Daily Math
Week 37 (2013-2014)
Mon. May 19, 2014
Tues. May 20, 2014
Wed. May 21, 2014
Thurs. May 22, 2014
1
Monday, May 19, 2014
1st
Given: 𝑓 𝑥 = 2𝑥
Find: 𝑓(3)
2
Monday, May 19, 2014
1st
Given: 𝑓 𝑥 = 2𝑥
Find: 𝑓(3)
Answer: Substitute 3 for x:
3
2 =𝟖
3
Monday, May 19, 2014
2nd
Given: 𝑓 𝑥 = 3𝑥
Find: 𝑓(2)
4
Monday, May 19, 2014
2nd
Given: 𝑓 𝑥 = 3𝑥
Find: 𝑓(2)
Answer: Substitute 2 for x:
2
3 =𝟗
5
Monday, May 19, 2014
3rd
Given: 𝑓 𝑥 = 2 𝑥 + 1 + 3
Find: 𝑓(3)
6
Monday, May 19, 2014
3rd
Given: 𝑓 𝑥 = 2 𝑥 + 1 + 3
Find: 𝑓(3)
Answer: Substitute 3 for x:
2 3+1 +3
2 4 + 3 = 𝟏𝟏
7
Monday, May 19, 2014
4th
Complete the table:
Term 1
Value 2
2
4
3
8
4
16
5
32
6
7
8
8
Monday, May 19, 2014
4th
Complete the table:
Term 1
Value 2
2
4
3
8
4
16
5
32
6
7
8
64 128 256
Answer:
Table shows a common ratio of 2.
(Each term is multiplied by 2 to get the next term).
Thus, the next terms are 64, 128, 256.
9
Monday, May 19, 2014
5th
Complete the table:
Term 1 2
Value 66 50
3
34
4
18
5
6
7
8
10
Monday, May 19, 2014
5th
Complete the table:
Term 1 2
Value 66 50
3
34
4
18
5
2
6
7
8
-14 -30 -46
Answer: Table shows a common difference
of -16.
Thus, the next terms are 2, -14, -30, -46.
11
Monday, May 19, 2014
6th
Complete the table:
Term 1
Value -3
2
9
3
-27
4
81
5
6
7
8
12
Monday, May 19, 2014
6th
Complete the table:
Term 1
Value -3
2
9
3
-27
4
81
5
6
7
8
-243 729 -2187 6561
Answer: Table shows a common ratio
of -3. Thus, the next terms are -243,
729, -2187, 6561.
13
Monday, May 19, 2014
7th
Complete the table:
Term 1
2 3 4
Value 160 80 40 20
5
6
7
8
14
Monday, May 19, 2014
7th
Complete the table:
Term 1
2
Value 160 80
3
40
4
20
5
10
6
5
7
8
2.5 1.25
Answer: Table shows a common ratio
1
.
2
of Thus, the next terms are 10, 5,
2.5, 1.25.
15
Tuesday, May 20, 2014
1st
Complete the table:
Term 1
Value -9
2
-2
3
5
4
12
5
6
7
8
16
Tuesday, May 20, 2014
1st
Complete the table:
Term 1
Value -9
2
-2
3
5
4
12
5
19
6
26
7
33
8
40
Answer: Table shows a common
difference of 7. Thus, the next terms
are 19, 26, 33, 40.
17
Tuesday, May 20, 2014
2nd
Complete the table for the equation:
𝑥
x
y
𝑦=4
1
2
3
4
5
18
Tuesday, May 20, 2014
2nd
Complete the table for the equation:
𝑥
𝑦=4
x
y
Answer: 41
42
43
44
45
=𝟒
= 𝟏𝟔
= 𝟔𝟒
= 𝟐𝟓𝟔
= 𝟏𝟎𝟐𝟒
1
4
2
3
4
16
64
256
5
1024
19
Tuesday, May 20, 2014
3rd
Complete the table for the equation:
𝑥
𝑦 = (−3)
x
y
1
2
3
4
5
20
Tuesday, May 20, 2014
3rd
Complete the table for the equation:
𝑥
𝑦 = (−3)
x
y
Answer: (−3)1 = −𝟑
(−3)2 = 𝟗
(−3)3 = −𝟐𝟕
(−3)4 = 𝟖𝟏
(−3)5 = −𝟐𝟒𝟑
1
-3
2
3
4
9
-27
81
5
-243
21
Tuesday, May 20, 2014
4th
Complete the table for the equation:
x
y
𝑦 = −3𝑥
1
2
3
4
5
22
Tuesday, May 20, 2014
4th
Complete the table for the equation:
𝑥
𝑦 = −3
x
y
Answer: −31 = −𝟑
2
−3 = −𝟗
3
−3 = −𝟐𝟕
−34 = −𝟖𝟏
5
−3 = −𝟐𝟒𝟑
1
-3
2
3
4
-9
-27
-81
5
-243
23
Tuesday, May 20, 2014
5th
Complete the table for the equation:
𝑦 = 10𝑥
x
y
1
2
3
4
5
24
Tuesday, May 20, 2014
5th
Complete the table for the equation:
𝑦 = 10𝑥
x
Answer: 101
102
103
104
105
= 𝟏𝟎
= 𝟏𝟎𝟎
= 𝟏𝟎𝟎𝟎
= 𝟏𝟎𝟎𝟎𝟎
= 𝟏𝟎𝟎𝟎𝟎𝟎
1
y
10
2
3
4
100
1000
10000
5
100000
25
Tuesday, May 20, 2014
6th
Solve this equation for x:
3 𝑥 − 1 = 2(𝑥 + 3)
26
Tuesday, May 20, 2014
6th
Solve this equation for x:
3 𝑥 − 1 = 2(𝑥 + 3)
Answer: 3 𝑥 − 1 = 2(𝑥 + 3)
3𝑥 − 3 = 2𝑥 + 6
3𝑥 − 3 + 3 = 2𝑥 + 6 + 3
3𝑥 = 2𝑥 + 9
3𝑥 − 2𝑥 = 2𝑥 − 2𝑥 + 9
𝒙=𝟗
27
Tuesday, May 20, 2014
7th
Solve this equation for x:
7 𝑥 + 20 = 𝑥 + 5
28
Tuesday, May 20, 2014
Solve this equation for x:
7 𝑥 + 20 = 𝑥 + 5
Answer: 7 𝑥 + 20 = 𝑥 + 5
7𝑥 + 140 = 𝑥 + 5
7𝑥 − 𝑥 + 140 = 𝑥 − 𝑥 + 5
6𝑥 + 140 = 5
6𝑥 + 140 − 140 = 5 − 140
6𝑥 = −135
6𝑥 ÷ 6 = −135 ÷ 6
𝒙 = −𝟐𝟐. 𝟓
7th
29
Wednesday, May 21, 2014
1st
Solve this equation for x:
9 𝑥 − 2 = 3𝑥 + 3
30
Wednesday, May 21, 2014
1st
Solve this equation for x:
9 𝑥 − 2 = 3𝑥 + 3
Answer: 9 𝑥 − 2 = 3𝑥 + 3
9𝑥 − 18 = 3𝑥 + 3
9𝑥 − 3𝑥 − 18 = 3𝑥 − 3𝑥 + 3
6𝑥 − 18 = 3
6𝑥 − 18 + 18 = 3 + 18
6𝑥 = 21
6𝑥 ÷ 6 = 21 ÷ 6
𝒙 = 𝟑. 𝟓
31
Wednesday, May 21, 2014 2nd
Solve this equation for x:
1
2
2
2 𝑥−
=
𝑥+
3
5
3
32
Wednesday, May 21, 2014 2nd
Solve this equation for x:
1
2
2
2 𝑥−
=
𝑥+
3
5
3
Answer: 2𝑥 − 23 = 25 𝑥 + 154
10
2
2
2
2
𝑥− 𝑥− = 𝑥− 𝑥
5
5
3
5
5
8
2
4
𝑥 − 3 = 15
5
8
2
2
4
2
𝑥
−
+
=
+
5
3
3
15
3
8
4
10
𝑥= +
5
15
15
8
14
𝑥 = 15
5
5 8
5 14
𝑥
=
8 5
8 15
70
𝟕
𝑥=
=
120
𝟏𝟐
+
4
15
33
Wednesday, May 21, 2014 3rd
Solve this equation for x:
3 𝑥+3 −2 𝑥−1 =0
34
Wednesday, May 21, 2014
3rd
Solve this equation for x:
3 𝑥+3 −2 𝑥−1 =0
Answer: 3 𝑥 + 3 − 2 𝑥 − 1 = 0
3𝑥 + 9 − 2𝑥 + 2 = 0
𝑥 + 11 = 0
𝑥 + 11 − 11 = 0 − 11
𝒙 = −𝟏𝟏
35
Wednesday, May 21, 2014
4th
Find the slope of the line that contains
these points: (3, 7) and (5, 10).
36
Wednesday, May 21, 2014
4th
Find the slope of the line that contains
these points: (3, 7) and (5, 10).
Answer: 𝑆𝑙𝑜𝑝𝑒 =
𝑦2 −𝑦1
𝑥2 −𝑥1
𝑆𝑙𝑜𝑝𝑒 =
10−7
5−3
=
𝟑
𝟐
37
Wednesday, May 21, 2014
5th
Find the slope of the line that contains
these points: (-1, 4) and (3, 3).
38
Wednesday, May 21, 2014
5th
Find the slope of the line that contains
these points: (-1, 4) and (3, 3).
Answer: 𝑆𝑙𝑜𝑝𝑒 =
𝑆𝑙𝑜𝑝𝑒 =
𝑦2 −𝑦1
𝑥2 −𝑥1
3−4
3−(−1)
=
−1
4
=
𝟏
−
𝟒
39
Wednesday, May 21, 2014
6th
Find the slope of the line that contains
these points: (0, 0) and (-2, 5).
40
Wednesday, May 21, 2014
6th
Find the slope of the line that contains
these points: (0, 0) and (-2, 5).
Answer: 𝑆𝑙𝑜𝑝𝑒 =
𝑦2 −𝑦1
𝑥2 −𝑥1
𝑆𝑙𝑜𝑝𝑒 =
5−0
−2−0
=
5
−2
=
𝟓
−
𝟐
41
Wednesday, May 21, 2014
7th
Find the slope of the line that contains
these points: (-1, -5) and (-4, -5).
42
Wednesday, May 21, 2014
7th
Find the slope of the line that contains
these points: (-1, -5) and (-4, -5).
Answer: 𝑆𝑙𝑜𝑝𝑒 =
𝑆𝑙𝑜𝑝𝑒 =
𝑦2 −𝑦1
𝑥2 −𝑥1
−5−(−5)
−4−(−1)
=
0
−3
=𝟎
43
Thursday, May 22, 2014
1st
Find the next 3 terms in this sequence
and identify the common difference.
3, 8, 13, 18, 23, __, __, __
Common difference = ___
44
Thursday, May 22, 2014
1st
Find the next 3 terms in this sequence and
identify the common difference.
3, 8, 13, 18, 23, __, __, __
Common difference = ___
Answer: Common difference is 8 – 3 = 5
23 + 5 = 28; 28 + 5 = 33; 33 + 5 = 38
3, 8, 13, 18, 23, 28, 33, 38
45
Thursday, May 22, 2014
2nd
Find the next 3 terms in this sequence
and identify the common difference.
11, 9, 7, 5, 3, __, __, __
Common difference = ___
46
Thursday, May 22, 2014
2nd
Find the next 3 terms in this sequence and
identify the common difference.
11, 9, 7, 5, 3, __, __, __
Common difference = ___
Answer:
Common difference is 9 – 11 = -2
3 + (-2) = 1; 1 + (-2) = -1; -1 + (-2) = -3
11, 9, 7, 5, 3, 1, -1, -3
47
Thursday, May 22, 2014
3rd
Find the next 3 terms in this sequence
and identify the common difference.
3, 1.5, 0, -1.5, -3, __, __, __
Common difference = ___
48
Thursday, May 22, 2014
3rd
Find the next 3 terms in this sequence and
identify the common difference.
3, 1.5, 0, -1.5, -3, __, __, __
Common difference = ___
Answer:
Common difference is 1.5 – 3 = -1.5
-3 + (-1.5) = -4.5;
-4.5 + (-1.5) = -6;
-6 + (-1.5) = -7.5
3, 1.5, 0, -1.5, -3, -4.5, -6, -7.5
49
Thursday, May 22, 2014
4th
Find the missing terms in the sequence
and state the common difference:
5, 11, ___, 23, 29, ___
Common difference = ___
50
Thursday, May 22, 2014
4th
Find the missing terms in the sequence
and state the common difference:
5, 11, ___, 23, 29, ___
Common difference = ___
Answer:
Common difference = 11 – 5 = 6
So… 5, 11, 17, 23, 29, 35
51
Thursday, May 22, 2014
5th
Find the missing terms in the sequence
and state the common difference:
7, 3, -1, ___, ___, -13
Common difference = ___
52
Thursday, May 22, 2014
5th
Find the missing terms in the sequence
and state the common difference:
7, 3, -1, ___, ___, -13
Common difference = ___
Answer:
Common difference = 3 – 7 = -4
7, 3, -1, -5, -9, -13
53
Thursday, May 22, 2014
6th
Find the missing terms in the sequence
and state the common difference:
8, ___, ___, 47, 60
Common difference = ___
54
Thursday, May 22, 2014
6th
Find the missing terms in the sequence
and state the common difference:
8, ___, ___, 47, 60
Common difference = ___
Answer:
Common difference = 60 – 47 = 13
8, 21, 34, 47, 60
55
Thursday, May 22, 2014
7th
Find the missing terms in the sequence
and state the common difference:
0, ___, ___, 2,
8
3
Common difference = ___
56
Thursday, May 22, 2014
7th
Find the missing terms in the sequence
and state the common difference:
0, ___, ___, 2,
8
3
Common difference = ___
Answer:
8
3
Common difference = − 2 =
0,
𝟐 𝟒
8
, , 2,
𝟑 𝟑
3
2
3
57