Pure Mathematics Year 2 (A Level) Unit Test 5: The Binomial Theorem
1 a Find the binomial expansion of in ascending powers of x up to and
including the x2 term, simplifying each term. (4 marks)
b State the set of values of x for which the expansion is valid. (1 mark)
c Show that when , the exact value of is . (2 marks)
d Substitute into the binomial expansion in part a and hence obtain an
approximation to . Give your answer to 5 decimal places. (3 marks)
2 Given that in the expansion of the coefficient of the x2 term is 75 find:
a the possible values of a (4 marks)
3
b the corresponding coefficients of the x term. (2 marks)
3 The first three terms in the binomial expansion of are
a Find the values of a and b. (5 marks)
b State the range of values of x for which the expansion is valid. (2 marks)
c Find the value of c. (2 marks)
4
a Show that the first three terms in the series expansion of f(x) can be written as
(7 marks)
b Find the exact value of f (0.01). Round your answer to 7 decimal places. (2 marks)
c Find the percentage error made in using the series expansion in part a to
estimate the value of f (0.01). Give your answer to 2 significant figures. (3 marks)
5
a Find the values of the constants A, B and C. (6 marks)
b Hence, or otherwise, expand in ascending powers of x, as far as
the x2 term. (6 marks)
c Explain why the expansion is not valid for . (1 mark)
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1 a Find the binomial expansion of in ascending powers of x up to and
including the x2 term, simplifying each term. (4 marks)
b State the set of values of x for which the expansion is valid. (1 mark)
c Show that when , the exact value of is . (2 marks)
d Substitute into the binomial expansion in part a and hence obtain an
approximation to . Give your answer to 5 decimal places. (3 marks)
2 Given that in the expansion of the coefficient of the x2 term is 75 find:
a the possible values of a (4 marks)
3
b the corresponding coefficients of the x term. (2 marks)
3 The first three terms in the binomial expansion of are
a Find the values of a and b. (5 marks)
b State the range of values of x for which the expansion is valid. (2 marks)
c Find the value of c. (2 marks)
4
a Show that the first three terms in the series expansion of f(x) can be written as
(7 marks)
b Find the exact value of f (0.01). Round your answer to 7 decimal places. (2 marks)
c Find the percentage error made in using the series expansion in part a to
estimate the value of f (0.01). Give your answer to 2 significant figures. (3 marks)
5
a Find the values of the constants A, B and C. (6 marks)
b Hence, or otherwise, expand in ascending powers of x, as far as
the x2 term. (6 marks)
c Explain why the expansion is not valid for . (1 mark)
© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 1
