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
Which statements are true?
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All 3 statements are true.
Did you get it right?
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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
Which statements are true?
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All three statements are true.
Choose a new starter
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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
Which statements are true?
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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
Choose a new topic
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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
Which statements are true?
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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.
Which statements are true?
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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
Which statements are true?
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Did you get it right?
Statements 1 & 3 are true
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
Which statements are true?
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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
Which statements are true?
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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
Which statements are true?
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Did you get it right?
Statements 1 & 2 are true.
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.
Which statements are true?
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Only statement 1 is true.
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
Which statements are true?
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Statements 1 & 2 are true.
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
Which statements are true?
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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
Which statements are true?
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Only statement 2 is true.
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
Which statements are true?
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Only statement 3 is true.
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
Which statements are true?
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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
Age in years Frequency
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
Which statements are true?
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Statements 1 & 2 are true.
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
Which statements are true?
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Try another
Statements 1 & 3 are true.
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
Age in years 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
Which statements are true?
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Statements 1 & 3 are true.
Statement 2 is not true.
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.
Which statements are true?
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
Statement 3 is not true.
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
Which statements are true?
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Statements 1 is true.
Statement 2 is not true
(probabilities are 0.3 and 0.25)
Statement 3 is not true.
(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.
Which statements are true?
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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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Check
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
Which statements are true?
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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
Statements 2 & 3 are true.
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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
Which statements are true?
5cm
3cm
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Statements 1 & 2 are true
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
Which statements are true?
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Choose a new starter
All three statements are true.
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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
Which statements are true?
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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
Which statements are true?
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)
Which statements are true?
B k
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Choose a new starter.
All three statements are true.
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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)
Which statements are true?
S
P
Q
B k
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Statements 1 & 3 are true
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)
Which statements are true?
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
Which statements are true?
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
Which statements are true?
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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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
Which statements are true?
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All three statements are true.
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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
Which statements are true?
Back Si il Q ti
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All three statements are true.
You need to use the Sine Rule
for this question.
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NorthNorth
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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
Which statements are true?
30 km
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All three statements are true.
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