Math 151 – Project 1 (60 points)
Due Thursday 5th January
This Project is to help you to review some of the concepts from Precalc I and II that you will use in this class.
These questions need to be done by hand but you may ask the Tutors and your fellow students to help you solve
any of these problems, but it is important that you are able to do all of these types of questions on your own as
we will be using all of them at some point during the course.
Students Name:_____________________________________________________
Section I
1.
The expression 3x2 – 10x + 3 when factored fully is:A. (3x – 1)(x – 3)
2.
3.
4.
5.
6.
The expression
B. (3x – 1)(x + 3)
C. (3x + 1)(x – 3)
D. (3x + 1)(x + 3)
100y2 – 400x2 when factored fully is:-
A. 100(y2 – 4x2)
B. 100(y + 2x)(y – 2x)
C. (2y + 20x)(2y – 20x)
D. Can’t be factored
The expression 4a2b3 – 8a3b3 when factored fully is:A. 4a2b3(1 – 2a)
B. 4a2b3(– 2a)
D. 4ab(ab2 – 2a2b2)
E some other answer
The expression
3x2 + 10x – 8 when factored fully is:-
A. (3x + 8)(x + 2)
B. (3x – 2)(x + 4)
D. (3x + 2)(x + 4)
E some other answer
2
Simplify x  4 x
x 2  16
x
A
x4
B
x
x4
Add and simplify the following expression
A
–1
C. a2b3(4 – 8a)
B1
C. (3x – 4)(x – 2)
C
1
4
D
x
4
C
4 x
4x
D
4x
4 x
x
4

x4 x4
7.
The equation of the line that passes through the points A(1,7) and B(– 2,1) is
A. y = 2x – 5
8.
B y = ½x + 2
Simplify the following radical expression
A. 2 24
9.
C y = 2x + 5
B. 16 3
The quadratic equation x2 – 4x + 9 =
A 0 solutions
B 1 solution
D y = ½x + 5
48
2 12
C.
D. 4 3
0 has the following number of real number solutions
C 2 solutions
D 3 solutions
10. The solution(s) to the quadratic equation 2x2 + 9 = 59 is:A x = 5 and x = – 5
B. x = 625
C. x = 25
D x = 12.5 and x = – 12.5
Section II
1.
Evaluate the following functions Give your answer as an
(a) For f(x) = x4 – 4x2
+7
x2 1
(b) For g(x) =
x4
(c) For h(x) =
sin x  cos x
cos(2 x)
(d) For h(x) = (e4x – sin x)(e2x + cos x)
exact value in its simplest form
evaluate f(√10)
evaluate g(2)
evaluate h(

)
4
evaluate h(0)
2.
For the function f(x) = x2 – 4x
(a) Find an expression for f(a)
(b) Find an expression for f(a + h)
(c) Find and simplify an expression for
3.
f ( a  h)  f ( a )
h
For the function f(x) = x3
(a) Find an expression for f(a)
(b) Find an expression for f(a + h)
(c) Find and simplify an expression for
f ( a  h)  f ( a )
h
4.
The following question is for a graphing calculator. No working is needed.
For the function f(x) = x3 – 2x2 + x using x-values in the interval (-10,10) answer the following questions.
(i) List the x – intercepts?
Answer = x-intercepts are ……………………..
(ii) List the y – intercept.
Answer = y-intercept is ……………………..
(iii) Give the coordinates of any local minimums (if they exist).
Answer = ……………………………………….
(iv) Give the coordinates of any local maximums (if they exist).
Answer = ……………………………………….
5.
Find the quotient and remainder for the division 4x5 – 8x3 + 6x2 + 12 divided by 2x2 + 1
6.
Factor each of the following expressions as much as possible.
(a) x3 – 5x2 + 6x
(b)
4x2 – 9 =
(b) x4 – 8x2 + 16
7
=
=
Solve the equation 2cos2x – 3cos x + 1 =
8. Verify the identity
(sin t  cos t ) 2
sin t cos t
=
0 (Give all solutions in the range 0  x  2 )
sec t csc t – 2