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Transcript
P, Q and R are points on the circumference of a circle, centre, O. The straight line POS has been drawn to help you. Prove that Angle QOR is twice the size of angle QPR Prove that 2n 1 2n 1 is a multiple of 8 for all integer values of n. 2 2 Prove algebraically that the difference between the squares of any two consecutive even numbers is always a multiple of 4. Jordan thinks that the sum How can you represent the of any 3 consecutive following algebraically? numbers is always a multiple of 3. i. An even number ii. An odd number Test to see if she is right. iii. A multiple of 3 Now prove it. Prove that (n 3)2 (n 5) (n 3)(n 4) 2 Prove algebraically that the sum of the squares of any two consecutive odd numbers cannot be a multiple of 4. How can you represent the following algebraically? Prove that the product of any two odd numbers is always odd. i. ii. iii. Two consecutive numbers Two odd numbers Two consecutive odd numbers PR and QS are two chords of a circle that meet at the point T. Prove that triangles PTS and QTR are similar. Given that PT = 3cm, TR = 8cm, and QT = 4cm, calculate the length ST.