Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
4A - Angles 4 89 Geometrical reasoning 4A - Angles LIN 2, 19, 27, 29, 31, 33 MOD 7, 18, 29, 34, 39, 41 o Distinguish between alternate and corresponding angles on parallel lines o Find angles in a triangle knowing that their sum is 180o, exterior angles = sum of interior opposites and base angles of an isosceles triangle are equal Use trigonometry to find the size of an angle in a right–angled triangle, given the length of two sides o o o Use trigonometry in complex problems o Find the exterior angle using the sum of the exterior angles of a polygon is 360o o Make simple sketches of graphs of sine, cosine and tangent o Find the size of interior and exterior angles of a regular polygon o Use trigonometry graphs to solve simple trigonometry equations o Solve geometric configurations using circle theorems of chord and tangents o Compare corresponding sides in similar triangles to calculate missing lengths o Solve geometric configurations using circle theorems o Prove that two triangles are similar triangles o Use trigonometry to find the length of a side of a right–angled triangle, given the length of one side and the size of an angle (not 90°) o Use ratio of length = a:b, ratio of area = a2:b2 and ratio of volume = a3:b3 o Find the conditions in order to prove that two triangles are congruent A03 - Shape, space and measures Use sine, cosine and area of a triangle rules to find unknowns in a scalene triangle This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited Topic Tutor GCSE Higher Maths St89 89 19/12/06 14:35:37 4A - Angles 90 1. 6. Leave blank Diagram NOT accurately drawn BEG and CFG are straight lines. ABC is parallel to DEF. Angle ABE = 48°. Angle BCF = 30°. (a) (i) Write down the size of the angle marked x. x = .............° (ii) Give a reason for your answer. ................................................................................................................................ (2) (b) (i) Write down the size of the angle marked y. y = .............° (ii) Give a reason for your answer. ................................................................................................................................ (2) Q6 (Total 4 marks) *N16915A0720* This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited Topic Tutor GCSE Higher Maths St90 90 7 Turn over 19/12/06 14:35:39 4A - Angles 2. 5. 91 Leave blank D C x Diagram NOT accurately drawn B A y 103° F E ABCD and AFE are straight lines. BF is parallel to CE. Angle CBF = 103o. AB = AF. ................................... o (ii) Give a reason for your answer. ................................................................................................................................ ................................................................................................................................ (2) (b) Find the size of angle y. ................................... o (2) A03 - Shape, space and measures (a) (i) Find the size of angle x. Q5 (Total 4 marks) *M22892A0508* This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited Topic Tutor GCSE Higher Maths St91 91 5 Turn over 19/12/06 14:35:40 y = .................... (2) 4A - Angles 92 Q2 (Total 3 marks) 3. 3. Diagram NOT accurately drawn a° 138° 65° Leave Leave blank blank Work out the value of a. SECTION B B SECTION Answer ALLALL SEVEN questions. Answer SEVEN questions. WriteWrite youryour answers in theinspaces provided. answers the spaces provided. 4. You must NOTNOT use ause calculator for this You must a calculator for section. this section. a = .................... (3) (Total 3 marks) You must writewrite downdown all stages in your working. You must all stages in your working. 1. 1. Q3 N17482A 4 WorkWork out the angle x. x. outsize the of size of angle x = ...................° x = ...................° Give Give reasons for your answer. reasons for your answer. .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. Q1 Q1 .............................................................................................................................................. .............................................................................................................................................. (3) (Total 3 marks) (Total 3 marks) 2. Given that that 2. Given 36003600 × 5.8×=5.8 20 =880 20 880 WriteWrite downdown the value of of the value This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited (i) 36 0.58 (i) × 36 × 0.58 Topic Tutor GCSE Higher Maths St92 92 ........................... ...........................19/12/06 14:35:45 4A - Angles 5. 2. 93 Leave blank The diagram shows the exterior angles of a quadrilateral. 88º Diagram NOT accurately drawn bº 121º 57º Work out the value of b. 3. (a) Expand 3(4x – 5) .................................... (1) (b) Factorise A03 - Shape, space and measures b = ............................. (2) (Total 2 marks) Q2 5y + 40 .................................... (1) (c) Simplify 3a + 7b + 9a – 4b .................................... (2) Q3 (Total 4 marks) 4 *M22891A0408* This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited Topic Tutor GCSE Higher Maths St93 93 19/12/06 14:35:46 7. 94 Put a ring around each fraction which gave a recurring decimal. 4A - Angles Q6 (Total 2 marks) 6. 7. x 7. 7. Diagram NOT accurately drawn N N Diagram NOT Diagram accurately drawn Diagram NOT NOT accurately accurately drawn drawn A A x Leave blank Leave blank 63° 63° 138° 138° P P B B Work out the bearing of Work out the bearing of The diagram shows a regular octagon. (i) B from P, (i) B from P, Work out the size of the angle marked x. ° ............................° ............................ The diagram shows a regular octagon. (ii) P from A. size of the angle marked x. Work out the (ii) P from A. Q7 ° ............................° Q7 ............................° x = ............................. Q7 (Total 3 marks) (4) (Total 3 marks) (Total 4 marks) 8. 7. 8. 6 TOTAL FOR SECTION B: 19 MARKS x = ............................. ° Diagram NOT Diagram NOT TOTAL FOR PAPER: 38 MARKS accurately drawn (Total 4 marks) accurately drawn END Q7 TOTAL FOR SECTION B: 19 MARKS *M22884A008* Calculate the size of an exterior angle of a regular hexagon. TOTAL FOR PAPER: 38 MARKS Calculate the size of an exterior angle of a regular hexagon. END Maths147303_M22884A.indd 6 6 05/09/2005 09:55:31 *M22884A008* Maths147303_M22884A.indd 6 05/09/2005 09:55:31 ° Q8 ............................° Q8 ............................ (Total 2 marks)(3) (Total 2 marks) This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited N17481A N17481A Topic Tutor GCSE Higher Maths St94 94 8 8 19/12/06 14:35:52 4A - Angles 8. 6. 95 Leave blank C Diagram NOT accurately drawn 5.4 cm A 2.3 cm B ABC is a right-angled triangle. Angle A = 90º. AB = 2.3 cm. BC = 5.4 cm. Work out the size of angle B. Give your answer correct to 3 significant figures. A03 - Shape, space and measures º .................................. (3) (Total 3 marks) Q6 TOTAL FOR SECTION B: 19 MARKS TOTAL FOR PAPER: 38 MARKS END *M22898A0708* 7 This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited Topic Tutor GCSE Higher Maths St95 95 19/12/06 14:35:53 4A - Angles 96 9. 5. B Leave blank C 6m Diagram NOT accurately drawn A 56º 10 m E F D 6m ABCDE is a pentagon. BC = ED = 6 m. Angle BCD = angle CDE = 90º. Angle BAE = 56º. The point F lies on CD so that AF is the line of symmetry of the pentagon and AF = 10 m. Calculate the perimeter of the pentagon. Give your answer correct to 3 significant figures. ........................... m (6) Q5 (Total 6 marks) TOTAL FOR SECTION B: 19 MARKS TOTAL FOR PAPER: 38 MARKS END 6 *M22882A0608* This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited Topic Tutor GCSE Higher Maths St96 96 19/12/06 14:35:55 4A - Angles 10. Leave 97 blank 15. H G E F 3cm A D 5 cm Diagram NOT accurately drawn C 7 cm B The diagram represents a cuboid ABCDEFGH. AB = 5 cm. BC = 7 cm. AE = 3 cm. (a) Calculate the length of AG. Give your answer correct to 3 significant figures. (b) Calculate the size of the angle between AG and the face ABCD. Give your answer correct to 1 decimal place. ° .......................... (2) A03 - Shape, space and measures ...................... cm (2) Q15 (Total 4 marks) N17484A 18 This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited Topic Tutor GCSE Higher Maths St97 97 19/12/06 14:35:56 4A - Angles 98 LeaveLeave blank blank 11. 19. 19. The The diagram shows somesome of the on aon baseball field.field. diagram shows of markings the markings a baseball 29 m29 m 29 m29 m 18.418.4 m m Diagram NOTNOT Diagram accurately drawn accurately drawn ABCD is a square. ABCD is a square. AC isAC a diagonal of ABCD. is a diagonal of ABCD. P is P a point on AC. is a point on AC. ADEADE and ABF are straight lines.lines. and ABF are straight AP =AP 18.4 m. m. = 18.4 Angle PAE = 45°. Angle PAE = 45°. EF isEF anisarc centre P and 29 m. an of arcthe of circle, the circle, centre P radius and radius 29 m. (a) (a) By considering triangle PAE,PAE, calculate the size of angle AEP.AEP. By considering triangle calculate the size of angle GiveGive youryour answer correct to 3 to significant figures. answer correct 3 significant figures. …………………..° …………………..° (3) (3) (3) 18 18 *N20905A01820* *N20905A01820* This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited Topic Tutor GCSE Higher Maths St98 98 19/12/06 14:35:59 ............................................. 4A - Angles 12. 17. (Total 3 marks) Q16 99 Diagram NOT accurately drawn The diagram shows a sketch of part of the curve y = sin x°. (a) Write down the coordinates of point A. ( ............ , ..............) (1) *N20904A01320* (2) (Total 3 marks) A03 - Shape, space and measures (b) On the same diagram, sketch the graph of y = sin 2x°. Q17 13 Turn over This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited Topic Tutor GCSE Higher Maths St99 99 19/12/06 14:36:01 4A - Angles 100 Leave blank 13. 20. Diagram 1 is a sketch of part of the graph of y = sin x°. y P Q Diagram 1 x O (a) Write down the coordinates of (i) P, ( ......... , ......... ) (ii) Q. ( ......... , ......... ) (2) Diagram 2 is a sketch of part of the graph of y = 3cos 2x°. y R O Diagram 2 x S (b) Write down the coordinates of (i) R, ( ......... , ......... ) (ii) S. ( ......... , ......... ) (2) (Total 4 marks) 16 Q20 *N20835A01620* This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited Topic Tutor GCSE Higher Maths St100 100 19/12/06 14:36:03 4A - Angles 101 Leave blank 14. 20. Diagram NOT accurately drawn The diagram shows part of two graphs. The equation of one graph is The equation of the other graph is y = a sin x° y = cos x° + b (a) Use the graphs to find the value of a and the value of b. b = .................... (2) (b) Use the graphs to find the values of x in the range 0° - x -720° when a sin x° = cos x° + b A03 - Shape, space and measures a = .................... x = ............................................ (2) (c) Use the graphs to find the value of a sin x° – (cos x° + b) when x = 450°. .......................... (2) Q20 (Total 6 marks) N17483RA Topic Tutor GCSE Higher Maths St101 101 19 This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited Turn over 19/12/06 14:36:05 4A - Angles 102 15. Leave blank 6. Diagram NOT accurately drawn AB is parallel to DE. ACE and BCD are straight lines. AB = 6 cm, AC = 8 cm, CD = 13.5 cm, DE = 9 cm. (i) Work out the length of CE. ………………… cm (ii) Work out the length of BC. ………………… cm (3) (Total 3 marks) *N20905A0720* Q6 7 Turn over This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited Topic Tutor GCSE Higher Maths St102 102 19/12/06 14:36:07 4A - Angles 16. 24. 103 Leave blank A Diagram NOT accurately drawn X B C D ABC is an equilateral triangle. AD is the perpendicular bisector of BC. BX is the angle bisector of angle ABC. (a) Show that triangle BXD is similar to triangle ACD. In triangle ACD, AC = 2 cm, AD = √3 cm. (b) Show that XD = 1 cm. 3 (3) A03 - Shape, space and measures (2) Q24 (Total 5 marks) END 20 TOTAL FOR PAPER: 100 MARKS *N20904A02020* This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited Topic Tutor GCSE Higher Maths St103 103 19/12/06 14:36:08 5 cm5 cm 4A - Angles The The diagram shows a model. diagram shows a model. The The model is a cuboid withwith a pyramid on top. model is a cuboid a pyramid on top. 18. The base of the model is a square with sides of length 5 cm. The base of the model is a square with sides of length 5 cm. 17. The The height of the cuboid in the model is 10 cm. height of the cuboid in the model is 10 cm. The The height the in the is 6 is cm. height of pyramid the pyramid in model the model 6 cm. 6ofcm Diagram NOT accurately drawn (a) (a) Calculate the volume of the Calculate the volume of model. the model. 104 Leave blank 10 cm 5 cm 5 cm ................................ cm3 cm3 ................................ The diagram shows a model. (3) (3) The model is a cuboid with a pyramid on top. The base of the model is a square with sides of length 5 cm. The The model represents a concrete post. The model represents a concrete post. is 10 cm. height of the cuboid in the model The The model is built to a scale of 1:30 The height model of is built to a scale the pyramid in of the1:30 model is 6 cm. The The surface area area of the is 290 cm2.cm2. surface of model the model is 290 (a) Calculate the volume of the model. (b) (b) Calculate the surface area area of the Calculate the surface of post. the post. GiveGive youryour answer in square metres. answer in square metres. ................................ cm3 (3) The model represents a concrete post. The model is built to a scale of 1:30 The surface area of the model is 290 cm2. 14 14 (b) Calculate the surface area of the post. Give your answer in square metres. ................................. m2 m2 ................................. (3) (3)Q18Q18 (Total 6 marks) (Total 6 marks) *N20904A01420* *N20904A01420* ................................. m2 (3) Q18 (Total 6 marks) 14 *N20904A01420* This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited Topic Tutor GCSE Higher Maths St104 104 19/12/06 14:36:12 4A - Angles 105 Leave blank 18. 18. Diagram NOT accurately drawn Q P 4 cm Two cylinders, P and Q, are mathematically similar. The total surface area of cylinder P is 90π cm2. The total surface area of cylinder Q is 810π cm2. The length of cylinder P is 4 cm. (a) Work out the length of cylinder Q. The volume of cylinder P is 100π cm3. (b) Work out the volume of cylinder Q. Give your answer as a multiple of π . .................. cm3 (2) A03 - Shape, space and measures .................... cm (3) Q18 (Total 5 marks) 14 *N20835A01420* This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited Topic Tutor GCSE Higher Maths St105 105 19/12/06 14:36:13 4A - Angles 106 T = .................... Q16 (Total 4 marks) 19. 17. X and Y are two geometrically similar solid shapes. The total surface area of shape X is 450 cm2. The total surface area of shape Y is 800 cm2. The volume of shape X is 1350 cm3. Calculate the volume of shape Y. Leave 17. Two similar tins have heights 12 cm and 20 cm. The volume of the smaller tin is 162 cm3. 3 .................... cm (3) (Total 3 marks) 20. 17. Calculate thetins volume, in cm3, 12 of the Two similar have heights cm larger and 20tin. cm. 3 N17484AThe volume of the smaller tin is 162 cm . 19 blank Q17 Leave blank Turn over Calculate the volume, in cm3, of the larger tin. ...................................... cm3 (3) (Total 3 marks) ...................................... cm3 TOTAL FOR SECTION A: 60 MARKS Q17 Q17 This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited END Topic Tutor GCSE Higher Maths St106 106 (Total 3 marks) TOTAL FOR SECTION A: 60 MARKS 19/12/06 14:36:17 4A - Angles Leave 107 blank 5. 21. Diagram NOT accurately drawn B A O C D A, B, C and D are four points on a circle, centre O. AOC and BOD are straight lines. A03 - Shape, space and measures Prove that triangle AOD and triangle BOC are congruent. You must give reasons for each stage of your proof. Q5 (Total 3 marks) (3) *M22877A0508* 5 Turn over This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited Topic Tutor GCSE Higher Maths St107 107 19/12/06 14:36:18 Q14Q14 .................... cm2 cm2 .................... (Total 3 marks) (Total 3 marks) 4B - Properties of shapes 108 22. 15. 15. PQRS is a quadrilateral. PQRS is a quadrilateral. P Q P Q Leave blank Leave blank Answer ALL SEVENTEEN questions. Answer SEVENTEEN questions. Write yourALL answers in the spaces provided. instages the spaces provided. YouWrite mustyour writeanswers down all in your working. S You R Rin your working. down some all stages S must write 1. Here is a list of ingredients for making Greek food for 6 people. PQ is parallel to SR. PQ is parallel to SR. 1. isSP is aof listgarlic of ingredients for making some Greek food for 6 people. SP parallel to RQ. is parallel to RQ. 2Here cloves 4 ounces of chick peas cloves garlic (a) (a) Prove thatofthat triangle PQSoil is congruent to triangle RSQ.RSQ. Prove triangle PQS is congruent to triangle 42 tablespoons of olive 4 ounces of chick peas 5 fluid ounces of Tahina paste 4 tablespoons of olive oil 5 fluidout ounces of Tahina paste Work the amount of ingredients to make the Greek food for 9 people. Work out the amount of ingredients to make the Greek food for 9 people. .......... cloves of garlic (3) (3) (3) .......... ounces cloves of .......... of garlic chick peas (b) (b) In quadrilateral PQRS, angleangle SPQ is obtuse. In quadrilateral PQRS, .......... ounces of chick peasoil SPQ is obtuse. .......... tablespoons of olive 4B - Properties shapes Explain whyof PQRS cannot be a be cyclic quadrilateral. Explain why PQRS cannot a cyclic quadrilateral. LIN 2 MOD 19 Q1 .......... fluid tablespoons oilpaste .......... ounces of of olive Tahina o Q1 (Total 2 marks) (2)Q15Q15 (Total 2 (2) marks) Find the number of sides of a polygon given .......... fluid ounces of Tahina paste exterior angles 2. A regular polygon has an exterior angle of 20° 1. 2. A regular polygon has an exterior angle of 20° ! N17483RA N17483RA ! 13 13 (Total 5 marks) (Total 5 marks) TurnTurn overover How many sides has this regular polygon? How many sides has this regular polygon? ........................... (2) ........................... (Total 2 marks) Q2 Q2 (Total 2 marks) This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited Topic Tutor GCSE Higher Maths St108 108 19/12/06 14:36:24 4C - 3-D Shapes and volumes 4C - 3-D shapes and volumes 1. o Draw and use plan and elevation of 3-D shapes o Find the surface area of shapes by using area of known 2-D shapes o o 109 LIN 22 MOD 31 Calculate volumes of prisms and cylinders Find the volume and surface area of a variety of complex shapes Leave blank 19. Here are the plan, front elevation and side elevation of a 3-D shape. plan front elevation side elevation A03 - Shape, space and measures In the space below, draw a sketch of the 3-D shape. Q19 (Total 2 marks) 637 20. Work out an estimate for the value of 3.2 × 9.8 (2) This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited Topic Tutor GCSE Higher Maths St109 109 19/12/06 14:36:26 4C - 3-D Shapes and volumes 110 Leave blank 2. 10. Here are the plan and front elevation of a prism. The front elevation shows the cross section of the prism. Plan Front Elevation In the space below, draw a 3-D sketch of the prism. Q10 (Total 2 marks) (2) 268 GCSE Mathematics 2540/2544 Sample Assessment Material UG017663 This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited Topic Tutor GCSE Higher Maths St110 110 19/12/06 14:36:27 4C - 3-D Shapes and volumes 3. 111 Leave blank 19. Diagram NOT accurately drawn 10 cm 8 cm 9 cm 6 cm Work out the surface area of the triangular prism. State the units with your answer. A03 - Shape, space and measures ............................ (4) (Total 4 marks) Q19 20. The table shows some expressions. a, b, c and d represent lengths. π and 3 are numbers which have no dimensions. 3a 2 πab 3 3d πbc ac + bd π (a + b) 3(c + d ) 3 3πbc 2 Q20 Tick () the boxes underneath the three expressions which could represent volumes. (Total 3 marks) *N20833A01520* 15 Turn over This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited Topic Tutor GCSE Higher Maths St111 111 19/12/06 14:36:30 Leave blank 4. 112 4C - 3-D Shapes volumes and 4. 4. 3. (ii) down the greatest possible height of the tower. WorkWrite out the surface area of the triangular prism. 3. A tower has a height of 124 m, correct to the nearest metre. (i) Write down the least possible height of the tower. Leave blank ............................. m Leave blank ............................. m Q3 (Total 2 marks) ............................. m (ii) Write down the greatest possible height of the tower. 4. 5. A tower has a height of 124 m, correct to the nearest metre. (i) Write down the least possible height of the tower. Work out the surface area ofthe triangular prism. 4. Leave blank r cm ............................. m Q3 (Total 2NOT marks) Diagram ................................. cm2 accurately drawn (3) (Total 3 marks) Q4 ................................. cm2 5. The distance of the Earth from the Sun is 93 000 000 miles. 10 cm (a) Write the number 93 000 000 in standard form. 5. The distance of the Earth from the Sun is 93 000 000 miles. The diagram shows a cylinder. The radius the of the cylinder is r 000 cm. in standard form. (a) Write number 000 r93cm The length of the cylinder is 10 cm. The volume of the cylinder is 140 cm3. 10 cm –6 One Angstrom unit is 3.94 × 10 inches. Work out the value of r. The showscorrect a cylinder. Givediagram your answer to 3 significant figures. (b) Write this as an ordinary number. –6 The radius of the cylinder inches. One Angstrom unit is 3.94 is× r10cm. The length of the cylinder is 10 cm. (b) Write this as an ordinary number.3 The volume of the cylinder is 140 cm . Work out the value of r. Give your answer correct to 3 significant figures. Q4 (Total 3 marks) Diagram NOT accurately drawn .............................................. (1) .............................................. (1) .............................................. (1) Q5 .............................................. (Total 2 marks) (1) Q5 (Total 2 marks) 193 GCSE Mathematics 2540/2544 Sample Assessment Material UG017663 r = ............................. Q4 (3) GCSE Mathematics 2540/2544 Sample Assessment Material UG017663 193 (Total 3 marks) This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited 5 Topic Tutor GCSE Higher Maths St112 112 *M22878A0508*r = .............................TurnQ4over 19/12/06 14:36:35 15. 4C - 3-D Shapes and volumes 6. 15. Diagram NOT accurately drawn 113 Leave blank 5 cm 4 cm 7 cm Diagram NOT accurately drawn 5 cm 3 cm 4 cm Calculate the volume of the triangular prism. 7 cm 3 cm Leave Leave blank blank Calculate the volume of the triangular prism. 5. 5. Leave blank 5. .......................... (4) (Total 4 marks) Q15 .......................... (Total 4 marks) Q15 7. 5. (a) (a) Calculate Calculate the the length length of of AC. AC. A03 - Shape, space and measures (a) Calculate the length of AC. Leave blank ........................................ ........................................ cm cm (2) (2) ........................................ cm (b) (b) ABC ABC isis the the side side of of aa triangular triangular prism prism of of length length 10cm. 10cm. (2) (a) Calculate the length of AC. Calculate Calculate the the volume volume of of the the triangular triangular prism. prism. (b) ABC is the side of a triangular prism of length 10cm. Calculate the volume of the triangular prism. ........................................ ........................................ cm cm (3) (3) cm Q5 Q5 ........................................ N17481A Turn over 13 (2)3 ........................................ cm (Total (Total 55 marks) marks) (3) Q5 (b) ABC is the side of a triangular prism of length 10cm. 6. 3x 6. Simplify Simplify 3x33yy22 ×× xx22yy33 (Total 5 marks) N17481A Turn over 13 Calculate the volume of the triangular prism. 6. This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited Simplify Topic Tutor GCSE Higher Maths St113 113 3x3y2 × x2y3 19/12/06 14:36:44 LeaveLeave blank blank 4C - 3-D Shapes and volumes 114 18. 18. 8. 6 cm6 cm Diagram NOTNOT Diagram accurately drawn accurately drawn 10 cm 10 cm 5 cm5 cm 5 cm5 cm The The diagram shows a model. diagram shows a model. The The model is a cuboid with a pyramid on top. model is a cuboid with a pyramid on top. The The basebase of the is a square withwith sidessides of length 5 cm.5 cm. ofmodel the model is a square of length The The height of the cuboid in the model is 10 cm. height of the cuboid in the model is 10 cm. The The height of the in theinmodel is 6 cm. height ofpyramid the pyramid the model is 6 cm. (a) Calculate the volume of the (a) Calculate the volume ofmodel. the model. ................................ cm3 cm3 ................................ (3) (3) The The model represents a concrete post.post. model represents a concrete The The model is built to a scale of 1:30 model is built to a scale of 1:30 2 The The surface area area of the is 290 surface ofmodel the model is cm 290.cm2. (b) Calculate the surface area area of the (b) Calculate the surface ofpost. the post. GiveGive youryour answer in square metres. answer in square metres. ................................. m2 m2 ................................. (3) (3)Q18Q18 (Total 6 marks) (Total 6 marks) 14 14 *N20904A01420* *N20904A01420* This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited Topic Tutor GCSE Higher Maths St114 114 19/12/06 14:36:47 Leave 115 blank 4C - 3-D Shapes and volumes 7. 9. Diagram NOT accurately drawn 10 cm 11 cm 3.5 cm 12 cm A rectangular container is 12 cm long, 11 cm wide and 10 cm high. The container is filled with water to a depth of 8 cm. A metal sphere of radius 3.5 cm is placed in the water. It sinks to the bottom. Calculate the rise in the water level. Give your answer correct to 3 significant figures. A03 - Shape, space and measures ......................... cm (4) (Total 4 marks) Q7 TOTAL FOR SECTION B: 19 MARKS TOTAL FOR PAPER: 38 MARKS END *M22900A008* 7 Turn over This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited Math147295_M22990A.indd 7 Topic Tutor GCSE Higher Maths St115 115 31/08/2005 14:0 19/12/06 14:36:48 116 Leave blank 4C - 3-D Shapes and volumes 21. 10. The radius of the base of a cone is x cm and its height is h cm. The radius of a sphere is 2x cm. The volume of the cone and the volume of the sphere are equal. Express h in terms of x. Give your answer in its simplest form. h = .................................... (3) (Total 3 marks) *N20835A01720* Q21 17 Turn over This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited Topic Tutor GCSE Higher Maths St116 116 19/12/06 14:36:49 4C - 3-D Shapes and volumes 117 Leave blank 11. 23. The diagram shows a sector of a circle with a radius of x cm and centre O. PQ is an arc of the circle. Angle POQ = 120°. Leave blank x cm O P The sector is the net of the curved surface of this cone. 120° Arc PQ forms the circumference of the circle that makes the base of the cone. Diagram NOT accurately drawn x cm Q h cm The sector is the net of the curved surface of this cone. Arc PQ forms the circumference of the circle that makes the base of the cone. The sector is the netexpression of the curved surface this xcone. π and for (a) Write down an in terms of of Arc PQ forms the circumference of the circle that makes the base of the cone. Leave blank (i) the area of this sector, x cm x cm .......................... (ii) the arc length of this sector. Given that V = 3A, (b) find the value of h. 2 The curved surface area of the cone is A cm . The volume of the cone is V cm3. 2 . The curved surface area ofofthe The height thecone coneisisAhcm cm. 3 The volume of the cone is V cm . The height of the conethat is hVcm. Given = 3A, .......................... (2) A03 - Shape, space and measures The curved surface area of the cone ishAcm cm2. 3 The volume of the cone is V cm . The height of the cone hiscm h cm. Given that V = (b) 3A, find the value of h. (b) find the value of h. .......................... (3) Q23 (Total 5 marks) N17483RA 22 TOTAL FOR PAPER: 100 MARKS This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited END Topic Tutor GCSE Higher Maths St117 117 19/12/06 14:36:55 4D - Pythagoras' theorem 118 4D - Pythagoras' theorem o 1. Use Pythagoras' theorem to find one side of a right– angled triangle given the other two sides 4. LIN 19, 31 MOD 29, 39 o Use Pythagoras' theorem in unstructured situations o Use Pythagoras' theorem in 3-D configurations Diagram NOT accurately drawn P Leave blank 5.7 cm Q 9.3 cm R In triangle PQR, QR = 9.3 cm. PQ = 5.7 cm. Angle PQR = 90º. Calculate the length of PR. Give your answer correct to 3 significant figures. ............................... cm (3) (Total 3 marks) 5. Q4 (a) Write 0.032 in standard form. .................................... (1) (b) Write 1.58 × 104 as an ordinary number. This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited Topic Tutor GCSE Higher Maths St118 118 .................................... (1) 19/12/06 Q5 14:36:57 accurately drawn accurately drawn Leave 119 blank 4D - Pythagoras' theorem O O 16 cm 16 cm A 19. 2. C C 12 cm 12 cm B Diagram NOT accurately drawn B O The diagram shows triangle ABC ABC and a16 circle, centre O. O. The diagram shows triangle and a circle, centre cm A, B A, andBCand areCpoints on the of theofcircle. are points oncircumference the circumference the circle. AB isAB a diameter of theofcircle. is a diameter the circle. 12 cm B AC =AC 16 =cm 12 =cm. 16and cmBC and=BC 12 cm. C (a) Angle ACB ACB = 90o=. 90o. (a) Angle The Give diagram shows triangle ABC and a circle, centre O. Give a reason why. why. a reason A, B and C are points on the circumference of the circle. AB is....................................................................................................................................... a diameter of the circle. ....................................................................................................................................... (1) (1) AC = 16 cm and BC = 12 cm. A03 - Shape, space and measures (a) ACB 90o. AB ofAB (b) Work out the diameter theofcircle. (b) Angle Work out the= diameter the circle. Give a reason why. ....................................................................................................................................... (1) (b) Work out the diameter AB of the circle. ............................ cm cm ............................ (3) (3) (c) Work out the theofcircle. (c) Work outarea the of area the circle. Give Give your your answer correct to 3 significant figures. answer correct to 3 significant figures. ............................ cm (3) (c) Work out the area of the circle. Give your answer correct to 3 significant figures. ............................ cm2 cm2 ............................ (3) (3)Q19 Q19 (Total 7 marks) (Total 7 marks) *M20834A01524* *M20834A01524* 15 15 TurnTurn over over ............................ cm2 Q19 (3) (Total 7 marks) *M20834A01524* 15 Turn over This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited Topic Tutor GCSE Higher Maths St119 119 19/12/06 14:37:02 120 Leave blank 4D - Pythagoras' theorem 20. A 3. 20. A 10 cm 17 cm 10 cm D 17 cm B Diagram NOT accurately drawn B Diagram NOT accurately drawn Leave blank C ABCD is a rectangle.D AC = 17 cm. AD = 10 cm. ABCD is a rectangle. AC = 17 cm. Calculate the length of the side CD. AD = 10 cm. Give your answer correct to one decimal place. C Calculate the length of the side CD. Give your answer correct to one decimal place. 5. 5. 5. 4. .....................cm Q20 Leave Leave (3) Leave blank blank blank (Total 3 marks) .....................cm Q20 (Total 3 marks) Calculate the length of AC. (a) (a) Calculate the length of AC. (a) Calculate the length of AC. N17482A 22 ........................................ ........................................ cm cm ........................................ cm (2) (2) (2) (b) ABC is the side a triangular prism of length 10cm. of a of triangular prism of length 10cm. side of a triangular prism of length 10cm. 22 (b) ABC is theisside (b) ABC the N17482A This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited Calculate the volume of triangular the triangular prism. Calculate the volume of the prism. Calculate the volume of the triangular prism. Topic Tutor GCSE Higher Maths St120 120 19/12/06 14:37:09 LeaveLeave blank121 blank 4D - Pythagoras' theorem 15. 15. H 5. E E F A 5 cm5 cm D B G G Diagram NOTNOT Diagram accurately drawn accurately drawn C C F 3cm 3cm A H D 7 cm7 cm B The diagram represents a cuboid ABCDEFGH. The diagram represents a cuboid ABCDEFGH. AB =AB 5 cm. = 5 cm. BC =BC 7 cm. = 7 cm. AE =AE 3 cm. = 3 cm. (a) Calculate the length of AG. (a) Calculate the length of AG. GiveGive youryour answer correct to 3 significant figures. answer correct to 3 significant figures. (b) Calculate the size between AG and ABCD. (b) Calculate the of sizetheofangle the angle between AG the andface the face ABCD. GiveGive youryour answer correct to 1 decimal place. answer correct to 1 decimal place. A03 - Shape, space and measures ...................... cm cm ...................... (2) (2) ° ° .......................... .......................... (2) (2)Q15 Q15 (Total 4 marks) (Total 4 marks) N17484A N17484A 18 18 This publication may be reproduced only in accordance with Edexcel Limited copyright policy. © 2006 Edexcel limited Topic Tutor GCSE Higher Maths St121 121 19/12/06 14:37:12