Calculus Readiness Multiple Choice Test Answer Key Wrong?

[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

My Answer: E

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

My Answer: A

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

My Answer: C.

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}

My Answer B.

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

My Answer A.

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

My Answer C.

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

My Answer C.

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

My Answer: E.

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

My Answer C.

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

My Answer: E.

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.

My Answer: E

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

My Answer: B

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

My Answer: E.

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

My Answer: D.

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

My Answer: E.

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

My Answer: B.

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

My Answer: E.

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

My Answer: D

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

My Answer: A.

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

My Answer: E.

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

My Answer: E.

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

My Answer: B.

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]

My Answer: C.

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

My Answer: B.

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

 

[Mark44]

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.

 

[eumyang]

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

My Answer A.

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.

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.

My Answer: E

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.

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

My Answer: B.

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.

 

[GreenPrint]

Thank you very much. No they didn't tell me which ones I got wrong =(.

 

[GreenPrint]

Is my answer to 19 wrong?

 

[eumyang]

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.

 

[gb7nash]

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.

 

[eumyang]

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.

 

[Dick]

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.

 

[GreenPrint]

ya i think they ripped me off

 

[BloodyFrozen]

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)

 

[SammyS]

Is there a penalty for "guessing".

They may deduct 1.25 for each wrong answer.

 

[GreenPrint]

nope