Arithemic sequence
In the arithmetic sequence: 5, 9, 13, 17, ...
a) What is the common difference?
b) What is the 7th term?
a) Common difference: 4
b) 7th term: 5 + 6(4) = 29
The data set is: 4, 7, 9, 10, 12, 13, 15 Find the five‑number summary for the box plot.
Minimum = 4
Q1 = 7
Median = 10
Q3 = 13
Maximum = 15
Given the quadratic function f(x) = x² − 6x + 5, find the vertex.
f(3) = 9 − 18 + 5 = −4
Vertex: (3, −4)
The data set is: 4, 7, 10, 12, 15 Find the range.
Max = 15
Min = 4
Range = 15 − 4 = 11
The relation is given as a set of ordered pairs: { (2, 5), (3, 7), (4, 9), (2, 8) } Is this relation a function?
No — it is not a function because the input 2 has two different outputs (5 and 8).
An arithmetic sequence has first term 12 and common difference 3. Find the 10th term.
a₁ = 12, d = 3
a₁₀ = 12 + 9(3) = 39
The data set is: 20, 25, 30, 35, 40, 45, 50, 55 Find the five‑number summary.
Minimum = 2
Q1 = 27.5
Median = 37.5
Q3 = 47.5
Maximum = 55
The quadratic function g(x) = 2x² + 8x + 1 is given. Find the vertex.
g(−2) = 2(4) − 16 + 1 = −7
Vertex: (−2, −7)
The test scores are: 65, 70, 72, 80, 85, 90 What is the range of the scores
Max = 90
Min = 65
Range = 90 − 65 = 25
Given the function f(x) = 3x − 4, find f(6).
f(6) = 3(6) − 4 = 18 − 4 = 14
In an arithmetic sequence, the first term is –2 and the 6th term is 18. Find the common difference.
a₆ = a₁ + 5d
18 = –2 + 5d
20 = 5d
d = 4
The data set is: 3, 5, 8, 11, 14, 18 Find the five‑number summary.
Minimum = 3
Q1 = 5
Median = 9.5
Q3 = 14
Maximum = 18
Find the vertex of the parabola h(x) = −3x² + 12x − 9.
h(2) = −12 + 24 − 9 = 3
Vertex: (2, 3)
A group of students recorded the number of books they read: 2, 5, 3, 8, 6, 9 Find the range.
Max = 9
Min = 2
Range = 9 − 2 = 7
The table shows a relation:
x,y
1,4
2,6
3,8
3,10
Is this relation a function?
No — it is not a function because the input 3 has two outputs (8 and 10).
The arithmetic sequence is defined by: a₁ = 7 and d = –2. Find the first 5 terms.
7, 5, 3, 1, –1
The data set is: 9, 12, 15, 17, 22, 25, 29, 30, 33 Find the five‑number summary.
Minimum = 9
Q1 = 15
Median = 22
Q3 = 29
Maximum = 33
p(x) = x² + 4x + 7. Find the vertex.
p(−2) = 4 − 8 + 7 = 3
Vertex: (−2, 3)
The temperatures for the week were: 58°, 62°, 65°, 60°, 70°, 68°, 64° Find the range of the temperatures.
Max = 70
Min = 58
Range = 70 − 58 = 12
Given the function g(x) = x² + 2x + 1, find g(−3).
g(−3) = 9 − 6 + 1 = 4
In an arithmetic sequence, the common difference is 6 and the 4th term is 25. Find the first term.
a₄ = a₁ + 3d
25 = a₁ + 18
a₁ = 7
The data set is: 6, 8, 10, 10, 12, 14, 16, 18 Find the five‑number summary.
Minimum = 6
Q1 = 9
Median = 11
Q3 = 15
Maximum = 18
k(x) = −2x² − 4x + 1, find the vertex.
k(−1) = −2(1) + 4 + 1 = 3
Vertex: (−1, 3)
The heights (in inches) of plants are: 10, 14, 12, 18, 20, 16 Find the range.
Max = 20
Min = 10
Range = 20 − 10 = 10
A mapping diagram shows: 1 -7 2 - 9 3 - 11 4 - 13 Is this relation a function?
Yes — it is a function because each input has exactly one output.