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Transcript
```Miss Bβs Maths
DIRT Bank
Created by teachers for teachers, to help improve the work life
balance and also the consistent quality of feedback our
This aims to be a continuously evolving document.
Please contribute to the DIRT Bank simply by emailing your
to missbsresources@gmail.com and I will update weekly.
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Template
Sub Topic
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Template
Subtopic
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Contents
Number
Topic
Contributor
Multiplying 3 digit by 1 digit (grid)
Danielle Bartram
@Missbsresources
Multiplying 3 digit by 1 digit (Long)
Danielle Bartram
@Missbsresources
Multiplying 3 digit by 2 digit (grid)
Danielle Bartram
@Missbsresources
Multiplying 3 digit by 2 digit (Long)
Danielle Bartram
@Missbsresources
Multiplying by scalars of 10
Danielle Bartram
@Missbsresources
Multiplying decimals
Danielle Bartram
@Missbsresources
Dividing decimals
Danielle Bartram
@Missbsresources
Functional division 1
Danielle Bartram
@Missbsresources
Functional division 2
Danielle Bartram
@Missbsresources
Danielle Bartram
@Missbsresources
Danielle Bartram
@Missbsresources
Directed numbers four rules
Danielle Bartram
@Missbsresources
Functional Temperature 1
Danielle Bartram
@Missbsresources
Functional Temperature 2
Danielle Bartram
@Missbsresources
Ordering Decimals
Danielle Bartram
@Missbsresources
Rounding nearest 10
Danielle Bartram
@Missbsresources
Significant Figures
Danielle Bartram
@Missbsresources
Rounding using a calculator 1
Danielle Bartram
@Missbsresources
Rounding using a calculator 2
Danielle Bartram
@Missbsresources
Laws of Indices
Danielle Bartram
@Missbsresources
Inequality Notation 1
Danielle Bartram
@Missbsresources
Inequality Notation 2
Danielle Bartram
@Missbsresources
Solving Inequalities
Danielle Bartram
@Missbsresources
Bounds nearest unit
Danielle Bartram
@Missbsresources
Bounds nearest (1dp)
Danielle Bartram
@Missbsresources
Bounds nearest (1dp)
Danielle Bartram
@Missbsresources
Bounds Area
Danielle Bartram
@Missbsresources
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Contents
Number
Topic
Contributor
Simplifying Fractions
Peter Hall
@MathsAST
Simplifying Fractions
Peter Hall
@MathsAST
Calculate missing numerator
Peter Hall
@MathsAST
Calculate missing numerator
Peter Hall
@MathsAST
www.missbsresources.com
Contents
Geometry
Topic
Contributor
Area and Perimeter (ππ2 ππππ)
Danielle Bartram
@Missbsresources
Area and Perimeter half squares (ππ2 ππππ)
Danielle Bartram
@Missbsresources
Area of a Triangle
Danielle Bartram
@Missbsresources
Area of a Parallelogram
Danielle Bartram
@Missbsresources
Area of a Trapezium
Danielle Bartram
@Missbsresources
Parts of a Circle
Danielle Bartram
@Missbsresources
Circumference of a Circle
Danielle Bartram
@Missbsresources
Area of a Circle
Danielle Bartram
@Missbsresources
Arc Length
Danielle Bartram
@Missbsresources
Area of a Sector 1
Danielle Bartram
@Missbsresources
Area of a Sector 2
Danielle Bartram
@Missbsresources
Perimeter of Rectilinear Shapes
Danielle Bartram
@Missbsresources
Area of Rectilinear Shapes
Danielle Bartram
@Missbsresources
Area of Compound Shapes
Danielle Bartram
@Missbsresources
Volume β Counting Cubes
Danielle Bartram
@Missbsresources
Volume β Cuboid
Danielle Bartram
@Missbsresources
Volume β Triangular Prism
Danielle Bartram
@Missbsresources
Volume β Cylinder
Danielle Bartram
@Missbsresources
Volume β Hemisphere
Danielle Bartram
@Missbsresources
Volume β Sphere/Cone (Ice Cream)
Danielle Bartram
@Missbsresources
Dimensions
Danielle Bartram
@Missbsresources
Surface Area β Cuboid
Danielle Bartram
@Missbsresources
Surface Area β Cylinder
Danielle Bartram
@Missbsresources
Pythagoras β Identify Hypotenuse
Danielle Bartram
@Missbsresources
Pythagoras β Missing Hypotenuse 1
Danielle Bartram
@Missbsresources
Pythagoras β Missing Hypotenuse 2
Danielle Bartram
@Missbsresources
Pythagoras β Missing Short Side
Danielle Bartram
@Missbsresources
Pythagoras β 3D Cuboid
Danielle Bartram
@Missbsresources
Pythagoras β Isosceles Triangle
Danielle Bartram
@Missbsresources
Danielle Bartram
@Missbsresources
Trigonometry β 3D Square-based pyramid
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Contents
Geometry
Topic
Contributor
Missing Angle inside a Triangle
Peter Hall
@MathsAST
Peter Hall
@MathsAST
Missing Angle on a Straight Line
Peter Hall
@MathsAST
Missing Angle around a point
Peter Hall
@MathsAST
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Contents
Algebra
Topic
Contributor
Sequences β Worded Rule
Caroline Beale
@cbeale83
Sequences β Missing Number
Caroline Beale
@cbeale83
Sequences β Finding term numbers
from given rule.
Caroline Beale
@cbeale83
Sequences β Geometric and Arithmetic
Caroline Beale
@cbeale83
Sequences β nth term rule
Caroline Beale
@cbeale83
Danielle Bartram
@Missbsresources
Forming an expression (multiply/divide)
Danielle Bartram
@Missbsresources
Simplifying Expressions
Danielle Bartram
@Missbsresources
Expanding single brackets
Danielle Bartram
@Missbsresources
Expand and Simplify single brackets
Danielle Bartram
@Missbsresources
Expanding Single brackets
Danielle Bartram
@Missbsresources
Expanding double brackets
Danielle Bartram
@Missbsresources
Expanding double brackets
Danielle Bartram
@Missbsresources
Factorising Single Brackets (HCF)
Danielle Bartram
@Missbsresources
Factorising Single Brackets (Division)
Danielle Bartram
@Missbsresources
Factorising Single Bracket (Variable)
Danielle Bartram
@Missbsresources
Factorising double brackets
Danielle Bartram
@Missbsresources
Algebraic Fractions - Multiply
Danielle Bartram
@Missbsresources
Danielle Bartram
@Missbsresources
Algebraic Fractions - Factorise
Danielle Bartram
@Missbsresources
Substitute into an Expression
Danielle Bartram
@Missbsresources
Substitute into worded formula
Danielle Bartram
@Missbsresources
Substitute and reverse worded formula
Danielle Bartram
@Missbsresources
with a coefficient.
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Contents
Algebra
Topic
Contributor
Substitute into science formula
Danielle Bartram
@Missbsresources
Deduce possible variables.
Danielle Bartram
@Missbsresources
Write a formula in words
Danielle Bartram
@Missbsresources
Substitute into scientific formula
Danielle Bartram
@Missbsresources
Form and solve Equations
Perimeter
Danielle Bartram
@Missbsresources
Form and solve Equations
Simple Functional
Danielle Bartram
@Missbsresources
Form and solve Equations
I think of a numberβ¦
Danielle Bartram
@Missbsresources
Form and solve Equations
Rectangles have same Area.
Danielle Bartram
@Missbsresources
Solving one-step equations
Danielle Bartram
@Missbsresources
Solving one-step equations
Multiply/Divide
Danielle Bartram
@Missbsresources
Solving two-step equations
Danielle Bartram
@Missbsresources
Solving two-step equations
With Brackets
Danielle Bartram
@Missbsresources
Solve Equations
Unknowns on both sides
Danielle Bartram
@Missbsresources
Solve Equations
Unknowns on both sides
Danielle Bartram
@Missbsresources
Solve Equations with bracket
Unknowns on both sides
Danielle Bartram
@Missbsresources
Solve Equations with brackets
Unknowns on both sides
Danielle Bartram
@Missbsresources
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Contents
Algebra
Topic
Contributor
Solving Inequalities
Unknowns on both sides
Danielle Bartram
@Missbsresources
Represent the solution set
Danielle Bartram
@Missbsresources
Solving Inequalities with brackets
Unknowns on both sides
Danielle Bartram
@Missbsresources
Danielle Bartram
@Missbsresources
Simultaneous Equations
Multiply both
Danielle Bartram
@Missbsresources
Simultaneous Equations
Worded
Danielle Bartram
@Missbsresources
Trial and improvement
Danielle Bartram
@Missbsresources
Change the subject β simple
Danielle Bartram
@Missbsresources
Change the subject
Square and Square Root
Danielle Bartram
@Missbsresources
Change the subject
Factorise
Danielle Bartram
@Missbsresources
Danielle Bartram
@Missbsresources
Danielle Bartram
@Missbsresources
Danielle Bartram
@Missbsresources
Mid Point of Coordinates
Danielle Bartram
@Missbsresources
Identify the rule of a line
Danielle Bartram
@Missbsresources
Plotting rules of a line
Danielle Bartram
@Missbsresources
Plotting straight line graphs
Danielle Bartram
@Missbsresources
Identifying graphs and features
Danielle Bartram
@Missbsresources
Danielle Bartram
@Missbsresources
Equation of a line.
Danielle Bartram
@Missbsresources
Identifying parallel lines
from an equation
Danielle Bartram
@Missbsresources
Danielle Bartram
@Missbsresources
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Contents
Algebra
Topic
Contributor
Equation of line parallel when
given coordinate
Danielle Bartram
@Missbsresources
Equations of perpendicular lines
Danielle Bartram
@Missbsresources
reciprocal and exponential graphs
Danielle Bartram
@Missbsresources
Plotting exponential graphs
Danielle Bartram
@Missbsresources
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Contents
Data Handling
Topic
Contributor
www.missbsresources.com
Contents
Algebra
Topic
Contributor
www.missbsresources.com
Contents
Problem Solving
and Functional
Topic
Contributor
www.missbsresources.com
Number
Multiplication
Calculate 273 x 4
Calculate 247 x 3
×
4
800
70
3
Calculate 247 × 3
Calculate 273 × 4
2 7
3
1
4
×
2
Complete the
multiplication and
(carried) numbers.
Calculate 354 × 27
×
Calculate 634 × 52
20
300
2100
1000
4
Calculate 354 × 27
3 5
4
2
7
2 4 7
8
0
×
+
Calculate 634 × 52
Complete the
multiplication and
(carried) numbers.
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Number
Multiplication
Calculate 3.9 × 100
Th
Calculate 2.7 × 1000
H T U . 1
10
3
3
. 9
Calculate 0.97 × 100
.
Fill in the gaps. Calculate 15 × 0.6
9 x 0.3
Show all working out.
9 x 3 = 27
1dp in the question, so 1dp in
Calculate 0.15 × 0.6
9 x 0.3 = 2.7
Show all working out.
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Number
Division
The school minibus seats 14 children. 60
children need to go to the cricket tournament.
How many times must the bus make the trip.
60 ÷ 14 =
14
14
14
14
?
The school minibus seats 14 children. 365
children need to go to the cricket tournament.
How many times must the bus make the trip.
365 ÷ 14 =
50 people are going to a meeting in the
school hall. We need chocolate brownies for
everyone but they come in packs of 6.
How many packs do we need to buy?
359 people are going to a meeting in the
school hall. We need chocolate brownies for
everyone but they come in packs of 6.
How many packs do we need to buy?
14
Calculate 518 ÷ 0.7
Calculate 245 ÷ 0.4
Show all working out.
Show all working out.
0.7 518
7 5180
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Number
Subtraction
Work out the following.
4
+3
+
3
1
6
8
Subtraction
7
5
β
5
3
8
2
4
7
2
6
5
6
8
5
7
2
4
7
Work out the following.
4
+3
1
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2
6
4
7
5
5
7
2
4
7
Number
Directed Numbers
How much
Factor 1
is this?
+ + +
-
2
1
0
Factor 2
+
+
--
--
--
+
+
--
Product
Overnight, the temperature
dropped from 2 ºC to -4 ºC.
By how many degrees did the
temperature fall?
-1
-2
+4 β +3 =
+4 β β3 =
+4 + β3 =
β 4 β +3 =
β 4 β β3 =
β 4 + β3 =
+5 × +3 =
β5 × +3 =
β5 × β3 =
+6 ÷ β2 =
β6 ÷ β2 =
One day the level of the water in a
river was 8cm above its average level.
One week later it was 6cm below its
average level.
How far did the water level drop in
the week?
-3
-4
1
0
-1
-2
-3
-4
-5
The table shows the temperatures
in four cities. Calculate the
difference between he highest and
lowest temperature.
Highest:
London
0π πΆ
Lowest:
π
Moscow
β9 πΆ
Difference:
Paris
6π πΆ
Berlin
At 7am, Joe recorded the temperature in his
garden as being β4°C. He went back outside
at 1pm and found that the temperature had
increased by 12°C. What was the
temperature at 1pm?
β3π πΆ
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Number
Place Value
Place the decimals in ascending order.
Units
.
1
10
1
100
1
1000
0
.
4
5
0
.
0
0
4
0
.
4
0
5
0
.
5
Place the decimals in ascending order.
0.602, 0.26, 6.02, 0.026, 0.06, 0.6
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Number
Rounding
73
70
73 rounded to the nearest ten is 70,
because 73 is closer to 70 than to 80.
76
80
1) Round 148 miles to the nearest
hundred miles.
2) To the nearest 10p how much is
in Sianβs purse?
76 goes up to 80, because 76 is closer
to ____ than to _____.
3.9 + 4.1
7
1.14285714
Round to 2
significant figures.
Calculate
11.7β3.1
9.6β2.4
Write down the full calculator display.
Round to 3 significant figures.
Place holder
9.83β1.622
Calculate
23.8β4.47×5.12
Calculate
Work out the numerator:
8.95+ 7,84
2.03×1.49
Write down the full calculator display.
Work out the denominator:
Write down the full calculator display.
Round the following numbers
to 3 significant figures.
Third
1)
significant
figure Place
holder
2)
35260
2.347
Correct to 3 significant figures.
Round the following numbers
to 3 significant figures.
1)
2)
3)
4)
3568
42062
0.024537
0.0034078
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Number
Fractions
Simplify
14
21
Simplify
Calculate the HCF of 14 and 21.
Factors of 14 Factors of 21
1 x 14
2x7
HCF =
To simplify divide the numerator and
_____________ of the fraction by the HCF.
Simplify
14
28
1 x 14
2x7
π)
=
To simplify divide the numerator and
_____________ of the fraction by the HCF.
Find the missing value
πππ€ π·ππππππππ‘ππ
πππ π·ππππππππ‘ππ
ππππππ =
30
=
Find the missing value
ππππππ =
πππ€ π·ππππππππ‘ππ
πππ π·ππππππππ‘ππ
ππππππ =
9
π)
15
Simplify
Calculate the HCF of 14 and 28.
Factors of 14 Factors of 28
HCF
ππππππ =
12
π)
18
30
=
×
24
π)
30
Find the missing value
2 ??
=
5 30
×
3 ??
π)
=
5 15
π)
4 ??
=
5 60
Find the missing value
×
2 ??
=
5 30
×
42
56
3 ??
π) =
8 48
4 ??
π) =
7 28
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Number
Indices
Fill in the missing gaps.
34 × 37 = 3
29 ÷ 25 = 2
2β1
1
=
2
=3
58 × 56 = _________
=2
79 × 7β3 = _________
412 ÷ 43 = _________
6β1 = _________
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Number
Inequalities
Match the inequality notation with the
correct definition.
<
Less than or equal to
β₯
β€
Greater than
Greater than or equal to
>
Less than
Match the inequality notation with the
correct definition.
β₯
Greater than
<
Less than or equal to
β€
Less than
>
Greater than or equal to
Find the maximum and minimum
values for π₯ when 15 < 5π₯ < 20.
What is the largest and smallest value
π₯ can be?
Minimum
Maximum
a) β5 < π₯ β€ 2
b)β3 β€ π₯ β€ 0
c) β9 < π₯ < β1
What is the largest and smallest value
π₯ can be?
Minimum
Maximum
a) β4 < π₯ β€ 3
b)β5 β€ π₯ < 0
c) β8 < π₯ < β1
Find the maximum and minimum values
for π₯ when 20 < 4π₯ < 56.
15 < 5π₯ < 20
3< π₯ <4
Minimum: _______
Minimum: _______
Maximum: _______
Maximum: _______
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Number
Bounds
Lower Bound
21.5m
Upper Bound
22.5m
Amjadβs height is given as 162cm,
correct to the nearest cm. Between
lie?
A fence is
m long to the
nearest metre.
Lower Bound
£1.55
Upper Bound
£1.65
A box is 8.5cm wide measured to
the nearest tenth of a cm. What
are the upper and lower bounds?
A Krispy Crème doughnut
costs £
to the nearest
10p.
Lower Bound
£1.45
Upper Bound
£1.55
A box is 10.6cm wide measured to
the nearest tenth of a cm. What
are the upper and lower bounds?
A Krispy Crème doughnut
costs £
to the nearest
10p.
A rectangle has a length of 20cm and height of
30cm to the nearest 10cm. What is the
maximum and minimum area of the rectangle?
Minimum
Length
Width
Area
The dimensions of a piece of carpet are given as
127cm x 68cm. Both lengths are correct to the
nearest cm. Between what limits does the area of the
carpet lie?
Maximum
25cm
25cm
875ππ2
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Geometry
Area and Perimeter
Complete the sentences
Area is the _____ of a shape.
Find the area and perimeter of the
Perimeter is the ________ of
a shape.
Complete the sentences
Count the _________ to find
the area.
Find the area and perimeter of this
shape.
Count the _________ to find
the perimeter.
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Geometry
Area and Perimeter
Calculate the area of the triangle.
Calculate the area of the triangle.
8 ππ
6 ππ
π
Area=______ππ
11 ππ
1
2
Area = × πππ π × βπππβπ‘
5 ππ
Area=__________
Calculate the area of the parallelogram.
8 ππ
A right angled triangle is translated to
the position shown to make a rectangles.
The formula for the area of a parallelogram
is the _________ as a rectangle.
Half the _____ of the
parallel sides.
________ the distance
between them.
That is how you calculate,
area of a ___________.
11ππ
Calculate the area of the trapezium.
6 ππ
5 ππ
10 ππ
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Geometry
Circles
Match the key terms to the diagrams.
Complete the sentences
diameter.
Diameter
Circumference
The diameter is _______ the
Calculate the circumference of the circle. Calculate the circumference of the circle
10 ππ
Diameter=
12 ππ
Circumference= ππ
Circumference= π × diameter
Circumference=______πm
Circumference=______
Calculate the area of the circle.
Calculate the area of the circle.
3ππ Diameter=
4 ππ
Area = ππ 2
Area = π × πππππ’π  × πππππ’π
Area = π × 3 ×
Area =______πππ
Area =______
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Geometry
Circles
The formula for circumference in
Calculate the arc lengths.
A
The expression for arc length is
B
Calculate the arc length AB.
360
× 2 × π × 10
The formula for the area of a
circle is
Calculate the area of the sectors.
A
The formula for the area of a
sector is
B
Calculate the area of the sector.
360
× π × 10
2
The formula for the area of a
circle is
A
The formula for the area of a
sector is
B
Calculate the area of the sector.
× π × 10
2
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Geometry
Area and Perimeter
Find the perimeter of the shape.
Not to scale.
b
Not to scale.
Length a = 15 -6
=____
Length b = 11 =____
Perimeter=_____cm
Perimeter=______
12 ππ
11 ππ
5 ππ Find the area of the shape.
14 ππ
15 ππ
Not to scale.
6 ππ
6 ππ
b
Area a = 5 ×
=____
Area b = 6 × 11
=____
Find the area of the shape.
7 ππ
Not to scale.
a
6 ππ
6 ππ
15 ππ
a
Find the perimeter of the shape.
7 ππ
14 ππ
5 ππ
Area=____πππ
11 ππ
12 ππ
Calculate the total area.
Calculate the total area.
The formula for area of a circle is_______
Area A = ___ x ___ =______ππ2
B
20 cm
5 cm
A
π_____2
Diagram not drawn accurately.
10 cm
ππ 2
Area B =
=
=_____ππ2
2
2
Total area= Area A + Area B
= _____+______
=________ππ2
10 cm
Diagram not
drawn accurately.
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Area=______
Geometry
Volume
Find the volume of the solid prism.
Here is a solid prism made from centimetre
cubes.
Volume:_____πππ
Find the volume of the solid prism.
Calculate the volume of the cuboid.
Calculate the volume of the cuboid.
4 ππ
4 ππ
Volume = length × width × height
3ππ
7ππ
Volume=______πππ
Volume=______
CSA is an abbreviation for cross sectional ________.
Calculate the volume of the cylinder.
5 cm
CSA =
4 ×____
2
4 cm
4 cm
6 cm
5 cm
Volume = CSA x
5 cm
Volume = ____ x 10
= _____ππ3
Find the volume of the cylinder.
4cm
10cm
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Geometry
Volume
Calculate the surface area of the
sphere.
2
SA=4ππ
Calculate the surface area of the sphere
hemisphere with a radius of 8cm.
8cm
10cm
Calculate the volume of this
strawberry ice cream and cone.
Clearly show all working out.
The formula for the volume of a sphere
is
The formula for the volume of a cone is
Area is measured in units
_______, because it has ____
dimensions.
a, b and c are representations of lengths.
Which expressions represent volume?
π2 π
Volume is measured in units
_______, because it has ____
dimensions.
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π(π2 + π)
2πππ
4ππ3
Geometry
Surface Area
Surface area is the area of each face
Sketch a net of the prism before calculating the
Write the
dimensions.
A
3cm
B
C
C
4cm
A
B
A
dimensions on the
net.
3cm
Calculate the surface area of the cuboid.
4cm
Diagram not
drawn accurately.
C
B
What is the completed formula for the surface area
of a cylinder?
Find the surface area of the cylinder.
ππ 2
β
Circumference = π × ππππππ‘ππ
4cm
ππ· × β
10cm
ππ 2
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Geometry
Pythagoras
Accurately label the hypotenuse
with a C on each of these triangles.
Pythagorasβ theorem is
+
=
The hypotenuse is the
___________ side. It is also the
side opposite the ________ angle.
Pythagorasβ theorem is
+
=
π = 4
2
+3
Pythagorasβ theorem is
+
=
π = 4
2
+3
Calculate the missing lengths.
(Clearly show all working out)
2
12cm
π 2 = 16 + 9 =
π = 25 β¦ =
To find the length of a shorter side in a right-angled
triangle we rearrange Pythagorasβ theorem.
π
Pythagorasβ theorem is
=
π =
π
2
2
β
2
β
2
Calculate the missing lengths of the shorter
sides. (Clearly show all working out)
π§
π
4.2 cm
2
π€
9cm
π2 = 9
π2 =
π₯
12 cm
2
+
π₯
6cm
π2 = 9
π2 = 16
π€
8cm
π 2 = 16 + 9 =
π = 25 β¦ =
π2 = 16
7 cm
2
10 cm
2
Calculate the missing hypotenuse lengths.
(Clearly show all working out)
π¦
12 cm
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Geometry
Pythagoras and Trigonometry Problems
Pythagorasβ theorem is
Second diagonal
+
Calculate the length of the line segment AF.
=
2cm
Remember to find a
logical order to
3cm
6cm
First diagonal
What is the formula for area of a
triangle?
Calculate the are of the triangle.
16 cm
πππ π =
π‘πππ =
Calculate the angle between the length AE and the
base ABCD in the pyramid pictured below, giving
Opposite
Remember
πππ
π πππ =
βπ¦π
π
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Geometry
Missing Angles
Find the missing angle
The angles in a triangle add up
to _________.
Find the missing angle
The angles on a straight line
The angles around a point add
up to _________.
Find the missing
angle
Find the missing
angle
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Algebra
Sequences
Match the sequence to its rule
Write down the next three terms
Fill in the blanks
Fill in the blanks
Mark each sequence with A (arithmetic)
or G (Geometric)
Write down the formula for the nth term of
these sequences
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Algebra
Notation & Expressions
Fill in the blanks from the word bank below to
complete the sentences.
Six
Match each statement to the correct
expression.
π+3
Subtract
a from 3
πβ3
Subtract
The expression π + 5 means we
five to π.
3 to a
The expression π β 5 means we
five to π.
The expression 6 β π means we subtract
a from
.
Fill in the blanks from the expression bank
below to complete the sentences.
c÷7
π×π
7×π
The expression π means
.
The expression 7π means
.
π
The expression means
.
7
When simplifying expressions
we collect like terms together.
For example
1) π‘ + π‘ + + +
= 5t
= 5π‘
Multiply
b by 3
Divide
b by 3
Multiply b
by itself
Simplify the following
1) π + π + π + π =
2) 7π₯ β 2π₯ =
3) 3 × 5π =
4) 3π₯ + 4π¦ β π₯ + 2π¦ =
3) 8 ×
3βπ
Match each statement to the correct
expression.
π2
2
2) 2π‘+
Subtract
3 from a
3
π = 16π
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3
π
3π
π
3
Algebra
Expansion
Expand the following brackets.
Expand means you need to
___________ out the brackets.
1) 3 π₯ + 5
πΈπ₯ππππ 2(π₯ + 3)
Use the method your teacher has taught.
π
2 π₯+3
= 2π₯
+π
2) 2 3π¦ β 4
2
=
3) π₯ π₯ + 2
Expand and simplify
Expand and simplify
1) 2 π₯ β 5 + 4 π₯ + 2
4 π₯β5 β3 π₯+7
Expand each
bracket first.
= 4π₯ β 20 β 3π₯
=π₯
2) 5 π₯ + 3 β 2(π₯ β 4)
Simplify by
collecting like
terms
together.
What does the word expand in
mathematics mean you need to do?
Expand
1) 3 π₯ + 2
2) 4(π₯ β 3)
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Algebra
Expansion
Expand and simplify:
Expand π₯ + 4 π₯ β 7
×
π₯
π₯
β7
a) ( x + 4 )( x + 9 )
β7π₯
b) ( x + 3 )( x β 5 )
+4
=
π₯2
c) ( 3x + 4 )( x β-2 )
β7π₯
=
First Outside Inside Last
Expand and simplify:
(2π₯ + 5)(4π₯ β 3)
a) ( 2x + 1 )( x + 3 )
β6π₯
b) ( 5x β 3 )( x β 5 )
=
= 8π₯ 2
c) ( 3x + 5 )
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2
Algebra
Factorisation
Factorise the following expression:
12 a + 8
Find the numerical highest common factor
between each term(12 and 8) = 4
4(3a + 2)
12 a + 8
4 goes outside
the bracket
4 x 3a = 12a and 4 x 2 = 8
Factorise the following expression:
12 a + 18
Find the numerical highest common factor
between each term(12 and 18) =
Factorise fully:
a) 6b β 9
b) 36 β 6c
c) 27a β 18b β 9c
Factorise fully:
a) 4b β 12
b) 24 β 6c
6 12π + 18
c) 14a β 21b +7c
So
(
+
)
Factorise the following expression:
4π2 + 8π
Factorise fully:
a) 3π2 + 2π
×π×
+
×2×
b) 10π + 15π 2
So
4a(
+
)
c) 12ππ 2 + 18π
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Algebra
Factorisation
Factorise
2
π₯ + π₯ β 12
What factor pairs
Times to make
multiply to make -12
End
= ( π₯+ )( π₯β )
Middle
Be careful of the signs.
Factorise
1) π₯ 2 β 8π₯ + 15
2) π₯ 2 β 3π₯ β 18
3) 2π₯ 2 + 10π₯ + 8
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Algebra
Algebraic Fractions
Express
3
π₯+4
×
2π₯+5
2
as a single fraction.
3 2x + 5
=
2 x+4
=
Express
2
π₯β7
×
3π₯+6
4
as a single fraction.
When multiplying
expressions, watch
out for expanding
brackets.
3 2x + 5
2 x+4
Express
2
π₯β2
+
3
π₯+5
as a single fraction.
Express
3
π₯+6
+
4
π₯β8
as a single fraction.
2 π₯+5 +3
β
+
π₯β2
Expand
Simplify
Simplify fully
π₯+
=
π₯+
π₯+
=
π₯β
π₯ 2 +3π₯+2
π₯ 2 βπ₯β6
π₯+
π₯β
Simplify fully
Factorise the
numerator and
denominator.
Simplify
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π₯ 2 β7π₯β8
π₯ 2 +5π₯+4
Algebra
Substitution
Evaluate the following expressions
when π = π πππ π = π
1) 2π₯ + π¦ =
π2 = π ×
3π 2 =
×
×
If π = 3 what is the value of
4π2 = 4 × 3 ×
=
2) 2π¦ 2 =
3) 2π₯ 2 β 2π¦ =
Use this rule to work out the total cost
of hiring a bouncy castle.
πππ‘ππ πππ π‘ = £10 πππ βππ’π πππ’π  £15
Michelle hires a bouncy castle for 6 hours.
πππ‘ππ πππ π‘ = £10 ×
πππ‘ππ πππ π‘ =
Use this rule to work out the total cost
of a taxis journey.
πππ‘ππ πππ π‘ = £3 πππ ππππ πππ’π  £2
Maria travels 5 miles in a taxis. Work
out the total cost.
+ £15
+ £15
πππ‘ππ πππ π‘ =
The total cost is £125, how many hours did
Adam hire the bouncy castle for?.
πππ‘ππ πππ π‘ = £10 πππ βππ’π πππ’π  £15
Cost
× 10
+15
Hire
Cost
÷ 10
β15
Hire
The total cost of a taxis journey is £23.
How many miles did Abdul drive?
πππ‘ππ πππ π‘ = £3 πππ ππππ πππ’π  £2
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Algebra
Formulae
When we follow a rule we substitute the terms
with the corresponding values.
The rule is
Power = Voltage × Current
If the voltage is 12 volts and
the current is 5 amperes.
What the is the power in watts?
Aiman wants to calculate the
momentum of a curling stone.
The stone had a mass of 8kg
and velocity of 3 m/s.
Use the rule below to
calculate the momentum.
Momentum = Mass × Velocity
Power = 12 ×
=
watts
π + π = 15
πβπ =8
c & d could be π = ππ and π = π
because ππ + π = ππ
Write down two different pairs of
π = ______ and d = ______
Write down two different pairs of
π = ______ and π = ______
π = ______ and π = ______
π = ______ and π = ______
A taxis cost £5 for each mile that
it travels. Write this as a formula.
Cost =
It costs £10 per hour to rent a
bouncy castle. Express this as a
formula.
×
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Algebra
Formulae
Find the value of s when
π = 3, π‘ = 2 πππ π’ = 4
1
π  = π’π‘ + ππ‘ 2
2
1
π =π’×
+ ×
× π‘2
2
1
π  = 4×
+ ×
× 22
2
Find the value of s when
π = 2, π‘ = 5 πππ π’ = 3
1
π  = π’π‘ + ππ‘ 2
2
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Algebra
Forming Equations
Write down an expression for the
perimeter of this shape.
Write down an expression for the
perimeter of this shape.
2π₯
then collect like terms.
3π₯ + 2
π₯+4
The perimeter=26cm what is the value of π₯?
= 26
The perimeter=54cm what is the value of π₯?
Solve for π₯.
Iqbal has 17 pencils all together.
He has a box of pencils and 5 extra
pencils.
Emily has a 20 sweets all together.
She has two bags of sweets.
Write this as an equation.
Write this as an equation.
How many pencils are in the box?
I think of a number
I multiply it by 5
and then subtract 6.
n
5n
5n
How many sweets are in a bag?
Julie thinks of a number. She multiplies
it by 4 and adds 16. The result is also six
times as big as the number.
What is the number?
The result is also two times the
number Iβm thinking.
The equation is
What is the number?
π₯+5
6
Both rectangles have the same area.
What is the value of the missing length?
5
2π₯ β 4
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Algebra
Solving Equations
Solve the equations
Solve the equations
π+5=9
π‘ + 12 = 15
Solve the equations
5π¦ = 15
2π€ = 14
πβ8=7
Solve the equations
π
=4
5
π€
=6
2
Solve
2π₯ + 8 = 22
Solve
3π₯ + 5 = 23
π β 11 = 14
5π₯ β 3 = 17
3π₯ =
π₯=
Solve 2 π₯ + 5 = 24
+
Solve
3 π₯ + 4 = 27
= 24
2π₯ =
π₯=
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Algebra
Solving Equations
Solve the equation
3π‘ β 9 = 5π‘ β 17
β3π‘
β3π‘
β9 = 2π‘ + 17
Solve the equation
5π‘ + 12 = 7π‘ + 8
Solve the following equation
Solve the following equation
3π‘ β 8 = 5π‘ + 20
β3π‘
β3π‘
2π‘ β 6 = 6π‘ + 12
β8 = 2π‘ + 20
Solve the following equation
Solve the following equation
2 π₯ + 2 = 6π₯ β 8
3 π₯ + 2 = 4π₯ β 7
Expand
3π₯ + 6 =
Solve the following equation
Solve the following equation
3 π₯ β 4 = 5(π₯ + 7)
Expand
3π₯ β 12 =
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5 π₯ β 7 = 4(2π₯ β 3)
Algebra
Solving Inequalities
Solve
6π₯ + 5 β₯ 4π₯ β 11
Solve
4π₯ + 15 < 8π₯ β 16
β₯
β₯
β₯
Represent the following solution sets on a number line.
π₯>5
2π₯ + 4 < 10
π₯ β€ β4
Expand
1) 3 π₯ + 5
Solve the following and
represent the solution set on a
number line.
4 3π₯ β 5 > 2π₯ β 35
2) 2(3π₯ β 5)
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Algebra
Factorise π₯ 2 β 2π₯ β 15
(π₯
)(π₯
Solve π₯ 2 + 4π₯ β 21 = 0
)
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Algebra
Simultaneous Equations
Solve 3π₯ + 2π¦ = 4
4π₯ + 5π¦ = 17
Aim to get one
coefficient value
the same.
1000 tickets were sold. Adult tickets cost £8.50, children's
cost £4.50, and a total of £7300 was collected. How many
tickets of each kind were sold?
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Algebra
Trial and Improvement
The equation π₯ 3 + 3π₯ = 4
Has solutions between 3 and 4.
π₯
Output
The equation π₯ 3 β 6π₯ = 72
Has solutions between 4 and 5.
Big/Small
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Algebra
Change the Subject
To rearrange equations you follow
the reverse order of operations.
Rearrange these formulae to make m the
subject.
Make π₯ the subject
1) π = π β 4
π§ = 5π₯ β 3
2) q = 7π + 5
+3
π¦=π₯+4
β4
π§ + 3 = 5π₯
÷5
β4
π§+3
π¦
=π₯
So π₯ =
=π₯
Make π₯ the subject of the formula.
Make π₯ the subject of the formula.
π¦ = 4π₯ + π§
π¦=
The opposite to the square root is to
_____________ a number.
4π₯
5
π¦ 2 = 4π₯ + z
Rearrange to make π₯ the subject of the formula
Rearrange to make π₯ the subject of the formula
3 π₯ β π‘ = π§(π β π₯)
= π§π β π§π₯
Factorise
3π₯ + π§π₯ = π§π + 3π‘
p π¦ + π₯ = π‘(π€ β ππ₯)
Expand
Rearrange
(3 + π§) = π§π + 3π‘
Rearrange
π₯=
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Algebra
Coordinates
Plot the missing coordinate to make a square.
What is the coordinate? _______
When plotting coordinates we
need to remember the rhyme .
Plot the missing coordinate to make a
rectangle.
What is the coordinate? _______
Plot the coordinates
A (3,4) B (2,5) C (0, 3) D (4,0)
Along the
____________ and
up the ___________.
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Algebra
Coordinates
Write down the coordinates of the points
1) A _________
B
2) B _________
(-3, 2)
3) C _________
A
Plot and label the following coordinates
4) D (0, 5)
5) E (β2, 4)
6) F (β3, β4)
7) G (5, β6)
C
(3, -3)
(-4, -6)
What is the midpoint between these
pairs of numbers?
Here are a set of coordinates
A (0, 4) B (4, 8) C (-2, 1) D (3, -4)
(Midpoint means halfway between)
4
8
5
10
-6
What is the midpoint of the
coordinates
a) A and B
b) C and B
c) A and D
-2
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Algebra
Line Graphs
B
What do you notice about the 3 points?
What is the equation of the line? π₯ =
C
D
A
What are the equations of the lines
a)
c)
b)
d)
Plot and connect the following coordinates
on the grid. (-2, 5) (1, 5) (3, 5) (6, 5)
What is the equation of the line they make?
Draw and label the lines of
1) π¦ = 4
2) π₯ = 2
3) π¦ = β5
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Algebra
Straight Line Graphs
π = ππ
π = ππ
π
β2 β1
0
1
2
π
β2
4
Complete the table, draw and label the graph.
π = ππ β π
π
β2
β1
π
0
1
β3
Circle the graphs with a positive gradient.
π¦
π¦
a
2
Match the equation with the correct sketches.
π¦
π¦
π¦ = 3π₯ +4
c
π₯
π₯
b
π¦
Circle the graphs with the intercept of 4.
π¦
π¦
a
π₯
2
π₯
π¦ = βπ₯ β1
π¦
c
4
-2
π₯
π₯
4
π₯
b
-4
4
Identify the gradient (m) and intercept (c)
of these equations.
1) π¦ = 3π₯ β 5
Intercept =
2) π¦ = β2π₯ + 6
Intercept =
π₯
π¦ = 2π₯ β4
π¦
π₯
π¦
π₯
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π¦ = β2π₯ +5
Algebra
Graphs
Complete the table, draw and label the graphs
π = ππ
π
β2
β1
π
0
1
1
2
3
4
π = ππ β π
π
β2
β1
π
0
1
β5
2
β1
π = ππ β ππ β π
π
β2
π
5
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β1
0
β3
1
2
β3
3
Algebra
Equations of a Line
The equation of a straight line is
normally in the form.
π¦=
What is the gradient of the equations?
a) 2π¦ = 8π₯ + 10
π₯+
If I have 2 lots of an equation I
need to divide the equation by 2.
b) 4π¦ = 12π₯ β 20
2π¦ = 6π₯ β 8
÷π
÷π
π¦=
π₯β4
What is the same when lines are parallel?
Which of these lines are parallel?
A
C
π¦ = 3π₯ + 2
B
4π¦ = 12π₯ β 20
3π¦ = 12π₯ β 15
E
D
π¦ = 2π₯ β 3
πβππππ ππ π¦
πβππππ ππ π₯
What is the intercept of the graph?
Calculate the gradient of this line.
What is the equation of the line?
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5π¦ β 10π₯ = 20
Algebra
Equation of a Line
When lines are parallel they have the
same ________________.
Calculate the equation of a line parallel to
π¦ = 3π₯ +5, passing through the point (2, 6).
E.g. Calculate the equation of a line parallel to
π¦ = 2π₯ + 4, passing through the point (1,3).
So,
π¦ = 2π₯ + π
Substitute in the
3= 2×1+π
coordinate
values to find c.
3=2+π
1=π
So, y = 2π₯ + 1
When line graphs are perpendicular to
multiply together to make βπ.
Are these pairs of lines perpendicular to
each other? (True or False)
π¦ = 5π₯ + 8
What are the missing numbers?
1) 4 ×
1
2) 3 ×
= β1
= β1
π¦ = β3π₯ + 6
1
π¦= π₯+3
2
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1
π¦=β π₯β3
5
1
π¦ = 3π₯ β
3
π¦ = β2π₯ + 4
T
F
Algebra
Graphs
Match the graphs to the equations.
π¦=3
π
Given that π π₯ is the
graph above math the
following graphs with
the functions.
π¦=π₯
π¦ = π₯3
2
π π₯ +3
π π₯ β3
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π¦=
π π₯+3
1
π₯
π π₯β3
Algebra
Exponential and Reciprocal Graphs
Complete the table of values for π¦ = 0.6
π₯
0
1
π¦
1
0.8
2
3
π₯
Note β the
variable that
changes is the
power
4
0.13
1
Draw the graph π¦ = 0.6
0.8
Use your graph to solve the
equation
0.6
0.6
π₯
= 0.4
0.4
Draw the line π¦ = 0.4,
because π¦ has been
replaced with 0.4 so
π¦ = 0.4
0.2
0
π₯
1
2
3
4
5
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