Mathematical Background Sample Questions - Mathematics Assignment Help

Assignment Task:

Task:

1. Evaluate -2(2-6)/(4-7)

2. Simplify the expression: (y 2 -9) / [ -(y-3)(y+2) / (3y 3 ) ]

3. Expand in increasing powers of y -1 : (1+3y -1 ) 3

4. Which of the following are correct?
a) |y-3| = y+3,
b) |y-3| = y-3,
c) |y-3| = the greater of 3-y and y+3
d) |y-3| = the greater of –y+3 and -3+y
e) |y-3| = the lesser of 3-y and y+3
f) |y-3| = the lesser of –y+3 and -3+y

5. Consider the following product: 2a 2 ?3b 3 . To which of the following expressions is it equivalent (there may be more than one):
a) 6a 2 b 3
b) 5a 2 b 3
c) 5(ab) 3 /a
d) 6(a 2 b 2 ) 2 /(a 2 b)

6. Consider the following expression: (3a -1 ) 2 /(6ab -3/2 ) 2 . To which of the following expressions is it equivalent:

a) (-3a) 2 /(-6ab 3/2 ) 2
b) 4b -3
c) 4b 3
d) 1/(4b 3 )
e) b 3 /(4a 4 )
f) 4a -4 b -3

7. This question concerns square roots.

(i) ?(a 2 +b 2 ) = a+b True or False?
(ii) ?(4a+12b) = 4?(a+3b) True of False?

8. In scientific notation, the expression: 3.24E-02 means

(a) 324,
(b) 3.24
(c) 0.0324
(d) 1/(32.4) 2
(e) 1/(64.8)
(f) 1.24

9. Check the appropriate boxes for each of the following numbers (in some cases several boxes may be checked for the one number; in other cases, none may be checked).

Note: i = ?(-1)

real integer rational irrational
-3 ? ? ? ?
5 / 7 ? ? ? ?
1.4037 ? ? ? ?
e ? ? ? ?
2/π ? ? ? ?
2+3i ? ? ? ?

10. Find the roots of each of the following equations (i.e. find the values of x for which the equality holds):
(a) 2x + 3 = 5
(b) x 2 - 5x + 6 = 0

11. Solve the pair of equations below
(in other words, find the point (x,y) that is common to the two lines)
y = x + 4
2y = 3x – 12

12. The following functions

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