1. Colour each number that ends in 2 in one colour. Make a list of the possible multiples (the first few have been done for you):

Transcription

1 Exercise.7 You will need a calculator for this exercise. Complete the table square and then take ten different colours. Follow the instructions in questions to and colour the relevant numbers in the table square below Colour each number that ends in in one colour. Make a list of the possible multiples (the first few have been done for ou):... =... =... =... Page

2 Exercise.7 (cont.). Colour each number that ends in with another colour. Make a list of the multiples:. Continue with numbers that end with through to 9, then do 0 and. (a) Multiples that end in : (b) Multiples that end in : (c) Multiples that end in : (d) Multiples that end in 7: Page

3 Exercise.7 (cont.) (e) Multiples that end in 8: (f) Multiples that end in 9: (g) Multiples that end in 0: (h) Multiples that end in : Page

4 Exercise.7 (cont.). (a) The column that is the times table has the same pattern as which other column?... (b) The column that is the times table has the same pattern as which other column?... (c) Look at the to 00 square below: (i) Colour number (ii) Colour the multiples of (iii) Colour the multiples of (iv) Colour the multiples of (v) Colour the multiples of 7 What is the name given to the numbers in the to 00 square that are not coloured?... Page

5 End of chapter activit: The number game (For instructions, see Maths Prep page.) Game Your number: Your opponents number: Game Your number: Your opponents number: Game Your number: Your opponents number: Page

6 End of chapter activit: Equivalent fraction dominoes Cut out the dominoes and pla the game as described on page 7 of Maths Prep The puzzle Place the dominoes in a continuous rectangle. All touching squares must be equal in value. Can ou make this rectangle? Page

7 Exercise 8.. (a) On each of the polgons below, mark an exterior angle, an interior angle and the angle at the centre. Give each polgon its correct name and state whether it is regular or irregular. Name... Name... regular/irregular regular/irregular Name... Name... regular/irregular regular/irregular Name... Name... regular/irregular regular/irregular Page 0

8 Exercise 8. (cont.). On the polgons below, measure each exterior angle and add them up. What do ou notice?... b c f a a d e b e c d a =... b =... c =... d =... e =... Sum =... a =... b =... c =... d =... e =... f =... Sum =... a b b i c a c h d g e d f a =... b =... c =... d =... e =... f =... g =... h =... i =... Sum =... a =... b =... c =... d =... Sum =... Complete the word formula: The sum of the exterior angle of an polgon =... Page

9 Exercise 8.. Divide each of these polgons into triangles with all lines drawn from the same vertex to find the sum of their interior angles. Fill in the results. For example: (a) Name of polgon: Pentagon Number of sides: Number of triangles: Name of polgon:... Number of sides:... Number of triangles:... (b) (c) Name of polgon:... Number of sides:... Number of triangles:... Name of polgon:... Number of sides:... Number of triangles:... (d) (e) Name of polgon:... Number of sides:... Number of triangles:... Name of polgon:... Number of sides:... Number of triangles:... Page

10 Exercise 8. (cont.) (f) (g) Name of polgon:... Number of sides:... Number of triangles:... Name of polgon:... Number of sides:... Number of triangles:.... Now fill in the table below to calculate the angle sum of the triangles of each of the polgons in question. You ma want to draw some more polgons of our own and add our results to the table. No. of sides No. of Angle sum of Name of polgon of polgon triangles the triangles pentagon 80 = 0 (a) hexagon =... (b) =... (c) =... (d) =... (e) =... (f) =... (g) =... (h) =... (i) =... What relationship do ou notice between the number of triangles and the number of sides of the polgons? Use our results and the numbers and signs shown below to complete this formula: 80, n,,, Angle sum of a polgon with n sides = ( ) Page

11 End of chapter 9 activit: Tormenting tessellations Read the instructions on page 87 of Maths Prep. Use this grid as the base for our tessellation design. Page

12 Exercise 0.: Enlargement on a grid. Find the centres of enlargement and the scale factor for each pair of shapes. (a) x (b) x Centre of enlargement (...,...) Centre of enlargement (...,...) Scale factor... Scale factor... (c) 0 9 (d) x x Centre of enlargement (...,...) Centre of enlargement (...,...) Scale factor... Scale factor... (e) 0 9 (f) x x Centre of enlargement (...,...) Centre of enlargement (...,...) Scale factor... Scale factor... Page

13 Exercise 0.: Enlargement on a grid (cont.). (a) Draw ABC such that A(, ), B(, ) and C (, ) and DEF such that D(, 7), E(, 7) and F(, 9). (b) Find the centre of enlargement and the scale factor for the enlargement that maps ABC to DEF. Centre of enlargement (...,...) Scale factor x (a) Draw GHI such that G(, ), H(, ) and I(, ) and JKL such that J(, 9), K(, ) and L(8, ). (b) Find the centre of enlargement and the scale factor for the enlargement that maps GHI to JKL. Centre of enlargement (...,...) Scale factor x (a) Draw LMN such that L(, ), M(, ) and N(, ) and PQR such that P(, 8), Q(, ) and R(, ). (b) Find the centre of enlargement and the scale factor for the enlargement that maps LMN to PQR. Centre of enlargement (...,...) Scale factor x Page

14 Exercise 0.: Enlargement on a grid (cont.). (a) Draw a square ABCD such that A(7, ), B(7, ), C(8, ) and D(8, ) and a square EFGH such that E(, 7), F(, ), G(7, ) and H(7, 7). (b) Find the centre of enlargement and the scale factor for the enlargement that maps ABCD to EFGH. Centre of enlargement (...,...) Scale factor.... (a) Draw a square PQRS such that P(, ), Q(, ), R(, ) and S(, ) and a square WXYZ such that W(, 8), X(, ), Y(8, ) and Z(8, 8). (b) Find the centre of enlargement and the scale factor for the enlargement that maps PQRS to WXYZ. Centre of enlargement (...,...) Scale factor (a) Draw a square ABCD such that A(, ), B(, ), C(, ) and D(, ) and a square EFGH such that E(, 9), F(, ), G(, ) and H(, 9). (b) Find the centre of enlargement and the scale factor for the enlargement that maps ABCD to EFGH. (You will notice that points C and F are the same which should give ou a clue!) Centre of enlargement (...,...) x x x Scale factor... Page 7

15 End of chapter activit: Dungeons and dragons (Read the instructions on pages - of Maths Prep.). Use this isometric paper to draw the paths of: (a) a (,) dragon (b) a (,) dragon (c) a (,) dragon (d) a (,) dragon Some of the lines have been drawn for ou. (,) Dragon cell (,) Dragon cells (a) (,) Dragon cells (b) (,) Dragon 7 cells Page 0

16 End of chapter activit: Dungeons and dragons (cont.). Complete this table: Dragon Units walked Dungeons in one circuit guarded (,) (,) 9 (,) (,) (,). Without drawing, tr to work out the numbers in the next two lines: Dragon Units walked Dungeons in one circuit guarded (,) (,7) Page

17 End of chapter activit: Dungeons and dragons (cont.). Now draw and check our answers to question.. How man dungeons will a (,0) dragon guard?.... What is the formula to see how man dungeons a (,n) dragon will guard?... Page

18 End of chapter activit: Dungeons and dragons (cont.) Use this isometric paper to draw the paths of the megadragons. (a) a (,) dragon (b) a (,) dragon (c) a (,) dragon (d) a (,) dragon (done for ou) (,) Dragon cells (,) Dragon cells (a) (,) Dragon 0 cells (b) Page

19 End of chapter activit: Dungeons and dragons (cont.) (cont.) Dragon Units walked Dungeons in one circuit guarded (,) 9 (,) (,) (,) (,) (,) (,7) (,8) (,9) (,0) The formula for a megadragon is What is the formula that tells ou how man dungeons an (m,n) dragon can patrol and how far he walks in one circuit?... Page

20 Exercise.: Using bearings The diagram represents a map showing our acht in the middle of a ba. Around ou are another boat, a tanker, a lighthouse and a hilltop. You have to find the bearing of each one from our own position. Here is a chart of our position: Hilltop Boat Your acht Lighthouse Tanker Scale cm to 00 m Scale cm to 00 m Use a protractor to find the bearing of each object from the acht. Use our ruler to find the distance of each object from the acht. Note the scale cm represents 00 metres. Fill our results in this table: Object Bearing Distance Measured Actual Boat cm m Tanker cm m Lighthouse cm m Hilltop cm m Page

21 Exercise.7. You are sailing a boat in the middle of a lake. On the edge of the lake there is a boathouse, a rescue station, a jett and a public telephone. With our compass ou take a bearing of each of these. This table shows the bearings: Bearing Bearing from Object of object object Boathouse 08 Rescue station 8 Jett Telephone 8 Use this information to plot our position on this chart of the lake: Telephone N Boathouse LAKE Jett Rescue station The lake is drawn to a scale of cm to 0 m. Use this information and work out the distance of each object from our boat. Fill in this information table: Object Distance Measured Actual Boathouse cm m Rescue station cm m Jett cm m Telephone cm m Page

22 Exercise.7 (cont.). You are going treasure hunting. The instructions for finding the buried treasure are given here on an old piece of parchment: To find the buried treasure e must walk 70 paces from the centre of the White tower on a bearing of 0. Fom here e must take paces towards the Red tower. At this point. Here be e must walk the buried treasure. 90 paces on a bearing of Here is the treasure map. One pace is represented b one millimetre. Happ treasure hunting! Blood tower Tower of sculls N Kreep keepe Red tower White tower Gatewa of terror Page 7

23 Exercise.7 (cont.). You are going orienteering, this means that ou have to find our wa around the countr side using a compass and a map. Because this is our first time our group leader has given ou this list of bearings and distances to help ou to find our wa through the Hazardous Wood: Distance Leg no: Bearing Actual To scale m cm 0 m cm 80 m cm 7 7. m cm 07 m cm m cm Here is the map, drawn to a scale of cm to m. First ou should work out the scaled distance on the map and fill in the last column on the table! Plot our wa through the wood following the above instructions. Marsh N Marsh Marsh Bottomless pond Marsh Quicksand Page 8

24 Exercise.7 (cont.). Having found our wa through the wood without mishap, ou find that ou have left our lunch back at the start of our journe. You have to get back to it, but ou must not cross our original path or even go close to it because gremlins ma be ling in wait for ou. Using the map in question, work out another path that will take ou back to the beginning. Fill in our instructions in the table below. Once ou are sure that our route will keep ou out of danger, give it to a friend to test for ou. Distance Leg no: Bearing Actual To scale Page 9

25 Exercise.: Tangram. Cut out the 7 pieces of the tangram and rearrange them to make this shape:. Cut out the 7 pieces of the tangram and rearrange them to make this shape:. Cut out the 7 pieces of the tangram and rearrange them to make this shape:. Cut out the 7 pieces of the tangram and rearrange them to make this shape: Page

26 Exercise. (cont.). Use these squares to make up some designs of our own. Be as creative as ou can. Page

27 Exercise. Cut out the 7 pieces of the tangram to answer the following questions:. Make a square using: (a) two tangram pieces (b) three tangram pieces (c) four tangram pieces (d) five tangram pieces (e) six tangram pieces. Using all seven pieces, write down whether it is possible to make: (a) a trapezium (but not the one in Exercise.) (b) a rectangle that is not a square (c) a parallelogram that is not a square (d) a triangle Page

28 Exercise.. and. Each of these triangles has a base or a height marked on it. Draw and measure the height or base so that the area of the triangle can be calculated. Now calculate the area of each triangle. (a) (b) Measurement: base:... cm Measurement: base:... cm height:... cm height:... cm Area:... Area:... (c) (d) Measurement: base:... cm Measurement: base:... cm height:... cm height:... cm Area:... Area:... (e) (f) Measurement: base:... cm Measurement: base:... cm height:... cm height:... cm Area:... Area:... Page

29 Exercise. (cont.) (g) (h) Measurement: base:... cm Measurement: base:... cm height:... cm height:... cm Area:... Area:... Page

30 End of chapter activit: The shape game Read the instructions on page 9 of Maths Prep. Choose a shape for ourself. Think hard about its properties. Now tr amd work out our opponent s shape before he guesses ours! Page

31 Exercise.7. (a) For the equation = x - complete this table of values for x and. x 0 Plot the five points ou have calculated above on this grid. (b) Draw the graph of = x b drawing a line through the points. Draw the line as long as possible and label it = x 0 x -. (a) For the equation = x + complete this table of values for x and. x 0 (b) Draw the graph of = x + (c) From our graph find: (i) the value of when x =. (ii) the value of x when = 0 - x Page 9

32 Exercise.7 (cont.). (a) For the equation = x complete this table of values for x and. x 0 (b) Draw the graph of = x (c) From our graph find: (i) the value of when x = 0. (ii) the value of x when =. 0 x -. (a) For the function = + x complete this table of values for x and. x 0 (b) Draw the graph of = + x (c) From our graph find: (i) the value of when x =. (ii) the value of x when = x Page 0

33 Exercise.7 (cont.). (a) For the function = x complete this table of values for x and. x 0 x 0 (b) Draw the graph of = x (c) From our graph find: (i) the value of when x =. (ii) the value of x when = x (a) For the function = - x complete this table of values for x and. x 0 x 0 (b) Draw the graph of = x (c) From our graph find: (i) the value of when x =. (ii) the value of x when = x Page

34 Exercise.7 (cont.) 7. (a) For the function = complete this table of values for x and. x 0 (b) Draw the graph of = (c) From our graph find: (i) the value of when x =. (ii) the value of x when = x - 8. (a) For the function = complete this table of values for x and. x 0 (b) Draw the graph of = (c) From our graph find: (i) the value of when x =. (ii) the value of x when =. 0 x - Page

35 Exercise 7.: Summar exercise. A B C D 0 x E F (a) The transformation that maps A to D is (b) The transformation that maps E to F is (c) The transformation that maps B to C is (d) The transformation that maps E to C is (e) The transformation that maps E to B is (f) The transformation that maps B to D is Page

36 Exercise 7. (cont.).. A 0 x - A triangle A has been drawn: (a) Draw the reflection of the triangle in the x-axis and label this image B. (b) Draw the rotation of A b 80 about the origin, and label this image C. (c) The translation of A given b the vector and label this image D. 0 x - A triangle P has been drawn: (a) Draw the image Q, the reflection of P in the line x = (b) Draw the image R, the rotation of P b 90 clockwise about the point (, ). (c) Draw the image S, the translation of P P given b the vector Page

37 Exercise 7. (cont.).. 0 x - W A square W has been drawn: (a) Draw the enlargement of W b scale factor and centre of enlargement the origin. Label this image X (b) Draw the translation of X b the vector. Label this image Y. (c) Describe the enlargement that maps W to Y: x - Draw the kite K with vertices at (, ) (, ) (, ) and (, ). (a) Draw the reflection of K in the line = and label the image L. (b) Draw the reflection of L in the line x = and label the image M. (c) Describe the transformation that maps K to M: x Draw the triangle Z with vertices at (, ) (, ) and (, 0). (a) Draw the image Y, the reflection of Z in the line = (b) Draw the image X, the rotation of Y 80 about the point (0, ). (c) Draw the image W, the translation of X b the vector (d) Describe the transformation that maps W to Z: Page

38 End of chapter 7 activit: The four colour theorem Colour these maps with the minimum number of colours possible, so that no two adjacent regions are coloured with the same colour Page

39 End of chapter 7 activit: The four colour theorem (cont.) Colour these maps with the minimum number of colours possible, so that no two adjacent regions are coloured with the same colour Page

40 End of chapter 7 activit: The four colour theorem (cont.). Colour this map of Europe with the minimum number of colours possible, so that no two adjacent regions are coloured with the same colour. Page 7

41 End of chapter 7 activit: The four colour theorem (cont.). Colour this map of the United States of America with the minimum number of colours possible, so that no two adjacent regions are coloured with the same colour. Page 8