School of Mathematics and Statistics
Junior
The University of Sydney
Maths & Stats Home / Teaching program / Junior / MATH1011 / Quizzes / Quiz 3
The University of Sydney
Usyd Home
MyUni
MyUni
Library
Sitemap
spcr
   Questions




right first
    attempt
right
wrong

Quiz 3: Exponential and logarithmic functions

Last unanswered question  Question  Next unanswered question
 

Question 1

 
 
Write 3sinx + 4cosx in the form R sin(x + α).
a) √- 7sin(x + 0.64)   b) √ - 7sin(x + 0.93)
c) 5sin(x + 0.64)   d) 5sin(x + 0.93)

 

Not correct. Choice (a) is false.
Not correct. Choice (b) is false.
Not correct. Choice (c) is false.
Your answer is correct.
R cosα = 3, R sinα = 4, R = √ ------ 32 + 42 = 5, α = tan-14∕3 = 0.93
 

Question 2

 
 
Write √- 1cosx - -3-sin x 2 2 in the form R sin(x + α).
a) sin(x+ π) 6   b) π sin(x - 6)
c) sin(x + 5π) 6   d) sin(x - 5π) 6

 

Not correct. Choice (a) is false.
Not correct. Choice (b) is false.
Your answer is correct.
R cosα = -√ - -23, R sinα = 12, R = ∘ ----- 13 + 34 = 1, tanα = -√13- and α is in the 2nd quadrant.
Not correct. Choice (d) is false.
 

Question 3

 
 
Which of the following graphs indicates that y is proportional to x2.
a)
PIC
   b)
PIC
c)
PIC
   d)
PIC

 

Not correct. Choice (a) is false.
Not correct. Choice (b) is false.
Your answer is correct.
Not correct. Choice (d) is false.
 

Question 4

 
 
The experimental data
| -t-|-1---2----3---4-----5-- y 0.9 3.6 8.1 14.4 22.5
appears to show that y is proportional to t2. Find the relationship between y and t.
a) y = 0.9t2   b) y = 2.7t2
c) y = 0.9t   d) y = 2.7t

 

Your answer is correct.
Scaling the data gives
| -t2 =-T|-1----4---9---16----25-- y 0.9 3.6 8.1 14.4 22.5
A scatter plot of y against T is a straight line through (0,0) with slope 3.6- 0.9 --4--1--= 0.9 .
therefore,y = 0.9T = 0.9t2.
Not correct. Choice (b) is false.
Not correct. Choice (c) is false.
Not correct. Choice (d) is false.
 

Question 5

 
 
Given the experimental data
| -t-|1.1--1.6--2.1--2.6--3.1- y 2.9 4.4 5.9 7.4 8.9
which of the following statements is correct ?
a) y is proportional to t.
b) y is proportional to t2.
c) y is a linear function of t.
d) There is no recognisable relationship between y and t.

 

Not correct. Choice (a) is false.
Not correct. Choice (b) is false.
Your answer is correct.
The equation of the line satisfying the data is y = 3t - 0.4.
Not correct. Choice (d) is false.
 

Question 6

 
 
Solve 3ex = 5 .
a) x = ln-5 3   b) ln5 x = --- ln3
c) x = ln 5+ ln(- 3)   d) x = ln5 - ln3

 

Not correct. Choice (a) is false.
Not correct. Choice (b) is false.
Not correct. Choice (c) is false.
Your answer is correct.
5 3ex = 5 ⇒ ex = 3 ( 5) lnex = ln - 3 x = ln5 - ln 3.
 

Question 7

 
 
Solve 1 ln 8x3 = 2.5 3 .
a) 2.5 x = e-- 2   b) x = 3√7.5--ln8-
c) x = 3e7.5-ln8   d) x = 1e7.5∕8 3

 

Your answer is correct.
1 ln 8x3 = 2.5 3 ln[(2x)3]1∕3 = 2.5 ln2x = 2.5 2.5 2x = e2.5 x = e--. 2
Not correct. Choice (b) is false.
Not correct. Choice (c) is false.
Not correct. Choice (d) is false.
 

Question 8

 
 
Simplify 2ln√x3 e .
a) 3 2x   b) e2 + x3∕2
c) x3   d) √ -- 2 x3

 

Not correct. Choice (a) is false.
Not correct. Choice (b) is false.
Your answer is correct.
√-- e2ln x3 = e2lnx3∕2 = eln(x3∕2)2 = elnx3 = x3 .
Not correct. Choice (d) is false.
 

Question 9

 
 
It is expected that the set of experimental data
| -x-|0.8--1.4--2.0---2.6--3.2---3.8-- y 1.0 5.5 16.0 35.1 65.5 109.7
follows a power law. Find the best approximation for the given data.
a) - 27.5x y = 10 e   b) y = 2× 10-3e7.5x
c) y = 1.1x1∕3   d) y = 2x3

 

Not correct. Choice (a) is false.
This equation does not follow a power law.
Not correct. Choice (b) is false.
This equation does not follow a power law.
Not correct. Choice (c) is false.
Your answer is correct.
We do a log-log transformation and to 2 decimal places we find
lnx = X |- 0.22 0.34 0.69 0.96 1.16 1.34 --lny-=-Y--|--0---1.70--2.77--3.56--4.18-4.70-
A scatterplot shows that the relationship between X and Y is linear.You should draw the scatterplot to verify this. So putting Y = mX + b we find m = 3 thus Y = 3X + b. Now 0 = -0.66 + b therefore 0.66 3 3 y = e x ≈ 2x .
 

Question 10

 
 
It is expected that the set of experimental data
| -x-|-1---2----3----4----5--- y 3.0 8.5 15.6 24.0 33.5
follows a power law. Find the best approximation for the given data.
a) x y = 1.1e   b) y = 1.2e0.9x
c) y = 3x3∕2   d) 2∕3 y = 3x

 

Not correct. Choice (a) is false.
This equation does not follow a power law.
Not correct. Choice (b) is false.
This equation does not follow a power law.
Your answer is correct.
We do a log-log transformation and to 2 decimal places we find
ln x = X | 0 0.69 1.10 1.39 1.61 ---------|-------------------------- ln y = Y 1.10 2.14 2.75 3.18 3.51
A scatterplot shows that the relationship between X and Y is linear. You should draw the scatterplot to verify this. So letting Y = mX + b we find m = 1.5 and b = 1.1. Thus y = e1.1x1.5 ≈ 3x1.5 = 3x3∕2 .
Not correct. Choice (d) is false.