{"id":1041,"date":"2020-03-04T10:28:07","date_gmt":"2020-03-04T10:28:07","guid":{"rendered":"http:\/\/ibalmaths.com\/?post_type=knowledgebase&p=1041"},"modified":"2020-05-28T04:18:29","modified_gmt":"2020-05-28T04:18:29","slug":"ibdp-practice-questions-binomial-theorem","status":"publish","type":"knowledgebase","link":"https:\/\/ibalmaths.com\/index.php\/ibdp-math-hl-2\/binomial-theorem\/ibdp-practice-questions-binomial-theorem\/","title":{"rendered":"Binomial Theorem – Practice Questions"},"content":{"rendered":"

1.\u00a0 In the expansion of \r\na<\/mi>–<\/mo>3<\/mn>b<\/mi><\/mrow><\/mfenced>n<\/mi><\/msup><\/math>\r\n , the sum of 9th<\/sup> and 10th<\/sup> term is zero. Find the value of\u00a0 \r\na<\/mi>b<\/mi><\/mfrac><\/math>\r\n in terms of\u00a0 \r\nn<\/mi><\/math>\r\n .<\/p>\r\n

2.\u00a0 If the coefficient of 4th,<\/sup> 5th<\/sup> and 6th<\/sup> terms in the expansion of\u00a0 \r\n1<\/mn>+<\/mo>x<\/mi><\/mrow><\/mfenced>n<\/mi><\/msup><\/math>\r\n are in arithmetic sequence, then find the value(s) of \r\nn<\/mi><\/math>\r\n .<\/p>\r\n

3.\u00a0 If the last term in the expansion of\u00a0 \r\n3<\/mn> <\/mo><\/msqrt>–<\/mo> <\/mo>1<\/mn>3<\/mn><\/msqrt><\/mfrac><\/mrow><\/mfenced>n<\/mi><\/msup><\/math>\r\n is \r\n–<\/mo>log<\/mi>2<\/mn><\/msub>81<\/mn><\/mrow>2<\/mn>3<\/mn>4<\/mn><\/mfrac><\/mstyle><\/msup><\/mfrac><\/math>\r\n , find the value of\u00a0 \r\nn<\/mi><\/math>\r\n .<\/p>\r\n

4.\u00a0 Find the remainder when\u00a0 \r\n2<\/mn>1003<\/mn><\/msup><\/math>\r\n is divided by 7. (Non Calculator question)<\/p>\r\n

5.\u00a0 If\u00a0 \r\nx<\/mi>n<\/mi><\/msub>–<\/mo>y<\/mi>n<\/mi><\/msub>2<\/mn><\/msqrt>=<\/mo>1<\/mn>–<\/mo>2<\/mn><\/msqrt><\/mrow><\/mfenced>n<\/mi><\/msup><\/math>\r\n \u00a0, then show that<\/p>\r\n

\u00a0 \u00a0 \u00a0 \u00a0a.\u00a0<\/strong> \r\nx<\/mi>n<\/mi><\/msub>2<\/mn><\/msup>–<\/mo>2<\/mn>y<\/mi>n<\/mi><\/msub>2<\/mn><\/msup>=<\/mo>–<\/mo>1<\/mn><\/mrow><\/mfenced>n<\/mi><\/msup><\/math>\r\n<\/p>\r\n

6. (i) Find the first three terms in the expansion, in ascending powers of \r\nx<\/mi><\/math>\r\n , of \r\n1<\/mn>–<\/mo>2<\/mn>x<\/mi><\/mrow><\/mfenced>5<\/mn><\/msup><\/math>\r\n . [2 marks]<\/p>\r\n


\r\n(ii) Given that the coefficient of \r\nx<\/mi>2<\/mn><\/msup><\/math>\r\n in the expansion of \r\n1<\/mn>+<\/mo>a<\/mi>x<\/mi>+<\/mo>2<\/mn>x<\/mi>2<\/mn><\/msup><\/mrow><\/mfenced>1<\/mn>–<\/mo>2<\/mn>x<\/mi><\/mrow><\/mfenced>5<\/mn><\/msup><\/math>\r\n \u00a0is 12, find the value of the constant \r\na<\/mi><\/math>\r\n . [ 3 marks]<\/p>\r\n