Hello Mike,

I have a question regarding the order you follow in the PWN guide for the Official SAT Tests. Do you follow the order of the College Board website? I have a blue book The Official SAT Study Guide 2020 edition, with eight SAT tests. The order of the tests does not follow the same order as the one listed in the College Board website, and does not include tests 2 and 4 listed there. Thank you. Regards,

Elizabeth

# f(x) = √x and g(x) = 3x – b…

f(x) = √x

g(x) = 3x – b

If the graph of y = f(g(x)) passes through (6, 5) in the standard (x, y) coordinate plane, what is the value of b?

# In a certain class of 70 students, 4/7 of the students are boys, and the ratio of students 10 years or older to students less than 10 years is 2:3. If 2/3 of the girls are less than 10 years old, how many boys are 10 years old or older?

OK, so you have 40 boys and 30 girls. That’s easy enough to calculate because you’re given a part:whole ratio (boys to total students) and you already know the total number of students is 70. Be careful about the second ratio, though, because it’s a part:part ratio! If the ratio of older to younger is (more…)

# The polygon ABCDEFGHI is a regular 9-sided polygon with consecutive vertices labeled in alphabetical order. What is the measure of angle ACE?

OK, so when you have a regular n-gon, you can figure out each angle in it using this formula: [(n-2)180]/n. In this case, 7*180/9 = 140, so we know each angle in the polygon is 140°. I couldn’t draw this quickly on the computer I’m on, so I found a good n-gon picture to mark (more…)

# A triangle with angle measures 30°, 60°, 90° has a perimeter of 18+6√3…

A triangle with angle measures 30°, 60°, 90° has a perimeter of 18+6√3. What is the length of the longest side of the triangle?

# Students in a Science lab are working in groups to build both a small and a large electrical circuit…

Students in a Science lab are working in groups to build both a small and a large electrical circuit. A large circuit uses 4 resistors and 2 capacitors, and a small circuit uses 3 resistors and 1 capacitor. There are 100 resistors and 70 capacitors available, and each group must have enough resistors and capacitors to make one large and one small circuit. What is the maximum number of groups that could work on this lab project?

# 4, 7, 3, 4,….In the sequence above, the first term is 4, the second term is 7, and each term after the second term is the nonnegative difference…

4, 7, 3, 4,….

In the sequence above, the first term is 4, the second term is 7, and each term after the second term is the nonnegative difference between the previous two terms. If the nth term is the first term of the sequence that is equal to zero, what is the value of n?

Okay I know this number can be solved through first principles(finding each number in the sequence manually) but I can’t help but wonder if there’s a certain algebraic formula or method one can utilize to solve it.

# On page 28, question 8, when I looked at the solutions, the number 1 was plugged in to solve the problem…

On page 28, question 8, when I looked at the solutions, the number 1 was plugged in to solve the problem. However, on the beginning of the book the author said to never plug 0 and 1…Anyhow, my question is, if never plugging 1 is suggested, how did you know that plugging 1 in would work in your favor for the question(btw I got it right but I didn’t plug 1 in, I thought of other numbers but it did take me longer to figure out the numbers that’d add up to 11)

# In the system of equations above, a and b represent the distance, in meters, two marathon runners are…

a = 4800 – 6t

b = 5400 – 8t

In the system of equations above, a and b represent the distance, in meters, two marathon runners are from the finish line after running for four hours and t seconds. How far will runner a be from the finish line when runner b passes her?

A. 300 meters

B. 500 meters

C. 100 meters

D. 3000 meters

# A rideshare app charges $2 per trip plus $0.4 per mile…

A rideshare app charges $2 per trip plus $0.4 per mile. A competitor charges $1 for the first 6 miles plus $0.5 per mile for every additional mile. For what length trip would the two services charge the same amount?

A. 10 miles

B. 18 miles

C. 20 miles

D. 40 miles

Can you craft an algebraic equation to solve this directly – or is plugging in the answers the way to go?

# This may be a little advanced for the SAT…

This may be a little advanced for the SAT, but complex numbers sometimes show up –as do cubic polynomials– so hopefully you can address this for me! TIA!

Which of the following could be the full set of complex roots of a cubic polynomial with real coefficients?

A. { 0, 1, i}

B. {1, i, 2i}

C. {2, i}

D. {3, 2 + i, 2 – i}

# Do you have the techniques and concepts for each question as your book only goes to Test #6?

Hi Mike! Your SAT book is amazing. Thank you. My daughter is prepping and is on Test #7 of the official tests. Do you have the techniques and concepts for each question as your book only goes to Test #6. I remember reading you had supplement, but now can’t find the link. Please let me know. Thank you!

Lisa

# A question about composite functions

A question about composite functions:

If f(x) = √x and g(x) = x^2, and you are solving for f(g(x)), ordinarily you solve for g(x) and then plug that value into f(x) to solve for f(g(x)). But what if x is a negative number? When you square it, you’ll get a positive value and then when you take the square root of that to solve for g(f(x)), the final answer will be positive only. Is that correct?

# Can you help me with Question #29 in Practice Test 3, Section 4?

Can you help me with Question #29 in Practice Test 3, Section 4? I found the answer by subtracting multiples of 9 from 122 to find one that was divisible by 5. Is there a better way?

# How do you solve number 2 on page 28 with the plugging in method?

How do you solve number 2 on page 28 with the plugging in method?