Honors Pre-Calculus Summer Review Packet
The following problems are a review of some of the material in Honors Algebra II. You are
encouraged to refer to your Honors Algebra II notes to guide you through this assignment.
Complete the entire packet on loose leaf, showing all steps. You must bring this work with you
to the first class in September.
Check your answers, which are listed at the end of the packet.
Page 1
Honors Pre-Calculus Summer Review
Linear Equations
1. Find the equation of the line, in standard form, that is perpendicular to the line containing
(6,1) and (4,-3) and has the same y-intercept as 2x-3y = 6.
2. Find the equation of the line, in standard form, that goes through the vertex of the parabola
= 2 − 12 + 16 and that is parallel to 2 − 3 = 6.
Solve each equation for x.
3.
3x 2 1
5
+ = x−
4
3 2
6
4.
2 x −1 2
=
4x + 3 3
5.
x+3 x
+ =7
5
3
6.
x
1
+
=3
x −4 x+2
7.
2 x − 1 + 11 =16
2
8. −5 x − 7 + 2 = − 13
9.
−2 x + 5 =13
10. 2 x + 1 − 2 = x
11.
2x − 5 − 5 = 0
12.
4x + 1 = 5 − x
Page 2
13. 2√ − 5 + 4 = 0
14. 3( + 1) − 9 = 15
15. − 3 + 2 = 0
Solve each inequality for x, using interval notation.
16. 2 −
3x
1
≥x−
2
4
17. −3(2 − 5) > 2( + 1) − 7
18. −3 ≤ 2 + 5 < 7
19. 3x − 2 > 7
20. 12 x 2 − 3 ≥ − 5 x
21.
3x + 2
≤1
4
x
1
22. - 3 + < − 2
3
2
23. 4 ≤
5
3
− 2n −
4
4
Honors Pre-Calculus Review
Page 3
Honors Pre-Calculus Review
Mixed Review:
24. Given () = − − 3 − 10, evaluate , (−2), and (5).
25. Find the sum and the product of
26. Solve for p: # =
$
%&'
!
and
"
.
.
27. Factor Completely (u-substitution): ( − 7 − 8.
28. Factor Completely (u-substitution): 3(* + 5) + 2(* + 5) − 21.
29. Reduce to lowest terms:
30. Reduce to lowest terms:
+ , ""+
.
. /".
. ". /
31. Simplify by rationalizing:
!√
.
..
√("√
32. Simplify √ − 6 + 9.
33. Determine the domain and range of the function: 0() = 2√ − 1 + 3.
34. Determine the domain of the function: 0() =
, "-
, "
.
"
35. Determine the domain and range of the relation: ( + 4) + ( − 9) = 25.
Page 4
Honors Pre-Calculus Review
36. Given 0() = + 2 and () = 4 − , determine 0((−4)).
37. Given 0() = + 2 and () = 4 − , determine (0()).
38. Determine the inverse of ℎ() =
"
.
39. Determine the inverse of () = − 1.
40. Determine the end behavior of 0() = −6 + 2 2 − 3 + 5 + 4.
ANSWERS TO THE HONORS PRE-CALCULUS SUMMER REVIEW
1. x + 2 y = − 4
2. 2 x − 3 y = 12
3. x = − 6
4. x = − 4.5
5.
x = 12
6.
x=
7.
1 ± 31
3
x = 3, x = − 2
8.
x = 4, x = 10
9.
x=±4
10. x = ± 1
11. x = 15
12. x = 2
13. x = − 3
14. x = 15
15. x = 0, x = ± 1, x = ± 2
16. ( −∞,0.9]
17. ( −∞, 2.5 )
18. [ −4,1)
5

19.  −∞, −  ∪ (3, ∞ )
3

3
1
20. (−∞, − ] ∪ [ ∞)
4
3,
2
21. [ −2, ]
3
22. ( −∞, − 18) ∪ (6, ∞)
7
23. ( −∞, − ] ∪ [3, ∞)
4
100
1
24. g   = −
, g ( −2 ) = − 8, g ( 5 ) = − 50
9
 3
12
9
25. a)
, b)
2
4− x
4 − x2
2W
26. p = 2
V CA
27. ( x − 2 ) ( x 2 + 2 x + 4 ) ( x + 1) ( x 2 − x + 1)
28. ( 3n + 8 )( n + 8 )
29. − ( y + 3)
30. −
31.
1
m
3 6 5 2
+
or ≈ 3.605
4
4
32. x − 3
33. D : x ≥ 1; R : y ≥ 3
34. D : x ≠ −1,3
35. D :[−9,1]; R :[4,14]
36. −10
37. − x 2 − 4 x
38.
2 x − 5 −2 x + 5
or
−3
3
39. y = 3 2 x + 2
40. Up on left, down on right or x → −∞ as y → ∞; x → ∞ as y → − ∞