrease/ original value. X 100

What is the equation for percentage increase?

Actual increase/original value. X 100 Eg: Old=7.50 New=9 9-7.5=1.5=percentage increase 1.5/7.5. X100=20%

Midpoint of a line on a graph:

Add the X coordinates of the end and beginning coordinates of the line and then divide it by 2. Then do the same for the y coordinate

How do you get a resultant vector when you have two vectors already?

Add the two vectors by adding the corresponding X and y coordinates which gives a new vector. Then draw these lines starting from the same point on a graph paper. Then draw the new vector also starting on the same point as the other vectors but one should also be moving this vector around so that a triangle is formed and this would be called the resultant vector.

frequency table

Age; Frequency; Age × Frequency 11 6 66 12 7 84 13 5 65 14 7 98 15 3 45 16 2 32 Totals 30 390 Mean = 390 ÷ 30 = 13

How do you find the solution to an iterative process?

Keep on repeating the U values until the answers being produced can become the same when the rounded up by the amount of decimal places stated in the question. Example: X=5+2/x^2 Forth of X= 5.07870 Fifth of X= 5.0775 These two rounded to 1 dp gives the same answer of X=5.1

Who can the scale factor of the enlargement be found? (Equation)

Length of a side on one shape/length of a corresponding side on other shape

What is required to draw a box plot?

Lowest LQ Median UQ Highest

is n+1 odd number?

No

Can you convert m^3 into cm^3 by multiplying the m^3 value by 100?

No, you must convert all the sides of the shape from meters to centimetres and then multiply them together to get a volume of cm^3

In an exponential graph what is the X axis called?

Asymptote As its never touched by curve

The line AB has midpoint (3,5). A has coordinate (6, -3). Find the coordinates of B:

B=(X,Y) (6 + X)/2=3 6+X=6 So X is 0 (-3+y)/2=5 -3+y=10 Y=13 B= (0,13)

What is the product of the roots of the quadratic equation given by?

C/a

What do you do when your asked for the error interval of X?

Calculate the upper and lower bound and then organise an equation where X is greater than or equal to the lower bound but also less than the upper bound

How do you compare medians/ IQR and range of box plots?

Comparing median: If Median is garage in X, then the average 'variable' is greater Comparing IQR: if IQR is greater in X, then it covers a larger span of box plot than y Comparing range: if X and y have same min and max value, then they have the same range

Tan rule for graphs and eg?

Tan40=tan(180+40)=tan220

Circle theorems; semicircle

The angle in a semicircle is a right angle

Circle theorems; angle at centre and circumferance

The angle subtended at the centre of the circle is twice the angle at the circumferance. This circle theorem can look ANOTHER WAY ALSO--LOOK OUT FOR THIS.

What are tessellations? How is something tesselate?

The interior angles of the corners of each regular shape much add at to 360 at a point

What must you include in a stem and leaf diagram?

The key

What does stratified sample mean?

The number in the sample are in proportion for each category.

A horizontal line on a velocity time graph means?

The object is travelling at constant velocity as acceleration is 0

How can a similar shapes question be in disguise?

The shape may be for example a triangle with a line horizontally across it. The first shape is the entire shape of the triangle and the second is from the top of the triangle with the base angles being where the horizontal line touches the original shape . SEPARATE THE TRIANGLES NEXT TO Q

The ratio of the number of red counters to the number of blue counters is 1 : 4 Linda takes at random 2 counters from the box. The probability that she takes 2 red counters is 6 / 155 How many red counters did John put into the box?

x/ 5x multiplied by x-1/5x-1 = 6/155 155x − 155 = 150x - 30 solve for x = 25 so 25 red counters

x is directly proportional to y. y is inversely proportional to z. prove that z is inversely proportional to x.

x=ky y=j/z sub the second into the first one. x= k [j/z] = kj/z z = kj/x so z in inversely proportional to x.

Show that the difference of the squares of two odd numbers are always even?

(2n+1)^2 - (2m+1)^2= (2n+1)(2n+1) - (2m+1)(2m+1)= 4n^2 +4n+1-(4m^2+4m+1) 4n^2 +4n-4m^2-4m 2(2n^2+2n-2m^2-2m) is a multiple of 2 so it's always even

The equation of a curve is y=x^​2-8x-21 . Write down the coordinates of the minimum point of the curve

(x-4)^​2 plus 5 so the coordinates would be 4,5 HOWEVER, you need to sub x=4 into the equation to find y which would get you 5.

What is the percentage of the 4 sections of the box plot?

1. 25% = from lowest to lower quartile 2. 50%= from lower quartile to median 3. 75%= from median to upper quartile 4. 100%= from upper quartile to highest

What are the two answers to simplifying: 6n^2m^6/2n^6m^2?

1. 3n^-4m^4 2. 3m^4/n^4

How to draw a triangle ABC with AB of length 10cm, AC of length 8cm and BC of length 6cm?

1. AB is already drawn 2. Measure 8cm on a ruler with the compass and lengthen it to 8cm then put this compass point on A 3. Draw an arc with the compass 4. Then to draw BC, measure 6cm with the compass and draw an arc which collides with the other arc 5. Connect the lines from where the two arcs cross with points A and B

Pie chart: how to create a pie chart with information of different ways to travel to school and their frequency?

1. Add up frequency 2. Divide total frequency by 360 to given you a number 3. Multiply this number by each frequency of each different way of travelling to give you their angle 4. Draw these angles on a pie chart

At a school: number of boys to girls is 9:7. There are 116 more boys than girls so work out total number of students at the school.

1. Divide the 166 by 2 to get 58 2. Multiply 58 by 9 and 7 for both boy and girl to get 522 and 406 3. Add these together to get 928 students

Exact trigonometric values-what are the two triangles involved;

1. Equilateral triangle = all outer sides=2 inner side= root 3 2. right angle triangle = adjacent sides= 1 hypotenuse side= root 2

What three rules do you need to know for bearings?

1. North line 2. Three digits 3. Clockwise

Circle theorem proof = Opposite angles of cyclic quad add up to 180

Extra= - Angle 80 is labelled point B -Angle 100 is labelled point D - Bottom right point is labelled A -Upper left point is labelled C - O is centre 1. Draw radius from DO and OB and mark the angle at C as X. 2. Angle subtended at centre theorem is formed so angle DOB is 2x 3. remainder of DOB angle is 360-2x 4. Angle at A will be half of 360-2x......so A= 180-x 5. Add up angle C which is X and angle A which is 180-x and you get 180

Circle theorem: angle subtended at centre is twice angle at circumference Prove it :

Extra= - 75 degree point is labelled point C - Opposite angles of 150 degrees are labelled A[on left] and [on right] -O is the centre 1. Draw line through the arrow shape like a diameter 2. OC=OB= OA as they are radii 3. Angle ACO=Angle CAO= X 4. So Angle COA = 180-2x 5. the diameter has angles that add up to 180 degrees so the angle between side OA and the diameter is 2x as 180-2x plus 2x = 180 6. Do all the again for the opposite isosceles triangle but swap x for y so that angle at centre is 2x plus 2y and circumferance is x plus y which is half centre angle.

Circle theorems; point outside circle

From a point outside a circle, two tangents can be drawn. From the point to where they touch the circle, the two tangents are equal in length

Inequalities on a number line: how do you show a number can be less than or greater than on a number line? How do you show a number is less than/ greater than and equal to? How do you show a number is continuous on a number line?

Less than/ greater than= uncoloured circle Less than and equal to or greater than and equal to= coloured in circle. Number is continuous= draw an arrow in the correct direction

At a concert the ratio of men to women is 5:3. The ratio of women to children is 7:4. Show that more than half of the people at the concert are men.

M:w= 5:3 W:C=7:4 Find lowest multiple for both women values in both ratios which is 21, then multiply the individual ratio by that factor. M:w=35:21 W:C=21:12 So m:w:c= 35:21:12 35+21+12=68 1/2 of 68=34 35>34

The density of an iron rod is 7.5 g per cm^3. The volume of the rod is 14000cm^3. What is the mass of the rod in Kg?

M=7.5 X 14000 = 105000g/1000 =105kg

Mass=

Mass= density X volume

What does an indirect proportion graph look like?

Negative correlation with a curve inwards

Sin0=? Cos0=? Tan0=?

Sin0=0 Cos0=1 Tan0=0

Reciprocal function?

Y= a/x IN OTHER WORDS ==== f(x) = 1/x

Exponential function?

Y= a^x where a>0 Or F(X) =a^x

What do you do when asked to round a number to 2 significant figures? Example: when number is 560 is rounded to 2 sf:

You add a five or subtract 5 after the amount of significant figures stated. Eg. 10/2=5 UB of 560=565 LB = 555

How do you find the magnitude of a vector?

You draw a right angled triangle from the line and calculate the hypotenuse through Pythagoras

How is a in y=a^x worked out?

You find out the y value when X is 1 and that is the y value is a

What happens in a Geometric progression sequence? What is the first term and common ratio called?

You multiply to get the next term The first term is called a The number that we multiply by is called the common ratio and is labelled r.

To get the next term in the Fibonacci sequence what must you do?

You must add the preceding two terms together

ware house has 3 different types of flooring. 30 diff wood floorings 24 diff vinyl floorings 18 diff tile floorings. harry choses one of each of two different types of flooring. work out different no. of combinations he can choose

[ 30 x 24] plus [30 x 18] plus [24 x 18] =1692

When there is an interpretation question, e.g. give an interpretation of the intercept of the graph of on the x-axis, What should you do

do not simply state the y- intercept. YOU NEED TO GIVE A REASONING INSTEAD 1. e.g. state that the y-intercept is ..... when x=0. 2. e.g. interpretation of gradient of graph; for every value of x, y increases by 0.5 3. e.g. give interpretation of intercept of graph on y-axis for a mins[x]/ pound[y] graph= At 0 pounds = there is a fixed charge. - give interpretation of gradient= As cost increases, so does the amount of mins.

how do you prove that a point is an outlier on a graph

don't just state it is not near the line of best fit, refer to its x and y coordinates

When it says write down the beating of b FROM a what does that mean?

draw the north line at A

A (−2, 1), B (6, 5) and C (4, k) are the vertices of a right-angled triangle ABC Angle ABC is the right angle. Find an equation of the line that passes through A and C Give your answer in the form ay + bx = c

process to start to solve problem eg. draw a diagram, find gradient of AB (0.5) find gradient of BC (−2) Process to find y coordinate of C (9) Process to find equation of AC 3y - 4x = 11

How to draw a line perpendicular to line AB at point C?

1. From point C using a compass make a mark on the line on both sides of C making C in the middle of the two arcs. 2. Put the compass point on the arcs and then draw an arc in vertical direction to point C so as to get two curvy crosses 3. Connect the two crosses which produces a line perpendicular

What are the 4 ways to prove two triangles are congruent?

1. SSS 2. SAS 3. ASA 4. RHS

How would you answer a congruency question for two triangles?

1. Separate the two triangles 2. Say what is common 3. Need to make 3 points of 4. If info is given in question then write in brackets (given)

What are the three types of simplifying algebraic fractions?

1. Straightforward cancelling 2. Factorise then cancel 3. Adding and subtracting fractions

How do you bisect a line?

1. Using a compass draw an arc over half the length of the line and do the same for the other side point 2. This forms two curvy cross which when connected bisects the line in a right angle

Describe the features of a histogram?

1. Vertical axis is labelled frequency density 2. Area rather than height of bars matters 3. Histogram is similar to frequent Diagram 4. Area of bar represents frequency 5. Class intervals often not equal

Basic laws of indices:

1. X^a x X^b= X^a+b 2. X^a / X^b= X^a-b 3. (X^a)^b=X^ab 4. X^-a = 1/x^a

Pressure =force / area Find the pressure extered by a force of 900 newtons on an area of 60 cm2 Give your answer in newtons/m 2

150 000 AS = 10000cm squared = 1 m squared 60cm squared is therefore = 0.006 900/0.006 = 150,000

In a class of 20 students : 10 have cat 12 have dog 4 have neither Find probability that student owns cat and dog:

20-4=16 10+12=22 22-16=6 You find both cat and dog by subtracting Those with neither from total number and then adding those who have both cat and dog and subtracting this number number from the total number without neither people. Answer=6/20

What represents an even number? How is this made odd?

2n (must be multiple of 2) Odd number: 2n+1

Show that sum of two odd numbers is always an even number?

2n+1 + 2m+1=2n+2m+2 2(n+m+1) is a multiple of 2 so it's always even

Show that the sum of two even numbers is always an even number?

2n+2m 2(n+m) is a multiple of 2 so always even

area of right angled triangle

A= ab/ 2

Area of a triangle using sine Equation;

Angle included in equation does not have its opposite side included in equation. Original equation; 1/2abSinC

Circle theorems; alternate segments

Angles in alternate segments are equal

Circle theorems; same segment

Angles in same segment are equal, if all 4 points touch circumferance-even 3 angles in same segment are equal

Cuboid with dimensions 1m by 0.5m by 0.2m. Marble has a density of 2.7 g/cm^3. What's the mass of the marble in kg?

Convert 0.5,0.2,1 meters into centimetres and multiply them giving you 100000cm^3. Multiply this by 2.7 giving you: 270,000g Divide this number by 1000 giving you: 270kg

Cos rule (not trig) for graphs? Eg:

Cos x =cos(360-x) Eg: Cos40= cos(360-40)=cos 320

Surface area of cone

Curved surface area = Pie x r x l

How do you find the median of a cf graph?

Divide the total frequency by 2 and then find the coordinating X coordinate

What happens when you multiply an odd and even number or an even number and even number?

Even number

Two corresponding angles on similar shapes are what?

Exactly the same (only sides change in similar shapes)

If a line is sloping down in a velocity time graph, what is the gradient?

Negative

What should you do in a trial and improvement method question?

Show each trial and answer (also including if one answer of a certain trial is too big or small or right)

What is the sin rule For graphs? Eg?

Sin x = sin (180-x) Eg: Sin45=sin(180-45)=sin135 Sin8=sin172 Sin42=sin138

Sin 90=? Cos90=? Tan90=?

Sin90=1 Cos90=0 Tan90=undefined

What does a direct proportion graph look like?

Straight or partially curved positive correlation graph

What is the reverse of subtract from 20?

Subtract from 20

What does equidistant mean?

There's equal distance away from A and B

What does f^-1(x) mean?

This is a function that reverses f(x)----it's the inverse of f(x)

If one vector is a multiply of another one then...

Those two vectors are parallel.

What does and mean in probability?

Times

How is interquartile range calculated?

UQ-LQ=IQR

How do you bisect an angle between two lines?

Using a compass mark an arc on both lines using the same length. And then from the point where the arc touches the line draw another arc with the compass for both lines until there is a curvy cross which is then connected at the point where the lines meet so that the angle is cut in half

What are factors?

What we can multiply to get the number. Eg. 1,2,3,6 are all factors of 6

What are multiples?

What we get after multiplying the number by an integer (not a fraction). Eg. Multiples of 5 are 5,10,15,20,25....

Circle theorems; tangent

When a radius meets a tangent, the angle will always be 90 degrees

What is the exponential graph flipped to the opposite side in reflected by y axis?

When the number is less than 1 eg: Y=0.5^x

When looking at a pie chart what does the different sections and shape on the pie chart represent?

When the pie chart is split in half then half of the frequency are in that category. Divide the pie chart as each piece of the pie chart represents a certain amount

What does extrapolation mean?

When you extend the line of best fit beyond the range of data you already have to make an estimate which is less reliable -- the further out the range of data then the less reliable it is

What does interpolation mean?

When you make an estimate using the line best fit and the estimate is within the range of data you have Which is reliable

What is an iterative method? Give example:

Where the previous answer is fed back into the formula to produce the next result. EG.: Un+1=Un+5 U1=3 (usually given this) U2=8 (done by substituting 3 into un +5) U3=13

What can the quadratic expression be written as when including the sum and product equations?

X^2 - (sum of the roots)X + (product of the roots) =0 or x^2- (-b/a)x + (c/a)=0 If the sum and product expressions are fractions then to get them to be a whole number make sure they have the same denominator and then multiply the coefficient of X by the denominator

The difference of two squares: what is the equation? Factories 9x^2-16=0

X^2-a^2= (X-a)(X+a) 9x^2-16=0 (3x-4)(3x+4)=0

In the exponential equation, what is the y value when X power is 0?

Y is 1

Coordinates question: when you need to find coordinate of T on a line but your not told either its x or y coordinate, but your given two other coordinates of B and S on the line what do you do? Also TB:BS= 2:3

You subtract the larger x coordinate of S from the smaller x coordinate of B (31-19) and divide by the ratio of BS which is 3 (12/3 gives 4) and then subtract 4 from 19 by the amount stated in the ratio (2) so you get 19-8= 11 which is the x coordinate for T Then do same with y coordinate

ratio of no. of cola sweets to orange sweets in a jar is 2; 3 simon eats 3 of the cola sweets. ratio of no. of cola to orange is now 7; 12 work out total no. of sweets originally in jar

at start ; 2x cola sweets and 3x orange sweets. after 3 sweets eaten 2x-3 cola and 3x orange. 2x-3/ 3x = 7/12 24x - 36 = 21x 3x= 36 x = 12 5x = 5 x 12 = 60 sweets originally

A table gives info about the speeds of 85 motorbikes on the road. The first record is = speed / frequency / fx 30 ≤ s < 40 / 9 / ............. 1. Calculate the fx= 2. IF given the remaining records how would the mean speed be found out

midpoint of class interval = 35 35 x 9 = 315 2. calculate the fx for all the records then add them up and divide by total frequency which is 85