Revision Test 3
This Revision Test covers the material contained in Chapters 8 to 10. The marks for each question are shown in
brackets at the end of each question.
1. Use Maclaurin’s series to determine a power series
for e 2x cos 3x as far as the term in x 2 .
( 9 )
2. Show, using Maclaurin’s series, that the first four
terms of the power series for cosh 2x is given by:
cosh 2x = 1 + 2x
2
+
2
3
x
4
+
4
45
x
6
.
(10)
3. Expand the function x
2 ln(1 + sin x) using
Maclaurin’s series and hence evaluate:
1
2
0
x
2 ln(1 + sin x) dx correct to 2 significant
figures.
(13)
4. Use the method of bisection to evaluate the root
of the equation: x 3 + 5x = 11 in the range x = 1 to
x = 2, correct to 3 significant figures.
(11)
5. Repeat question 4 using an algebraic method of
successive approximations.
(16)
6. The solution to a differential equation associated
with the path taken by a projectile for which the
resistance to motion is proportional to the velocity
is given by:
y = 2.5(e
x
− e
−x
) + x − 25
Use Newton’s method to determine the value of x,
correct to 2 decimal places, for which the value of
y is zero.
(10)
7. Convert the following binary numbers to decimal
form:
(a) 1101 (b) 101101.0101
(5)
8. Convert the following decimal number to binary
form:
(a) 27 (b) 44.1875
(9)
9. Convert the following decimal numbers to binary,
via octal:
(a) 479 (b) 185.2890625
(9)
10. Convert
(a) 5F 16 into its decimal equivalent
(b) 132 10 into its hexadecimal equivalent
(c) 110101011 2 into its hexadecimal equivalent
(8)