Calculus with Applications Summer Review Packet
This packet is a review of the entering objectives for Calculus/Applications and is due on the first
day back to school. Please show all work NEATLY and on a SEPARATE sheet of paper.
Have a great summer!!
1. Simplify. Show work that leads to your answer.
x3  8
b)
x2
x4
a) 2
x  3x  4
5 x
c)
x
2
 25
2. Trigonometric Pythagorean Identities: a) ______________ b) ______________ c) ______________
3. Simplify each expression. Write answers with positive exponents where applicable:
1
1

a)
xh x
1
f) log
100
2
2
b) x
10
x5
g) ln e
12 x 3 y 2
c)
18 xy  1
7
h) 27
2
3
2
3
3
2
5
3
d) (5a )( 4a )
e) (4a )
I) log 1 8
j) ln 1
3
2
2
4. Solve 4x + 10yz – 3 = 0 for z
5. Given: f(x) = {(3, 5), (2, 4), (1, 7)}
a) h(g(x))
g ( x)  x  3
h(x) = x 2  5 find, simplified:
c) f -1 (x) (inverse)
b) g(h(-2))
d) to find g-1 (x) (inverse) you switch _____ and then solve for _____. Fill in the blanks and then
find the inverse.
5
6. Expand and simplify:
 3n  6
n2
(remember

means sum)
7. Using EITHER the slope/intercept (y = mx + b) or the point slope ( y  y1  m( x  x1 )) form of a line,
write an equation for the lines described: SHOW ALL WORK
a) with slope -2, containing the point (3, 4)
b) containing the points (1, -3) and (-5, 2)
c) with slope 0, containing the point (4, 2)
d) parallel to 2x – 3y = 7 and passes through (5,1)
e) perpendicular to the line in problem #7 a, containing the point (3, 4)
8. Without a calculator, determine the exact value of each expression:
a)
sin
e) cos

2

3
b) sin
3
4
c) cos 
f) tan
7
4
g) tan
2
3
9. For each function: Make a neat sketch, putting numers on each axis
For #d, e, f and g also write the equations of the asymptotes
a) y = sin x
7
6
d) cos
h) tan

2
Name the Domain and Range
b) y  x 3  2 x 2  3x
c) y  x 2  6 x  1
f) y  e x
d) y 
x4
x 1
e) y = ln x
g) y 
1
x
h) y 
j) y  x  3  2
k) y 
x2  4
x2
x4
i) y  3 x
l) y 
x2  4
10. Make a neat sketch of the piecewise function:
x 2 if x < 0
y = x + 2 if 0 < x < 3
4 if x > 3
11. Solve for x, where x is a real number. Show the work that leads to your solution:
a) 2 x 2  5 x  3
b) ( x  5) 2  9
c) (x + 3)(x – 3) > 0
d) log x + log(x – 3) = 1
e) x  3 < 7
f) ln x = 2t – 3
g) 12 x 2  3 x
h) 27 2 x  9 x 3
i) x 2  2 x  15 < 0
12. Determine all points of intersection:
a) parabola y  x 2  3x  4 and the line y = 5x + 11
b) y = cos x and y = sin x in the first quadrant