Download AppCalcSummer Work.tst

Summer Work for Students Entering AP Calculus
Please show all your work.Algebra is the backbone of
Calculus. Take this seriously.
Perform the indicated operation.
1) (6n5 + 18n4 - 19) - (3n5 - 15n4 - 12)
2) -2(q2 - 4q + 2) + 2(-1q2 + q - 5)
3) (x - 2y)(-4x + 8y)
4)
2
5
m - 2 m + 2
3
3
1
5) (3x + 4y)(4x - 11y + 1)
6) (2x - y)3
Factor out the greatest common factor.
7) 14m2 - 15r3
Factor completely. State that the polynomial is prime if it cannot be factored.
8) 15y2 + 22y + 8
9) 108x2 + 63xy + 9y2
2
10) 147a4 - 27b2
11) x2 - 15x + 225
Factor completely.
12) 1000y3 - 343
Write the expression in lowest terms.
(y + 4)(y - 2)
13)
(y - 2)(y + 3)
3
14)
a2 - 8a
(a + 2)(a - 8)
15)
y2 + 2y - 15
y2 - 4y - 45
Perform the indicated operation and simplify.
k2 + 14k + 45
k2 + 7k
16)
· k2 + 16k + 63 k2 + 12k + 35
4
Perform the indicated operations and simplify.
3
5
17) + r r - 1
18)
4
6
- z2 z
19)
2ab
b
6
- + a2 - b2 a - b 2
5
Solve the equation.
3
1 2
20) z - 4z + = 10
5 5
1
1
21) (6x - 8) = (16x - 12)
2
4
Solve the equation. If the solutions involve square roots, give both the exact solutions and the
approximate solutions to three decimal places.
22) 8k2 - 39k - 5 = 0
6
23) x2 - x = 56
2
t
24) = t -3t - 4
25)
4
x2 - 3x + 2
+ 5
x2 + 4x - 5
= 1
x2 + 3x - 10
Write the expression in interval notation. Graph the interval.
26) 2 < x ≤ 3
7
Using the variable x, write the interval as an inequality.
5
27) -∞, 3
Solve the inequality, then graph the solution.
21x + 21
28)
> 6x + 6
3
29) -2 < 10 - 5x
≤ 5
4
Solve the quadratic inequality. Graph the solution.
30) s2 - 3s - 28 < 0
8
Solve the inequality. Write your answer using fractions or decimal numbers rounded to the
nearest hundredth, as appropriate.
x2 + x
31)
≤ 2
x2 - 1
Evaluate the expression. Write your answer without exponents.
4-3
32)
3-4
33) -(-2-3)
Simplify the expression. If the expression contains any variables, assume that they represent
positive real numbers. Write your answer with only positive exponents.
x-5
34)
(9x)-5
9
35)
x-2y-2
x2y-6
1/2
Simplify the expression, writing the answer as a single term without negative exponents.
m-1 + z-1
36)
m-1 - z-1
37)
x-2
x-2 - y-2
Evaluate the expression.
38) 2561/4
10
39) 815/4
Simplify the expression. Write the answer with only positive exponents. Assume that all variables
represent positive real numbers.
x6/5 · y3/2
40)
x4/5 · y-7/2
Factor the expression.
41) (9q + 7)(3q + 7) + (9q + 7)(q - 7)
42) 15(p + 1)2 + 17(p + 1) + 4
11
-1/2
43) x(3x + 2)2(x2 - 3)
+ 3(x2 - 3)1/2(3x + 2)
44) 10x2(x2 + 2)2 - 2x(2x3 + 1)(x2 + 2)
Simplify. Assume that all variables represent positive real numbers.
4
45) - 512
46)
3
216x4y5
12
Rationalize the denominator. Assume that all radicands represent positive real numbers.
3
47)
5 + 9
48)
x + 1
2 x - 4
Rationalize the numerator.
x + y
49)
8x
Simplify the expression, writing the answer as a single term without negative exponents.
(3m + 2n)-1
50)
4m-2 - 9n-2
13
Perform the indicated operations and simplify. Assume all variables represent positive real
numbers.
51) 3 + 7 147 + 5 192
4
4
52) 9 x7 - 4x x3
14