1. A function f(x) is defined as: (0.5 x^2) if x < 1 , and (-2) if x = 1 , and (3 - x) if x > 1 . Which statement is false about this piece-wise defined function?

a) The function f(x) is defined for all values of x.

b) The function is discontinuous.

c) The value of the function at x = 4 equals 8.

d) The function has a jump discontinuity at x = 1 .

e) The graph of the function passes through the point A(5 , - 2 ).

2. Given the exponential equation (9/4)^(x+3) = (8/27)^(-5) , the exact value of the square root of the equation's single root equals:

a) 2 (2 ) / 3

b) 9 (2 )

c) (2 )

d) (2 ) / 2

e) 3 (2 ) / 2

f) - 2 (2 ) / 3

g) 4 (2 )

h) None of the given options are correct.

i) - 3 (2 ) / 2

3. If the common logarithm of x , that is log x equals 8, then the logarithm of (x^2) to the base 0.1 equals:

a) -1

b) 10

c) 1

d) - 24

e) - 4

f) - 16

g) 80

h) 0.8

i) - 8

j) 8

k) 16

l) - 32

4. Given that p = 5 q , the value of [log (p)^(-1) - log (q)^(-1)] correct to 3 decimal places equals:

a) - 0.278

b) - 0.2

c) - 2.796

d) 5

e) 2.796

f) 1.398

g) - 1.398

h) 0.699

i) 0.278

j) 0.2

5. Which one of the following numbers equals to the common logarithm of R, that is log (R), given that 3 ^ [ log(1/R)+(1/2) log(1/10000)] = 1 / 81 ?

a) 10000

b) - 4

c) 1

d) 100

e) log(4)

f) 0.25

g) 4

h) 0.1

i) -0.01

j) 0.25 log (4)

6. When the polynomial (2a^3 - 7a + 6) , is divided by the binomial (7a - 4), the remainder is:

a) 343/814

b) 814 / 343

c) 407 / 343

d) 343 / 407

e) - 343 / 407

f) - 407 / 343

g) - 814 / 343

h) - 343/814

i) 37821 / 1184

j) -37821 / 1184

k) None of the given options are correct.

7. The binomial (x^2 - 3x - 4) is a factor of the cubic polynomial (x^3 - 6 x^2 + m x + n), where m and n are integers. The value of (m+n) equals:

a) 7

b) 5

c) 12

d) 17

e) 8

f) - 7

g) - 5

h) 18

i) 3

8. Which one of the following is NOT an exact root of the equation x^4 - 8 x^3 + 13 x^2 = 18 - 12x ?

a) 1

b) 2 + 25

c) 3

d) 2 - 10

e) All of the given options are the roots of the equation.

9. The sum of the periods of the functions y = 4 tan (16 x) and y = 16 cot (4 x) equals 5 / 8 .

a) True

b) False

10. A quartic function f(x) = x^4 has undergone some transformations and its equation has become g(x) = 3(x+6)^4 - 48 . The average (arithmetic mean) of ALL zeros of this quartic function equals:

a) 6

b) - 2

c) 8

d) None of the given options are correct.

e) - 6

f) - 8

g) 0

h) - 4

i) 12

j) 32