E3 Revision www.mathsrevision.com Revision Area Revision Weight and Volume Revision Scale Drawings & Angles www.mathsrevision.com Revision Triangular and square numbers Revision Patterns Revision Fractions and %’s and Ratio’s

General Jack’s Carpets Problem… General Jack’s Carpets www.mathsrevision.com How much for this one? ? Only £5 a square metre!

How much for 18 square metres? Problem… 1m 1m = 1 square metre 6 m 6 square metres 3 m 6 square metres 6 square metres www.mathsrevision.com 3 rows of 6 squares = 3 x 6 = 18 square metres 18 x £5 = £90 How much for 18 square metres?

6 3 Area of a rectangle 6 x 3 = 18 m² Area = length x breadth www.mathsrevision.com 6 x 3 = 18 m² Area = length x breadth

Example 1 11 cm 6 cm Area = length x breadth A = l x b A = 11 x 6 A = 66 cm² www.mathsrevision.com Find the area of the rectangle

right-angled triangle Area of a right-angled triangle 4 cm 7 cm www.mathsrevision.com Area of rectangle = l x b = 7 x 4 = 28 cm² Area of triangle = ½ x Area of rectangle = ½ x 28 = 14 cm²

Example 1 10 cm 15 cm Area Δ=½ x base x height AΔ =½ x b x h AΔ = ½ x 15 x 10 10 cm AΔ = 75 cm² www.mathsrevision.com 15 cm Find the area of the triangle

Composite shapes 10 cm 6 cm ? ? www.mathsrevision.com 3 cm 13 cm

Composite shapes www.mathsrevision.com Area (1) = l x b = 10 x 6 10 cm 6 cm (1) 6 cm ? (2) 3 cm www.mathsrevision.com Area (1) = l x b = 10 x 6 = 60 cm² Area (2) = ½ x b x h = ½ x 3 x 6 = 9 cm² Area of shape = (1) + (2) = 60 + 9 = 69 cm²

Example 1 Area (1)= l x b =15 x 8 = 120 cm² Area (2) = l x b =9 x 3 ? 8cm (1) Area (2) = l x b =9 x 3 = 27 cm² (2) Area of shape = (1) + (2) = 120 + 27 ? 9cm = 147 cm² Find the area of the shape

Example 2 Area (1)= l x b =20 x 12 = 240 cm² Area (2) = l x b =10 x 6 Area of shape = (1) – (2) = 240 -60 (1) = 180 cm² Find the area of the shape

Compiled by Mr. Lafferty Maths Dept. Volume of a cuboid 3cm 4cm 6cm 18 cubes fit the base. = 1 centimetre cube = 1 cm³ 4 layers of 18 cubes = 4 x 18 = 72 centimetre cubes = 72 cm³ 20-Sep-18 Compiled by Mr. Lafferty Maths Dept.

Compiled by Mr. Lafferty Maths Dept. A short cut ! 3cm 4cm 6cm height Area of rectangle breadth length Volume = 6 x 3 x 4 = 72 cm³ Volume = length x breadth x height 20-Sep-18 Compiled by Mr. Lafferty Maths Dept.

Compiled by Mr. Lafferty Maths Dept. Example 1 Working Volume = l x b x h V = 18 x 5 x 27 Heilander’s Porridge Oats V = 2430 cm³ 27cm 5 cm 18 cm 20-Sep-18 Compiled by Mr. Lafferty Maths Dept.

Compiled by Mr. Lafferty Maths Dept. Example 2 Working Volume = l x b x h How many of the small cubes fit into the big cuboid. V = 5 x 5 x 5 V = 125 cm³ 5 cm Volume = l x b x h V = 10 x180 x 5 www.mathsrevision.com V = 9000 cm³ 10 cm 5cm 180 cm 9000 ÷ 125 = 72 cubes 20-Sep-18 Compiled by Mr. Lafferty Maths Dept.

Compiled by Mr. Lafferty Maths Dept. Example 2 Working Cube = 2.5g If each cube weighs 2.5g How much does the big cuboid weigh in : (i) Grams (ii) kg (ii) Tonnes Cuboid = 72 x2.5g Weight = 180 g 2.5g = 180 ÷1000 = 0.18Kg www.mathsrevision.com = 0.18 ÷ 1000 = 0.00018T 10cm 5cm 180cm 20-Sep-18 Compiled by Mr. Lafferty Maths Dept.

Scaled Drawings Definition A scale of www.mathsrevision.com 1 cm = 2m This simply means for every 1cm measured on a drawing this represents 2m in real-life. 20-Sep-18 Created by Mr. Lafferty Maths Dept.

Scaled Drawings 4cm www.mathsrevision.com 2cm 2x25 = 50cm 4x25= 100cm The scale of this drawing is 1cm = 25cm What is the actual length and breadth of the TV ?

Angle Properties www.mathsrevision.com Revision of Level E 65o 115o Two angles making a straight line add to 180o 145o Angles round a point Add up to 360o 50o 40o www.mathsrevision.com 90o 146o 34o 146o 3 angles in a triangle ALWAYS add up to 180o. angles opposite each other at a cross are equal. 20-Sep-18 Created by Mr. Lafferty

Angle Properties www.mathsrevision.com Revision of Level E h b c e ALL angles in an equilateral triangle are 60o Two angles in a isosceles Are equal d = 115o ao co bo go fo ho eo www.mathsrevision.com h is corresponding to d and must be 115o b is opposite to d and must be 115o c is must be 65o (straight line) e is alternate to c and must also be 65o 20-Sep-18 Created by Mr. Lafferty

Sum of Angles in a Triangle Level E Find the missing angles. 50o 38o 40o www.mathsrevision.com xo xo xo Remember all the angles in a triangle add up to 180o 20-Sep-18 Created by Mr.Lafferty Math Dept

Triangular and square Numbers Level E 1 3 6 10 1 4 9 www.mathsrevision.com 12 22 32 2 3 4 Write the number that are triangular or square for the list 4 25 15 49 21 17 36 28 20-Sep-18 Created by Mr.Lafferty Math Dept

Complicated Linear Patterns using diagrams and tables Level E nth terms 1st terms 2 4 5 1 3 Pattern Number P 6 10 12 8 Number of Dots Pattern 1 Pattern 3 Pattern 2 nth D = 2P +2 48 = 2xP +2 P =23 D = 2x35 +2 =72 Find the nth term ( the rule) of the pattern How many dots for pattern number 35? What is the pattern number for 48 dots?

Complicated Linear Patterns using diagrams and tables Level E Find the nth term ( the rule) of the patterns A 1 2 3 4 50 B 5 7 9 11 B = 2A + 3 103 Find A if B = 87 A = 42 x 1 2 3 4 100 y 6 11 16 21 y = 5x + 1 501 Find x if y = 96 x = 19

Fractions Percentages Decimals & Ratios Level E Percentages Fraction Decimal 50% 0.5 25% 0.25 75% 0.75 100

Fractions Percentages Decimals & Rations Level E Fill in the missing values. Percentages Fraction Decimal 40% 0.4 70% 0.7 80% 0.8

Fractions Percentages Decimals & Ratios Level E 2 4 1 + x 2. Mixed Number improper Decimal fraction 2.25 1.6 6.5

Created by Mr.Lafferty Math Dept Percentages Level E A TV shop has 15% off the normal price of TV. The normal price was £300. Calculate the sale price. 10% = 300 ÷ 10 = £30 5% = 30 ÷ 2 = £15 www.mathsrevision.com 15% £45 Sale price is £300 - £45 = £255 20-Sep-18 Created by Mr.Lafferty Math Dept

Created by Mr. Lafferty Math Dept Ratios A way of comparing things Level E A survey of people sitting their driving test found that in one week 96 people passed and 24 failed. Calculate the ratio of: pass to fail The pass rate is defined as the amount of people that passed out of the total who sat their test. Find the pass rate as a : Ratio (iii) Fraction (iv) Percentage Simplify were possible 96 : 24 = 4 : 1 www.mathsrevision.com 4 5 80% 96 : 120 = 4 : 5 20-Sep-18 Created by Mr. Lafferty Math Dept