SAT Official Practice Test #6 Section 4 Question 32 (Grid-In)
2(5x − 20) − (15 + 8x) = 7
What value of x satisfies the equation above?
CAS Solution
solve(2(5x − 20) − (15 + 8x) = 7,x) Enter
Returns
x=31
SAT Official Practice Test #6 Section 4 Question 35 (Grid-In)
The line with the equation 4/5 x + 1/3 y = 1 is graphed
in the xy‐plane. What is the x-coordinate of the x‐intercept of the line?
If you know that the x-intercept is the x-value of the equation when y=0, it is very easy to solve this problem algebraically without the calculator. It only make sense to use the method below if you know how to use a calculator to identify the zeroes of a function but do not know how to do it algebraically. Some students fall into this category, maybe because they use their calculators for graphing all the time but have done algebra 1 too long ago to remember its basic concepts well.
To those people who protest that everyone knows how to do this problem without a graphing calculator, I note that this problem appears as the fifth of eight grid-ins. I take this to mean that fewer than half of the students answer it correctly.
CAS Graphing Solution
Step 1: Open a graphing page, then select
Menu-Graph Entry/Edit-Relation and copy the equation 4/5 x + 1/3 y = 1 onto the relation line
The calculator will graph the line. Since the x-intercept is not an integer, complete Step 2.
Step 2: Menu-Analyze Graph- Zero
Set the lower and upper limits near the x-intercept. The calculator returns (1.25,0).
Answer: 1.25
SAT Official Practice Test #6 Section 4 Question 27
In the xy-plane, the graph of 2x^2 − 6x + 2y^2 + 2y = 45 is a circle. What is the
radius of the circle?
A) 5
B) 6.5
C) sqrt 40
D) sqrt 50
CAS Solution
Algebraic:
Steo 1: completesquare(2x^2 − 6x + 2y^2 + 2y = 45,x,y) Enter
Returns
2(x-3/2)^2+2(y+1/2)^2=50
Step 2: Divide both sides by 2 to put the circle equation in center form
(x-3/2)^2+(y+1/2)^2=25
Step 3: r=sqrt 25=5
Answer: A
Graphing:
Step 1: Open a graphing page, then select
Menu-Graph Entry/Edit-Equation Templates-Circle-Standard Form and copy the constants into the equation template.
The calculator will graph the circle.
Step 2:
Menu-Analyze Graph-Analyze Conics-Radius
Returns
5
SAT Official Practice Test #6 Section 4 Question 11
7x+3y = 8
6x−3y = 5
For the solution (x, y) to the system of equations above, what is the value of x-y?
A) − 4/3
B) 2/3
C) 4/3
D) 22/3
CAS Solution
solve(7x+3y = 8
6x−3y = 5, (x,y)) Enter
Returns
x=1 and y=1/3
Answer: B
SAT Official Practice Test #6 Section 4 Question 1
Which expression is equivalent to (2x^2−4)−(−3x^2+2x−7) ?
A) 5x^2−2x+3
B) 5x^2+2x−3
C) −x^2−2x−11
D) −x^2+2x−11
CAS Solution
2x^2−4)−(−3x^2+2x−7) Enter
Returns
5x^2-2x+3
Answer: A
SAT Official Practice Test #5 Section 4 Question 8
Which of the following is an equivalent form of (1.5x − 2.4)^2 − (5.2x^2 − 6.4) ?
A) -2.2x^2+1.6
B) -2.2x^2+11.2
C) -2.95x^2-7.2x+12.16
D) -2.95x^2-7.2x+0.64
CAS Solution: Subtract answer choices from given expression to see if the difference is 0. Test the most complicated answer choices first.
D: (1.5x − 2.4)^2 − (5.2x^2 − 6.4) - (-2.95x^2-7.2x+0.64) Enter
Returns 11.52
C): (1.5x − 2.4)^2 − (5.2x^2 − 6.4) - (-2.95x^2-7.2x+12.16) Enter
Returns 0
Answer: C
@Plotinus
Where are the scoring guidelines for this new practice test #2? I took the test but the scoring sheet (aka the curve) isn’t included.
I haven’t seen the scoring curve for PSAT Practice Test #2 anywhere. You might try the Scan & Score feature of the SAT Daily Practice App. I haven’t tried this myself yet so I don’t know if it works for this test.
In any case, if this is a practice test that has never been administered, it may not be possible to produce a reliable scoring curve that gives a definite score for each raw score. The unadministered practice tests in the old SAT Official Guide and Online Course did not have definite scoring curves either – the curves gave score ranges for each raw score. I would take curved scores from unadministered tests cum grano salis.
PSAT October 2016
Question 26 (Difficulty Level “Hard”)
y= -x^2+10x-27
y+9=x
Which of the following gives all of the ordered pairs (x, y) that satisfy the system of equations above?
CAS Solution:
Solve(y= -x^2+10x-27
y+9=x, x,y)
returns
x=3 and y=-6 or x=6 and y= -3
Question 29 (Difficulty Level “Hard”)
t^2-7t+12=0
What is the positive difference of the two values of t that satisfy the equation above?
CAS Solution:
solve (t^2-7t+12=0,t)
returns
t=3 or t=4
Answer: 4-3=1
Question 19 (Difficulty Level “Medium”)
T=3(ak-1)+4
In the equation above, which of the following is equal to ak?
CAS Solution
solve(T=3(ak-1)+4,ak)
returns
ak=(t-1)/3
^Not that it matters this time, but should that be “a*k” rather than just “ak”? I thought that you could not leave out the multiplication symbol when you are talking about multiplying variables…It works this time, but I believe that, as entered, the calculator thinks that “ak” is the two-letter name of a single variable and not the product of two separate variables. But I know you are more familiar with this than I am, so I could be wrong.
@pckeller You are completely right: the calculator interprets “ak” as a single two-letter variable name. I exploited that feature in this solution to find the value of ak in one step. Essentially, in my solution, I substitute the single variable ak for the two-variable expression ak.
Otherwise, I could have written two equations:
solve (T=3(ak-1)+4
z=ak,a,k,z)
returns
t=1 and z=0 and a=c2 and k=0 or z=(t-1)/3 and a=(t-1)/3c1 and k=c1.
or also directly
solve (T=3(z-1)+4,z)
returns
z=(t-1)/3
Students commonly learn substitution of variables in calculus, so probably the kind of student who is tempted to use the calculator for this baby algebra problem will have to go the define-a-new-variable-and-write-another-equation route. That methods always works, also for much harder problems.
Official SAT Practice Test #7, Section 4, Question 35 (Grid-In)
y = x^2 - 4x + 4
y=4-x
If the ordered pair (x, y) satisfies the system of equations above, what is one possible value of x ?
CAS Solution
solve(y = x^2 - 4x + 4
y=4-x, x,y)
returns x=0 and y = 4 or x=3 and y=1
Test 7 Section 4 Question 2
(x^2- 3) - (-3x^2 + 5)
Which of the following expressions is equivalent to the one above?
CAS Solution
(x^2- 3) - (-3x^2 + 5) Enter
returns
4x^2-8
Test 7 Section 4 Question 5
Which of the following ordered pairs (x, y) satisfies the inequality 5x -3y < 4 ?
I. (1,1) II. (2,5) III. (3,2)
CAS Solution
Graph the given inequality using the “relation” option. Turn on lined grid. Check whether the given points are in the shaded area of the graph. Answer: I and II
Test 7 Section 4 Question 29
A circle in the xy-plane has equation (x + 3)^2 + (y - 1)^2 = 25. Which of the following points does NOT lie in the interior of the circle?
A) (-7,3) B) (-3, 1) C) (0,0) D) (3,2)
CAS Solution
Graph the given circle using the circle equation template. Turn on lined grid. Check whether the given points lie inside or outside the circle. Answer: D
PSAT October 15, 2016
Section 4 Question 29
7<0.04x-2y<8
In the inequality above, if x=320, what is one possible value for y?
CAS Solution
solve(7<0.04*(320)-2y<8,y)
returns
2.4<y<2.9
PSAT October 15, 2016
Section 4 Question 27
y=10x^2-25x-60
The graph of the equation above is a parabola in the xy-plane. In which of the following equivalent forms of the equation does the minimum value of y appear as a term?
A) y=5(2x+3)(x-4)
B) 5(4x-5)^2-8y=605
C) (x-5/4)^2=y/10-121/16
D) y=10(x-5/4)^2-605/8
CAS Solution:
CompleteSquare(y=10x^2-25x-60,x)
returns
y=10(x-5/4)^2-605/8
PSAT October 15, 2016
Section 4 Question 26
x-y=1
x^2=1+y
A system consisting of a linear equation and a quadratic equation is shown above. If (x,y)=(a,b) is a solution to the system, which of the following could be the value of a?
A) 1 B) 0 C) -1 D) -2
CAS Solution:
solve (x-y=1
x^2=1+y,x,y)
returns
x=-1 and y=0 or x=2 and y=3
Answer: C