masl1 christmas practice
TRANSCRIPT
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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
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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) ..................................................................
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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.
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(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) ..................................................................
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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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