• GreenPrint
In summary, the conversation was about a calculus readiness test and the participant's answers and justifications for certain questions on the test. The test was quick and designed for someone who already knows calculus. The questions and answers discussed were about finding the point of intersection of two graphs, determining when a function is positive, solving for x in a logarithmic equation, simplifying an expression, finding the height of a pole using ratios, finding the distance between two points, determining proportional relationships, and solving for x in an equation involving polynomials.
GreenPrint
Hi, for spring break homework I had to take this "calculus readiness test" thingy and I got a score of 19/24 and I'm trying to go through the test and see which ones I got wrong. I'm however perplexed because I don't see which ones I got wrong. I guess I got five wrong but don't see which ones. I don't even see how I got one wrong. I was hoping someone could point out to me which ones I got wrong and what the right answers are, thanks. Also note that this test took me about 10 minutes to do and you it's a very quick test for someone that already knows calculus so don't be scared by it... I just would like to know which ones I got wrong... below you'll find my answers along with my justifications... thanks for any help

1.

The x-coordinate of the point of intersection of the graphs of x + 2y = 3 and -3x + y = -2

A. 2
B. 0
C. -2
D. -1
E. 1

Justification:
x + 2y = 3
x - x + 2y = 3 - x
2y = 3 - x
1/2 (2y) = 1/2(3-x)
y = 1/2(3 - x)

-3x + y = -2
3x - 3x + y = -2 + 3x
y = -2 + 3x

-2 + 3x = 1/2(3 - x)
-4 + 6x = 3 - x
-4 + 6x + x = 3 - x + x
-4 + 7x = 3
-4 + 4 + 7x = 3 + 4
7x = 7
(1/7)7x = (1/7)7
x = 1

2.

If f is a function whose graph is the parabola sketched below, then f(x) > 0 whenever

[PLAIN]http://img703.imageshack.us/img703/1189/capturezd.jpg

A. -1 < x < 3
B. x< -1 or x > 3
C. x > -1
D. x < 3
E. x > 3

Justification:
The answer is not E. because by inspection of the graph provided of the function x values greater than 3 are negative, for example f(6) is clearly negative, hence the answer choice doesn't agree with f(x) > 0.

The answer is not D. because by inspection of the graph provided of the function x values less than 3 are not always positive, for example f(-4) is clearly negative, hence the answer choice doesn't agree with f(x) > 0.

The answer is not C. because by inspection of the graph provided of the function x values greater than -1 are not always positive, for example f(6) is clearly negative, hence the answer choice doesn't agree with f(x) > 0.

The answer is not B. because by inspection of the graph provided of the function x values less than negative one or greater than 3 are negative, for example f(6) is clearly negative as well as f(-4) , hence the answer choice doesn't agree with f(x) > 0.

The only answer choice left is A.

3.

If log base 3 of (2x + 1) = 2, then x =

A. 10
B. 9
C. 4
D. 2/log(3) - 2
E. 5

Justification
log base 3 of (2x + 1) = 2
3^2 = 2x + 1
9 = 2x + 1
9 -1 = 2x + 1 - 1
8 = 2x
1/2(8) = 1/2(2x)
4 = x

4.

x^2 - 2x can be represented as (x + a)^2 + b where

A. {a = -1, b = 1}
B. {a = -1, b = -1}
C. {a = 1, b = -1}
D. {a = -2, b = 2}
E. {a = 2, b = 2}

Justification
(x - 1)^2 - 1
(x -1)(x -1) - 1
x^2 - x - x + 1 - 1
X^2 -2x

5.

A certain cougar population increases by a factor of 1.2 every year. (for example, if there are 100 cougars now, a year from now there will be 120.) Of the following, which best approximates the factor by which the population will increase over a 15-year period?

A. 18.000
B. 15.000
C. 7.400
D. 15.407
E. 26.986

Justification
1.2 = 6/5
15(6/5)
3(6)
18

6.

If a^2 is approximately equal to 3000, then, of the following, which best approximates a^4?

A. 9,000
B. 900,000
C. 9,000,000
D. 3000^4
E. 6,000

Justification
3000^2 = 9,000,000

7.

The algebraic quantity x - y is a factor of how many of the following?
{x^2 - y^2} {x^2 + y^2} {x^3 - y^3} {x^3 + y^3}

A. none
B. one only
C. two only
D. three only
E. all four

Justification
x^2 - y^2 = (x - y)(x + y)
x^2 + y^2, cannot be factored
x^3 - y^3 = (x - y)(x^2 + xy + y^2)
x^3 + y^3 = (x + y)(x^2 - xy + y^2), cannot be factored further
hence there are only two that have x - y as a factor

8.

Simplify the expression SQRT(9u^6 + 36v^4), if u > 0 and v > 0.

A. 3u^3 + 6v^2
B. 3SQRT(u^6 + 2v^2)
C. 18u^3 v^2
D. Cannot be simplified more.
E. None of these

Justification
SQRT(9u^6 + 36v^4)
SQRT(9(u^6 + 4v^4))
3SQRT(u^6 + 4v^4)
I chose E. because this cannot be simplified further and is not one of the other options

9.

A child 4 feet high casts a shadow 6 feet long. At the same time, the length of the shadow cast by a pole is 12 feet. what is the height of the pole in feet?

A. 18
B. 16
C. 8
D. 6
E. 14

Justification
tan^-1 (4/6) = Ans
tan(Ans) = x/12
12 tan(Ans) = x
8 = x

10.

In the figure shown below, what is the distance between (-2, 4) and (2, 7)?

[PLAIN]http://img69.imageshack.us/img69/8663/capturellc.jpg

A. 9
B. 8
C. 7
D. 6
E. 5

Justification:
SQRT( (7 - 4)^2 + (2 + 2)^2 )
SQRT( 3^2 + 4^2 )
SQRT( 9 + 16 )
SQRT( 25 )
5

11.

If P is proportional to T and P = 4 when T = 1/3, then when P = 1, what is T equal to?

A. 1/12
B. 1/3
C. 3
D. 12
E. None of these.

Justification:
PT = (1/3) 4 = 4/3
1T = 4/3
1/1 (1T) = 1/1 (4/3)
T = 4/3

12.

If ( (3x - 3)(x + 2) )/(x - 2) = 0, then x =

A. 2 or -1
B. -2 or 1
C. 2 or 1
D. -2, 1, or 2
E. -1, 2, or -2

Justification:
3x - 3 = 0
3x - 3 + 3 = 3
3x = 3
1/3 (3x) = 1/3 (3)
x = 1
x + 2 = 0
x = -2

13.

In the standard coordinate system, the graph of a line with slope 2/3 is

A. a vertical line
B. a horizontal line
C. a line through the origin
D. a line falling to the right
E. a line rising to the right

Justification:
A line with a first derivative that is positive is "rising to the right" I guess... I thought the term was funny

!4.

What is the area of the rectangle shown below (not drawn to scale)?

[PLAIN]http://img225.imageshack.us/img225/97/capturewl.jpg

A. 1.320
B. 1705
C. 4.774
D. 1.023
E. 0.990

Justification:
1.1 = 11/10
(11/10)^2 + 2(11/10)
121/100 + 22/10
121/100 + 220/100
341/100
341/100(1.4 - 1.1)
341/100(.3)
341/100(3/10)
1023/1000
should be slightly greater than 1 so I chose D

15.

The width of a certain rectangle is 1 inch more than its length. What is the length of the rectangle if the perimeter of the rectangle is 26 inches?

A. 5 inches
B. 8 inches
C. 5.5 inches
D. 6.5 inches
E. 6 inches

Justification:
26 = 2(L + W)
W = L + 1
26 = 2(L + L + 1)
26 = 2(2L + 1)
13 = 2L + 1
13 - 1 = 2L + 1 - 1
12 = 2L
1/2(12) = 1/2(2L)
6 = L

16.

Definition: A function f has a maximum value at c if f(c) => f(x) for every x if in the domain of f. The domain of the function whose graph is shown below is [-1, 2]. At which of the following numbers does the function appear to have a maximum value?

[PLAIN]http://img189.imageshack.us/img189/8938/capturejg.jpg

A. -1
B. 0
C. 1
D. 1.5
E. 2

Justification:
I don't like how the defined maximum value of a function but either way based off of observation of the graph the function has a maximum value at would appear to be a number close to 0.

17.

The inequality |x - 6| <= 9 is equivalent to:

A. -6 <= x <= 9
B. -9 <= x <= 6
C. x <= -3 and x => 15
D. -3 <= x <= 6
E. -3 <= x <= 15

Justification:
x - 6 <= 9
x -6 + 6 <= 9 + 6
x <= 15
6 - x <= 9
6 - 6 - x <= 9 - 6
- x <= 3
1/-1 (- x) => 1/-1 (3)
x => -3
-3 <= x <= 15

18.

If f(x) = x^2 for all x, then f(x+h) - f(x) =

A. h^2
B. f(h)
C. 2hx
D. 2hx + h^2
E. x^2

Justification:
f(x+h) - f(x) = (x + h)^2 - x^2
= (x + h)(x + h) - x^2
= x^2 + 2xh + h^2 - x^2
= 2xh + h^2

19.

How many distinct numbers in the interval 1 <= x <= 3 are solutions to the equation x(x^2 + 1)sinx = 0?

A. 0
B. 1
C. 2
D. 3
E. 4

Justification:
x(x^2 + 1)sinx = 0 has only one real solution at x = 0, which isn't in the domain the question provided.

20.

Simplify: ( x^2/( 2 x^(1/3) ) )^-3

A. x^-3/8
B. 8x^-5
C. 8x^3
D. X^3/8
E. None of these

Justification:
( x^2/( 2 x^(1/3) ) )^-3 = ( 8x )/ x^6 = 8/x^5
Most would consider answer B unsimplified because of the negative exponent.

21.

The equation of the line passing through points (1, 5/2) and (4, 10) is y = mx + b, what is b equal to?

A. 2/5
B. -5/2
C. 5/2
D. 23/10
E. 0

first derivative = (10 - 5/2)/(4 - 1) = (20/2 - 5/2)/3 = (15/2)/3 = 15/6 = 5/2
y = 5/2 x + b
5/2 = 5/2 (1) + b
5/2 - 5/2 = 5/2 - 5/2 + b
0 = b

22.

Of the following, which best approximates the radian measure of the angle [theta] shown? (Note: the picture is not drawn to scale."
[PLAIN]http://img846.imageshack.us/img846/6394/capturecvv.jpg

A. 0.197
B. 1.373
C. 0.201
D. 1.369
E. -3.381

Justification:
tan^-1(5/1) = 1.373

23.

For all [theta] defined, sin^2[theta] - cos^2[theta] =

A. -1
B. (sin[theta] - cos[theta])^2
C. -cos2[theta]
D. 1 + cos2[theta]
E. sin2[theta]

Justification:
sin^2[theta] - cos^2[theta] = -cos2[theta]

24.

If f(y) = (2y - 3)/y, then for which value of y does f(y) = 1?

A. 1/3
B. 3
C. -3
D. -1
E. 1

Justification:
f(y) = (2y - 3)/y = 2 - 3/y = 1
2 - 2 - 3/y = 1 - 2
-3/y = -1
3/y = 1
y/3 = 1
y = 3

Last edited by a moderator:
They didn't tell you which ones were wrong? I would rather not check all 24 of your problems to see which 5 you got wrong. Surely the person/computer program who graded your work could tell you which ones are wrong.

GreenPrint said:
5.

A certain cougar population increases by a factor of 1.2 every year. (for example, if there are 100 cougars now, a year from now there will be 120.) Of the following, which best approximates the factor by which the population will increase over a 15-year period?

A. 18.000
B. 15.000
C. 7.400
D. 15.407
E. 26.986

Justification
1.2 = 6/5
15(6/5)
3(6)
18

This is wrong. You should have done 1.215 instead of 1.2 × 15.

GreenPrint said:
11.

If P is proportional to T and P = 4 when T = 1/3, then when P = 1, what is T equal to?

A. 1/12
B. 1/3
C. 3
D. 12
E. None of these.

Justification:
PT = (1/3) 4 = 4/3
1T = 4/3
1/1 (1T) = 1/1 (4/3)
T = 4/3

This is wrong too. "P is proportional to T" translates to
P = kT
for some k. Plug in P = 4 and T = 1/3 to solve for k. Then find your new value of T.

GreenPrint said:
22.

Of the following, which best approximates the radian measure of the angle [theta] shown? (Note: the picture is not drawn to scale."
[PLAIN]http://img846.imageshack.us/img846/6394/capturecvv.jpg

A. 0.197
B. 1.373
C. 0.201
D. 1.369
E. -3.381

Justification:
tan^-1(5/1) = 1.373

Oops! tan θ = y/x. You switched the numbers.It's also possible that even though what you said about #20 is right (no negative exponents), B may be the answer that the test was looking for.

Last edited by a moderator:
Thank you very much. No they didn't tell me which ones I got wrong =(.

Is my answer to 19 wrong?

GreenPrint said:
Is my answer to 19 wrong?

Invoke the zero product property:
x(x^2 + 1)sin x = 0

x = 0, OR
x^2 + 1 = 0 => no real solutions, OR
sin x = 0 => nπ, n is an integer

None of these solutions are in the interval 1 ≤ x ≤ 3.

Like Eumyang said, a lot of us don't have the time to check all 24 questions (like me). Try to get it narrowed down which are wrong and we can help you better.

Actually, it was Mark44 who said that, not me.

I'm a little concerned that I couldn't find all of the answers that were wrong. Even if we were to count #20 (with the negative exponents), that makes 4 wrong, not 5.

eumyang said:
Actually, it was Mark44 who said that, not me.

I'm a little concerned that I couldn't find all of the answers that were wrong. Even if we were to count #20 (with the negative exponents), that makes 4 wrong, not 5.

Hmm. I got 4 wrong as well, same as eumyang.

ya i think they ripped me off

Don't forget early mathematic skills

For some questions, there are easier ways to solve them. Examples include Questions #9,10

9-- Can be solved with proportions
10-- May not be easier, but I personally think so. Use pythagorean theorem

EDIT-- Just incase you want to save time (atleast it's easier for, IDK about you)

Last edited:
Is there a penalty for "guessing".

They may deduct 1.25 for each wrong answer.

nope

## What is a calculus readiness multiple choice test?

A calculus readiness multiple choice test is an assessment used to evaluate a student's proficiency in the fundamental concepts and skills necessary for success in a calculus course.

## What types of questions are included in a calculus readiness multiple choice test?

A calculus readiness multiple choice test typically includes questions covering topics such as algebra, trigonometry, functions, and limits, which are all foundational concepts for calculus.

## Why is a calculus readiness multiple choice test important?

A calculus readiness multiple choice test is important because it helps identify areas where a student may need additional support before starting a calculus course. This can improve the student's chances of success and help them build a strong foundation for future math courses.

## How can I prepare for a calculus readiness multiple choice test?

To prepare for a calculus readiness multiple choice test, it is important to review and practice fundamental concepts such as algebra and trigonometry. Additionally, familiarizing yourself with the format and types of questions typically found on these tests can also be helpful.

## What happens if I do not do well on a calculus readiness multiple choice test?

If you do not do well on a calculus readiness multiple choice test, it is important to not get discouraged. Instead, use the results as a guide to identify areas where you need to improve and seek additional support and resources to help you better understand the concepts. With practice and determination, you can improve your skills and be better prepared for a calculus course.

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