Question 34 (Grid-in) (CB Rating: Hard)
1/2 x = a
x + y = 5a
In the system of equations above, a is a constant such that 0 < a < 1/3. If (x,y) is a solution to the system of equations, what is one possible value of y?
CAS Solution
Pick any value for a between 0 and 1/3, say 1/4.
solve(1/2 x = 1/4
x + y = 5(1/4), x, y)
returns x = 1/2 and y = 3/4.
Answer: 3/4
Question 35 (Grid-in) (CB Rating: Hard)
(x^2+17x+66)/(x+6)
If the expression above is equivalent to an expression of the form x+a, where x is not equal to -6, what will be the value of a?
CAS Solution
(x^2+17x+66)/(x+6) Enter
returns x+11
Answer: 11
Thanks a lot for sharing. Going through the thread I sympathize with the views not looking favorable to the atypical use of the calculator on the SAT. As educators we want our charges to learn truly the math as they would have a better chance to max out their score and the knowledge would probably be useful in college and later. Yet,we need to help the students get the best score by means best for them. The more tools they can use competently use the better think. Also, I am guessing that this generation is less comfortable with calculations, multi step work throughs. Calculators are introduced earlier and they seem more comfortable punching numbers than handwriting it out. Just my limited observation.
PSAT Oct. 11, 2017
Question 13
Which of the following is equivalent to nthroot(2^3n x 5^(n+2)), where n>0?
A. 200
B. 40 x nthroot(25)
C. 40 + nthroot(25)
D. 10,000 x nthroot(100)
CAS Solution
nthroot(2^3n x 5^(n+2)) Enter
Returns 40x(25^1/n)
PSAT Oct. 11, 2017
Question 18
x+2y=5
3x+4y=15
if (x,y) is the solution to the system of equations above, what is the value of y?
A. -5
B. 0
C. 2
D. 5
CAS Solution
solve(x+2y=5
3x+4y=15, (x,y)) Enter
Returns
x=5 and y=0
PSAT Oct. 11, 2017
4a^2 + 20ab + 25b^2
Which of the following is a factor of the polynomial above?
A. a+b
B. 2a+5b
C. 4a+5b
D. 4a+25b
CAS Solution
factor(4a^2 + 20a x b + 25b^2,a) Enter
Returns (2a+5b)^2
PSAT Oct. 11, 2017
Which of the following is equivalent to (x^2+x)+(x^2-x)?
A. x^2
B. 2x^2
C. 2x^2+x
D. 2x^2+2x
CAS Solution
(x^2+x)+(x^2-x) Enter
Returns 2x^2
PSAT Oct. 14, 2017
17. If a=b+2, what is the value of (3^a)(3^-b)?
A. 0
B. 1
C. 3
D. 9
CAS Solution
solve(a=b+2 and z=(3^a)(3^-b),z) Enter
Returns z= 9 and a=b+2
PSAT Oct. 14, 2017
4x+5y=100
5x+4y=62
If the system of equations above has solution (x,y), what is the value of x+y?
A. 0
B. 9
C. 18
D. 38
CAS Solution
solve(4x+5y=100
5x+4y=62, (x,y)) Enter
Returns x=-10 and y=28
x+y=-10+28=18
Some questions ask you to convert from metric to American units or vice-versa. The latest operating system (4.5.0) has a Conversion Assistant that makes these conversions very easy. Enter the number to be converted, then access the Conversion Assistant: press the catalogue button (looks like an open book), then c, then Conversion Assistant. Choose the units to be converted, press enter.
For example,
SAT Oct 2017 Question 12
Biologists found a new species of pale shrimp at the world’s deepest undersea vent, the Breebe Vent Field. The vent is 3.1 miles below the sea’s surface. Approximately how many kilometers below the sea’s surface is the vent? (1 kilometer=0.6214 miles)
A. 2 B. 3 C. 4 D. 5
CAS Solution:
3.1 Enter
Conversion Assistant
Category Length
From: miles
To: kilometers Enter
Returns 4.98897 km
Question 24
If f(x)=5x^2-3 and f(x+a)=5x^2+30x+42, what is the value of a?
A. -30 B. -3 C. 3 D. 30
CAS Solution (Forward Solve)
Define f(x)=5x^2-3 Enter
returns OK
solve(f(x+a)=5x^2+30x+42,a)
Returns a=(2x+3) or a=3
CAS Solution (Backsolve)
Define f(x)=5x^2-3 Enter
returns OK
A: f(x-30) Enter
returns 5x^2-300x+4497
B: f(x-3) Enter
returns 5x^2-30x+42
C: f(x+3) Enter
returns 5x^2+30x+42
Question 17
If 2w+4t=14 and 4w+5t=25, what is the value of 2w+3t?
A. 6 B. 10 C. 13 D. 17
CAS Solution
solve(2w+4t=14 and 4w+5t=25 and z=2w+3t,w,t,z) Enter
returns w=5 and t=1 and z=13
Question 16
(4x+4)(ax-1)-x^2+4
In the expression above, a is a constant. If the expression is equal to bx, where b is a constant, what is the value of b?
A.-5 B. -3 C. 0 D. 12
CAS Solution
expand((4x+4) ( a x-1)) Enter
returns 4ax^2+4ax-4x-4
Ans-x^2+4 Enter
returns (4a-1)x^2 +(4a-4)x
solve(4a-1=0 and b=4a-4,a,b) Enter
returns a=1/4 and b=-3
Question 25
If sin x°=a, which of the following must be true for all values of x?
A. cos x°=a
B. sin(90°-x°)=a
C. cos(90°-x°)=a
D. sin (x^2)°=a^2
CAS Solution (Backsolve)
Solve each equation for x. If the equation is true for all x, the calculator will return “true”. If the calculator is in degree mode, you can omit the degree signs. If the calculator is in radian mode, you must include all the degree signs.
A: solve(cos x°=sin x°,x) Enter
returns x=45(4n1-3)
B:solve(sin(90°-x°)=sin x°, x) Enter
returns x= 45(4n2-3)
C: solve(cos(90°-x°)=sin x°, x) Enter
returns true
In average cases, I encourage students to learn how to solve problems both with and without the calculator. Students who are very strong in algebra often can solve questions faster by hand, while students who are very weak may have trouble without the calculator. However, during homework practice, I don’t encourage students to solve questions with the calculator that they are unable to solve without it. On the day of the test, the student can use whatever method seems easier.