Question ID a5663025
Assessment Test Domain Skill Difficulty
SAT Math Advanced Math Nonlinear
equations in one
variable and
systems of
equations in two
variables
ID: a5663025
PR
A system of equations consists of a quadratic equation and a linear equation. The
equations in this system are graphed in the xy-plane above. How many solutions
does this system have?
A. 0
O
B. 1
FD
C. 2
D. 3
ID: a5663025 Answer
O
Correct Answer: C
C
Rationale
Choice C is correct. The solutions to a system of two equations correspond to points where the graphs of the
equations intersect. The given graphs intersect at 2 points; therefore, the system has 2 solutions.
Choice A is incorrect because the graphs intersect. Choice B is incorrect because the graphs intersect more
than once. Choice D is incorrect. It’s not possible for the graph of a quadratic equation and the graph of a linear
equation to intersect more than twice.
Question Difficulty: Medium
,Question ID d0a7871e
Assessment Test Domain Skill Difficulty
SAT Math Advanced Math Nonlinear
equations in one
variable and
systems of
equations in two
variables
ID: d0a7871e
y equals, x plus 1, and, y equals, x squared plus x
If is a solution to the system of equations above, which of the
following could be the value of x ?
A. –1
PR
B. 0
C. 2
D. 3
O
ID: d0a7871e Answer
FD
Correct Answer: A
Rationale
2
Choice A is correct. It is given that y = x + 1 and y = x + x. Setting the values for y equal to each other yields x + 1
2 2
O
= x + x. Subtracting x from each side of this equation yields x = 1. Therefore, x can equal 1 or –1. Of these, only
–1 is given as a choice.
2 2
C
Choice B is incorrect. If x = 0, then x + 1 = 1, but x + x = 0 + 0 = 0 ≠ 1. Choice C is incorrect. If x = 2, then x + 1 = 3,
2 2 2 2
but x + x = 2 + 2 = 6 ≠ 3. Choice D is incorrect. If x = 3, then x + 1 = 4, but x + x = 3 + 3 = 12 ≠ 4.
Question Difficulty: Medium
,Question ID 7f81d0c3
Assessment Test Domain Skill Difficulty
SAT Math Advanced Math Nonlinear
equations in one
variable and
systems of
equations in two
variables
ID: 7f81d0c3
x squared, minus x, minus 1, equals 0
What values satisfy the equation above?
A. and
x equals 1
PR
B. and
x equals negative one half
C. and
x equals, the fraction with numerator 1 plus the square root of 5, and denominator 2
O
D. and
FD
x equals, the fraction with numerator negative 1 plus the square root of 5, and denominator 2
ID: 7f81d0c3 Answer
Correct Answer: C
O
Rationale
C
Choice C is correct. Using the quadratic formula to solve the given expression yields
. Therefore, and satisfy the given
equation.
Choices A and B are incorrect and may result from incorrectly factoring or incorrectly applying the quadratic
formula. Choice D is incorrect and may result from a sign error.
Question Difficulty: Medium
, Question ID ff2c1431
Assessment Test Domain Skill Difficulty
SAT Math Advanced Math Nonlinear
equations in one
variable and
systems of
equations in two
variables
ID: ff2c1431
The given equation relates the positive numbers , , and . Which equation correctly gives in terms of and ?
A.
B.
PR
C.
D.
O
ID: ff2c1431 Answer
Correct Answer: B
FD
Rationale
Choice B is correct. It's given that the equation relates the positive numbers , , and . Dividing
both sides of the given equation by yields . Subtracting from both sides of this equation yields
, or . It follows that the equation correctly gives in terms of and .
O
Choice A is incorrect and may result from conceptual or calculation errors.
C
Choice C is incorrect and may result from conceptual or calculation errors.
Choice D is incorrect and may result from conceptual or calculation errors.
Question Difficulty: Medium
Assessment Test Domain Skill Difficulty
SAT Math Advanced Math Nonlinear
equations in one
variable and
systems of
equations in two
variables
ID: a5663025
PR
A system of equations consists of a quadratic equation and a linear equation. The
equations in this system are graphed in the xy-plane above. How many solutions
does this system have?
A. 0
O
B. 1
FD
C. 2
D. 3
ID: a5663025 Answer
O
Correct Answer: C
C
Rationale
Choice C is correct. The solutions to a system of two equations correspond to points where the graphs of the
equations intersect. The given graphs intersect at 2 points; therefore, the system has 2 solutions.
Choice A is incorrect because the graphs intersect. Choice B is incorrect because the graphs intersect more
than once. Choice D is incorrect. It’s not possible for the graph of a quadratic equation and the graph of a linear
equation to intersect more than twice.
Question Difficulty: Medium
,Question ID d0a7871e
Assessment Test Domain Skill Difficulty
SAT Math Advanced Math Nonlinear
equations in one
variable and
systems of
equations in two
variables
ID: d0a7871e
y equals, x plus 1, and, y equals, x squared plus x
If is a solution to the system of equations above, which of the
following could be the value of x ?
A. –1
PR
B. 0
C. 2
D. 3
O
ID: d0a7871e Answer
FD
Correct Answer: A
Rationale
2
Choice A is correct. It is given that y = x + 1 and y = x + x. Setting the values for y equal to each other yields x + 1
2 2
O
= x + x. Subtracting x from each side of this equation yields x = 1. Therefore, x can equal 1 or –1. Of these, only
–1 is given as a choice.
2 2
C
Choice B is incorrect. If x = 0, then x + 1 = 1, but x + x = 0 + 0 = 0 ≠ 1. Choice C is incorrect. If x = 2, then x + 1 = 3,
2 2 2 2
but x + x = 2 + 2 = 6 ≠ 3. Choice D is incorrect. If x = 3, then x + 1 = 4, but x + x = 3 + 3 = 12 ≠ 4.
Question Difficulty: Medium
,Question ID 7f81d0c3
Assessment Test Domain Skill Difficulty
SAT Math Advanced Math Nonlinear
equations in one
variable and
systems of
equations in two
variables
ID: 7f81d0c3
x squared, minus x, minus 1, equals 0
What values satisfy the equation above?
A. and
x equals 1
PR
B. and
x equals negative one half
C. and
x equals, the fraction with numerator 1 plus the square root of 5, and denominator 2
O
D. and
FD
x equals, the fraction with numerator negative 1 plus the square root of 5, and denominator 2
ID: 7f81d0c3 Answer
Correct Answer: C
O
Rationale
C
Choice C is correct. Using the quadratic formula to solve the given expression yields
. Therefore, and satisfy the given
equation.
Choices A and B are incorrect and may result from incorrectly factoring or incorrectly applying the quadratic
formula. Choice D is incorrect and may result from a sign error.
Question Difficulty: Medium
, Question ID ff2c1431
Assessment Test Domain Skill Difficulty
SAT Math Advanced Math Nonlinear
equations in one
variable and
systems of
equations in two
variables
ID: ff2c1431
The given equation relates the positive numbers , , and . Which equation correctly gives in terms of and ?
A.
B.
PR
C.
D.
O
ID: ff2c1431 Answer
Correct Answer: B
FD
Rationale
Choice B is correct. It's given that the equation relates the positive numbers , , and . Dividing
both sides of the given equation by yields . Subtracting from both sides of this equation yields
, or . It follows that the equation correctly gives in terms of and .
O
Choice A is incorrect and may result from conceptual or calculation errors.
C
Choice C is incorrect and may result from conceptual or calculation errors.
Choice D is incorrect and may result from conceptual or calculation errors.
Question Difficulty: Medium
