Trials Preparation - Learn from your mistakes.
Studied by 0 people
Learn
Practice Test
Spaced Repetition
Match
Flashcards1/20
There's no tags or description
Looks like no tags are added yet.
Name | Mastery | Learn | Test | Matching | Spaced |
|---|
No study sessions yet.
21 Terms
2023 Trial Exam Question 1
x2 + y2 - 2y = 2
x2 + (y2 - 2y) = 2
x2 + (y2 - 2y +1 - 1) = 2
x2 + (y - 1)2 - 1 = 2
x2 + (y - 1)2 = 3
Radius = Root 3
2023 Trial Exam Question 5
f(x) = logex becomes g(x) = loge2x
What is this transformation?
Vertical translation.
Cause loge2x = loge2 + logex
2023 Trial Exam Question 6
Second derivative of 2x
f’’(x) = (ln2)2 2x
(Remember, ln2 is a constant and does not need to be differentiated like 2x.
2023 Trial Exam Question 8
∫ (sin2x + cos2x + tan2x) dx
∫ (1 + tan2x) dx
∫ (sec2x) dx
= tanx + c
2023 Trial Exam Question 9
100 x (1 + 0.1)n x (1 - 0.1)n
= 100 x (1.1 × 0.9)n
= 100 x (0.99)n
2023 Trial Exam Question 10
(5/3)2cos2π + (5/3)3cos3π + (5/3)4cos4π + (5/3)5cos5π + … ?
Explanation
The cos functions are just alternating between 1 and -1. Therefore…
Geometric Series with a = (3/5)2 and r = -3/5
Sum is just limiting sum formula a/1-r
(3/5)2/1-(-3/5) = 9/40
2023 Trial Exam Question 13
I struggled with discrete random variable X table. I needed to fill in the blanks.
Lesson:
When given the mean, set up the equation with what you have. Which you know is the sum of all the varibles multiplied by their probability.
You also know the p(x) section all added together adds to one.
2023 Trial Exam Question 15
Lessons:
You can tell what to use between degrees and radians because it is in the question!
For sectors (radians)…
Area = ½ x r2 x theta
Perimeter = 2r + r theta
Arc Length = r theta
2023 Trial Exam Question 16
I got the question wrong, just made one mistake.
Lessons:
Check for restrictions when solving for x. I found two answers when only one was correct.
In this case, it was that the log could not be negative.
2023 Trial Exam Question 18
Lessons:
General form means it all equates to zero as well as the rule of no fractions.
2023 Trial Exam Question 19
Read!
2023 Trial Exam Question 20
You need to learn a reverse power rule!
∫(ax+b)ndx = (ax+b)n+1/a(n+1) + c
2023 Trial Exam Question 23
Lessons:
Assume radians
Full circle is 2 pi
Area of triangle in radians is ½ a x b x sin c.
Take triangles from point to point. Do not assume it goes to the centre.
My mistake was taking EABO instead of EAB.
It ended being area of triangle minus another small triangle, using same formula A = ½ ab sinc.
2023 Trial Exam Question 24
Lesson
I knew the math, I just didn’t trust it or see it through.
Trial Exam Question 25
Lessons:
I got part a incorrect.
Blanked on setup. Use T! Like Tn…
Read the question.
Trial Exam Question 27
Lessons:
I forgot that in an annuity future value table, it already accounts for n. For example, I was meant to put in 1000 x that interest factor (which accounted for eight years), when instead I did 8000 by that interest factor doing the n myself.
Trial Exam Question 28
Lessons
When answering a question about correlation, comment on stength, sign and form.
Always look to see where you can use simultaneous equations.
You can use one least regression line formula to find another.
Trial Exam Question 29
Lessons:
Trust your ability to differentiate.
Simplest form by factorisation.
For something to be speeding up in the negative direction, velocity must be negative and acceleration must be negative (concave down)
When describing limiting behaviour, describe what x and y approach.
Trial Exam Question 30
Lesson:
How to find percentage of interest paid as a percentage of total cost of repaying the loan.
n (number of periods) x M (monthly repayments) - 1 000 000 / nM
This gives you what extra you paid divided by what you paid which is how we usually find percentage. The smaller divided by the larger. Than multiply by a 100.
Trial Exam Question 31
Lesson:
To solve trig equations, take the trig function and solve it equal to what it needs to be.
Always try to simplify an integral equation when you can, for example, if symmetrical take 2x.
Trial Exam Question 33
Lessons:
In Min/Max problems, always solve for one variable.
Then subtitute known value to prove what question will ask you to prove.
Differentiate to find the minimum or maximum. Solve first derivative to zero (know its a stationary point) then test when it is greater/less than that value to see if it goes from increasing to decreasing (maximum) or from decreasing to increasing (minimum).