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.
1. Evaluate correct to 4 significant figures:
(a) sinh 2.47 (b) tanh 0.6439
(c) sech 1.385 (d) cosech 0.874
(6)
2. The increase in resistance of strip conductors
due to eddy currents at power frequencies is
given by:
λ =
αt
2
sinh αt + sin αt
cosh αt − cos αt
Calculate λ, correct to 5 significant figures, when
α = 1.08 and t = 1.
(5)
3. If A ch x − B sh x ≡ 4e
x
− 3e
−x determine the
values of A and B.
( 6 )
4. Solve the following equation:
3.52 ch x + 8.42 sh x = 5.32
correct to 4 decimal places.
(7)
5. Determine the 20th term of the series 15.6, 15,
14.4, 13.8, ...
(3)
6. 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)
7. An engineer earns £21000 per 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)
8. 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)
10. Determine the sum to infinity of the series
5, 1,
1
5 , ...
(3)
11. A machine is to have seven speeds ranging from
25 rev/min to 500 rev/min. If the speeds form a
geometric progression, determine their value, each
correct to the nearest whole number.
(8)
12. Use the binomial series to expand (2a − 3b) 6 .
(7)
13. Determine the middle term of
3x −
1
3y
18
.
(6)
14. Expand the following in ascending powers of t as
far as the term in t 3
(a)
1
1 + t
(b)
1
√ (1 − 3t )
For each case, state the limits for which the
expansion is valid.
(12)
15. When x is very small show that:
1
(1 + x) 2 √
(1 − x)
≈ 1 −
3
2
x
(5)
16. The modulus of rigidity G is given by G =
R 4 θ
L
where R is the radius, θ the angle of twist and
L the length. Find the approximate percentage
error in G when R is measured 1.5% too large,
θ is measured 3% too small and L is measured
1% too small.
(7)
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.
1. Evaluate correct to 4 significant figures:
(a) sinh 2.47 (b) tanh 0.6439
(c) sech 1.385 (d) cosech 0.874
(6)
2. The increase in resistance of strip conductors
due to eddy currents at power frequencies is
given by:
λ =
αt
2
sinh αt + sin αt
cosh αt − cos αt
Calculate λ, correct to 5 significant figures, when
α = 1.08 and t = 1.
(5)
3. If A ch x − B sh x ≡ 4e
x
− 3e
−x determine the
values of A and B.
( 6 )
4. Solve the following equation:
3.52 ch x + 8.42 sh x = 5.32
correct to 4 decimal places.
(7)
5. Determine the 20th term of the series 15.6, 15,
14.4, 13.8, ...
(3)
6. 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)
7. An engineer earns £21000 per 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)
8. 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)
10. Determine the sum to infinity of the series
5, 1,
1
5 , ...
(3)
11. A machine is to have seven speeds ranging from
25 rev/min to 500 rev/min. If the speeds form a
geometric progression, determine their value, each
correct to the nearest whole number.
(8)
12. Use the binomial series to expand (2a − 3b) 6 .
(7)
13. Determine the middle term of
3x −
1
3y
18
.
(6)
14. Expand the following in ascending powers of t as
far as the term in t 3
(a)
1
1 + t
(b)
1
√ (1 − 3t )
For each case, state the limits for which the
expansion is valid.
(12)
15. When x is very small show that:
1
(1 + x) 2 √
(1 − x)
≈ 1 −
3
2
x
(5)
16. The modulus of rigidity G is given by G =
R 4 θ
L
where R is the radius, θ the angle of twist and
L the length. Find the approximate percentage
error in G when R is measured 1.5% too large,
θ is measured 3% too small and L is measured
1% too small.
(7)