CHRISTMAS NEW YEAR’S PRACTICE

BINOMIAL

1.Find the coefficient of x5 in the expansion of (3x – 2)8

Working:

Answers:

....……………………………………..........

2. Find the coefficient of a3b4 in the expansion of (5a + b)7.

Working:

Answers:

....……………………………………..........

3. Find the coefficient of a5b7 in the expansion of (a + b)12.

Working:

Answers:

....……………………………………..........

4. Determine the constant term in the expansion of .

2–

9

2

xx

1

Working:

Answers:

…………………………………………..

5. Use the binomial theorem to complete this expansion.

(3x +2y)4 = 81x4 + 216x3 y +...

Working:

Answers:

…………………………………………..

6. Consider the binomial expansion .

3

4

2

4

1

41)1( 4324 xxxxx

(a) By substituting x = 1 into both sides, or otherwise, evaluate .

3

4

2

4

1

4

(b) Evaluate

8

9

7

9

6

9

5

9

4

9

3

9

2

9

1

9

.

Working:

Answers:

(a) …………………………………………..

(b) ..................................................................

2

7. Consider the expansion of .

1–3

92

xx

(a) How many terms are there in this expansion?

(b) Find the constant term in this expansion.

Working:

Answers:

(a) …………………………………………..

(b) ..................................................................

8. Find the coefficient of x3 in the expansion of (2 – x)5.

Working:

Answer:

…………………………………………..

9. Find the term containing x10 in the expansion of (5 + 2x2)7.

Working:

Answer:

…………………………………………..

10. Complete the following expansion.

3

(2 + ax)4 = 16 + 32ax + …

Working:

Answer:

…………………………………………..

11. Find the term containing x3 in the expansion of (2 – 3x)8.

Working:

Answer:

…………………………………………........

12. Consider the expansion of (x2 – 2)5.

(a) Write down the number of terms in this expansion.

(b) The first four terms of the expansion in descending powers of x are

x10 – 10x8 + 40x6 + Ax4 + ...

Find the value of A.

Working:

Answers:

(a) ..................................................................

(b) ..................................................................

4

13. The equation x2 – 2kx + 1 = 0 has two distinct real roots. Find the set of all possible values of k.

Working:

Answer:

…………………………………………..

14. Consider the function f(x) = 2x2 – 8x + 5.

(a) Express f(x) in the form a (x – p)2 + q, where a, p, q .

(b) Find the minimum value of f(x).

Working:

Answers:

(a) …………………………………………..

(b) ..................................................................

PLEASE READ CAREFULLY AND PRACTICE WITH YOUR GRAPHIC CALCULATOR DEDICATE TIME IT IS VEY

IMPORTANT TOREPEAT THE STEPS UNTIL YOU KNOW THEM BY HEART!!!

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