Download Honors Algebra 2 Summer Worksheet # 1. Due the first day

Honors Algebra 2 Summer Worksheet # 1.
#
=
#
Due the first day of class.
= .
Always reduce fractions!!!!
Adding/Subtracting Fractions: The denominators have to be the same. Then add/subtract the top.
2 10
12
2 1
2 2 4
1
5
1
1 12 1 13
+
→
→ 42. + + → = .3 + →
+ →
3 3
3
5 10
5 2 10 10
10 2
4
4 4
4
+1
5
3( + 1) 5
3 +3 8 +3
−3
4(3 )
−3
12 + − 3
→
+
→
+
→
$.3 +
→
+
→
. +
3
5
5(3)
3(5)
15
15
15
4
4(1)
4
4
13 − 3
→
4
' $'
'
.'
.' $' /'
.'
&'
.' &'
0'
&. +
(()*+ ,- ) → +
=
/.
+ .'(()*+.',- ) →
+
→
&
&
&
&
&
Be careful of the “-“ in front of the second fraction. It implies to multiply everything by -1
5
+1 5
− −1
4 −1
3
4 −1 9
−2(4 − 1) 9 − 8 + 2
+2
−
→
+
→
1.
−
→
+
→
→
0.
3
3
3
3
3
2
3
6
6
6
6
1.
Multiplying Fractions: Multiply the numerators; Multiply the denominators.
Reduce any numerator with any
denominator. Add exponents when multiplying monomials. Subtract exponents when dividing…
4
7
47; :<;
47
7
:<
4
7;∗4;
9; F
∗ :9 =>?@A? :9 B 5 CD@ :8 B 5E → 5∗5 → G
:8
(;H:)
: 4(;H:)
5;
8; J 5;
; J 5;
5; K
∗
→ I 13.5 7 ∗ → ∗ →
=
5
4
:<
:
:<
: 4
4
9
10. 5 ∗ 8 = :8 11.
7;
:<(;H:)
9;
12. :8 ∗
→
Dividing Fractions: Find the reciprocal of the second fraction (flip it) and then multiply.
8
8<
8
7;
:∗:
:
9;
9;
14. 9; ÷ 7; → 9; ∗ 8< → 4∗:< = 4< 15. 48 ÷ 16 → 48 ÷
Multi-tiered Fractions:
16.
17.
JU
V
FW
X
4
X
K
=
=
7;
Y
F
Z
X
K
÷
4<
5
4∗8
:∗5
=
M
N
O
P
Q
S
Q
T
= R÷T = R∗S =
→
=
7;
Y
5
;5
QT
RS
so a shortcut is
5;
M
N
O
P
9;
:
;
:
;
→ 48 ∗ :I = 48 ∗ 4 = 8<
QT
= RS
∗ 4< → Y(8) = 58 Or use the shortcut
:<
5
:I
:
JU
V
FW
X
7;∗5
5;
= Y∗4< = 58
Substituting in fractions. Just plug them in and simplify carefully.
18. f(x) = 2x2 – 3x – 4. Find f(-1/2) 2(-1/2)2 – 3(-1/2) – 4 2(-1/2)(-1/2) – 3(-1/2) – 4 2(1/4) +3/2 – 4 ½ + 3/2 + 8/2 12/2 6
Factoring Fractions: Sometimes in Algebra, the number in front of x2 needs to be 1 so the number in front of x2 is
factored
19. 2x2 – 11x 2(x2 – 11x/2)
20. 1/2x2 – 8x ½ (x2 – 16x) (8 divided by ½ is 16!)
Simplifying Radicals.Look for the radicand sets of the coefficients. Bring one number out and discard the others.
Multiply anything that comes out together; multiply anything left inside together. For exponents, divide the exponent
by the radicand. The quotient comes out and the remainder stays in.
\
√#n is the radicand.
X
21. √54
:5 (>C@ACD@]3): X√3
Answer: a √.a
22. 5b96
J
If ‘n’ isn’t there then the radicand is a ‘2’
Y9
∗ 3 ∗ 3 ∗ 23AB?]B&2]C]D. :5
]4`1]Bx4
5
Y
J
9
comes out; x1 stays in
→ 5√2 ∗ 2 ∗ 2 ∗ 2 ∗ 2 ∗ 32AB?]B&(2 ∗ 3)]C]D. 7 ]1`3; 7 ]2`0]BDB]C]D.
J
Answer: 5 ∗ 2 4 √6
5
→ dae. √&a
:
Y
23. 5b72 Y (>C@ACD@]2) → √2 ∗ 2 ∗ 2 ∗ 3 ∗ 3(2 ∗ 3)AB?]B2]C]D. 4 ]0`1; 4 ]3`1
Answer: 5 ∗ 2 ∗ 3 5 b2 = e b.ae
Adding Radicals: Simplify the inside of the radicals. Add the outsides if the insides are the same.
24.5√3 − 2√5 − √5 + 3√3 → 0√ − √$
25. 8√12 − 5√75 → 8√2 ∗ 2 ∗ 3 − 5√3 ∗ 5 ∗ 5 → 16√3 − 25√3 → −1√
Multiplying Radicals: Multipliy the outside numbers.Mulitply the inside numbers. Simplify the inside.
26. 5√6 ∗ 3√2 = 5 ∗ 3√6 ∗ 2 = 15√2 ∗ 3 ∗ 2 = √
X
X
X
X
27.14√20 ∗ √2 = 14√2 ∗ 2 ∗ 5 ∗ 2 = 28√5
Dividing Radicals: Divide/Reduce outside numbers. Divide reduce inside numbers. If there is a radical in the
denominator then multiply top and bottom by the bottom radical.
√Y √5
√4:
√4:
∗ →
→
5
√5 √5
√G
:8
5
5 √5
√5
→
∗ =
29.
:<√5
4 √5 √5
4 √5 √5
28.
=
5 √5
4√5∗5
→
5 √5
4∗5
=
√5
4
You are also expected to be able to add, multiply, and divide up to 3-digit numbers without a calculator.
Simplify the following on separate paper without using your calculator. Show work. Use your calculator to check
your answers. Some of the answers will be on-line for you to check your answers also.
1. 5/3 + 7/3
6.
11.
x
4
−
4 x 8x
8g
9
∗
:9<
g
16. 4b120
2. ¾ - 2
7.
5g
7
−
8
3. 1/5 – 4/7 + 13/35
8g
I
12. I; ÷
IG
20. (4√5)(√10)
4<;
:8
8.
21. (3√10)4
8
− 2h
9. I ∗
8
13. 9 ÷ 100
17. b−250 :I
X
5g
7
x x +1
−
4
4
4.
18. 5√8 − 3√2
9 √5
√4
22. 7
14.
4<;
:8
KU
ZF
ZW
iUF
23.
4 √5
8 √I
28. F(x) = -2x2 + 4x + 1. Find f(3/2)
29-30. Multiply without a calculator. Show work:
29. 29(345)
30. (-123)(.00014)
31-32. Perform the long division without a calculator. Leave answers with remainders:
31. 165 divide by 12 32. 14567/15
Recall that the distance formula is: b(a. − ad ). + (e. − ed ).
33. Find the distance between (-2,3) and (-1,4)
34. Find the radius of the circle that has the endpoints (-3,5) and (-1,3)
10.
15.
19. 5√18 − √50 + √240
24-26. Factor out the number so that x2 is by itself. (See examples 19 & 20)
24. -3x2 – 16x
25. ½ x2 – 7x
26. ¾ x2 – 21x
27-28. Simplify:
27. f(x) = 3x2 – 2x – 10. Find f(-1/2)
5.
x x +1
−
4
3
8
9
∗6
4<
K
jU