By the end of this set of exercises, you should be able to:
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1 BASIC GEOMETRIC PROPERTIES By the end of this set of exercises, you should be able to: find the area of a simple composite shape find the volume of a cube or a cuboid find the area and circumference of a circle. Mathematics: Mathematics 1 (Int 1) Student Materials 15
2 Mathematics: Mathematics 1 (Int 1) Student Materials 16
3 A. Areas of Simple Composite Shapes Triangles and Quadrilaterals Exercise 1 1. Find the areas of the following triangles: (d) (e) 4 (f) (g) (h) (i) cm 6 2. Find the areas of the following squares and rectangles: (d) 12 cm square 1 12 cm Find the areas of the following quadrilaterals: (d) 1 12 (e) (f) (g) 12 cm 1 8 (h) (i) 6 (j) Mathematics: Mathematics 1 (Int 1) Student Materials 17
4 Composite Shapes Exercise 2 1. For the following composite shapes, (i) split each one into two or three parts, showing each part clearly (ii) calculate the area of each part (iii) find the total area of the composite shape. (d) 1 (e) (f) (g) (h) 20 cm (i) (j) (k) (l) 22 cm For each of the following shapes, (i) find the area of the outer shape (ii) find the area(s) of the hole(s) (iii) find the total shaded area, (the remaining area) cm cm (d) (e) (f) 1 12 cm 1 Mathematics: Mathematics 1 (Int 1) Student Materials 18
5 B. Volumes of Cubes and Cuboids Exercise 3 1. Use a simple counting process to find the volume of each of these cubes or cuboids (each box represents 1 centimetre): (d) (e) (f) 2. Use your formula for the volume of a cuboid to calculate the volumes of these cubes and cuboids. 2 5 m 7 m 6 m (d) 20 cm 20 cm (e) 6 (f) 8 3. The cardboard box, used to pack a microwave, measures 50 centimetres by 40 centimetres and is 45 centimetres high. Calculate the volume of the box (in cm 3 ) cm 40 cm Mathematics: Mathematics 1 (Int 1) Student Materials 19
6 (i) A rectangular water tank measures 7 metres long, 6 metres wide and 2 5 metres high. 2 5 m 7 m 6 m (ii) Calculate the volume of water in the tank (in m 3 ). Given that 1 m 3 = 1000 litres, find how many litres the tank holds. A rectangular swimming pool is 25 metres long, 12 metres wide and 1 2 metres deep. (i) How many cubic metres does it hold when full? (ii) Calculate the number of litres it will hold. 4. Calculate the volume of plaster, in cm 3, needed to make the following mathematical sculptures: 2 cm 2 cm 2 cm 2 cm 2 cm 2 cm (d) This shape consists of a large cuboid with a smaller cube cut out from it. Find the volume of the remaining shape. Mathematics: Mathematics 1 (Int 1) Student Materials 20
7 C. Circumferences and Areas of Circles Circumference of a Circle (C = π D) Exercise 4 1. Calculate the circumferences of the following: (use π = 3 14) 14 mm 2 (d) a circle with diameter 15 centimetres (e) a circle with diameter 22 millimetres (f) a circle with diameter 10 5 millimetres (g) a circle with diameter 85 metres. 2. Calculate the circumferences of the following: 7 mm 2 (d) a circle with radius 6 centimetres (e) a circle with radius 32 millimetres (f) a circle with radius 8 5 millimetres (g) a circle with radius 4 3 metres. 3. The diameter of a 10p piece is 24 millimetres. Calculate its circumference. 4. The centre circle of a football pitch has a radius of 3 metres. Calculate the length of the white line forming this circle. 5. A boy flies a model aeroplane around his head attached to a piece of wire 15 metres long. Calculate how far the plane flies on one circuit of its circular path around him when the piece of string is perfectly horizontal. 15 m 6. The diameter of a CD is 12 centimetres. Calculate the length of its circumference. Mathematics: Mathematics 1 (Int 1) Student Materials 21
8 7. Calculate the lengths of the arcs of the following semi-circles: (i) (ii) (iii) 20 cm 18 mm Calculate the lengths of the arcs of the following quarter circles: (i) (ii) (iii) 8. For each of the following: (i) split each shape up, showing the various lines and curves which form it 6 mm 12 (ii) (iii) calculate the length of each part calculate the total perimeter of the shape mm (d) 2 9 mm (e) (f) (g) 6 4 mm 16 mm 30 mm Mathematics: Mathematics 1 (Int 1) Student Materials 22
9 Area of a Circle (A = π r 2 ) Exercise 5 1. Calculate the area of each of the following: 7 mm 8 1 cm (d) a circle with radius 11 centimetres (e) a circle with radius 15 metres (f) a circle with radius 6 5 millimetres (g) a circle with radius 30 millimetres. 2. Calculate the areas of the following: 12 cm 40 cm 23 mm (d) a circle with diameter 16 centimetres (e) a circle with diameter 3 millimetres (f) a circle with diameter 24 millimetres (g) a circle with diameter 4 5 metres. 3. A ten pence piece has diameter 2 4 centimetres. Calculate its area. 4. A roundabout has a diameter of 18 metres. Calculate its area. 5. A circular metal drain cover has a diameter of 350 millimetres. Calculate its area. 6. A circular rug has diameter 1 4 metres. Calculate the area of the rug. 7. Calculate the areas of the following part circles. 6 2 cm 22 mm (d) (e) (f) 13 mm 5 14 mm Mathematics: Mathematics 1 (Int 1) Student Materials 23
10 8. Composite Shapes. For each of the following shapes: (i) split each one up showing the various parts (ii) calculate the area of each part (iii) write down the total area of the shape. 6 mm 1 12 mm (d) (e) (f) 23 mm 20 mm (g) (h) (i) 15 mm 21 cm 6 mm 1 (j) (k) 20 mm 12 mm Mathematics: Mathematics 1 (Int 1) Student Materials 24
11 MATHEMATICS 1 (INTERMEDIATE 1) Checkup for Basic Geometric Properties 1. Find the areas of the following triangles: 5 mm 13 mm 11 mm mm 2. Find the areas of the following quadrilaterals: 6 1 (d) (e) (f) 7 mm 10 mm 22 mm 40 cm 1 19 mm 5 mm 22 mm 11 mm 3. Split the following shapes into triangles and rectangles and from this, calculate the areas of each of the shapes. 1 (d) 12 cm 1 22 cm 1 20 cm Mathematics: Mathematics 1 (Int 1) Student Materials 25
12 4. Calculate the volumes of the following boxes, (in cm 3 ) cm 5. How many litres of water will this tray hold? 50 cm 20 cm 6. Calculate the circumferences of the following two circles: 16 mm 7. A car s tax disc has a diameter of 7 5 centimetres. Calculate its circumference. 8. Calculate the perimeter of the following two shapes: 60 cm 23 mm 9. Calculate the areas of the following two circles: 5 mm 22 cm 10. A circular badge has a radius of 2 3 centimetres. Calculate its area. 11. Calculate the area of the following three shapes: 1 7 mm 2 Mathematics: Mathematics 1 (Int 1) Student Materials 26
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