E-Math 2015 Paper 2 Worked Solutions

Difference of two squares

11 marks: (a) 1, (b) 1 + 2, (c) 3, (d) 1 + 3 · number & algebra (algebraic manipulation, quadratic)

Locate points from given vectors

8 marks: (a) 1 + 1, (b) 1, (c) 3, (d) 2 · geometry & measurement (vectors, similar triangles)

Wage + percentage bonus

12 marks: (a) 2, (b) 2 + 2, (c) 3 + 3 · number & algebra (everyday percentage & money)

Angles in the same segment

9 marks: (a) 1 + 1 + 2 + 2, (b) 3 · geometry & measurement (circle properties, sector)

Distance = speed × time to form an equation

7 marks: (a) 1, (b) 1, (c) 3, (d) 2 · number & algebra (simultaneous equations, rate)

Height of a pyramid via 3D Pythagoras

9 marks: (a) 4, (b) 2, (c) 3 · geometry & measurement (3d mensuration, similar/equal volumes)

Nth term of an arithmetic sequence

9 marks: (a) 2 + 1, (b) 1 + 2 + 3 · number & algebra (sequences, number-grid proof)

Pythagoras and tan in a right triangle

13 marks: (a) 2, (b) 4, (c) 4, (d) 3 · geometry & measurement (trigonometry, bearings/3d)

Median & quartiles from a CF curve

10 marks: (a)(i) 1 + 2 + 2, (a)(ii) 1, (b)(i) 1 + 1, (b)(ii) 2 · statistics & probability