1.1 

2.1 

(a) comma should be replaced by decimal point

(e) asterisk should be omitted

(f) exponent must be integer

(h) comma should be replaced by decimal point

2.2 

(b) decimal point not allowed

(c) first character must be a letter

(d) quotes not allowed

(h) blanks not allowed

(i) allowed but not recommended!

(k) asterisk not allowed

(l) allowed but not recommended!

.

2.3 

2.4 

2.5 

(a) expression not allowed on left-hand side

(b) left-hand side must be valid variable name

(c) ditto

2.6 

2.7 

2.8 

2.9 

 t = a;

 a = b;

 b = t;

2.10 

2.11 

2.12 

2.13 

2.14 

2.15 

 sum(2: 2: 200)

2.16 

 m = [5 8 0 10 3 8 5 7 9 4];

 disp( mean(m) )

2.17 

x = 2.0833, a = 4.

2.18 

2.19 

2.21 

 r = 5;

 c = 10;

 l = 4;

 e = 2;

 w = 2;

i = e / sqrt(r ^ 2 + (2 * pi * W * l-1 / (2 * pi * w * c))^ 2)

2.22 

2.24 

2.26 

2.27 

2.28 

3.1 You should get a picture of tangents to a curve.

3.2 

(a) 4(b)2

(c)  The algorithm (attributed to Euclid) finds the HCF (Highest Common Factor) of two numbers by using the fact that the HCF divides exactly into the difference between the two numbers, and that if the numbers are equal, they are equal to their HCF.

3.3 

3.4 

3.6 

4.2 

4.3 

4.5 

4.6 

5.2 

5.3 

5.7 

6.5 

7.1 

 function pretty(n, ch)

 line = char(double(ch)*ones(1,n));

 disp(line)

7.2 

7.3 

 function y = double(x)

 y = x * 2;

7.4 

 function [xout, yout] = swop(x,y)

 xout = y;

 yout = x;

7.6 

7.8 

8.1 

8.2 

8.3 

8.5 

8.6 

8.8 

8.10 

9.1 

9.2 

9.4 

9.6 

11.1 

13.1 

13.2 

13.4 

14.1 

(a)  Real roots at 1.856 and −1.697, complex roots at −0.0791 ± 1.780i.

(b)  0.589, 3.096, 6.285, …(roots get closer to multiples of π).

(c)  1, 2, 5.

(d)  1.303.

(e)  −3.997, 4.988, 2.241, 1.768.

14.2 Successive bisections are: 1.5, 1.25, 1.375, 1.4375, and 1.40625. The exact answer is 1.414214…, so the last bisection is within the required error.

14.3 22 (exact answer is 21.3333).

14.4 After 30 years the exact answer is 2117 ().

14.6 The differential equations to be solved are:

The exact solution after 8 h is and .

14.8 

14.9