grade 8 revision booklet

7/31/2019 Grade 8 Revision Booklet

1/24


2/24

common factor.12 in prime factor form is 2 x 2 x 3 and 90 in prime factor form is 2 x 3 x 3 x 5.Both numbers can 'fit' 2 x 3 into their prime factor form, so that is their commonfactor ( e.g 2 x3 = 6)

The least common multiple of these numbers can be found by using all multiplyingtogether all the factors or taking the greatest number of each of those factors. e.g inthis case 2 x 2 x 3 x 3 x 5 = 180. Both numbers have to 'fit' completely into the LCM.

Another example : the prime factor form of 40 is 2 x 2 x 2 x 5 and the prime factorform of 70 is 2 x 5 x 7.The GCF is 2 x 5 = 10.The LCM is 2 x 2 x 2 x 5 x 7.

USING BASE TEN TO SOLVE PERCENTAGE PROBLEMSMultiplying something by 1 will give you 100 %, multiplying by 1.1 will give you 110 %.You can use this to solve problems such as ' a shirt with 15 % tax was $23. Find theprice before tax.Divide the new price by the multiplicative factor ( in this case 1.15 ) and you get theoriginal23 / 1.15 = 20. The original price was $20

MULTIPLYING AND DIVIDING DECIMALS BY POWERS OF TEN

To multiply by ten and powers of ten, move the decimal right and add zeroes if needed.

e.g 5.6899 x 10 = 5.6899 x 1000 = 5689.9 ( move the decimal 3 places right )

or3.4x 10 = 340

Dividingpowers of ten moves the decimal place left.

Eg, 5624 / 10 = 5624 / 100 = 56.24

or 4.355 / 10 = 0.004355

OPERATIONS WITH FRACTIONS

Adding and Subtracting fractions requires that you have the same denominators. This is


3/24

done by finding the common multiples of the denominators.. In the case of 2/3 + 4/5you would find the LCM of 3 and 5. Both fractions would then be converted into'fifteeths'.2/3 becomes 10/15 as you multiply both top and bottom by 5.4/5 becomes 12/15 as you multiply both top and bottom by 3.

Now the fractions can be added as 10/15 and 12/15 to become 22/15 or 1 and 7/15

Multiplying fractions just means multiply the top by the top, and the bottom by thebottom.In the case of 2/3 times 4/5, this is ( 2 x 4) / ( 3 x 5) = 8 /15

Dividing fractions is the same as multiplying except that you multiplying except that youturn the second fraction upside down. eg.2/3 divided by 4/5 = 2/3 x 5 / 4 = 10/12 = 5/6

ORDER OF OPERATIONS

BEDMAS stands for brackets first, then exponents, then multiplication or division, thensubtraction or addition ( note these last two categories are equal ranking and performedleft to right ).

e.g Evaluate the following expression : 3 ( 4 x 3 ) - 6

3 ( 4 x 9 ) - 6 = 3 ( 36) 6 = 108 6 = 2

PROPORTIONAL RELATIONSHIPS

Proportional relationships can be solved like fractions. If the ratio 2 : 3 is raised to x :15 , the ratio was multiplied by 5 and so x = 10.

Comparing unit costs : Find the cost of one unit to compare unit costs. Usually problemslike these involve dividing price by quantity. e.g a 800ml can of juice costs $4.99 . A300ml can of juice costs $ 1.99. To find which is more economical find the cost of 1 mlfor each can. 800/499 = 1. 6 cents per ml.300 / 199 = 1.5 cents per ml. Therefore the smaller can is more value for money.

NOW YOU TRY 2 :

1) Find the GCF of 72 and 40 using prime factor form.2) A shirt after 15 % taxes cost $58. Find the original price.3) Subtract : 4/5 1/7


4/24

4) Divide : 6/7 divided by 3/45) Evaluate : 3 + 8 x 2 36) Find the price per ml of a litre of milk at $ 3.99


5/24

SECTION B : MEASUREMENT

The Metric System

-The metric system is based on tens and multiples of ten with standard prefixes, so

most conversions can be done by moving a decimal point or adding zeroes.-For example, with grams we have milli grams ( a thousandthof a gram ) and kilograms( one thousand grams ).

E.g - To convert 4.23 grams into milligrams, multiplyby a 1000, or move the decimal 3places right( milligrams are smaller, so there are moreof them ) :4.23 x 1000 = 4230 milligrams.

E.g 2 - To convert 1600 metres into kilometres, divideby 1000 or move the decimal left

( kilometres are larger so there are fewer of them ):16000m / 1000 = 1.6 kilometres

Know the following prefixes which tell you if something is ten times smaller/larger orsome multiple of :

Giga = 1 000 000 000

Mega = 1 000 000

Kilo = 1000

hecto = 100deka = 10

deci = 0.1

centi = 0.01

m1 = 0.001

micro- (mu) = 0.000 001

NOW YOU TRY 3: : i) Convert 0.459 Litres into millilitresii) Convert 330 millilitre into Litres

iii) Convert 500 megabytes into gigabytesii) Convert 20 km into miles

SQUARE AND CUBIC MILLIMETRES, CENTIMETRES AND METRES

The Golden Rule here is square or cube the number you are multiplying or dividing by.


6/24

If 1metre = 100cm, then 1 m = 1 x 100 = 100cm x 100cm = 10,000cm.

Similarly, if 1 m = 1 x 100= 100cm x 100cm x 100cm = 1, 000,000 cm

To change from cm back to metres, divide by 100 or 100, depending on whether you

are finding converting cm or cm. e.g ' Convert 260cm into m '. : 260/ 10. ( Asa shortcut move the decimal point 6 places to the left )

260 cm = 0. 000260m

For conversion of mm, similarly find use 1cm = 10mm and 1metre = 1000mm and square orcube those conversions depending on whether you are looking for area or volume.e.g ' Convert 45cm into mm ' : 45cm = 45 x 10 = 45000mm

Convert 20mm into cm. Since 1mm = 0.1cm, then 1mm = 0.01cm.So, 20mm = 20 x 0.01 or 20 / 10 = 0.2cm

NOW YOU TRY 4:

Convert :1) 45m into mm2) 300cm into metres3) 4m into cm

CIRCLES ; CIRCUMFERENCE AND AREA OF A CIRCLE

The line that goes from the edge of a circle to the middle is called the radius.

This radius can be used to calculate both the circumference ( the perimeter or distancearound the circle ) by using Circumference = 2 x radius x 3.14 or C = 2 rYou can 22/7 instead of 3.14, OR if using a calculator use the pi or button


7/24

e.g with a circle of radius 5cm the circumference is 2 x 5 x 3.14 = 31.4 cm

The Area of a Circle is calculated by using A = r The Area of a circle with radius 4cm is : A = 3.14 x 4 = 50.24 cm

NOW YOU TRY 5 :1) Find the circumference of a circle that has a diameter 10cm2) Find the Area of a circle that has radius 3cm.

Surface Area and Volume

Most of these problems involve 3-D shapes. Think of volume as how many slices you haveof a shape, and surface area as the area of the outside faces only. You will often have toapply trigonometry to these problems.

Eg. 1 Surface area and volume of a simple rectangular prism that measures 3cm( height ) by 4cm ( length) by 5cm ( width ).

The surface area is the total of the faces.Note there are two of each face, e.g front and back are the same, the sides are thesame, and the top and bottom are equal too.S.A = 2 [ ( l x w ) + ( l x h ) + (w x h ) ]

S.A = 2 [ ( 4 x 5 ) + ( 4 x 3 ) + ( 5 x 3 ) ]S.A = 2 [ 20 + 12 + 15 ] = 2 x 47S.A = 94cm.

SURFACE AREA AND VOLUME OF CYLINDERS

When you find the volume of a cube, one way is to find the area of a face or 'slice' ofthe cube and then multiply by the 3rd dimension.Cylinders involve a slightly differentformula but the idea of multiplying by slices is the same.Look at a cylinder of diameter 8 cm and height 6cm.

Find the area of the circle top or bottom using pi x r.


8/24

In this case A = 3.142 x 4 = 157.95 cmMultiply this answer by the height 6 cm to find volume :

V = 6 x 157.95 = 947.73 cm( Note * : I have rounded answers to 2 d.p to save space, but you should only round

FINAL answers. Use the Ans button on your calculator to use previous answers andretain accuracy.)

To find surface area, use the circumference times the height to find the wrap aroundsection ( if you peel a label off a can you will see this is height x length , where length =circumference ).Area of curved surface area of a cylinder is : 2 x pi x r x h

In this case the curved surface area is 6cm x 3.142 x 8 = 150.816 cm

Then add the top and bottom using A = 2 x pi x r

So the total surface area of this cylinder is : SA = (2 x pi x r ) + ( 2 x pi x r x h )

In this case the total surface area is : S.A = (2 x 3.142 x 4) + ( 2 x 3.142 x 4 x 6 ) =251.36 cm

NOW YOU TRY 6 :

1) A cylinder has diameter 30cm and height 4cm. Find the total surface area.2) A cylinder has radius 6cm and height 7cm. Find the volume


9/24

SECTION C : GEOMETRY AND SPATIAL SENSE

SORTING QUADRILATERALS BY GEOMETRIC PROPERTIES INVOLVING

DIAGONALS

The diagonals of the square and rhombus are congruent and bisect each other at 90 (perpendicularto each other ).The diagonals of the rectangle, trapezoid and parallelogram are congruent and bisect too, butnot at 90.The kite is the odd one out in that the diagonals are NOT congruent, but they do bisect at 90

Angles in Polygons

A polygon is a straight sided shape, such as triangle, but not a circle.Any polygon can be broken into triangles, and this helps you calculate the total interiordegrees, as each triangle has 180 inside.A polygon always has 2 less triangles inside than its number of sides. For example, a fivesided shape can be split into three triangles. Therefore, a pentagon has 3 x 180 degreesinside.Total interior degrees of a pentagon = 540.

The exterior angle of a polygon is 180 minus the interior.In a regular pentagon, there are a total of 540 and five sides, so each interior angle is108.Each related exterior angle is 180-108 = 72


10/24

Exterior angles are also directly related to the number of sides of the polygon.360 / exterior angle = the number of sides.e.gIn a hexagon each exterior angle is 360 / 6 = 60

Note how you could also then quickly find the interior 120.

NOW YOU TRY 7 ;

Calculate the i) exterior and ii) total interior angles in a Nonagon ( 9 sided shape ).

Angles around a vertex or corner can generally be calculated by using 4 fundamentalgeometry rules :

2. The angles on a straight line add to 1803. Angles opposite crossed lines are equal.


11/24

To these rules are added 2 more useful Angle Geometry principles that occur whenparallel lines are crossed or traversed by the same line :

NOW YOU TRY 8 :

Apply the four angle rules above to find the labelled angles in the diagram below :


12/24

FACES, EDGES AND VERTICES OF POLYHEDRONS ( 3 -D polygons )

For a simple polyhedron F - E + V = 2. (This is also called the Euler's Formula.)

That is, Faces minus Edges + Vertices = 2For instance, in a cube, there are 6 faces, 12 edges and 4 vertices ( 4 corners ).This formula can be rearranged :

F = 2 -V + EE = F 2 + VV = 2 F + E

Similar Triangles and Congruency

-Similartriangles are triangles that are larger or smaller versions of each other thathave the same anglesand same ratiosof sides.-Congruenttriangles have exactly the same angles ANDsize.

eg. 1:The triangle that has sides 3, 4 and 5 cm is a smaller but similartriangle to that whichhas sides 6, 8 and 10 cm ( allsides on the larger triangle are twice as big)

eg. 2 Triangles which have allthe same angles inside are similar, regardless of size.

We will now see how we can know with less information, but it is important thatcorrespondingsides are similar for the triangle to qualify.

10 cm

6 cm

8 cm


13/24

Finding corresponding sides if triangles are similar

If you have 3 out of 4 corresponding sides then you can use ratios to find the missingside. For example if a triangle has height 3cm and width 4cm, and a similar triangle has

height 5cm and width 'x' , you can set up a ratio :3/4 = 5/x

(3/4) x = 5 ( multiply both sides by x ; x cancels on the right side )x = 5 / ( 3/4) ( divide both sides by , ;x = 20/3 ( dividing by is the same as multiplying by 4/3 )x = 6.67 cm

NOW YOU TRY 9: i) A triangle has hypotenuse 7m and height 4m. Another triangle

has hypotenuse 20 m and height 11.4m . Are they similar, and how would you prove it ?ii) A triangle has width 5m and height 6m. A similar triangle has height 10m. What isthe width of the larger triangle ?

The volume can be found simply using V = l x w x hor V = 5 x 4 x 3 = 60cm.

It is also useful to think of taking a slice of the shape and multiplying by the 3rd

dimension. The area of the front face is 3 x 5 = 15cm. Now multiply by 4cm, or imagine4 slices through the shape. V = 4 x 15cm = 60cm.

Volume of cones :, Cones are just one third of a regular prism that has the same heightand width.E.g A cone has one third the volume of a cylinder that has the same dimensions. So justuse the cylinder formula then divide by 3.

Surface area of a cone uses the slant length instead of height, and you may need to usePythagoras with the height to calculate slant length. Slant length is then used tocalculate the curved part of the cone using A = pi x r x S.In this cone the slant length can be found using the radius as the base.S = h + r , in this case S = 4 + 2.5 = 4.72 cm


14/24

Slant length ( S) is now used in the surface area formula : S.A = pi x r ( for the circlebase) + ( pi x r x S).S.A = (3.142 x 2.5 ) + ( 3.142 x 2.5 x 4.72 ) = 56.71 cm

A pyramid uses the same principle as a cone for volume ; just find one third the volume

of a regular prism that has the same dimensions.

The surface area of a pyramid involves finding the slant length which is used as theheight of a face. In this case slant length means the line which runs down the middle ofeach face.Like a cone, use Pythagoras with half the width to find slant length.In this case use height 5cm with width 6cm : S = 5 + 3 ; S = 34 = 5.83cmOnce you found the slant length use it as the height of each face. In this case the areaof each face is A = 34 x 6 = 35cm.

The total area of a square based pyramid is the base plus 4 times the face area.S. A = (6 x 6 ) + 4 ( 34 x 6 ) = 175.94 cm

For balls or Spheres use S.A = 4 x 3.142 x r ( think of 4 circles )For volume of spheres use V = 4/3 x 3.142 x r ( remember the 3s are in the volumeformula )

Sample Mixed problem : A cone has a height of 16 cm and diameter 10 cm. What is thesurface area in square inches ?

- We need slant length, which is S = 16 + 5 ; S = 16.76 cmS.A in cm is : S.A = ( 3.142 x 5) + ( 3.142 x 5 x 16.76 ) = 341.90cm. Since 2.5cm = 1 inch, 341.90/2.5 = approx. 137 inches

NOW YOU TRY 10: I) A swimming pool measures 8 feet by 4 feet by 20 feet.What is the volume of water it can hold in litres ?i) A basketball has a diameter of 28cm. What is its surface area in cm, andhow much air can it hold in litres ?ii) A cardboard pyramid has a square base of 5cm by 5cm. Each face has aslant length of 7cm. Find the volume of the pyramid.


15/24

The Pythagorean Theorem

i) In a right triangle, the two short sides squared and then added equal thelongest side squared. You can then square root this sum to find the long side.

eg. - If a triangle has short sides 8cm and 6cm, then the long side opposite thehypotenuse can be found using 8 + 6 = 64 +36 ( make sure you square the numbersbeforeyou add them ; remember BEDMAS ! )

64 + 36 = 100100 = 10 ; the long side is 10cm.

ii) You can re-arrange the formula a + b = c to find short sides.

The formula can be rewritten as c a = b , or long side squared minusshort sidesquared gives the other short side squared.

e.g : A triangle has hypotenuse 15 cm and width 9cm.The missing side can be found with 15 9 = 225 81225 81 = 169

169 = 13 cm

NOW YOU TRY 11: i) A right triangle has width and height 3m and 6m respectively.Find the length of the hypotenuseii) A right triangle has hypotenuse 8cm and height 7cm. Find the width.iii) A right triangle has hypotenuse 11m and width 9m. Find the height.

CARTESIAN GRAPHS AND TRANSFORMATIONS

A Cartesian graph is where points are plotted on x-y axis with 4 quadrants. The point( 5, -6 ) for example is 5 right, 6 down . This would put you in quadrant 3.

X cm

6 cm

8 cm


16/24

Transformations here are when you move a shape on a graph.

A TRANSLATION is moving something up, down or left or right.

Look at the triangle which is defined by the vertices ( 0.0), ( 1,0) and (1,2).If it is moved by the translation (1, 3) this means move all the points up 1, right 3.

A ROTATION is when you spin a shape round, usually around the origin ( 0, 0). If yourotate by 90 clockwise, your shape will be on it's side, but also move from quadrant 1 to4.A rotation of 180 will flip a shape upside down and move into the diagonally opposite

quadrant.A rotation of 270 will move a shape around by 3 quadrants. A shape will be on it' s sideagain, but the opposite way to a 90 rotation.

A rotation of 360 will return a shape to it's original position.

A REFLECTION is when a shape is reflected across a line and produces a mirror image.A reflection in the x ( horizontal ) axis will move a shape into the opposite quadrant.Notice the mirror effect will appear to flip the shape upside down.A reflection in the y (vertical ) axis will flip a shape from right to left or vice-versa.

NOW YOU TRY 12 :

For the triangle above ( 0.0), ( 1,0) and (1,2) apply the following transformations and listthe new co-ordinates

i) translate with ( - 3 , - 4)


17/24

ii) rotate 270 counter clockwiseiii) reflect in the y-axis


18/24

SECTION D : PATTERNING AND ALGEBRA

Representing the general term in a linear sequence

Suppose you were given a list of numbers and there appeared to be a pattern, such as 5,

8 , 11....etc.Clearly you can see the pattern is that you add 3 to get to the next term.Mathematics give you a way to predict far into the future. Because there is adifference of 3 this can be modeled with the 3 times tables.If you compare the 3 times tables to this sequence, you see this sequence is 2 more , iethe 3 times table with 2 added on.The 3 times table with 2 added on can be written ; 3n + 2. where n is the term.For example. The 100 term would be : 3 ( 100 ) + 2 = 302.

Some sequences will be times tables you are unfamiliar with, but nonetheless they can bemodeled with a simple multiplicative relationship.For example, consider the sequence 8, -3, 14. The difference between terms is -11, so we can use the ' -11' times table.Now compare the first term 8 to -11.8 is 19 bigger than -11, so we can use the formula -11n + 19 .The 30 term for example would be : -11( 30 ) + 19 = - 330 + 19 = - 311.

Translating statements using algebraic equations

Using x to represent an unknown quantity, and defining other unknowns in terms of x, wecan solve complex word problems.For example, suppose the age of Brett is unknown. But we do know Lisa is 2 years olderthan him, and Maria is twice as old as Lisa. The total of their ages is 30.Brett = xLisa = x + 2Maria = 2 ( x +2 ) = 2x + 4Total : x + ( x + 2) + 2x + 4 = 30

Add like terms and simplify : 4x + 6 = 304x = 24x = 6

So, Brett is 6, Lisa is 8, and Maria is 16

Solving Linear Equations using the balance model


19/24

Our aim here is to shuffle the equation around until we have x =

In the above example, we solved an equation using two basic steps ;

1) We subtracted the constant ( the number on its' own ). You can think of this as

balancing an equation by subtracting 6 from both sides.

4x + 6 6 = 30 6so: 4x = 24

2) Now that we have x only being multiplied by a number, we can reverse this bydividing both sides by that number.In this case 4x = 24so 4x/4 = 24 /4

x = 6

Most basic equations are solved this way, after collecting like terms.If you like formulae, you can think of this as if : ' ax + b = c,

then x = (c -b ) / a

Solving Advanced Equations

Using inverse/reverse operations to simplify and solve equations :Squaring and square rooting

Eg1. 5x - 4 = 215x = 21 +45x = 25x = 5 x = +/-2.24 ( 2.dp.)

e.g 2 : (4X) + 3 = 10It is a good idea to isolate the square root first.(4X) = 7

Now reverse the root by squaring :[(4X) ] = 74X = 49X = 49/4 = 12.25

NOW YOU TRY 13

Solve for x : i) 3x - 9 = 12ii) 2x - 4 = 8

Operations with monomials and polynomials.The golden rule for operating with algebraic expressions is : only add liketerms.


20/24

Xs can only add with Xs, and X can only add with other X.Eg :2X + 3y - X + X +4y y + 2X = ( 2X +X) +(-y) + (2X-X) + ( 3y +4y)

= 3X -y + X +7yExpanding with brackets

Every term inside the bracket must be multiplied by the term outside :2x ( x + 4 ) = 2x + 2x ( 4 ) = 2x + 8x

Remember to add exponents where appropriate : eg.22x ( 3x - 2x + 1 ) = 6x - 4x + 2xExpanding andSimplifying :After expanding, you must be careful to collect like terms and simplify if possible.E.g2x ( 4x +1 ) 3x ( x +2) = 8x +2 -3x - 6x = -3x + 2x + 2 ( note how x simplified

)There is one golden rule of manipulating all algebraic equations ; ' What you do to oneside of the equation you must also do the same to the other side'Most of the time this involves reversing operations to isolate a variable, and making sure

you apply the reverse operation to both sides.

For example, re-arrange the equation below so that y is the subject ( y = ...)

4x 3y = 12

- 3y = 12 - 4x ( subtract '4x' from both sides to start isolating 'y' ).

y = ( 12 4x )/ (- 3 ) ( divide both sides by -3 to get one single, positive y )

y = 4 + (4/3)x ( everypart of the equation on the left is divided by 3 )


21/24

SECTION E : DATA MANAGEMENT AND PROBABILITY

Discrete data

is data that can only have certain values, such as shoe size. You can only get shoe size8 or 9 for example, not shoe size 8.76

Continuous data is data that is in theory unending, because the units used can befurther divided. For example you might be 156cm, but your actual height might be156.75748210....cm etc.

A Population is the group that you are examining.

A Census is when you get data from everyone in the population.

A Sample is when you take data from just some of the population.

A Representative Sample is when your sample, even though it does not get data fromeveryone, is nonetheless a fair and accurate picture of the population. This is because ittries to get data in a fair way from each 'sub group' that might be in the population. Forexample, if a school has 25 girls and 15 boys, then a sample might aim to ask surveyquestions from 5 girls and 3 boys, because this is in the same proportion.

Histograms are bar charts where the bars are next to each other without gaps.

Scatterplots show correlation, that is a certain relationship between two data sets.

If you plot a set of data on an x-axis, and a corresponding set of data on a y-axis, youwill get a scatter-plot which helps you to visualise the relationship between them.Using the table of values below, plot the pairs as a co-ordinate on a graph.e.g . The first point would be ( 6, 100 )

X (age in years) 6 8 10 12 14

Y ( height in cm ) 100 110 120 130 140

Your graph should look something like the one below :


22/24

Whenever anything like a straight line is made on a scatter graph, you can assume thereis some kind of relationship. You now need to know how to describe that relationship in

mathematical terms :We talk of trend meaning there is some sort of relationship. If the dots line up at all,even roughly, then there is a trend.

The strength of a trend can be called correlation. Strong correlation looks like a line( perfect correlation is a straight line ) and weak correlation is where a rough , looserelationship occurs. In weak correlation the points are scattered but you can still see apattern.

The type of trend can be positive or negative. If both quantities increase together ( asthey do here ) then the trend is positive. If the trend line goes down as you read thegraph left to right, then the trend is negative. In our first graph we have an exampleperfect, positive correlation. Below is an example of weak, negative correlation.

.


23/24

Note that a line could be drawn roughly close to all points and this would be the line ofbest fit :

Measures of Central Tendency

Consider the data set : 5, 8 , 8, 9 , 3 , 1

Meanis when you add all the numbers and divide by how many there are ; in this case :( 5+8+8+9+1) / 6 = 5.67 ( 2 d.p )

Modeis the most commonly occurring number ; in this case 8

Medianis the middle of the data set, when they are in orderfrom smallest to largest. Inthis case : 1, 3, 5, 8, 8, 9. The middle is between 5 and 8 ; ie. 6.5

Theoretical probability is the probability of a desired outcome divided by the totalpossibilities. For example if you throw a dice, the chance of getting a 5 is 1 /6 because6 different things could happen but there is only one 5 on the dice.

Experimental probability is the calculation of probability from a real life experiment ortrial . For example, lets say you flipped a coin 10 times and you got 6 tails and 4 heads.In theory, the probability of getting a tail is 5/10 or 0.5, but in this trial theexperimental probability is 6/10 or 0.6

Note that if you repeat an experiment many times, the closer it will get to thetheoretical probability. In the example above, if we flipped the coin a hundred times, wewould likely get a probability much closer to the theory. We might for example get55/100 e.g 0.55

Complementary events are events that have to add together to make zero, and areusually the opposites of each other. For example, if the probability of it raining is 0.3,then the probability of it NOT raining is 1 0.3 = 0.7

NOW YOU TRY 14 :

1) Calculate the mode, median and mode of the following numbers : 4, 6,7,5,2,4, 92) Calculate the probability that a team wins a match, if the probability of losing is

0.3 and the probability of a tie is 0.2


24/24

SOLUTIONS TO EXERCISES

1)

2)

3)

4)

5)

6)

7)

8)

9)

10)

11)

12)

13)

14)

grade 8 revision booklet

Documents