V1.1 (40) Find the triple
(x, y, z) so that
x + 2y - z = 4
x - 4y + z = 2
x +2y
=0
V1.2. (30) The universe is
{1, 2, 3, 4, 5, 6, 7, 8, 9}
A = {1, 2, 3, 4, 5}
B = {2, 4, 6, 8}.
Find: ( A ' B ')'
V1.3 (30) We define a binary
operation by
x * y  2x  y.
Solve: 4*(x*4) = 6.
V1.4 (40) Give the equations
of all asymptotes to the graph:
2x  5
y 2
x  x2
2
V1.5 (15) Give, in interval
notation, the range of the
function
f ( x)  x  3x  5
3
V1.6 (40) Find the coefficient
2 2
of a b in the expansion of
( a  b)
4
V1.7. (30) Find the ycoordinate of the vertex of the
parabola
y  x  4x  2
2
V1.8 (30) Let
f ( x)  2 x  3 g ( x)  x  1
Find: f ( g ( f ( g ( x))))
V1.9 (30) Calculate

k  20
k 1
(2k  1)
V1.10 (30) (-2,0) and (2,0)
are the end points of the
hypotenuse of a right triangle.
Give, in standard form, the
equation of the locus of points
for the third vertex.
V1.11 (30) I roll two dice.
What is the probability their
product is 4?
V1.12 (45) Find all solutions
in [0, ) of
tan   cot 
V2.1. (40) How many
different ways are there to
arrange the letters
{a, b, c, d, e}
in order so there are no two
consecutive consonants.
V2.2. (40) Solve for x:
2x 2
2x
(
)  2(
) 1  0
3x  2
3x  2
V2.3 (30) What is the range
of the function?
f ( x)  x  4 x
4
2
V2.4 (30) Solve for x:
x  3  x  10  7
V2.5 (30) Simplify
log 2 27
log 2 9
V2.6 (40) If (3a  2b) is
multiplied out, what is the
2 2
coefficient of a b ?
4
V2.7 (30) Solve for x:
log3 ( x  1)  log 3 ( x  1)  3
5 1
V2.8 (40) cos36 
.
4
0
Write sin18 in radical form.
o
V2.9 (20) Give the area
inside the ellipse:
2
x
2
 y 1
4
V2.10 (30) If I roll two dice,
what is the probability the
product of the numbers is even?
V2.11 (30) What is tan 2 if
sin   3/ 5
 / 2  
V2.12. (30) Simplify
4
log 2 7
V3.1 (40) The numbers x, y,
and z are in ratio 2 to 3 to 4.
Their product is 3. What is x?
V3.2 (40) If we multiply out
the polynomial
(x-1)(x-2)(x-3)(x-4)
then what is the coefficient of
3
x?
V3.3 (40) . What is A if:
2x  1

2
x  3x  2
A

x2
B
x 1
V3.4 (20) Give a3 if
2
an  an 1 a0  8.
3
V3.5 (40) If i  1 then find
in simplified form
2
(1  i )
8
V3.6 (30) Find the
determinant:
2 1 1
1 4 2
6 3 3
V3.7 (30) Perform the base
five division:
4004 five /13 five  ???? five
V3.8. (30) Find the sum of
the binomial coefficients:
 4  4  4  4  4
 0   1    2    3    4 
         
V3.9. (30) Solve, giving your
answer in interval form:
| | x  1| 2 |  3
V3.10. (40) I draw 3 cards at
random from an ordinary deck.
What is the probability (in
lowest terms) that all three are
red?
V3.11 (30) A triangle has
0
0
0
angles 30 , 45 , and 105 . The
second longest side has length
2 . What is the length of the
shortest side?
V3.12. (20) Find the limit:
10
x
lim x
x  2
V4.1 (30)
f ( x)  3 x  8
1
g ( x)  2 x  1
1
Find f ( g (3))
V4.2. (30) If we multiply out
the polynomial
(x+1)(x+2)(x+3)(x+4)
what is the coefficient of x?
V4.3 (40) Two sides of a
triangle have lengths 2 and 3.
The angle between them is  / 3.
What is the length of the third
side?
V4.4. (40) 3  2 2 can be
written in the form a  b 2
where a and b are integers.
What is b?
V4.5 (30) i  1. Write in
simplest form:
2
( 3  i)
6
V4.6 (30) Find the sum of
the binomial coefficients:
 4  4  4  4  4
 0   1    2    3    4 
         
V4.7 (40) Give, in interval
notation, the range of the
function
f ( )  sin  cos
V4.8 (30) Three of the roots
of
f ( x)  x  ax  bx  cx  12
4
3
2
are 1, -1, and 2. What is the
fourth root?
V4.9 (40) Find the inverse
matrix of:
1 1 
1 2 


V4.10. (30) Give the
mathematicians A , B, C, and D
in correct historical order.
A.
B.
C.
D.
Hilbert
Gauss
Euclid
Fermat
3x  2
V4.11 (40) f ( x) 
x 1
Find f '(2)
V4.12 (30) What is the name
for the set of functions which,
for all a, satisfy:
lim f ( x)  f (a)
x a