Revision PPT maths

8/12/2019 Revision PPT maths

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1

Angles Area andperimeter

2

Algebra

3

4

Triangles

5

Statistics

6

Probability

7

Solids Graphs

9

Bearings

8


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Angles

Foundation Higher


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Check

B

D

C

A

Lines AB and CD are parallel.

EF is perpendicular to AB.

Angle FAE = 47o

Statements

1. Angle AFC is 47o

2. EF is perpendicular to CD3. Angle AFE is 47o

47o

F

E

Which statements are true?


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Statements 1 & 2 are true

Statement 3 is false.

Angle AFE = 43o

Did you get it right?

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Check

B

D

C

A

Lines AB and CD are parallel.

AF = AE.Angle AFE = 70o

Statements

1. Angle FAE is 40o

2. Angle EFD = 70o

3. Angle AFC is 40o

70o

F

E



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All 3 statements are true.


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Check

Chords AD and CB intersect atthe centre of the circle, O.

Angle CDA = 35oB

D

O

C

A

35o

Statements1. Angle BCD = 35o

2. Angle CBD = 55o

3. Angle AOC = 70o



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All three statements are true.

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Check

Chords AD and CB intersectat point E.

Angle CDA = 40o

B

DE

C

A

40o

Statements1. Angle DAB = 40o

2. Angle ABC = 40o

3. Angle AEC = 80o



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Statement 1 is false because the lines ABand CD are not parallel

Statement 2 is true (angles on same arc)

Statement 3 is false because E is not thecentre of the circle

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Area & Perimeter

Foundation Higher


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This large rectangle is made from 4 smallerrectangles, each measuring 2cm by 4cm

Check

Statements1. The perimeter of a small rectangle is 12cm2. The perimeter of the large rectangle is 48cm3. The area of the large rectangle is 24cm2



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Well done if you got it right

Only statement 1 is true.

The large rectangle measures

8cm by 4cm so its perimeter is24cm and its area is 32cm2

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This shape is made from 6 rectangles, eachmeasuring 3cm by 5cm and a red rectangle

Check

Statements1. The perimeter of the red rectangle is 18cm2. The area of the red rectangle is 14cm23. Less than 10% of the whole shape is red.



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Well done if you got it right

Statements 1 & 2 are true.

Statement 3 is not accurate.Over 13% is red.

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Statements1. The area of the trapezium is 15cm22. BC is 7 cm3. The perimeter of the trapezium is 18cm

D

B

C

AABCD is a trapezium.AB = AD = 3cmDC = 7cmBAD = ADC = 90o

3cm

7cm

3cm



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Statement 2 is false.

You need to use Pythagoras Theoremto find the length of BC.

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Statements1. Angle ABC = 70o2. Perimeter of the rhombus = 40 cm3. Area of rhombus = 96cm2

D

B

C

AABCD is a rhombus

Diagonal AC = 12cmDiagonal DB = 16cmAngle BAC = 55o

E55o



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All 3 statements are true.

The diagonals of a rhombus bisect

each other at right angles so you canuse Pythagoras Theorem to calculate

the length of a side.

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Al b


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Algebra

Foundation Higher


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Add two touching bricks to obtain theexpression in the brick above them.

Check

3x + 7

4x + 2

x - 5 5x + 3

Statements

1. (3x + 7) + (x 5) = 4x + 22. (x 5) + (5x + 3) = 6x + 23. The value of x must be 6

?

60



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This is 12m b 10m t l d O t


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This is a 12m by 10m rectangular garden. On twosides is a path of x metres width. The remainingtwo thirds of the garden is grass.

Check

xm

xm

10 m

12m

Statements1. x< 102. x 2- 22x+ 40 = 03. The width of the path is 2 cm



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Statement 3 is not true becausethe width is 2 metres (not cm)

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This is a 12m by 10m rectangular garden. A path of width ymetres surrounds a lawn at the centre of the garden.

Check

y m

8 m

12m

Statements

1. The area of the path is 64 cm

2

2. The area of the path is 44y cm23. y < 2

y m

The area of thepath is twicethe area of thelawn.



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The area of the path is8y 280y + 192

so y = 2

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Trian les


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Triangles

Foundation Higher


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15 m

ABC is a right angled triangle

Check

B

Statements1. You can use Pythagoras

Theorem to find AC

2. AC2

= 152

+ 82

3. AC =289 m

8 m

A

C



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Statement 3 is false.AC2= 289

AC = 289 = 17 m

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A 13 foot ladder leans against a 12 foot wall so that


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12 feet

A 13-foot ladder leans against a 12-foot wall so thatthe top of the ladder just reaches the top of the wall.

Check

13 feetStatements

1. You can use PythagorasTheorem to find x.

2. x2= 122+ 132

3. The value of x is 5

A bottom of the ladder is xfeet

from the base of the wall.

x feet



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A 13-foot ladder leans against a 12-foot wall so that


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Check

13 feetStatements

1. Tan = 12/132. Tan = 2.43. The value of is 67.3o

to 1 decimal place

A ladder makes an angle of with

the ground.

A 13-foot ladder leans against a 12-foot wall so thatthe top of the ladder just reaches the top of the wall.

12 feet



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Statement 1 is false because

Sin = 12/13

Statement 3 is false because

is 67.4oto 1 d.p.

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Check

Statements1. tan 12o = 75/x2. 75cm = 7.5 m

3. x = 3.53 to 3 s.f.

A wheel chair ramp rises by 75 cm. The angle ofthe ramp is 12o. The length of the ramp is xmetres.

75cm12o

x m



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75 cm = 0.75 m

So tan 12o= 0.75/x

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Statistics


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Statistics

Foundation Higher


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Check

Age in years Frequency

7 28910

11

347

5

This table shows the ages of children in a club.

Statements1. The mode is 7 years2. The median is 9 years3. The mean is 45 21



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None are trueThe mode is the most common age = 10 years

The median is the middle age in order (11thout of 21)Median = 10 years.

Sum of the ages = 14 + 24 + 36 + 70 + 55So the mean is 199 21 = 9.48

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Check


0 < x 20 320 < x 4040 < x 6060 < x 80

80 < x 100

946

3

This table shows the ages of people in a village.

Statements1. The ages of 25 people are recorded2. The modal class is 20 < x 403. The best estimate for the median is 50



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Statement 3 is not true.

The median value is the first of

the 4 values in the 40 < x 60 interval.

So 45 is a better estimate.

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Thi t bl h th b f b k d b


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This table shows the number of books read by aclass of pupils during a Charity Readathon

Check

Number of books Frequency

5 13678

9

943

1

Statements1. Altogether there were 30 pupils2. Altogether, they read 35 books3. Mean = 6 books



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Try another


Statement 2 is not true.The pupils read 180 books altogether

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Thi t bl h th f l h li i ill


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This table shows the ages of people who live in a village.

Check

Number of books Frequency


0 < x 20 3

20 < x 4040 < x 6060 < x 7070 < x 100

9463

Statements1. A good estimate for the mean is 45 years

2. The most densely populated class is 20 < x 403. On a histogram the relative frequency for theinterval 60 < x 70 would be 0.6



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20 < x 40 is the most populatedbut not the most denselypopulated

(relative frequency is 0.45)

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Probability


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Probability

Foundation Higher


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Check

Statements1. Probability that the lights are red or amber = 0.362. Probability that they are green = 0.553. Probability that they are not red = 0.75

The probabilitythe lights are

red is 0.35

Each day the schoolbus passes a set oftraffic lights.


The probabilitythe lights areamber is 0.1


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Statements 1 is not true

( 0.35 + 0.1 = 0.45)

Statement 2 is trueprob(green) = 1 0.45


prob (not red) = 1 prob (red) = 0.65

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A b ll i i k d d f h b


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Check

Statements1.The probability of picking a blueball from bag A is 0.32.You are more likely to pick a bluefrom bag B than bag A

3.You are more likely to pick greenfrom bag A than bag B

Bag A Bag B

A ball is picked at random from each bag



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Statements 1 is true.

Statement 2 is not true

(probabilities are 0.3 and 0.25)


(probabilities are 0.6 and 0.625)

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Each day the school bus passes two sets of traffic lights


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Check

The

probabilitythat thefirst lightsare red is

0.3

Statements1. The first set of lights are more likely to be green

than the second set.

2. The probability that bothlights are red is 0.63. The probability that only one set is red is 0.38

The

probabilitythat thesecond lights

are red is0.2

Each day the school bus passes two sets of traffic lights.



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Statements 1 & 2 are not true.Prob (RR) = 0.2 x 0.3 = 0.06

Statement 3 is true.

prob (one red) = prob (GR) + prob (RG)

= (0.7 x 0.2) + (0.3 x 0.8)

= 0.14 + 0.24 = 0.38

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Statements1. The probability of picking at least one yellow = 0.652. The probability that both are yellow = 0.13. If the ball from bag A is put into bag B beforea ball

ball is taken from bag B then the probability that theball from bag B is yellow = 0.28

Bag A Bag B

Two balls are picked at random one ball from each bag



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Statement 1 is not true.Prob (one yellow) = p(yy) + p(yy)

= (0.4 x 0.75) + (0.6 x 0.25) = 0.45


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Solids


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So s

Foundation Higher

This box has a 4 cm by 5 cm rectangular base


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Check

This box has a 4 cm by 5 cm rectangular baseand a height of 3 cm

4cm

Statements1. The area of the top is 20 cm2

2. The area of the front face is 15 cm2

3. The total surface area is 47 cm2


5cm

3cm


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but statement 3 is not true because

total surface area is 94cm2

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Each of these boxes has a 4cm by 5 cm rectangular base


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Check

Each of these boxes has a 4cm by 5 cm rectangular baseThe green box has a height of 3cmThe blue box has a height of h cm

hcm3cm

4cm

4cm 5cm5cm

Statements1. Volume of the green box is 60 cm3

2. Volume of the blue box is 20h cm3

3. If the volume of the blue box is 76 cm3then its height is 3.8 cm



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A This is a right angled


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8cm

Check

C

AB

D

E

9cm

12cm

This is a right-angledtriangular prism

Statements1. Area of cross section is 108 cm2

2. Volume = 864 cm3

3. Total surface area = 396 cm2

F



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Choose a newquestion

Only statement 3 is true

Statements 1& 2 is not true.

The area of the cross-section is

x 9 x 12 = 54 cm2

and so the Volume is 432 cm3

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AThis is a


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12 m

Check

C

AB

D

E

8cm

9cm

This is aright-angled

triangularprism

Statements1. Journey AF E D = 29cm

2. Journey AF D = 23cm3. Journey AB E = 29cm

F


Journeys

between twopoints are madealong theshortest paths


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Choose a newquestion

They are all true.

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Graphs


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p

Foundation Higher

y


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Check

x

A

B

Statements1. B = (-2, -1)

2. The mid point of line AB = (1, 1)3. AB = 52 units

A = (4, 3)


B k


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y


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Check

x

R

T

Statements1. PQ is parallel to TS

2. PQST is a rhombus3. Angle RTS is a right angle

P = (1, 3)


S

P

Q

B k


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Statement 2 is not true. The shapeis a parallelogram

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y


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Check

x

A

B

Statements1. Gradient of AB is 1

2. Equation of line AB is y = x + 13. Length AB = 510 units

A = (-2, 3)


B k


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None of the statements are true.

The gradient of the line is -1

Hence, the equation of the line is

y = -x + 1 or x + y = 1

AB = 50 units = 52 units

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y


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Check

x

Statements1. A = (-2,0)

2. Equation of line BC is y = 83. Equation of line through C perpendicularto AB is y = 14 - 2x

The equation of

line AB isy = x + 2


A

B

C

B k


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Statements 1 & 2 are not true

A = (-4, 0)

The equation of BC is x = 8

Statement 3 is true.

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Bearings


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Foundation Higher

NorthNorth


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Check

NorthNorth

Islandlighthouse

Port

A positions of aPort, a lighthouse

and an island areshown on this map.

The Island is on abearing of 045o

from the Port.

45o

Statements1. The Island is East of the lighthouse.

2. The Island is North-East of the Port

3. The Port is South-East of the Island


B k i il Q i


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Only statements 1 & 2 are true.

Statement 3 is false because the Port isSouth-West of the Island

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NorthNorth


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Check

NorthNorth

Islandlighthouse

Port

16 km34 km

A boat leaves thePort and sails 16km

North, goes round alighthouse and sailsEast to the Island.

The island is 34km

from the Port on abearing of 062o

62o

Statements1. The Island is 30km from the lighthouse

2. The bearing of the Island from the lighthouse is 090o

3. The bearing of the Port from the Island is 242o


B ck


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NorthNorth A boat leaves the Port at


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Check

NorthNorthHarbour

Buoy

Port

30 km

A boat leaves the Port atNoon, sails 30km North,goes round a Buoy and sailsto the Harbour on abearing of 080o.

The Harbour is on abearing of 060o from thePort.

The average speed of theboat is 20 km/hr

60o

Statements1.The bearing of the Buoy from the Harbour is 260o

2.The Harbour is 86.4 km from the Port (3sf)3.The Boat arrives at the Harbour at 17:18

80o


Back Si il Q ti


80/82


You need to use the Sine Rule

for this question.

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NorthNorth


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Check

NorthNorth

Wreck

Reef

Port

20 km

The Reef is 20kmNorth of the Port.

The wreck is 30 kmfrom the reef on abearing of 120o

Statements1. The Wreck is 26.5km from the Port (to 3sf)2. The bearing of the Wreck from the Port is 079o to the

nearest degree3. The area of sea within the triangle is 260 km2(3sf)

120o


30 km

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