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Form 3 Mathematics Questions and Answers on Binomial Expansions
Use binomial expansion to evaluate #(2 + 1 / sqrt2 )^5# +# (2 - 1/sqrt2 )^5#
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1.
Expand #(1+ 1/2x)^8# up to the term in #x^3#. By putting x= 0.1, find the approximate value of #(1.05)^8# to 2 decimal places.
2.
Write down the first four terms of #(p+q)^8# using binomial expansion. Use your expansion to evaluate #(9.99)^8# to the nearest 100.
3.
Obtain the binomial expansion for #(1-2x)^5#. Use your expansion to evaluate #(0.98)^5# to five places of decimal.
4.
Use binomial theorem to expand #(1 - 1/2x)^8# up to the fourth term. Use your expansion to evaluate #(0.98)^8# by taking x = 0.04
5.
By making use of binomial expansion, determine the value of #(2.002)^4# to four decimal places.
6.
Expand #(1+2x)^10# up to the term in #x^3#. Hence use your expansion to estimate #(0.95)^10# correct to three decimal places.
7.
Expand #(1+a)^5#. Use your expansion to estimate #(0.8)^5# correct to four decimal places.
8.
Expand and simplify #(1-3x)^5#, up to the term in #x^3#. Hence use your expansion to estimate #(0.97)^5# correct to 4 decimal places.
9.
(a) Write down the simplified expansion of #(1+x)^6#. (b) Use the expansion up to the fourth term to find the value of #(1.03)^6# to the nearest one thousandth.
10.
Expand #(1+x)^5#, hence, use the expansion to estimate #(1.04)^5# correct to 4 decimal places.
11.
Expand #(2+x)^5# in ascending powers of x up to the term in #x^3#. Hence, approximate the value of #(2.03)^5# to 4 s.f.
12.
(a) Expand #(a-b)^6# (b) Use the first three terms of the expansion in (a) to find the approximate value of #(1.98)^6#
13.
(a) Expand and simplify the binomial expression #(2-x)^6# (b) Use the expression up to the term in #x^2# to estimate #(1.99)^6#
14.
(a) Expand #(1+x)^5# (b) Use the first three terms of the expansion in (a) to find the approximate value of #(0.98)^5#
15.
Expand and simplify #(3x-y)^4#. Hence use the first three terms of the expansion to approximate the value of #(60.2)^4#
16.
Use binomial expansion to evaluate #(2 + 1 / sqrt2 )^5# +# (2 - 1/sqrt2 )^5#
17.
(a) Expand the expression #(1+ 1/2x)^5# in ascending powers of x, leaving the coefficients as fractions in their simplest form. (b) Use the first three terms of the expansion in (a) above to estimate the value of #(1 1/20)^5#
18.
(a) Expand and simplify the expression #(10+ 2 )^5# (b) Use the expansion in (a) above to find the value of #14^5#
19.
(a) Expand and simplify the binomial expression #(2-x)^7# in ascending powers of x. (b) Use the expansion up to the fourth term to evaluate #(1.97)^7# correct to 4 decimal places.
20.
(a) Expand and simplify #(2-x)^5# (b) Use the first 4 terms of the expansion in part (a) above to find the approximate the value of #(1.8)^5# to 2 decimal places
21.
Expand and simplify the expression #(a + 1/2)^4# + #(a - 1/2)^4#
22.
(a) Expand #(1+x)^7# up to the #4^(th)# term. (b) Use the expansion in part (a) above to find the approximate value of #(0.94)^7#
23.
(a) Expand #(1-x)^5#. (b) Use the expansion in (a) up to the term in #x^3# to approximate the value of #(0.98)^5#
24.
Expand #(3-x)^7# up to the term of containing #x^4#. Hence find the approximate value of #(2.8)^7#
25.
Use the expression of #(x-y)^5# to evaluate #(9.8)^5# correct to 4 decimal places.
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