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Form 3 Mathematics Questions and Answers on Binomial Expansions

Form 3 Mathematics Binomial Expansions Questions and Answers.
In this course, we are going to solve several questions on binomial expansion, which is a Form 3 Mathematics topic.

Lessons (25)

• 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.
  9m 21s

• 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.
  9m 35s

• 3.    Obtain the binomial expansion for #(1-2x)^5#. Use your expansion to evaluate #(0.98)^5# to five places of decimal.
  7m 19s

• 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
  7m 55s

• 5.    By making use of binomial expansion, determine the value of #(2.002)^4# to four decimal places.
  5m 46s

• 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.
  10m 39s

• 7.    Expand #(1+a)^5#. Use your expansion to estimate #(0.8)^5# correct to four decimal places.
  6m 51s

• 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.
  7m 37s

• 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.
  7m 27s

• 10.    Expand #(1+x)^5#, hence, use the expansion to estimate #(1.04)^5# correct to 4 decimal places.
  6m 15s

• 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.
  6m 40s

• 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#
  7m 3s

• 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#
  8m 43s

• 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#
  6m 21s

• 15.    Expand and simplify #(3x-y)^4#. Hence use the first three terms of the expansion to approximate the value of #(60.2)^4#
  7m 3s

• 16.    Use binomial expansion to evaluate #(2 + 1 / sqrt2 )^5# +# (2 - 1/sqrt2 )^5#
  7m 28s

• 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#
  7m 28s

• 18.    (a) Expand and simplify the expression #(10+ 2 )^5# (b) Use the expansion in (a) above to find the value of #14^5#
  7m 55s

• 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.
  7m 42s

• 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
  5m 49s

• 21.    Expand and simplify the expression #(a + 1/2)^4# + #(a - 1/2)^4#
  5m 28s

• 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#
  6m 11s

• 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#
  5m 14s

• 24.    Expand #(3-x)^7# up to the term of containing #x^4#. Hence find the approximate value of #(2.8)^7#
  7m 17s

• 25.    Use the expression of #(x-y)^5# to evaluate #(9.8)^5# correct to 4 decimal places.
  6m 14s