MENU
Educational Resources
Exam Papers
Form 1 Videos
Form 2 Videos
Form 3 Videos
Form 4 Videos
Grade 4 Videos
Grade 5 Videos
Grade 6 Videos
Grade 7 Videos
Class 8 Videos
Form 1 Exams
Form 2 Exams
Form 3 Exams
Form 4 Exams
KCSE Videos
Class 8 Exams
Grade 5 Exams
Grade 4 Exams
Grade 3 Exams
Grade 2 Exams
Grade 1 Exams
Online Tests
Online Tuition
Sign In
Join
Get access to thousands of educational resources
Get premium membership
and access revision papers with marking schemes, video lessons and live classes.
OR
Processing. Please wait.
Form 3 Mathematics Questions and Answers on Binomial Expansions
Expand
(
1
+
a
)
5
. Use your expansion to estimate
(
0.8
)
5
correct to four decimal places.
(6m 51s)
2107 Views
SHARE
|
« Previous
Next »
1.
Expand
(
1
+
1
2
x
)
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
-
2
x
)
5
. Use your expansion to evaluate
(
0.98
)
5
to five places of decimal.
4.
Use binomial theorem to expand
(
1
-
1
2
x
)
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
+
2
x
)
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
-
3
x
)
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
(
3
x
-
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
√
2
)
5
+
(
2
-
1
√
2
)
5
17.
(a) Expand the expression
(
1
+
1
2
x
)
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
t
h
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.
×
Share Content Via:
Facebook
Twitter
WhatsApp
Close
Get premium membership