1. GCSE Past Paper Questions & Solutions Dr J Frost (jfrost@tiffin.kingston.sch.uk) Last modified: 18 th April 2014

2. Index Click to visit section. Straight Line Equations Algebra Factorising, Simplifying & Solving Non-Right Angled Triangles Congruent Triangle Proofs Algebraic Proofs & Algebraic Geometry Right-Angled Triangles Number Includes bounds, direct/indirect proportion, standard form, %s ProbabilityCircle Theorems Mark Scheme Notes: M1Method mark.cao Correct Answer OnlyoeOr equivalent A1Accuracy mark.C1 ‘Communication Mark’ (used for *-ed questions) B1‘Independent mark’. Sort of a ‘miscellaneous’ mark, often used when an explanation is required. Volumes and Surface Area Functions and Graph Transformations More Topics >>

3. Index Click to visit section. Loci & ConstructionsAngles & Bearings Mark Scheme Notes: M1Method mark.cao Correct Answer OnlyoeOr equivalent A1Accuracy mark.C1 ‘Communication Mark’ (used for *-ed questions) B1‘Independent mark’. Sort of a ‘miscellaneous’ mark, often used when an explanation is required. Vectors

4. Straight Lines Gradient = -9/4 2y = -x + 1, so y = -0.5x + 0.5 So gradient is -0.5 y = 3x - 4 y = -3x + 16 y = 4x + 3 y = 4x – 5 ? ? ? ? ? ? << Return to Index

5. Straight Lines y = 4x - 11 y = (1/3)x + 2 y = -(1/2)x + c (where c can be anything) y = -(1/5)x – 1 ? ? ? ? << Return to Index

6. Straight Lines ? << Return to Index

7. Straight Lines ? << Return to Index

8. Straight Lines 3, 3.5 -9/5 ? ? << Return to Index

9. Straight Lines 51.5 ? Reveal << Return to Index

10. Straight Lines Reveal << Return to Index

11. Straight Lines 2/3 Gradient of 2y = 10 – 3x is -3/2 2/3 × -3/2 = -1 therefore perpendicular ? ? << Return to Index

12. Straight Lines 6 1.50 -3/2 ??? ? Reveal << Return to Index

13. Straight Lines -0.6, 5.5 -1.4, 6.4 x = 0.2, y = -3.8 x = 5.8, y = 1.8 ? ? ? << Return to Index

14. Straight Lines - 1/2 y = -(1/2)x – 1 ? ? << Return to Index

15. Straight Lines [June 2010 NonCalc] << Return to Index

16. Algebra ? << Return to Index

17. Algebra x 10 m 12 ? ? ? << Return to Index

18. Algebra ? ? << Return to Index

19. Algebra 3 ? ? << Return to Index

20. Algebra 12.5 4m 2 – 1 ? ? << Return to Index

21. Algebra ? << Return to Index

22. Algebra a9a9 3 9e 5 f 6 ? ? ? << Return to Index

23. Algebra ? << Return to Index

24. Algebra ? << Return to Index

25. Algebra 3(2 + 3x) (y + 4)(y – 4) (2p – 5)(p + 2) ? ? ? << Return to Index

26. Algebra -3 ? << Return to Index

27. Algebra 4 5 4, 5 ? ? ? << Return to Index

28. Algebra ? ? << Return to Index

29. Algebra ? ? << Return to Index

30. Algebra ? << Return to Index

31. Algebra ? << Return to Index

32. Algebra ? << Return to Index

33. Algebra ? << Return to Index

34. Algebra ? << Return to Index

35. Algebra ? << Return to Index

36. Algebra -3 < x ≤ 4 t > 7/2 ? ? ? << Return to Index

37. Algebra 2x(x – 2y) (p – 4)(p – 2) x + 2 6a 5 b 2 ? ? ? ? << Return to Index

38. Algebra ? << Return to Index

39. Algebra ? << Return to Index

40. Algebra x + 4 2x – 3 7x – 2 (x+2)(x-2) ? ? << Return to Index

41. Algebra (x + p)(x + q) (m + 2)(m – 2) x + 10 (x – 4)(x + 3) ? ? ? << Return to Index

42. Algebra x 2 + 3 = 7x x 2 – 7x + 3 = 0 x = (7 ±  37) / 2 ? << Return to Index

43. Algebra -2, -1, 0, 1, 2, 3, 4 x > 5/2 ? ? << Return to Index

44. Algebra 16n 12 ? << Return to Index

45. Algebra (2x – 1)(x – 4) (2x – 1)(x – 4) = (2x – 1) 2 x – 4 = 2x – 1 x = -3 ? ? << Return to Index

46. Algebra -160 ? ? << Return to Index

47. Algebra 4(3n + 1) 3(n + 4) 2n + 1 ? ? ? << Return to Index

48. Algebra ? << Return to Index

49. Algebra ? << Return to Index

50. Algebra 4x -1 or 4/x ? << Return to Index

51. Algebra 8x 2 + 6xy – 20y 2 x + 10 x – 5 x + 2 3-11 ? ? ? ?? << Return to Index

52. Algebra ? << Return to Index

53. Non-Right Angled Triangles ? << Return to Index

54. Non-Right Angled Triangles ? << Return to Index

55. Non-Right Angled Triangles ? << Return to Index

56. Non-Right Angled Triangles ? ? << Return to Index

57. Non-Right Angled Triangles ? << Return to Index

58. Non-Right Angled Triangles ? << Return to Index

59. Non-Right Angled Triangles ?

60. ? ?

61. ? ?

62. ? ?

63. Congruent Triangles ? << Return to Index

64. Congruent Triangles ? ?

65. ?

66. ?

67. ? ?

68. Algebraic Proofs and Geometry << Return to Index 21. ?

69. Algebraic Proofs and Geometry << Return to Index ? ?

70. Algebraic Proofs and Geometry << Return to Index ?

71. Algebraic Proofs and Geometry << Return to Index ?

72. Algebraic Proofs and Geometry << Return to Index 5x 2 ?

73. Algebraic Proofs and Geometry << Return to Index ?

74. Algebraic Proofs and Geometry << Return to Index ?

75. Algebraic Proofs and Geometry << Return to Index ?

76. Algebraic Proofs and Geometry << Return to Index ? ? ?

77. Algebraic Proofs and Geometry << Return to Index ? ?

78. Algebraic Proofs and Geometry << Return to Index ? ? ?

79. Right Angled Triangles << Return to Index ?

80. Right Angled Triangles << Return to Index 80.1 ?

81. Right Angled Triangles << Return to Index 11.547.2 ? ?

82. Right Angled Triangles << Return to Index ?

83. Right Angled Triangles << Return to Index 3.52 ?

84. Right Angled Triangles << Return to Index ?

85. Right Angled Triangles << Return to Index ?

86. Right Angled Triangles << Return to Index 33.7 9.44 ??

87. Right Angled Triangles << Return to Index 13.86 ?

88. Right Angled Triangles << Return to Index ?

89. Right Angled Triangles << Return to Index 48.2 ?

90. Right Angled Triangles << Return to Index ?

91. Right Angled Triangles << Return to Index ?

92. Number << Return to Index 0.00078 9.56 x 10 7 ? ? ?

93. Number << Return to Index ?

94. Number << Return to Index Remember, you choose the greatest degree of accuracy such that the two bounds are the same. ?

95. Number << Return to Index 820 000 3.76 x 10 -4 0.5 x 10 9 = 5 x 10 8 ? ? ?

96. Number << Return to Index ?

97. Number << Return to Index ?

98. Number << Return to Index ?

99. Number << Return to Index Non ?

100. Number << Return to Index Non ?

101. Number << Return to Index ?

102. Number << Return to Index ?

103. Number << Return to Index ?

104. Number << Return to Index ?

105. Number << Return to Index 643 000 16 x 10 -5 = 1.6 x 10 -4 ? ?

106. Number << Return to Index ?

107. Number << Return to Index ?

108. Number << Return to Index ?

109. Number << Return to Index 1 0.000067 2.7 x 10 14 2.4 x 10 16 6.4 x 10 8 ? ? ? ? ?

110. Number << Return to Index 109.8847047 ?

111. Number << Return to Index 8.25 x 10 7 1.456 x 10 -15 ? ?

112. Number << Return to Index ? ?

113. Probability << Return to Index ?

114. Probability << Return to Index ?

115. Probability << Return to Index ?

116. Probability << Return to Index 2 42 16 42 ? ?

117. Probability << Return to Index 222 380 ?

118. Probability << Return to Index 64 110 ? ?

119. Probability << Return to Index ?

120. Probability << Return to Index ?

121. Circle Theorems << Return to Index ?

122. Circle Theorems << Return to Index ?

123. Circle Theorems << Return to Index ?

124. Circle Theorems << Return to Index ? ?

125. Circle Theorems << Return to Index ?

126. Circle Theorems << Return to Index

127. Circle Theorems << Return to Index ? ?

128. Circle Theorems << Return to Index ?

129. Circle Theorems << Return to Index ? ?

130. Circle Theorems << Return to Index

131. Circle Theorems ? << Return to Index

132. Circle Theorems << Return to Index Angle DAB = 180 – 103 = 77 (opposite angles of cyclic quadrilateral) Angle DBA = 39 (Alternate Segment Theorem) Angle ADB = 180 – 77 – 39 = 64 ?

133. Circle Theorems << Return to Index 116 Angle OCB = (180 – 116)/2 = 32 Angle OCA = 74 – 32 = 42 ? ?

134. Circle Theorems << Return to Index Angle BOA = 152 Angle APB = 360 – 152 – 90 – 90 = 28 ?

135. Volumes and Surface Area << Return to Index ?

136. Volumes and Surface Area << Return to Index ?

137. Volumes and Surface Area << Return to Index ?

138. Volumes and Surface Area << Return to Index ?

139. Volumes and Surface Area << Return to Index ?

140. Volumes and Surface Area << Return to Index ?

141. Volumes and Surface Area << Return to Index 236 ? ?

142. Volumes and Surface Area << Return to Index ?

143. Volumes and Surface Area << Return to Index ? ? ?

144. Volumes and Surface Area << Return to Index ?

145. Volumes and Surface Area << Return to Index ?

146. Volumes and Surface Area << Return to Index ?

147. Volumes and Surface Area << Return to Index ?

148. Volumes and Surface Area << Return to Index ?

149. Volumes and Surface Area << Return to Index 32 4 1 ? ? ? ?

150. Volumes and Surface Area << Return to Index ? ?

151. Volumes and Surface Area << Return to Index Yes ? 8 x 100 3 = 8 000 000 ?

152. Functions and Graph Transformations << Return to Index General Tips: 1.When asked to sketch a transformed graph, e.g. f(x + 3), pick key points on the original graph to transform first (e.g. ones that go exactly through grid points, or y-intercepts, etc.) then join up with a line. This will ensure you draw it accurately. 2.Remember that changes inside the function brackets affect the x-axis and do the opposite of what you expect. 3.Learn the shape of y = sin(x), y = cos(x) and y = tan(x). In particular, learn that coordinates for which the graphs cross the x-axis, and the maximum/minimum points. On to questions >>>

153. Functions and Graph Transformations << Return to Index Reveal To get the curve perfectly mirrored, mirror points that go through squares first, i.e. (-4, 4), (-3, 1), (-1, 1), (0.4), then join up with a line.

154. Functions and Graph Transformations << Return to Index y = f(x – 6) ?

155. Functions and Graph Transformations << Return to Index 90 0 ? Reveal

156. Functions and Graph Transformations << Return to Index Reveal

157. Functions and Graph Transformations << Return to Index Reveal

158. Functions and Graph Transformations << Return to Index EBFCDAEBFCDA ?

159. Functions and Graph Transformations << Return to Index Reveal

160. Functions and Graph Transformations << Return to Index Reveal

161. Functions and Graph Transformations << Return to Index Reveal

162. Functions and Graph Transformations << Return to Index Reveal

163. Functions and Graph Transformations << Return to Index -15 -7 -6 1 Reveal ????

164. Functions and Graph Transformations << Return to Index Reveal x = -1.6, y = 2.6 x = 2.6, -1.6 ?

165. Functions and Graph Transformations << Return to Index f(x – 5) 4 3 ? ?

166. << Return to Index 3 -3 -1 ? ? ? Reveal

167. Vectors << Return to Index ? ?

168. Vectors << Return to Index ? ?

169. Vectors << Return to Index ? ?

170. Vectors << Return to Index ? ?

171. Vectors << Return to Index ? ?

172. Vectors << Return to Index ? ?

173. Vectors << Return to Index ? ?

174. Vectors << Return to Index ? ?

175. Loci & Constructions << Return to Index #1: Use compass the get some fixed distance across the lines AC and AB. #2: Find perpendicular bisector of these two points. Reveal

176. Loci & Constructions << Return to Index Reveal

177. Loci & Constructions << Return to Index #1: Use two arcs with radius the width of the line to form an equilateral triangle (only one side needed). This gives you an angle of 60 . #2: Find the angle bisector of these two lines in the usual way, in order to find the angle half of 60 . Reveal Step #1 Reveal Step #2

178. Loci & Constructions << Return to Index ?

179. Loci & Constructions << Return to Index 5cm 3cm Angle bisector of angle DAB Reveal

180. Angles & Bearings << Return to Index 40  Angle PQT = 70 (angles on straight line). Angle PTQ = 70 (isosceles triangle) Angle TPQ = 40 (angles in triangle add to 180) ? ?

181. Angles & Bearings << Return to Index 360 ÷ 5 = 72  ?

182. Angles & Bearings << Return to Index 112  Angle LNB = 68 (corresponding angles) so y = 112 (angles on straight line add to 180) OR Angle ANM = 68 (alternate angles) so y =... ? ?

183. Angles & Bearings << Return to Index 55  Corresponding angles. ? ?

184. Angles & Bearings << Return to Index 360 ÷ 30  = 12 ?

185. Angles & Bearings << Return to Index ?

186. Angles & Bearings << Return to Index 360 – 90 – 120 = 150  ?

187. Angles & Bearings << Return to Index 42  ?

188. Angles & Bearings << Return to Index Angle PBA = 180 – (x + 50) – (2x – 10) = 140 – 3x y = 180 – (140 – 3x) = 3x + 40 3x + 40 = 145 x = 35 35 + 50 = 85 ? ? ?

189. Angles & Bearings << Return to Index 3x – 15 = 2x + 24 x = 39 ?

190. Angles & Bearings << Return to Index Interior angle of hexagon = 180 – (360 / 6) = 120 Interior angle of octagon = 180 – (360 / 8) = 135 x = 360 – 120 – 135 = 105 ?

191. Angles & Bearings << Return to Index ? ? ?

192. Angles & Bearings << Return to Index ?

193. Angles & Bearings << Return to Index 150  ? ?

194. Angles & Bearings << Return to Index ?

195. Angles & Bearings << Return to Index ?

196. Angles & Bearings << Return to Index ?

197. Angles & Bearings << Return to Index ?

198. Angles & Bearings << Return to Index ?

199. Angles & Bearings << Return to Index ?

200. Angles & Bearings << Return to Index ?

201. Angles & Bearings << Return to Index ?