Revision Test 2
This Revision Test covers the material contained in Chapters 5 to 7.The marks for each question are shown in
brackets at the end of each question.
- Evaluate correct to 4 significant figures:
(a) sinh2.47 (b) tanh0. 6439
(c) sech 1.385 (d) cosech 0. 874 (6)
- The increase in resistance of strip conductors
due to eddy currents at power frequencies is
given by:
λ=
αt
2
[
sinhαt+sinαt
coshαt−cosαt
]
Calculateλ, correct to 5 significant figures, when
α= 1 .08 andt=1. (5)
- If Achx−Bshx≡4ex−3e−x determine the
values ofAandB.(6) - Solve the following equation:
3 .52chx+ 8 .42shx= 5. 32
correct to 4 decimal places. (7)
- Determine the 20th term of the series 15. 6 , 15 ,
14. 4 , 13. 8 ,... (3) - The sum of 13 terms of an arithmetic progression
is 286 and the common difference is 3. Determine
the first term of the series. (4) - An engineer earns £21000per annum and receives
annual increments of £600. Determine the salary
in the 9th year and calculate the total earnings in
the first 11 years. (5) - Determine the 11th term of the series 1. 5 , 3 , 6 ,
12 , ... (2)
9. Find the sum of the first eight terms of the series
1 , 2. 5 , 6. 25 ,...,correct to 1 decimal place. (4) - Determine the sum to infinity of the series
5 , 1 ,^15 ,... (3) - A machine is to have seven speeds ranging from
25rev/min to 500rev/min. If the speeds form a
geometricprogression,determinetheir value,each
correct to the nearest whole number. (8) - Use the binomial series to expand( 2 a− 3 b)^6.
(7) - Determine the middle term of
(
3 x−
1
3 y
) 18
.
(6)
- Expand the following in ascending powers oftas
far as the term int^3
(a)
1
1 +t
(b)
1
√
( 1 − 3 t)
For each case, state the limits for which the
expansion is valid. (12)
- Whenxis very small show that:
1
( 1 +x)^2
√
( 1 −x)
≈ 1 −
3
2
x (5)
- The modulus of rigidityGis given byG=
R^4 θ
L
whereRis the radius,θtheangleoftwistand
Lthe length. Find the approximate percentage
error inGwhenRis measured 1.5% too large,
θis measured 3% too small andLis measured
1% too small. (7)