Geometry and trigonometry
What equation is used to find angles and sides of triangles?
The Pythagorean Theorem
What does the imaginary unit βiβ represent?
Square root of -1
How do you decide if data is discrete or continuous?
Data that can be measured is continuous (5.6, 7.3, 862.22). Data that can be counted is discrete (1, 5, 8, 3).
What is the definition of a function?
A relationship or expression involving one or more variables.
If |π(π₯)|β€|π₯|2for all π₯ββ then prove f is differentiable at π₯=0
+1
If an angle of a right triangle is 57 degrees, then how many degrees does the other angle have?
33
In 1856 Andrew Waugh announced Mount Everest to be 8840m tall, then in 1875 the height was confirmed to be 8848m high. What was the percent error in the earlier observation?
0.09%
When do you reject the null hypothesis?
When the X^2 test statistics is greater than the critical value or when the p-value is less than the than significance level
A tree is 10 ft tall and will grow 2.5 ft every year. How tall will the tree be after 20 years?
f(x) = 2.5x+10
f(x) = 60ft
If πΆ0+πΆ1/2+β¦+πΆπ/(π+1)=0
where each πΆπβR , then prove that the equation πΆ0+πΆ1π₯+β¦+πΆππ₯π=0
has at least one real root between 0 and 1
If πΆ0+πΆ1/2+β¦+πΆπ/(π+1)=0
where each πΆπβR , then prove that the equation πΆ0+πΆ1π₯+β¦+πΆππ₯π=0
has at least one real root between 0 and 1
Complete and find the trigonometry identity?
1+tan2u
sec2u
One millilitre has about 15 drops. One drop of water as 1.67x1021 H2O molecules. Estimate the number of molecules in 1 litre of water, in standard form.
2.505x1025
What is a tree diagram?
A tree diagram is a way to represent all the possible outcomes of an event. The end of each branch represents a combined event.
An amount of $5,000 is invested at a simple interest rate of 3% per annum, for a period of 8 years.
Calculate the interest received after 8 years.
Find the total amount in the account after 8 years.
I = $1,200
2. $6,200
Find equation of the tangent line to the curve with equation sin(π¦2)=π₯2
sin at the point (0,πβΎβΎβ)
π¦=πβΎβΎβ
Ο
What are the x and y points located at 225 degrees on the unit circle?
(-β2 / 2 , -β2 / 2)
What is 3.429x10-13 in expanded form?
0.0000000000003429
A group of students is asked to rank six snack foods by taste and value for money. The ranks are averaged and recorded in the following table.
Calculate Spearman's rank correlation coefficient for the data and comment on your results.
Popcorn Chips Chocolate bar Chews Cookie
Taste 2 4 1 5 3
Value 5 3 2 4 1
rs=.02 This means that there is no clear correlation between the taste of a snack and its value for price.
Tom invests $80,000 in a bank that offers interest at 3% per annum compounded quarterly.
Calculate how much money is made in 6 years.
Calculate how long it will take for his original amount to double.
1. FV = $95,713.08
2. n = 23 years
Find the inverse of function π(π₯)=ππ(2π₯β3)+2
πβ1(π₯)=12(ππ₯β2+3)