Mass and Kg
THE COLLEGES OF OXFORD UNIVERSITY
PHYSICS
Wednesday 5 November 2008
Time allowed: 2 hours
For candidates applying for Physics, and Physics and Philosophy
There are two parts (A and B) to this test, carrying equal weight.
Attempt as many questions as you can from each part. Write on white A4 lined paper. At the end of the test put your answer sheets in order and collate with a treasury tag. Attach a cover sheet to your answers. DO NOT write your name anywhere except on the cover sheet.
Marks for each question are indicated in the right hand margin. There are a total of 100 marks available and total marks for each section are indicated at the start of a section. You are advised to divide your time according to the marks available, and to spend equal effort on parts A and B.
No calculators, tables or formula sheets may be used.
Answers in Part A should be given exactly unless indicated otherwise. Numeric answers in Part B should be calculated to 2 significant figures.
Use g = 10 m s−2 .
Do NOT turn over until told that you may do so.
Part A: Mathematics for Physics [50 Marks]
Answers in Part A should be given exactly unless indicated otherwise.
1. Evaluate the sum of integers 1 + 2 + 3 + · · · + 99 + 100.
[3]
2. Evaluate (0.25)−1/2 and (0.09)3/2
[4]
3. The first three terms of the series expansion of (1 + x)m are:
1 + mx +
m(m − 1)x2
.
2
Find the first three terms in the series expansion of (1+ x)m+1 (1 − 2x)m .
[5]
4. Find the set of values of x for which x2 + 2
< 3.
1 − x2
[3]
5. Given that x = log9 2, find, in terms of x, (i) log2 9; (ii) log8 3.
[4]
6. Find the two values of x for which 1, x2 , x are successive terms of an arithmetic progression.
[3]
2
3
4
7. Determine the value of a such that the curve y = x + x + x + x + · · ·
2
3
4
and the line y = ax have the same gradient at x = 0. What value will a have if instead they have the same gradient at x = 1 ?.
[4]
4
8. The points (5,2)
PHYSICS
Wednesday 5 November 2008
Time allowed: 2 hours
For candidates applying for Physics, and Physics and Philosophy
There are two parts (A and B) to this test, carrying equal weight.
Attempt as many questions as you can from each part. Write on white A4 lined paper. At the end of the test put your answer sheets in order and collate with a treasury tag. Attach a cover sheet to your answers. DO NOT write your name anywhere except on the cover sheet.
Marks for each question are indicated in the right hand margin. There are a total of 100 marks available and total marks for each section are indicated at the start of a section. You are advised to divide your time according to the marks available, and to spend equal effort on parts A and B.
No calculators, tables or formula sheets may be used.
Answers in Part A should be given exactly unless indicated otherwise. Numeric answers in Part B should be calculated to 2 significant figures.
Use g = 10 m s−2 .
Do NOT turn over until told that you may do so.
Part A: Mathematics for Physics [50 Marks]
Answers in Part A should be given exactly unless indicated otherwise.
1. Evaluate the sum of integers 1 + 2 + 3 + · · · + 99 + 100.
[3]
2. Evaluate (0.25)−1/2 and (0.09)3/2
[4]
3. The first three terms of the series expansion of (1 + x)m are:
1 + mx +
m(m − 1)x2
.
2
Find the first three terms in the series expansion of (1+ x)m+1 (1 − 2x)m .
[5]
4. Find the set of values of x for which x2 + 2
< 3.
1 − x2
[3]
5. Given that x = log9 2, find, in terms of x, (i) log2 9; (ii) log8 3.
[4]
6. Find the two values of x for which 1, x2 , x are successive terms of an arithmetic progression.
[3]
2
3
4
7. Determine the value of a such that the curve y = x + x + x + x + · · ·
2
3
4
and the line y = ax have the same gradient at x = 0. What value will a have if instead they have the same gradient at x = 1 ?.
[4]
4
8. The points (5,2)