 # E 3 Revision www mathsrevision com Revision Area

• Slides: 28 E 3 Revision www. mathsrevision. com Revision Area Revision Weight and Volume Revision Scale Drawings & Triangles Revision Triangular and square numbers Revision Patterns Revision Fractions and %’s and Ratio’s www. mathsrevision. com Problem… General Jack’s Carpets How much for this one? ? Only £ 5 a square metre! 1 m 1 m Problem… = 1 square metre www. mathsrevision. com 6 m 6 square metres 3 m 6 square metres 3 rows of 6 squares = 3 x 6 = 18 square metres How much for 18 square metres? 18 x £ 5 = £ 90 Area of a rectangle 6 www. mathsrevision. com 6 m length 3 3 m breadth 6 x 3 = 18 m² Area = length x breadth www. mathsrevision. com Example 1 11 cm 6 cm Find the area of the rectangle Area = length x breadth A=lxb A = 11 x 6 A = 66 cm² www. mathsrevision. com Area of a right-angled triangle 4 cm 7 cm 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 www. mathsrevision. com Area Δ=½ x base x height AΔ =½ x b x h 10 cm 15 cm Find the area of the triangle AΔ = ½ x 15 x 10 AΔ = 75 cm² Composite shapes www. mathsrevision. com 10 cm 6 cm ? 13 cm ? 3 cm Composite shapes www. mathsrevision. com 10 cm 6 cm (1) 6 cm ? Area (1) = l x b = 10 x 6 = 60 cm² (2) 3 cm 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 15 cm = 120 cm² ? 8 cm 11 cm 3 cm 6 cm (1) (2) ? 9 cm Find the area of the shape Area (2) = l x b =9 x 3 = 27 cm² Area of shape = (1) + (2) = 120 + 27 = 147 cm² Example 2 12 cm = 240 cm² (2) 10 cm Area (1)= l x b =20 x 12 20 cm 6 cm (1) Find the area of the shape Area (2) = l x b =10 x 6 = 60 cm² Area of shape = (1) – (2) = 240 -60 = 180 cm² A short cut ! height 4 cm Area of rectangle 6 cm 3 cm breadth length Volume = 6 x 3 x 4 = 72 cm³ Volume = length x breadth x height 07 -Oct-20 Compiled by Mr. Lafferty Maths Dept. Example 1 Working Volume = l x b x h V = 18 x 5 x 27 V = 2430 cm³ 27 cm 5 cm Heilander’s Porridge Oats 18 cm 07 -Oct-20 Compiled by Mr. Lafferty Maths Dept. Example 2 Working www. mathsrevision. com Volume = l x b x h How many of the small cubes fit into the big cuboid. 3 cm V=3 x 3 x 3 V = 9 cm³ Volume = l x b x h V = 10 x 180 x 5 V = 9000 cm³ 10 cm 180 cm 07 -Oct-20 5 cm 9000 ÷ 9 = 1000 cubes Compiled by Mr. Lafferty Maths Dept. www. mathsrevision. com Example 2 Working If each cube weighs 2. 5 g How much does the big cuboid weigh in : (i) Grams 2. 5 g (ii) kg (ii) Tonnes Cube = 2. 5 g Cuboid = 1000 x 2. 5 g Weight = 2500 g = 2500 ÷ 1000 = 2. 5 Kg = 2. 5 ÷ 1000 = 0. 0025 T 10 cm 18 cm 07 -Oct-20 5 cm Compiled by Mr. Lafferty Maths Dept. www. mathsrevision. com Scaled Drawings Definition A scale of 1 cm = 2 m This simply means for every 1 cm measured on a drawing this represents 2 m in real-life. 07 -Oct-20 Created by Mr. Lafferty Maths Dept. www. mathsrevision. com Scaled Drawings 4 cm 4 x 25= 100 cm 2 x 25 = 50 cm The scale of this drawing is 1 cm = 25 cm What is the actual length and breadth of the TV ? Angle Properties www. mathsrevision. com Revision of Level E 120 95 145 o o o Angles round a point o Add up to 360 146 o 34 146 o o 115 Two angles making a o straight line add to 180 50 90 o o angles opposite each other at a cross are equal. 07 -Oct-20 65 o o 40 o 3 angles in a triangle ALWAYS o add up to 180. Created by Mr. Lafferty Angle Properties www. mathsrevision. com Revision of Level E Two angles in a isosceles Are equal h b c e ALL angles in an equilateral o triangle are 60 is corresponding to d and must be 115 is opposite to d and must be 115 o o is alternate to c and must also be 65 07 -Oct-20 Created by Mr. Lafferty c h o is must be 65 (straight line) d = 115 o g o o o a o b e f o o Sum of Angles in a Triangle Level E www. mathsrevision. com Find the missing angles. 38 x o o 50 x o o x o 40 o Remember all the angles in a triangle add up to 180 07 -Oct-20 Created by Mr. Lafferty Math Dept o Triangular and square Numbers www. mathsrevision. com Level E 1 3 2 6 3 10 4 1 4 9 12 22 32 Write the number that are triangular or square for the list 4 07 -Oct-20 25 15 49 21 17 36 28 Created by Mr. Lafferty Math Dept Complicated Linear Patterns using diagrams and tables Level E www. mathsrevision. com 1 st D = 2 P +2 Pattern 1 terms Pattern 3 Pattern 2 Pattern Number P D = 2 x 35 +2 Number of=72 Dots nth terms 1 2 3 4 6 8 484 = 2 x. P +2 nth 5 P =23 10 12 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 www. mathsrevision. com Find the nth term ( the rule) of the patterns A B 1 5 2 7 1 6 Find x if y = 96 4 11 50 103 B = 2 A + 3 A = 42 Find A if B = 87 x y 3 9 2 11 3 16 x = 19 4 21 100 501 y = 5 x + 1 www. mathsrevision. com Level E Fractions Percentages Decimals & ratio Percentages Fraction Decimal 50% 0. 5 25% 0. 25 75% 0. 75 100 Level E Fractions Percentages Decimals & ratio www. mathsrevision. com Fill in the missing values. Percentages Fraction Decimal 40% 0. 4 70% 0. 7 80% 0. 8 www. mathsrevision. com Level E Fractions Percentages Decimals & ratio +1 2 x 4 Mixed Number 2. improper Decimal fraction 2. 25 6. 5 1. 6 Percentages www. mathsrevision. com 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% = £ 15 £ 45 Sale price is £ 300 - £ 45 = £ 255 07 -Oct-20 Created by Mr. Lafferty Math Dept Ratios A way of comparing things www. mathsrevision. com 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: (i) pass to fail 96 : 24 = 4 : 1 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 : 4 (iv) (ii) Ratio (iii) Fraction Percentage 80% 96 : 120 = 4 : 5 5 Simplify were possible 07 -Oct-20 Created by Mr. Lafferty Math Dept