March 21 QAS Sec 3 #11

Hi Mike …can you solve & explain? (from QAS March 2021)
Section 3; #11.
y = (x-1)(x+1)(x+2)
The graph in the xy plane of the equation above contains the point (a,b). If -1 < or = a < or = 1, which of the following is NOT a possible value of b?
A) -2
B) -1
C) 0
D) 1

Hi, Mike. How would you say the two math sections of the SAT are different (besides the obvious calculator use and the timing/number of questions)? I’m thinking in terms of content covered, types of questions, etc. Thanks!

Hi, Mike. How would you say the two math sections of the SAT are different (besides the obvious calculator use and the timing/number of questions)? I’m thinking in terms of content covered, types of questions, etc. Thanks!

Hi! Love your book so far. I just started reviewing…

Hi! Love your book so far. I just started reviewing. I looked at number 10 in the first section on page 29 and I was wondering how would you pick the correct answer if you chose to substitute 8 for d? Because both answer choices a and d work. Would you just try all the answer choices and choose different variable values and try again or is there a different way to approach it?

What am I not seeing?

4x + y = 7
2x – 7y = 1

If I multiply the second equation by 2, I can stack them and subtract:

4x + y = 7
4x – 14y = 2

So, 15y = 5, —> y = 3

Then: 2x – 7(3) = 1 –> 2x – 21 = 3 —> 2x = 24 –> x = 12
But: 4x + 3 = 7 –> 4x = 4 –> x = 1

What am I not seeing? The answer should be x= 5/3.

In this equation, k is a constant…

Some help please, Mike?

x^2 – 12x +k = 0 In this equation, k is a constant. For which values of k does the equation have only one solution? I know I can set the discriminant to zero and solve for k. But is there another way to solve? Thanks!

The lengths of the sides of a rectangle are a and b…

The lengths of the sides of a rectangle are a and b, where a > b The sum of the lengths of the two shorter sides and one of the longer sides of the rectangle is 36. What value of a maximizes the area of the rectangle?

A .9
B. 12
C. 18
D. 24

The answer is C. I suspect there is an easier way to solve than completing the square and finding the vertex of the resulting quadratic function. What is your most direct, easy to understand solution to this calculator-allowed question?