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You’ve studied and now you’re geared up for the ACT math section (whoo!). But are you ready to take on the most challenging math questions the ACT has to offer? Do you want to know exactly why these questions are so hard and how best to go about solving them? If you’ve got your heart set on that perfect score (or you’re just really curious to see what the most difficult questions will be), then this is the guide for you.

We’ve put together what we believe to be the most 21 most difficult questions the ACT has given to students in the past 10 years, with strategies and answer explanations for each. These are all real ACT math questions, so understanding and studying them is one of the best ways to improve your current ACT score and knock it out of the park on test day.



Brief Overview of the ACT Math Section
Like all topic sections on the ACT, the ACT math section is one complete section that you will take all at once. It will always be the second section on the test and you will have 60 minutes to completed 60 questions.

The ACT arranges its questions in order of ascending difficulty. As a general rule of thumb, questions 1-20 will be considered “easy,” questions 21-40 will be considered “medium-difficulty,” and questions 41-60 will be considered “difficult.”

The way the ACT classifies “easy” and “difficult” is by how long it takes the average student to solve a problem as well as the percentage of students who answer the question correctly. The faster and more accurately the average student solves a problem, the “easier” it is. The longer it takes to solve a problem and the fewer people who answer it correctly, the more “difficult” the problem.

(Note: we put the words “easy” and “difficult” in quotes for a reason—everyone has different areas of math strength and weakness, so not everyone will consider an “easy” question easy or a “difficult” question difficult. These categories are averaged across many students for a reason and not every student will fit into this exact mold.)

All that being said, with very few exceptions, the most difficult ACT math problems will be clustered in the far end of the test. Besides just their placement on the test, these questions share a few other commonalities. We'll take a look at example questions and how to solve them and at what these types of questions have in common, in just a moment.



But First: Should You Be Focusing on the Hardest Math Questions Right Now?
If you’re just getting started in your study prep, definitely stop and make some time to take a full practice test to gauge your current score level and percentile. The absolute best way to assess your current level is to simply take the ACT as if it were real, keeping strict timing and working straight through (we know—not the most thrilling way to spend four hours, but it will help tremendously in the long run). So print off one of the free ACT practice tests available online and then sit down to take it all at once.

Once you’ve got a good idea of your current level and percentile ranking, you can set milestones and goals for your ultimate ACT score. If you’re currently scoring in the 0-16 or 17-24 range, your best best is to first check out our guides on using the key math strategies of plugging in numbers and plugging in answers to help get your score up to where you want it to. Only once you've practiced and successfully improved your scores on questions 1-40 should you start in trying to tackle the most difficult math problems on the test.

If, however, you are already scoring a 25 or above and want to test your mettle for the real ACT, then definitely proceed to the rest of this guide. If you’re aiming for perfect (or close to), then you’ll need to know what the most difficult ACT math questions look like and how to solve them. And luckily, that’s exactly what we’re here for.

Answer:

The answer is the first matrix. Image attached.

Step-by-step explanation: Given that Dante is solving the system of equations:

In solving the above system of equations, Dante writes the row echelon form of the matrix. We are to select the correct row echelon of the matrix that he wrote.

We know that a matrix is said to be in row echelon form if the leading entry in each nonzero row is a 1 and each column containing a leading 1 has zeros everywhere else.

In the given options, these conditions are satisfied by the first option only. And also, if we write the solution from this matrix, we will have

r = -1,  s = 0  and  t = 3.

If we substitute these values in the given system, it will get satisfied.

Thus, the first matrix, attached herewith, is the correct matrix.

The skip interval should be 40 if the sampling frame has 2000 names and the desired sample size is 50.

Systematic sampling is a type of sampling which uses the probability method where researchers select members of the group or population at a regular interval.

To determine the skip interval, it is necessary to first determine the sample size. Then the skip interval can be determined by dividing the total population by the target/desired sample size. Therefore;

skip interval = population / target sample size

Substituting the given values;

skip interval = 2000 / 50

skip interval = 40

Hence, the skip interval is calculated to be 40 if the frame has 2000 names and the desired sample size is 50.

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Answer:

See below

Step-by-step explanation:

find slope between     0,1     and   10, -49

  m =  (-49-1) / (10-0) = -5

slope intercept form

  y = mx + b

  y = -5 x +1    re=arrange

5x + y = 1

The standard deviation lies in the range of 0 to 1. The numerical value of standard deviation can never be negative.

The standard deviation is a measure of amount of variation or dispersion of a set of values. When we compare two unequal observations, the result is always greater than zero i.e., always positive.

Standard deviation is the square root of the variance of the observations and the root always gives values either positive or zero, it can never be negative.

Therefore, the numerical value of the standard deviation can be positive. The value of standard deviation is always greater or equal to zero.

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The sum of their squares is (x)^2 + (x-d)^2 + (x-2d)^2.

According to the statement

we have given that the 3 integers are in an arithmetic progression and their product is prime.

And we have to find the sum of their squares.

So, let the three integers which is A, B, C.

And according to the arithmetic progression the

A = x and B = x-d, C = x-2d. here d is the common difference and x is a 1st term.

So, there product is prime

then

(x) (x-d) (x-2d) = c -(1)

And

their sum of square is

(x)^2 + (x-d)^2 + (x-2d)^2 - (2)

So, The sum of their squares is (x)^2 + (x-d)^2 + (x-2d)^2.

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Answer:

Step-by-step explanation:

so since he pours 295 grams and need to remove 12 spoonfuls the answer will me 1.7 milligrams

The factored version of the equation would be (b + 9) (b - 7) = 0.

We are given the equation:

b ^ 2 + 2b - 72 + 9 = 0

b ^ 2 + 2b - 63 = 0

We can rewrite this equation, based on two numbers that multiply to - 63 and add up to 2. These numbers would be 9 and 7 so the equation becomes :

(b + 9) (b - 7) = 0

The answers after the simplification would be:

b + 9 = 0

b = -9

b - 7 = 0

b = 7

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The standard thermometer reads 50°C, the reading of the thermocouple is  0.3922.

To find the reading of the thermocouple when the standard thermometer reads 50°C substitute T = 50 into the equation e = 0.4T - e(T - 100). Let's calculate it:

e = 0.4(50) - e(50 - 100)

e = 20 - e(-50)

e = 20 + 50e

to solve this equation for e. Let's rearrange it:

50e + e = 20

51e = 20

e = 20/51 ≈ 0.3922

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Answer:

130g

Step-by-step explanation:

Answer:.20

Step-by-step explanation:

According to what are written in the table the probability for x=-10 is .20

Answer:

Yes they both are equal

Answer:

the answer is d

Step-by-step explanation:

For 55 you times the average by the time it took and you get 55 same with kick 2 so kick 3 would be 2 seconds because 15 times 2 is 30

Answer:

x=7/5

Step-by-step explanation:

We can write it in exponential form

128= 2^2*2x * 2^x

2^4x+x=5x

2^5x=128

2^5x=2^7

5x=7

x=7/5

The value of x in the equation given is

\( \frac{7}{5} \)

To solve :

\(128 = {4}^{2x} \times {2}^{x} \)

Change all values to have the same root :

\( {2}^{7} = {2}^{2(2x)} \times {2}^{x} \)

\( {2}^{7} = {2}^{4x} \times {2}^{x} \)

\( {2}^{7} = {2}^{(4x + x)} \)

\( {2}^{7} = {2}^{5x} \)

The roots cancel out

\( 7 = 5x\)

Divide both sides by 5

\(x = \frac{7}{5} \)

Therefore, the value of

\(x = \frac{7}{5} \)

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Answer:

Step-by-step explanation:

Solving systems of equations gives the points of intersection when the equations are graphed.

The answer is 3.

Answer:

125

Step-by-step explanation:

Divide 50 by the 4 acres which is 12.5, then times 12.5 by 10 acres.  

Answer:

18.7

Step-by-step explanation:

First find the degree of J which is 6 (found this by doing 180=160+14=6

so then you make the fraction J/sin14=8.1/sin6

cross multiply so its Jsin6=8.1sin14

to get J by itself you divide by sin 6 so

J=8.1sin14 divided by sin6 which equals 18.7

The length of \(l\) is approximately 18.8 inches.

In this question we know the value of two angles, in sexagesimal degrees, and a length of the triangle, in inches, we must determine the length \(l\) by the law of sine:

\(\frac{l}{\sin \angle L} = \frac{j}{\sin \angle J}\) (1)

\(\angle J = 180^{\circ} - \angle K - \angle L\) (2)

If we know that \(j = 8.1\,in\), \(\angle K = 160^{\circ}\) and \(\angle L = 14^{\circ}\), then the length of \(l\) is:

\(\angle J = 180^{\circ}-160^{\circ}-14^{\circ}\)

\(\angle J = 6^{\circ}\)

\(l = j\cdot \left( \frac{\sin \angle L}{\sin \angle J} \right)\)

\(l = (8.1\,in)\cdot \left(\frac{\sin 14^{\circ}}{\sin 6^{\circ}} \right)\)

\(l \approx 18.8\,in\)

The length of \(l\) is approximately 18.8 inches.

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Thus, the value of the function for the given Laplace transformation is:

y(t)=(1/6)*∫[0,t]sin(6(t-u))du+30u(t-3)sin(6(t-3))

To take the Laplace transform of both sides of the given differential equation, we will use the fact that L{y''(t)}=s^2Y(s)-s*y(0)-y'(0) and L{g(t)}=G(s), where G(s) is the Laplace transform of g(t).

Thus, we have:
s^2Y(s)-s*0-0+36Y(s)=G(s)

Simplifying:
Y(s)(s^2+36)=G(s)

Solving for Y(s):
Y(s)=G(s)/(s^2+36)

To take the inverse Laplace transform of both sides, we will use the fact that L^-1{F(s)/s}=∫[0,∞]f(t)dt and L^-1{F(s)/(s^2+w^2)}=1/w*sin(wt).

Thus, we have:
y(t)=L^-1{Y(s)}=L^-1{G(s)/(s^2+36)}

Breaking up G(s) into two terms based on the definition of g(t), we have:
y(t)=L^-1{(t/(s^2+36))+(30e^(-3s)/(s^2+36))}

Taking the inverse Laplace transform of the first term:
L^-1{(t/(s^2+36))}=∫[0,t](1/6)*sin(6(t-u))du

Taking the inverse Laplace transform of the second term:
L^-1{(30e^(-3s)/(s^2+36))}=30u(t-3)sin(6(t-3))

Thus, our final solution for y(t) is:

y(t)=(1/6)*∫[0,t]sin(6(t-u))du+30u(t-3)sin(6(t-3))

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According to the 2002-2003 national surveys conducted in America, the estimated percentage of children living in poverty was approximately 16.7%. This figure is based on data collected during that time period, and it's important to note that poverty rates can change over time.

A survey is a set of questions used in human subject research with the goal of gathering specific information from a certain population. Surveys can be carried out via the phone, by mail, online, at street corners, and even in shopping centers. Surveys are used to collect data or learn more in areas like demography and social research.

Survey research is frequently used to evaluate ideas, beliefs, and emotions. Surveys might have narrow, focused objectives or they can have broad, more general objectives. In addition to being utilized to satisfy the more practical requirements of the media, such as evaluating political candidates, public health officials, professional organizations, and advertising and marketing directors, surveys are frequently employed by psychologists and sociologists to evaluate behavior.

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Nearest thousanth-.063

Nearest Hundranth-.06

Nearest Tenth-.1

Nearest whole-0

I think you meant to write

(2 × 10⁶) × 0.00009

First, convert 0.00009 to scientific notation:

0.00009 = 9 × 10 ⁻⁵

Then

(2 × 10⁶) × 0.00009 = (2 × 10⁶) × (9 × 10 ⁻⁵)

… = (2 × 9) × (10⁶ × 10 ⁻⁵)

… = 18 × 10¹

… = 1.8 × 10²

Answer:

39 homes

Step-by-step explanation:

The fraction of people having computers is

13/20

Multiply by the number of homes

13/20 * 60

13 * 60/20

13*3

39

39 homes

Answer:

39 Computers

Step-by-step explanation:

i never really understood how everyone does these types of question so i just do them my own way:

60/20 = 3  

13*3 = 39

ʕ•ᴥ•ʔ  (dats a bear)

Answer:

-4, 3

Step-by-step explanation:

you got's it :)

Volume of "region" which lies between the paraboloid z = 24 - x² - y² and the cone z = 2√x² + y² is 536.2 cubic units.

In order to find the volume, we first convert in the polar-coordinate;

We get,

Cone : z = 2√x² + y² ⇒ 2r;  and

Paraboloid : z = 24 - x² - y² ⇒ 24 - r²;

So, the point of intersection can be found by;

2r = 24 - r²,

r² - 24r + 2r = 0,

r = 4, -6.

Since, r≥0, we have r=4;

The intervals are : 0≤r≤4 and 0≤θ≤2π;

So, the Volume is written as : \(\int\limits^{2\pi}_0 \int\limits^4_0\) ((24-r²) - 2r)r.dr.dθ

⇒  \(\int\limits^{2\pi}_0 \int\limits^4_0\) (24 - 2r - r²)r.dr.dθ

⇒  \(\int\limits^{2\pi}_0 \int\limits^4_0\) (24r - 2r² - r³)dr.dθ

⇒  \(\int\limits^{2\pi}_0\) [12r² - 2r³/3 - r⁴/4]⁴₀,

⇒  2π [192 - 128/3 - 64] = 512π/3 ≈ 536.2 cubic units.

Therefore, the volume of the region is 536.2 cubic units.

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The given question is incomplete, the complete question is

Find the volume of the region that lies between the paraboloid z = 24 - x² - y² and the cone z = 2√x² + y².

Answer:

Answer is 18

Step-by-step explanation:

Substitute the variable.

2 x 9 =

Then solve

2 x 9 = 18

Answer:

Submarine must descend by 12 feet in the fifth minute.Average of the data:Average of a data set is calculated by dividing the sum of terms by the number of the terms of the set.From the table given in picture,Let the distance descended by submarine in 5th minute = x feetAverage distance descended by the submarine =                                                                                 =                                                                                 =  feet per minuteStatement given in the question → "Submarine must descend at an average rate of at least 10 feet per minute"So the inequality for the statement will be,38 + x ≥ 50x ≥ 50 - 38x ≥ 12    Therefore, submarine must descend 12 feet in the 5th minute.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

380

To create a work plan for the food intake of each person in the group, there needs to be the required 5600 calories and there needs to be a replacement for the caloric deficit.

This refers to the formal roadmap that is created for a project for the purposes of streamlining it.

Based on the fact that a map was not provided, there is insufficient data to solve the problem, so a general overview will be given about a work plan.

Because the group is 28,800 calories short and needs to complete the trip with their five members, then they need to ration their supplies.

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Answer:

57

Step-by-step explanation:

100 - 43 =

57

Answer:

He got 57% wrong

Step-by-step explanation:

If he got 43% correct, there is 100 percent on the assignment

100 -43 = 57

He got 57% wrong