ACT Practice Question - Math

Let's do another ACT math question:

First, let's write out the question mathematically. C will stand for copies and m will stand for minutes. Since the second machine starts 2 minutes after the first, it runs for a total of six minutes.

Let's multiply these out to see how many pages each machine makes.

They each make 480 copies. But that's not our answer. We want the total copies that both machines make together. So let's add the two amounts to get the correct answer: E. 960.

ACT Question of the Day - Writing

Now that the SAT and ACT are going to resemble each other more (no more memorizing SAT vocabulary), studying for one test is more like studying for both. You might see similar writing questions on the ACT and the SAT. Let's take a look at one:

In 1926, RCA paid the American Telephone & Telegraph Company one million dollars for station WEAF in New York City—and NBC was

born. Years later, the Radio Law of 1927 was

enacted. It authorized it's control for licensing and of policing the broadcasters.

Choose the best alternative for the underlined part 9.

A. NO CHANGE
B. A year later,
C. Factually,
D. In conclusion,

The underlined part nine needs to be changed, so we can rule out A. The previous sentence refers to the year 1926, and the next sentence mentions 1927, so the most logical choice would be B. Sometimes these writing questions can refer to tone. Make sure that the tone stays consistent throughout the piece. Here, however, it simply has to do with chronology and logic.

PSAT Math Practice - Geometry

The question is asking for the perimeter and it gives us the area. So we have two steps: 1. Determine the length of the sides using the area. 2. Determine the perimeter.

First, let's define the length of the sides with a variable.

We know that area = length * width, so let's use the given area to find the width (x). 

Now that we know the width (and the length), let's find the perimeter.

PSAT Math

The question is asking for the minimum value of the function, in other words, the y-value in a certain domain. Since we are looking for the minimum y-value when x is greater than -4 and less than 6, we can rule out choice A. We can also rule out choice B because that is an x-value and not a y-value. The lowest y-value given the domain limitations is going to be where x is -4. At that point, y is -2. That's our answer: -2.

ACT Question of the Day - Science

Let's look a little more closely at the ACT question of the day (a great place to visit daily if you aren't yet doing it):

Passage II

    The Sun's path from sunrise to sunset varies with the time of year. A student performed the following experiments on three clear, sunny days at three- or four-month intervals throughout the course of a year to study the path of the Sun through the sky.

Experiment 1

    At a chosen Northern Hemisphere location, the student placed a stick vertically into the ground so that 1 meter of its length was left above ground. The student knew that the length of the shadow was related to the height of the Sun above the horizon and that the shadow would point away from the direction of the Sun. The length in meters (m) and direction of the shadow cast by the stick were measured one hour after sunrise (Shadow A), at mid-morning (B), at noon (C), at mid-afternoon (D), and one hour before sunset (E) on each of the three days. The direction of each shadow was determined by placing a magnetic compass at the base of the stick and aligning the north arrow with the north mark on the compass. The direction of each shadow was then determined by a comparison with the compass face markings. The results are recorded in Table 1.

Table 1
Shadow	Day 1		Day 2		Day 3
	Length (m)	Shadow direction	Length (m)	Shadow direction	Length (m)	Shadow direction
A	5.0	SW	8.6	NW	6.8	W
B	1.2	W	2.9	NNW	1.7	NW
C	0.3	N	2.3	N	0.9	N
D	1.2	E	3.0	NNE	1.8	NE
E	5.0	SE	8.6	NE	6.9	E

Experiment 2     The following year, the student repeated Experiment 1 at a chosen location in the Southern Hemisphere. The results are in Table 2.

Table 2
Shadow	Day 1		Day 2		Day 3
	Length (m)	Shadow direction	Length (m)	Shadow direction	Length (m)	Shadow direction
A	9.0	SW	5.0	NW	6.9	W
B	3.2	SSW	1.1	W	1.8	SW
C	2.5	S	0.3	S	1.0	S
D	3.2	SSE	1.1	E	1.8	SE
E	9.1	SE	5.0	NE	6.9	E

Which of the following was a constant in both experiments?

F. Length of vertical stick exposed
G. Shadow direction
H. Day of the year
J. Shadow length

The ACT is a test not only of knowledge and aptitude, but one of time management. This question shows that looking at the actual question first can save you a lot of time. When I started this problem, I read through the paragraphs and all the experiment text, and then I looked through the data in the table... only to find that I could have saved a lot of time by figuring out what information I needed. Now, this isn't the best strategy for every ACT section, but in the science section, it can definitely help to skim over the questions before reading a passage.

The correct answer is F. Length of vertical stick exposed. It was stated in Experiment 1 that the length of the stick exposed above ground was one meter, and the procedure was repeated in Experiment 2. So the length isn't changing. It is constant. The shadow direction and length change constantly, so neither of those choices could work. As for choice H, six different days were used, and it is not clear from the information given if those same six days were used for Experiment 2.

Keep in mind, the ACT science section does not have so much to do with knowledge as with processing information you are given. There is a lot of chart and graph reading.

PSAT Practice Problem - Algebra

Let's work through a PSAT problem. (Click on any of the images to make them bigger).

First, let's find the equation of the parabola by putting the coordinate for the vertex into a vertex-form quadratic equation, y = a(x-h)2 + k, where the vertex is (h, k).

We need to find a, so let's use the other point given on the parabola (0,3) and plug it in the equation.

Let's put that back in the quadratic equation.

Now we need to find the equation of the linear function. First we'll find the slope of the line, and then we'll use the y-intercept of the line to complete the equation.

Now we need to solve the system of equations. We can find the solutions (the two places they touch) by setting both equations equal to each other.

Let's solve.

Since we want the point that's on the right side of the y-intercept, we know that x is going to be positive, so the answer we want is 6. v, which is representing the x-coordinate of the solution of the system of equations, is 6.

New SAT Practice on Khan Academy

There's a new SAT in town. Well, not quite yet, but soon! Starting in March of 2016, the SAT will have a lot of changes. One that I like is that there will no longer be a penalty for wrong answers. Go here to see a full list of changes.

To help you get used to the new format, the College Board has partnered up with Khan Academy to offer practice.

Click on the image below to practice for the new SAT on Khan Academy.

ACT Math Problem - Trig

Here's a problem from the ACT. Let's solve it!

Don't be thrown off by the cone. This is really just a triangle problem. To solve it, we need a little bit of trigonometry knowledge: 

SOH-CAH-TOA 

You should say this aloud to yourself until you've got it memorized. It stands for:

Sine = Opposite/Hypotenuse

Cosine = Adjacent/Hypotenuse

Tangent = Opposite/Adjacent

When you see a problem that requires this knowledge, write it down that you've got it all straight.

Now, if you're looking for the measure of the angle θ, you need to determine what the sides are relative to this angle. 

The side that measures 5 inches is adjacent to the angle. The side that measures 7 is opposite the angle. Now, using SOH-CAH-TOA, we can see that the function we'll use is tangent.

So now we can put the measures of the sides into the tangent equation to get our answer:

Regents Retakes

So you have to retake the Algebra I Regents... You probably want a tutor to help you through it this time. I have a lot of experience with Algebra I Common Core and can help you get a better score.

SAT or ACT?

Should I take the SAT or the ACT?

According ACT, the main difference between the two tests is that the SAT measures aptitude whereas the ACT measures high school achievement. This, however, only really applies to the math section. You do need a bit more knowledge in math to succeed on the ACT. But it's not necessarily true for the other parts. The writing and English sections are very similar in both tests (especially since the SAT is now changing), and the science section does not require much scientific knowledge (it is more about reading and interpreting graphs and charts).

One major difference is how the questions are presented. The SAT questions, although slightly easier than ACT questions, can be presented in a tricky way. Conversely, ACT questions, although they can be harder than SAT questions, are very straightforward.

Another MAJOR difference between the two tests is very obvious if you sit for a practice of each. You have to fly through the ACT to get it done. You cannot sit and linger over questions. Learning to be strategic with your time is essential to being successful on the ACT.

Want some help with either test? Contact me for a session or learn more on SlopeTutor.com.

Prepare for the New PSAT

What's different about the new PSAT?

One of the main changes in the English half is that vocabulary is no longer tested like it was before. If there are vocabulary questions, they will be about a word in context in a selection you are reading. No more memorizing long vocabulary lists!

As for math, there is less geometry and more algebra.

The new test is now 2 hours and 45 minutes (35 minutes longer than the old test).

Want to brush up on PSAT? Contact me for tutoring!