A LevelMaths: Pure 1CIEExam Questions4. Sequences & Series4.1 Binomial Expansion

Binomial Expansion (CIE A Level Maths: Pure 1)

Exam Questions

2 hours39 questions
Easy
Medium
Hard
Very Hard
1
Sme Calculator3 marks

Evaluate

(i)
4 factorial
(ii)
 C presuperscript 5 subscript 2
(iii)
 C presuperscript 6 subscript 3

How did you do?

Did this page help you?

2
Sme Calculator2 marks

Show that, for all values of k,

      C presuperscript k subscript 1 space equals k

How did you do?

Did this page help you?

3
Sme Calculator3 marks

Expand left parenthesis x plus 2 right parenthesis to the power of 4.

How did you do?

Did this page help you?

4
Sme Calculator3 marks

Find the first three terms, in ascending powers of x, in the expansion of left parenthesis 3 plus 2 x right parenthesis to the power of 8.

How did you do?

Did this page help you?

5
Sme Calculator3 marks

Find the coefficient of the x squared term in the expansion of left parenthesis 2 minus x right parenthesis to the power of 5.

How did you do?

Did this page help you?

6
Sme Calculator3 marks

Expand .left parenthesis 2 x minus 3 right parenthesis to the power of 6.

How did you do?

Did this page help you?

7
Sme Calculator3 marks

In the expansion of left parenthesis p plus x right parenthesis to the power of 12, the coefficient of the x to the power of 5 term is 12 976 128.
Find the value of p.

How did you do?

Did this page help you?

8a
Sme Calculator3 marks

Find the first three terms in the expansion of left parenthesis 5 plus 2 x right parenthesis to the power of 5.

How did you do?

8b
Sme Calculator2 marks

 Use your answer to part (a) to estimate the value of left parenthesis 5.04 right parenthesis to the power of 5.

How did you do?

Did this page help you?

9
Sme Calculator3 marks

In the expansion of left parenthesis p plus x right parenthesis to the power of 4, where p is a non-zero constant, the coefficient of the x squared term is twice the coefficient of the x term.  Find the value of p.

How did you do?

Did this page help you?

1
Sme Calculator3 marks

Expand left parenthesis 2 plus x right parenthesis to the power of 4.

How did you do?

Did this page help you?

2
Sme Calculator3 marks

Find the coefficient of the term in x cubed in the expansion of left parenthesis 2 minus x right parenthesis to the power of 8.

How did you do?

Did this page help you?

3a
Sme Calculator3 marks

Find the first three terms, in ascending powers of x, in the expansion of left parenthesis 3 plus x right parenthesis to the power of 4.

How did you do?

3b
Sme Calculator2 marks

Use your answer to part (a) to estimate left parenthesis 3.1 right parenthesis to the power of 4.

How did you do?

Did this page help you?

4
Sme Calculator2 marks

In the expansion of left parenthesis a minus x right parenthesis to the power of 4, the coefficient of the x squared term is 96.
Given that a greater than 0, find the value of a.

How did you do?

Did this page help you?

5a
Sme Calculator3 marks

Find the first three terms in the expansion of left parenthesis 9 minus 2 x right parenthesis to the power of 5.

How did you do?

5b
Sme Calculator2 marks

Use your answer to part (a) to estimate left parenthesis 8.9 right parenthesis to the power of 5.

How did you do?

Did this page help you?

6
Sme Calculator4 marks

In the expansion of left parenthesis a minus 2 x right parenthesis to the power of 5, the coefficient of the x squared term is equal to the coefficient of the x cubed term.  Find the value of a.

How did you do?

Did this page help you?

7
Sme Calculator3 marks

In the expansion of left parenthesis 3 plus p x right parenthesis to the power of 6, the coefficient of the x to the power of 4 term is four times the coefficient of the x squared term.  Find the possible values of p.

How did you do?

Did this page help you?

8a
Sme Calculator3 marks

Find the first three terms in the expansion of left parenthesis 3 plus 2 x right parenthesis to the power of 8.

How did you do?

8b
Sme Calculator3 marks

Given that x is small such that x cubedand higher powers of x can be ignored show that

         left parenthesis 1 plus x right parenthesis left parenthesis 3 plus 2 x right parenthesis to the power of 8 almost equal to 6561 plus 41553 x plus 116640 x squared 
                 

How did you do?

Did this page help you?

9
Sme Calculator4 marks

In the expansion of left parenthesis p plus q x right parenthesis to the power of 5, the coefficients of the x squared term and the x cubed term are equal.

Find p in terms of q.

How did you do?

Did this page help you?

10a
Sme Calculator3 marks

In the expansion of left parenthesis a plus b x right parenthesis to the power of 4, the coefficient of the x squared term is equal to the coefficient of the x cubed term.

Show that a over b equals 2 over 3.

How did you do?

10b
Sme Calculator2 marks

Given that a and b are integers, and that 10 less than b less than 15, find the values of a and b.

How did you do?

Did this page help you?

1
Sme Calculator3 marks

Fully expand left parenthesis 4 minus x right parenthesis to the power of 4.

How did you do?

Did this page help you?

2
Sme Calculator4 marks

Fully expand  left parenthesis 2 minus begin inline style 1 third end style x right parenthesis to the power of 4.

How did you do?

Did this page help you?

3
Sme Calculator3 marks

Find the coefficient of the term in x to the power of 4 in the expansion of left parenthesis 3 plus 2 x right parenthesis to the power of 9.

How did you do?

Did this page help you?

4a
Sme Calculator3 marks

Find the first three terms, in ascending powers of x, in the expansion of left parenthesis 5 minus 2 x right parenthesis to the power of 4.

How did you do?

4b
Sme Calculator2 marks

Use your answer to part (a) to estimate left parenthesis 4.5 right parenthesis to the power of 4.

How did you do?

Did this page help you?

5
Sme Calculator3 marks

In the expansion of left parenthesis 4 minus p x right parenthesis to the power of 6, the coefficient of the x to the power of 4 term is 19 440.
Given that p is a positive integer find the value of p.

How did you do?

Did this page help you?

6
Sme Calculator3 marks

In the expansion of left parenthesis 3 a minus 2 x right parenthesis to the power of 6 comma the coefficient of the x cubed term is equal to the coefficient of the x to the power of 4 term.  Find the value of a.

How did you do?

Did this page help you?

7a
Sme Calculator3 marks

Find the first three terms in the expansion of left parenthesis 2 minus 3 x right parenthesis to the power of 7.

How did you do?

7b
Sme Calculator3 marks

Given that x is small such that x cubed and higher powers of x can be ignored show that

         left parenthesis 1 minus 2 x right parenthesis left parenthesis 2 minus 3 x right parenthesis to the power of 7 almost equal to 128 minus 1600 x plus 8736 x squared 
                 

How did you do?

Did this page help you?

8
Sme Calculator3 marks

In the expansion of left parenthesis p plus q x right parenthesis to the power of 8, the coefficients of the x squared term and the x to the power of 6 term are equal.

Find p in terms of q.

How did you do?

Did this page help you?

9
Sme Calculator3 marks

In the expansion of left parenthesis 1 plus x right parenthesis to the power of n comma the coefficient of the x cubed term is 84.

Find the value of n.

How did you do?

Did this page help you?

10
Sme Calculator5 marks

In the expansion of left parenthesis a plus b x right parenthesis to the power of 4 comma the coefficient of the x cubed term is 216.

In the expansion of left parenthesis a plus b x right parenthesis to the power of 6 comma the coefficient of the x to the power of 4 term is 4860.

Find the possible values of a and b.

How did you do?

Did this page help you?

1
Sme Calculator3 marks

Expand .left parenthesis 3 minus 2 x right parenthesis to the power of 5

How did you do?

Did this page help you?

2
Sme Calculator3 marks

Find the coefficient of the term in x to the power of 4 in the expansion of left parenthesis 4 minus 3 x right parenthesis to the power of 7..

How did you do?

Did this page help you?

3
Sme Calculator3 marks

Given that C presuperscript n subscript 3 equals 35 find the value of n.

How did you do?

Did this page help you?

4a
Sme Calculator5 marks

Use the first three terms, in ascending powers of x, in the expansion of left parenthesis 3 minus 5 x right parenthesis to the power of 4 to find an approximation for left parenthesis 2.6 right parenthesis to the power of 4.

How did you do?

4b
Sme Calculator2 marks

Using your calculator, find the percentage error in the approximation from part (a) to the exact value of left parenthesis 2.6 right parenthesis to the power of 4.

How did you do?

Did this page help you?

5
Sme Calculator3 marks

In the expansion of left parenthesis m minus 1 fourth x right parenthesis to the power of 5, the coefficient of the x cubed term is -10.
Find the possible values of m.

How did you do?

Did this page help you?

6
Sme Calculator3 marks

In the expansion of  left parenthesis 3 a plus begin inline style 1 half end style x right parenthesis to the power of 6, the coefficient of the x cubed term is equal to the coefficient of the x to the power of 5 term.  Find the values of a, giving your answers in the form fraction numerator square root of m over denominator n end fraction, where m and n are integers to be found.

How did you do?

Did this page help you?

7a
Sme Calculator3 marks

Find the first three terms in the expansion of left parenthesis 4 minus 3 x right parenthesis to the power of 9.

How did you do?

7b
Sme Calculator3 marks

Given that x is small such that x cubed and higher powers of x can be ignored show that

            left parenthesis 3 minus 2 x squared right parenthesis left parenthesis 4 minus 3 x right parenthesis to the power of 9 almost equal to 786432 minus 5308416 x plus 15400960 x squared
                 

How did you do?

Did this page help you?

8
Sme Calculator3 marks

In the expansion of left parenthesis p plus q x right parenthesis to the power of 9, the coefficient of the x cubed term is double that of the x to the power of 5 term.  Find p in terms of q.

How did you do?

Did this page help you?

9
Sme Calculator4 marks

In the expansion of left parenthesis 1 minus 3 x right parenthesis to the power of n comma the coefficient of the x cubed term is -3240.

Find the value of n.

How did you do?

Did this page help you?

10
Sme Calculator5 marks

In the expansion of left parenthesis a plus b x right parenthesis to the power of 8 comma the coefficient of the x to the power of 5 term is -870 912.

In the expansion of left parenthesis a plus b x right parenthesis to the power of 12 comma the coefficient of the x cubed term is -1 557 135 360.

Find the possible values of a and b.

How did you do?

Did this page help you?