Abet Level 4 Summative Assessment

GENERAL EDUCATION AND TRAINING CERTIFICATE

NQF LEVEL 1

ABET LEVEL 4 SITE-BASED ASSESSMENT

LEARNING AREA:MATHEMATICAL LITERACY CODE :MLMS4 TASK:WORKSHEET DURATION:3 HOURS MARKS:50

This assessment task consists of 12 pages.

Copyright reserved Please turn over MLMS 4 -2- SBA Task: Worksheet 2017

INSTRUCTIONS AND INFORMATION

1. 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 cm

7 cm (1)

1.2 60 mm

30 mm 25 mm

50 mm (1)

1.3 A hexagon has sides with lengths 4 cm, 5 cm, 7 m, 2 cm, 8 cm and 3 cm.

1.4 A quadrilateral has sides with lengths 17,5 cm; 10,13 cm; 5,0 cm and 15,2 cm.

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.

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QUESTION 2: CALCULATING PERIMETER OF REGULAR POLYGONS

Regular 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 = 4l

2. A rectangle has two opposite sides equal. 2 cm

Then, 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 What is the perimeter of a rectangle that has a length of 15 cm and a breadth of 8 cm?

2.3 Calculate the perimeter of a regular hexagon that has one side equal to 5 cm.

2.4 If the perimeter of a square is 48 cm, determine the length of each side.

2.5 The perimeter of a regular hexagon is 108 m. Find the length of one side.

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QUESTION 3: CALCULATING AREAS OF POLYGONS

In 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 formula

Area (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 cm

O 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.

Calculate the areas of the following polygons:

3.2 Find the shaded area of this composite shape.

6 cm 2 cm

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QUESTION 4: CALCULATING THE PERIMETER AND AREA OF A CIRCLE

A 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 be

P = 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 cm2

Use 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 cm

4.1 Calculate the perimeter of the plate.

4.2 Calculate the area of the plate.

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 cm

If she charges 5c per cm2 of a pizza, how much would the following cost (in rands)?

4.3.1 One small pizza;

4.3.2 Half a large pizza;

4.3.3 One-third of a medium pizza.

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QUESTION 5: CALCULATING PERIMETERS AND AREAS OF DIFFERENT 2D SHAPES

The 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.

5.2 The area of the tile in mm2.

5.3 The number of tiles you will need to cover the floor.

5.4 If one tile cost R82,50 per square metre, determine the amount needed to tile a room.

5.5 The radius of each circle is given below:

6 cm 6 cm

Then, calculate the area of the rectangle.

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QUESTION 6: CLASSIFYING 2D SHAPES

Give the names of the following 2D shapes:

(1) [5] Copyright reserved Please turn over MLMS 4 -13- SBA Task: Worksheet 2017

TOTAL: 50

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