Abet Level 4 Summative Assessment

GENERAL EDUCATION AND TRAINING CERTIFICATENQF LEVEL 1ABET LEVEL 4 SITE-BASED ASSESSMENTLEARNING AREA:MATHEMATICAL LITERACY CODE :MLMS4 TASK:WORKSHEET DURATION:3 HOURS MARKS:50This assessment task consists of 12 pages.Copyright reserved Please turn over MLMS 4 -2- SBA Task: Worksheet 2017INSTRUCTIONS AND INFORMATION1. Answer ALL the questions on the worksheet.2. Calculators may be used.3. ALL calculations must be shown and answers should be rounded off to TWO decimal places unless otherwise stated.GEOMETRY OF 2D SHAPES (Polygons, e.g. triangles, quadrilaterals, circles, etc.)QUESTION 1: PERIMETERS OF IRREGULAR POLYGONS A polygon is a flat shape consisting of straight lines that are joined to form a closed shape. The word ' polygon' comes from the Greek word polus which means ' many' . There are two types of polygons, i.e. Regular polygon - an equiangular and equilateral polygon.  An equiangular polygon is a polygon whose vertex angels are equal.  An equilateral polygon is a polygon which has all sides of the same length.Irregular polygon - a polygon where all the sides or angles are not equal. The perimeter of any polygon is the distance around its outside. This distance can be measured in millimetres (mm), centimetres (cm), metres (m) or kilometres (km); etc. To find the perimeter of a polygon, you must calculate the total length of all the sides. A two-dimensional (2D) shape is flat with only a length (l) and a breadth (b). Another name for a breadth is a width (w).Example: a b Calculate the perimeter of the irregular pentagon alongside: e c Answer: Perimeter = a + b + c + d + e d Use the above information to calculate the perimeters of the following irregular polygons:1.1 5 cm 5 cm7 cm (1)1.2 60 mm30 mm 25 mm50 mm (1)Copyright reserved Please turn over MLMS 4 -3- SBA Task: Worksheet 20171.3 A hexagon has sides with lengths 4 cm, 5 cm, 7 m, 2 cm, 8 cm and 3 cm.(1)1.4 A quadrilateral has sides with lengths 17,5 cm; 10,13 cm; 5,0 cm and 15,2 cm.(1)1.5 An octagon has sides with lengths 5 mm, 6 mm, 4 mm, 10 mm, 9 mm, 10 mm, 2 mm and 3 mm. (1) [5]Copyright reserved Please turn over MLMS 4 -4- SBA Task: Worksheet 2017QUESTION 2: CALCULATING PERIMETER OF REGULAR POLYGONSRegular polygons are marked in a special way Examples: to show that they are regular. A line is drawn on each of the equal sides. 1. SQUARE 2 cm When calculating the perimeter of regular polygons, we often2 cm use a formula 2 cm which is an equation containing symbols and numbers to do specific calculations. 2cm 1. For example, a square has four equal sides, and then if you need to find its perimeter, you P = 4s can multiply the length of one side by the = 4 × 2 cm = 8 cm number of sides.2. RECTANGLE i.e. P = 4s, or P = 4l2. A rectangle has two opposite sides equal. 2 cmThen, P = 2l + 2b or 2(l + b) 3 cm P = 2l + 2b or 2(l + b) = (2 × 3 cm)+(2 × 2 cm) or 2(3 cm + 2 cm) = 6 cm + 4 cm = 10 cm 2. Calculate the following:2.1 The perimeter of a square if one side measures 10 cm. (2)2.2 What is the perimeter of a rectangle that has a length of 15 cm and a breadth of 8 cm?(2)Copyright reserved Please turn over MLMS 4 -5- SBA Task: Worksheet 20172.3 Calculate the perimeter of a regular hexagon that has one side equal to 5 cm. (2)2.4 If the perimeter of a square is 48 cm, determine the length of each side.(2)2.5 The perimeter of a regular hexagon is 108 m. Find the length of one side.(2) [10]Copyright reserved Please turn over MLMS 4 -6- SBA Task: Worksheet 2017QUESTION 3: CALCULATING AREAS OF POLYGONSIn geometry, area is defined as the amount of space that a Examples: flat surface or shape covers. Area is measured in the A B same units that is used to measure length. Area can be 1. expressed in units squared, i.e. mm2; cm2; m2 or km2; etc.1. In the given rectangle (ABCD), side AB= 18 cm and side AD =12 cm. D C The formula of area of a rectangle is: A = l × b Area (A) = length (l) × breadth (b), = 18 cm × 12 cm = 216 cm2 Can be used to calculate the area of a rectangle. 2 Therefore the area of rectangle ABCD is 216 cm . 2. E F If the size of a tile is 3 cm × 3 cm, then the number of tiles to cover an area of rectangle will be 216 cm2 ÷ 9 cm2 which gives 24 tiles. H G A = l × l or (l )2 = 6 cm × 6 cm 2. The area of a square (EFGH) can be given by the = 36 cm2 formulaArea (A) = length (l) × length (l) = length2, that is l2 3. M In a square, all sides have the length of 6 cm each. Then the area of a square is 36 cm2 4 cmO 6 cm N 3. The area of a triangle (MNO) is half the area of a rectangle. Then, the area of a triangle can be given 1 A = (b × h) by the formula: 2 1 1 Area (A) = × base (b) × height (h) = (6 cm × 4 cm) 2 2 1 24 = (b × h) = cm2 2 2 = 12 cm2 In the triangle (MNO) the height is 4 cm and the base is 6 cm. Then, area is 12 cm2.Copyright reserved Please turn over MLMS 4 -7- SBA Task: Worksheet 2017Calculate the areas of the following polygons:3.16 cm11 cm(2)3.27 mm5 mm(3)3.2 Find the shaded area of this composite shape.7 cm6 cm 2 cm2 cm(4) [9]Copyright reserved Please turn over MLMS 4 -8- SBA Task: Worksheet 2017QUESTION 4: CALCULATING THE PERIMETER AND AREA OF A CIRCLEA circle is a line that is curved so that its ends meet. 1. The diameter runs from one point on the circumference through the centre to the other side. It divides the circle in halves. 2. The radius is half a diameter. This also means that a diameter is twice the length of the radius. It is drawn from the centre of the circle to any point on the circumference.3. The circumference is the distance around the edge of a circle. It can form a perimeter of a circle though it is measured in degrees.We shall focus on the above-mentioned lines of the circle although there are some other lines like the chord and the tangent. A chord is a line segment that joins two points on the circumference of a circle. A tangent is a line that only touches the circle at exactly one and only one point perpendicular to a radius.When we calculate the perimeter of a circle, the following formula is used:P = 2× × r [where Pi( ) = 3,14] c = 2 r r ∙ d e.g. if a circle has a radius of 3 cm, then the perimeter will beP = 2 × 3,14 × 3 cm = 18,84 cm KEY: r-radius To calculate the area of a circle, we use the following formula: d-diameter c-circumference A =  × r2 =  r2 e.g. If a circle has a radius of 3 cm, then the area will be:A = 3,14 × (3 cm)2 = 28,26 cm2Copyright reserved Please turn over MLMS 4 -9- SBA Task: Worksheet 2017Use the above information to answer the following question:A plate of cookies on the right has the shape of a circle. The radius (r) of this plate is 8 cm as shown on the picture. 8 cm4.1 Calculate the perimeter of the plate.(2)4.2 Calculate the area of the plate.(2)4.3 Mrs Mongwe is running a pizza business. Her pizzas are circular in shape, with the following diameters:SMALL : 23 cm MEDIUM : 30 cm LARGE : 38 cmIf she charges 5c per cm2 of a pizza, how much would the following cost (in rands)?4.3.1 One small pizza;(2)Copyright reserved Please turn over MLMS 4 -10- SBA Task: Worksheet 20174.3.2 Half a large pizza;(2)4.3.3 One-third of a medium pizza.(2) [10]QUESTION 5: CALCULATING PERIMETERS AND AREAS OF DIFFERENT 2D SHAPESThe floor of a room is 4,5 m × 3,75 m. The area of the room should be covered with square carpet tiles with each side equal to 750 mm.Calculate the following:5.1 The area of the floor in m2.(1)5.2 The area of the tile in mm2.(2)Copyright reserved Please turn over MLMS 4 -11- SBA Task: Worksheet 20175.3 The number of tiles you will need to cover the floor.(2)5.4 If one tile cost R82,50 per square metre, determine the amount needed to tile a room.(2)5.5 The radius of each circle is given below:6 cm 6 cmThen, calculate the area of the rectangle.(4) [11]Copyright reserved Please turn over MLMS 4 -12- SBA Task: Worksheet 2017QUESTION 6: CLASSIFYING 2D SHAPESGive the names of the following 2D shapes:6.1(1)6.2(1)6.3(1)6.4 (1)6.5(1) [5] Copyright reserved Please turn over MLMS 4 -13- SBA Task: Worksheet 2017TOTAL: 50Copyright reserved Please turn over

Abet Level 4 Summative Assessment

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