Summer Preparation for PRECALCULUS
This worksheet is a review of the objectives for Precalculus and is due on the first day back to school.
It is to be done NEATLY and on a SEPARATE sheet of paper. Have a great summer!
In exercises 1 – 2 find the points that are symmetric to the given point (a) across the x-axis, (b) across
the y-axis, and (c) across the origin.
1.
(1, 4)
2.
(2, -3)
3.
Find equations for the vertical and horizontal lines through the point (1, 3).
4.
Graph each of the following. State the domain and range.
a.
b.
y  x3
y
c.
d.
y  e x e. y  ln x
y
Domain: ______________
Range: _______________
Absolute Max: ________________
Local Max: __________________
Absolute Min: _________________
Local Min: ___________________
Increasing interval(s): ____________
Decreasing interval(s): ____________
Bounded Above, Below or Both? _______
Function?(Explain)_________________
(5, 6)
(-4, 4)
(-6, 0)
(1.5, -1)
6.
x
1
g. y  x  1
x2
Determine the following properties for the function graphed.
f.
5.
y  ( x  1) 2  3
Write an equation for the polynomial graphed at right.
-2
7.
3
4
Find the domain restrictions for the following:
1
x
a.
f ( x) 
d.
f ( x)  x
b.
e.
f ( x) 
1
x2
f ( x)  x  1
c.
f.
f ( x)  log x
f ( x) 
g.
1
2
x  3x  2
f ( x)  log x  5
8.
Factor completely.
a. 4 x  4 x
b. 8 x  2 x  15
3
2
c.
49  25 x 2
d.
x 2  15 x  56
b.
 1 4


 625 
x  1 5x
1


3x  6 6 x  2
9.
Solve.
10.
11.
Solve by factoring: 3 x  10 x  13 x
12.
Solve by square root property: 3( x  5)  27
13.
Solve by completing the square: x  4 x  7  0
2
Solve by quadratic formula: 2 x
2
 5x  7
2
2
3
14.
Simplify:
a.
log 3 27
Determine the lengths of the missing sides of the special right triangles.
15. A 45- 45- 90 triangle.
16. A 30- 60- 90 triangle.
24
10
y
30
x
x
17. Given the right triangle below, determine the trig functions, using SOH CAH TOA:
sin  = __________
13
5

18.
Fill in blank.
cos  = __________
tan  = __________
12
a. The sum of the interior angles of a triangle is __________.
b. A 45-45-90 triangle has sides with ratio measures ____________.
c. A 30-60-90 triangle has sides with ratio measures ____________.
d. In a triangle, the largest angle is opposite the __________.
e. In a triangle, the smallest angle is opposite the ___________.
f. In a triangle, if two angles are equal in measure then __________.
y