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Area of Any Triangle Area of Parallelogram Area of Kite & Rhombus Volume of Solids www.mathsrevision.com Area of Trapezium Composite Area Volume & Surface Area Surface Area of a Cylinder Volume of a Cylinder Composite Volume Exam Type Questions

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Sunday, 26 April 2015 2Created by Mr.Lafferty Starter Questions Q1.True or false Q2.Write down the probability of picking out a number greater than 20 in the national lottery. Q3.If a = -3 and b = -4 does Q4.Calculate a 2 – 3b 2 = 57 www.mathsrevision.com

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Sunday, 26 April 2015 3Created by Mr.Lafferty Simple Areas Definition : Area is “ how much space a shape takes up” A few types of special Areas TrapeziumRhombus and kite ParallelogramAny Type of Triangle www.mathsrevision.com

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Sunday, 26 April 2015 4Created by Mr.Lafferty Learning Intention Success Criteria 1.To know the formula for the area of ANY triangle. 1. To develop a formula for the area of ANY triangle. 2.Use the formula to solve problems. 2.Apply formula correctly. (showing working) (showing working) 3.Answer containing appropriate units appropriate units www.mathsrevision.com Any Triangle Area

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Sunday, 26 April 2015 5Created by Mr.Lafferty Any Triangle Area h b Sometimes called the altitude h = vertical height www.mathsrevision.com

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Sunday, 26 April 2015 6Created by Mr.Lafferty Any Triangle Area 6cm 8cm Example 1 : Find the area of the triangle. www.mathsrevision.com

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Sunday, 26 April 2015 7Created by Mr.Lafferty Any Triangle Area 10cm 4cm Example 2 : Find the area of the triangle. Altitude h outside triangle this time. www.mathsrevision.com

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Sunday, 26 April 2015 8Created by Mr.Lafferty Any Triangle Area 5cm 8cm Example 3 : Find the area of the isosceles triangle. www.mathsrevision.com Hint : Use Pythagoras Theorem first ! 4cm

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Sunday, 26 April 2015 Created by Mr. Lafferty @www.mathsrevision.com Now try Ex 2.1 & 2.2 MIA Ch1 (page 6) www.mathsrevision.com Area & Volume 9

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Sunday, 26 April 2015 10Created by Mr.Lafferty Q3.True or false Starter Questions Q1.Find the area of the triangle. Q2.Expand out ( w - 5) (2w 2 + 2w – 5) Q4.Rearrange into the form y = y – 3x + 7 = 0 4cm 3cm www.mathsrevision.com 10cm

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Sunday, 26 April 2015 11Created by Mr.Lafferty Learning Intention Success Criteria 1.To know the formula for the area of a parallelogram. 1. To develop a formula for the area of a parallelogram. 2.Use the formula to solve problems. 2.Apply formula correctly. (showing working) (showing working) 3.Answer containing appropriate units appropriate units www.mathsrevision.com Parallelogram Area

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Sunday, 26 April 2015 12Created by Mr.Lafferty Parallelogram Area b Important NOTE h = vertical height www.mathsrevision.com h

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Sunday, 26 April 2015 13Created by Mr.Lafferty Parallelogram Area Example 1 : Find the area of parallelogram. 9cm 3cm www.mathsrevision.com

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Sunday, 26 April 2015 Created by Mr. Lafferty @www.mathsrevision.com Now try Ex 3.1 MIA Ch1 (page 6) www.mathsrevision.com Area & Volume 14

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Sunday, 26 April 2015 15Created by Mr.Lafferty Starter Questions Q1.True or false 2x 2 – 72 = 2(x – 6)(x + 6) Q2.Does 2.5 + 1.25 x 20 = 27.55 Explain your answer Q3.Expand ( y - 3) (2y 2 + 3y + 2) Q4.Calculate www.mathsrevision.com

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Sunday, 26 April 2015 Created by Mr.Lafferty Learning Intention Success Criteria 1.To know the formula for the area of ANY rhombus and kite. 1. To develop a single formula for the area of ANY rhombus and Kite. 2.Use the formula to solve problems. 2.Apply formulae correctly. (showing working) (showing working) 3.Answer containing appropriate units appropriate units www.mathsrevision.com Rhombus and Kite Area

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Sunday, 26 April 2015 17Created by Mr.Lafferty Area of a Rhombus D d www.mathsrevision.com This part of the rhombus is half of the small rectangle.

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Sunday, 26 April 2015 18Created by Mr.Lafferty Area of a Kite D d Exactly the same process as the rhombus www.mathsrevision.com

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Sunday, 26 April 2015 19Created by Mr.Lafferty Rhombus and Kite Area Example 1 : Find the area of the shapes. 5cm 2cm 9cm 4cm www.mathsrevision.com

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Sunday, 26 April 2015 20Created by Mr.Lafferty Rhombus and Kite Area Example 2 : Find the area of the V – shape kite. 7cm 4cm www.mathsrevision.com

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Sunday, 26 April 2015 Created by Mr. Lafferty @www.mathsrevision.com Now try Ex 4.1 MIA Ch1 (page 8) www.mathsrevision.com Area & Volume 21

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Sunday, 26 April 2015 22Created by Mr.Lafferty Starter Questions Q1.Find the area of the parallelogram Q2.Solve the equation (ie find the root) to 1 dp x 2 + 4x – 3 = 0 Q3.A can of beans is reduce by 15% to 25p. Find the price before the reduction. Q4.The speed of light is 300000000 metres per sec. True or false in scientific notation 3 x 10 8. 7 7 www.mathsrevision.com

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Sunday, 26 April 2015 23Created by Mr.Lafferty Learning Intention Success Criteria 1.To know the formula for the area of a trapezium. 1. To develop a formula for the area of a trapezium. 2.Use the formula to solve problems. 2.Apply formula correctly. (showing working) (showing working) 3.Answer containing appropriate units appropriate units www.mathsrevision.com Trapezium Area

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Sunday, 26 April 2015 24Created by Mr.Lafferty Trapezium Area W X Y Z 1 2 a cm b cm h cm Two triangles WXY and WYZ www.mathsrevision.com

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Sunday, 26 April 2015 25Created by Mr.Lafferty Trapezium Area Example 1 : Find the area of the trapezium. 6cm 4cm 5cm www.mathsrevision.com

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Sunday, 26 April 2015 Created by Mr. Lafferty @www.mathsrevision.com Now try Ex 5.1 MIA Ch1 (page 9) www.mathsrevision.com Area & Volume 26

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Sunday, 26 April 2015 27Created by Mr.Lafferty Starter Questions Q1.Find the area of the trapezium Q2.Explain why the perimeter of the shape is 25.24cm. Q3.y varies directly as the square of x. When y = 25, x = 4 Find the value of y when x = 10 7 9 8 www.mathsrevision.com 30 o r = 10cm

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Sunday, 26 April 2015 28Created by Mr.Lafferty Learning Intention Success Criteria 1.To know the term composite. 1. To show how we can apply basic area formulae to solve more complicated shapes. 2.To apply basic formulae to solve composite shapes. 3.Answer containing appropriate units appropriate units www.mathsrevision.com Composite Areas

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Sunday, 26 April 2015 29Created by Mr.Lafferty Composite Areas We can use our knowledge of the basic areas to work out more complicated shapes. 4cm 3cm 5cm 6cm Example 1 : Find the area of the arrow. www.mathsrevision.com

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Sunday, 26 April 2015 30Created by Mr.Lafferty Composite Areas Example 2 : Find the area of the shaded area. 11cm 10cm 8cm 4cm www.mathsrevision.com

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Sunday, 26 April 2015 Created by Mr. Lafferty @www.mathsrevision.com Now try Ex 6.1 MIA Ch1 (page 11) www.mathsrevision.com Area & Volume 31

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Summary Areas Trapezium Rhombus and kite Parallelogram Any Type of Triangle www.mathsrevision.com

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Sunday, 26 April 2015 Created by Mr. Lafferty @www.mathsrevision.com Now try Ex 6.2 MIA Ch1 (page 12) www.mathsrevision.com Area & Volume 33

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Sunday, 26 April 2015 34Created by Mr.Lafferty Starter Questions Q1.Find the area of the trapezium Q2.Calculate the perimeter of the shape. Q3.w varies inversely as the square of b. When w = 10, b = 2 Find the value of w when b = 10 7 9 8 www.mathsrevision.com 60 o r = 3cm

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Learning Intention Success Criteria 1.To know the volume formula for any prism. 1.To understand the prism formula for calculating volume. 2.Work out volumes for various prisms. 3.Answer to contain appropriate units and working. appropriate units and working. www.mathsrevision.com Volume of Solids Prisms

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www.mathsrevision.com Definition : A prism is a solid shape with uniform cross-section Cylinder (circular Prism) Pentagonal Prism Triangular Prism Hexagonal Prism Volume = Area of Cross section x length Volume of Solids

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www.mathsrevision.com Definition : A prism is a solid shape with uniform cross-section Triangular Prism Volume = Area x length Q. Find the volume the triangular prism. 20cm 2 10cm = 20 x 10 = 200 cm 3 Volume of Solids

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www.mathsrevision.com Definition : A prism is a solid shape with uniform cross-section Volume = Area x length Q. Find the volume the hexagonal prism. 43.2cm 2 20cm = 43.2 x 20 = 864 cm 3 Hexagonal Prism Volume of Solids

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26-Apr-15 Created by Mr. Lafferty Maths Dept. Back Front www.mathsrevision.com This is a NET for the triangular prism. 5 faces 3 congruent rectangles 2 congruent triangles 10cm 4cm Net and Surface Area Triangular Prism 4cm 10cm Bottom 4cm FT BT

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26-Apr-15 Compiled by Mr. Lafferty Maths Dept. = 2 x3 =6cm 2 Example Find the surface area of the right angle prism Working Rectangle 1 Area = l x b = 3 x10 =30cm 2 Rectangle 2 Area = l x b = 4 x 10 =40cm 2 Total Area = 6+6+30+40+50 = 132cm 2 2 triangles the same 1 rectangle 3cm by 10cm 1 rectangle 4cm by 10cm 3cm 4cm 10cm 1 rectangle 5cm by 10cm Triangle Area = Rectangle 3 Area = l x b = 5 x 10 =50cm 2 5cm www.mathsrevision.com

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26-Apr-15 Compiled by Mr. Lafferty Maths Dept. Bottom Top LS Back RS Front www.mathsrevision.com This is a NET for the cuboid Net and Surface Area The Cuboid 6 faces Top and bottom congruent Front and back congruent Left and right congruent 5cm 4cm 3cm 5cm 3cm 4cm 3cm 4cm

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26-Apr-15 Compiled by Mr. Lafferty Maths Dept. Front Area = l x b = 5 x 4 =20cm 2 Example Find the surface area of the cuboid Working 5cm 4cm 3cm Top Area = l x b = 5 x 3 =15cm 2 Side Area = l x b = 3 x 4 =12cm 2 Total Area = 20+20+15+15+12+12 = 94cm 2 Front and back are the same Top and bottom are the same Right and left are the same www.mathsrevision.com

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Now try MIA Ex 7.1 & 7.2 Ch1 (page 14) www.mathsrevision.com Volume of Solids

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Sunday, 26 April 2015 44Created by Mr.Lafferty Q3.True or false Starter Questions Q1.Expand out (x – 2) ( x 2 - 3x + 4) Q2.Factorise x 2 – 2x + 1 Q4.By rearranging in y =, find the gradient and where the straight line crosses the x-axis y + 4x - 3 = 0 www.mathsrevision.com

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Learning Intention Success Criteria 1.To know split up a cylinder. 1.To explain how to calculate the surface area of a cylinder by using basic area. 2.Calculate the surface area of a cylinder. www.mathsrevision.com Surface Area of a Cylinder

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www.mathsrevision.com Total Surface Area = 2πr 2 + 2πrh The surface area of a cylinder is made up of 2 basic shapes can you name them. Curved Area =2πrh Cylinder (circular Prism) h Surface Area of a Cylinder Roll out curve side 2πr Top Area =πr 2 Bottom Area =πr 2

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www.mathsrevision.com Example : Find the surface area of the cylinder below: = 2π(3) 2 + 2π x 3 x 10 3cm Cylinder (circular Prism) 10cm = 18π + 60π Surface Area of a Cylinder Surface Area = 2πr 2 + 2πrh = 78π cm

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www.mathsrevision.com Example : A net of a cylinder is given below. Find the diameter of the tin and the total surface area. 2r = Surface Area of a Cylinder 2πr = 25 25cm 9cm 25 π Diameter = 2r Surface Area = 2πr 2 + 2πrh = 2π(25/2π) 2 + 2π(25/2π) x 9 = 625/2π + 25 x 9 = 324.5 cm

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Now try MIA Ex 8.1 Ch1 (page 16) www.mathsrevision.com Surface Area of a Cylinder

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Sunday, 26 April 2015 50Created by Mr.Lafferty Q3.Calculate Starter Questions Q1.Find the area of the triangle. Q2.Factorise 9x 2 - 64 Q4.Find the gradient and where the straight line crosses the x-axis y – 2x + 5 = 0 6cm www.mathsrevision.com 10cm

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Learning Intention Success Criteria 1.To know formula. 1.To derive the formula for the volume of a cylinder and apply it to solve problems. 2.Apply formula correctly. 3.Work backwards using formula. www.mathsrevision.com Volume of a Cylinder

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www.mathsrevision.com Volume = Area x height The volume of a cylinder can be thought as being a pile of circles laid on top of each other. = πr 2 Volume of a Cylinder Cylinder (circular Prism) x h h = πr 2 h

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www.mathsrevision.com V = πr 2 h Example : Find the volume of the cylinder below. = π(5) 2 x 10 5cm Cylinder (circular Prism) 10cm = 250π cm Volume of a Cylinder

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Other Simple Volumes www.mathsrevision.com Composite volume is simply volumes that are made up from basic volumes. r D r h Cylinder = πr 2 h Cylinder (circular Prism) h r

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Now try MIA Ex 9.1 & 9.2 Ch1 (page 18) www.mathsrevision.com Volume of Solids

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Sunday, 26 April 2015 56Created by Mr.Lafferty Starter Questions Q1.Factorise Q2.Write down the probability of picking out a number less than 30 in the national lottery. Q3.True or false if a = -1 and b = -2 Q4.Explain why -(a 2 ) + b 2 = 5 www.mathsrevision.com

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Learning Intention Success Criteria 1.To know what a composite volume is. 1.To calculate volumes for composite shapes using knowledge from previous sections. 2.Work out composite volumes using previous knowledge of basic prisms. 3.Answer to contain appropriate units and working. appropriate units and working. www.mathsrevision.com Volume of Solids Prisms

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Other Simple Volumes www.mathsrevision.com Composite volume is simply volumes that are made up from basic volumes. r D r h Cylinder = πr 2 h Cylinder (circular Prism) h r

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Volume of a Solid www.mathsrevision.com Q. Find the volume the composite shape. Composite volume is simply volumes that are made up from basic volumes. Volume = Cylinder + half a sphere h = 6m r 2m

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Volume of a Solid www.mathsrevision.com Q. This child’s toy is made from 2 identical cones. Calculate the total volume. Composite Volumes are simply volumes that are made up from basic volumes. Volume = 2 x cone r = 10cm h = 60cm

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Now try MIA Ex 10.1 Ch1 (page 19) www.mathsrevision.com Volume of Solids

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_____(0-10 pts.) Describe how to find the areas of a square, rectangle, triangle, parallelogram, trapezoid, kite and rhombus. Give at least 3 examples.

_____(0-10 pts.) Describe how to find the areas of a square, rectangle, triangle, parallelogram, trapezoid, kite and rhombus. Give at least 3 examples.

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