What is the best way to solve this problem within ~1 minute? (given SAT time limit)

# 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

# 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 the xy-plane, the point (6,3) is the midpoint of the line segment with endpoints (x,5) and (9,y). What is the value of x+y ?

The midpoint formula tells you that the a segment with endpoints (a, b) and (c, d) will have a midpoint at ((a + c)/2,(b + d)/2) So we know that (x + 9)/2 = 6 and (5 + y)/2 = 3. We can solve those! (x + 9)/2 = 6 x + 9 = 12 x = 3 (5 + y)/2 = 3 5 + y = (more…)

# If A(-3,0) and C(5,2) are the endpoints of diagonal AC of rectangle ABCD, with B on the x-axis, what is the perimeter of rectangle ABCD?

Draw this out. Start with the two points you’re given. Now remember that the shape is a rectangle, and that you’re told that point B is on the x-axis. The only way that happens is if B is at (5, 0). Point D, by the same logic, must be at (–3, 2). Now draw the rectangle (more…)

# The function f is defined by f(r) = (r-4)(r+1)^2 . If f(h-3) = 0, what is one possible value for h? I don’t see the correlation between the two functions. Can you please elucidate? Thank you <3

The thing to remember about functions is that they do the same thing to whatever is inside the parentheses. So don’t worry about the r vs. the h. They could use x, or a little star symbol, or whatever else they want. What matters is that the function f, as defined here, will equal zero (more…)

# A question from the May 2018 SAT (Section 4 #18)

A question from the May 2018 SAT (Section 4 #18)

kx + y = 1

y = -x² + k

In the system of equations above, k is a constant. When the equations are graphed in the xy-plane, the graphs intersect at exactly two points. Which of the following CANNOT be the value of k?

A. 3

B. 2

C. 1

D. 0

# The function f is defined by f(x) is x^4 – 4x^2 + x + 1 for -5 ≤ x ≤ 5…

Here are a couple questions from the old official SAT Subject Test Math I practice exam:

The function f is defined by f(x) is x^4 – 4x^2 + x + 1 for -5 ≤ x ≤ 5. In which of the following intervals does the minimum value of f occur?

A) -5 ≤ x ≤ -3

B) -3 ≤ x ≤ -1

C) -1 ≤ x ≤ 1

D) 1 ≤ x ≤ 3

E) 3 ≤ x ≤ 5

Can you solve w/o graphing?

# Could you please explain SAT Past paper 3, section 4, question 12?

Could you please explain SAT Past paper 3, section 4, question 12? I don’t really understand why the double root is considered a ‘distinct’ zero.

Thank you for your time!

# Test 4 Section 4 Question 21

Can you help me with the Official Test 4 Question 21?

# Test 8 Section 4 #30

Test 8 Section 4 #30

# what is the difference between the maximum value of y=-x^4-2x^3+5 and the minimum value of y = x^4+x^2-4

what is the difference between the maximum value of y=-x^4-2x^3+5 and the minimum value of y = x^4+x^2-4

# PSAT #2, Section 4, #29

PSAT #2, Section 4, #29

# Test 5, Section 4, Question 20. How do you get to the answer?

Test 5, Section 4, Question 20. How do you get to the answer?

# If r>0 and (9r/2)^(1/3) = (1/2) r, what is the value of r?

If r>0 and (9r/2)^(1/3) = (1/2) r, what is the value of r?