Number Sets
Which number set contains the counting numbers 1, 2, 3, 4, 5, ...?
Natural Numbers
What does it mean for a set of numbers to be more dense?
It contains more numbers within the same interval.
x³ × x⁴
x7
On a scatter plot, which axis represents the independent variable?
x-axis
An independent variable is the cause or input that you change or control in an experiment, while a dependent variable is the effect or outcome that you measure to see how it responds.
Classify the number -7. Is it natural, whole, integer, rational or irrational?
Integer and rational
Which set is more dense between 0 and 10?
Set A: Counting by 1
Set B: Counting by 0.5
Counting by 0.5 produces more numbers within the same interval because the intervals between numbers are smaller.
a⁹ ÷ a⁵
a4
What type of correlation exists when one variable increases while the other variable decreases?
Negative correlation
Which number is irrational?
A. 0.5
B. -3
C. √2
D. 4
√2
How many numbers are there when counting by 0.5 from 0.5 to 3.0?
6 numbers.
Solution:
0.5, 1.0, 1.5, 2.0, 2.5, 3.0
(3x²)³
27x6
A student collects the following data:
Hours Studied (x) | Test Mark (y)
1 | 50
2 | 60
3 | 70
4 | 80
What type of correlation exists?
Positive correlation
List ALL the number sets that the number 5 belongs to.
Answer: Natural, whole, integer and rational.
Solution:
Natural: 5 is a counting number.
Whole: 5 is a whole number.
Integer: 5 is a positive integer.
Rational: 5= 5/1
True or False:
Between any two different real numbers, there are infinitely many real numbers
True.
Solution: There is always another real number between two different real numbers
(x⁸y⁶) ÷ (x³y²)
x5y4
A scatter plot has a line of best fit represented by:
y = 5x + 20
Predict the value of y when x = 6.
y= 5(6)+20
y= 50
Explain why every integer is rational, but not every rational number is an integer. Give an example to support your answer.
Every integer can be written as a fraction with a denominator of 1.
However, rational numbers can also be fractions or decimals that are not integers.
A sequence follows this pattern:
10, 5, 2.5, 1.25, 0.625, ...
What is the limit of this sequence? Explain your answer
Answer: 0.
Solution:
Each term is divided by 2.
The numbers get smaller and smaller.
They approach 0 without necessarily reaching it.
Therefore, the limit is 0.
(2x³)² ÷ (4x⁸)
1/x2
A scatter plot shows the following data:
Hours of Exercise | Resting Heart Rate
1 | 85
2 | 80
3 | 75
4 | 70
5 | 65
10 | 95
What type of correlation does the main data pattern show?
Write a trend statement describing the relationship
Negative correlation.
As hours of exercise increase, resting heart rate generally decreases. This indicates a negative correlation.