AdaAda

Home / Library / Synthetic quiz

Digital SAT Math Practice Quiz

10 multiple-choice questions assessing linear systems, quadratics, Desmos shortcuts, and geometry for the Digital SAT Math section.

10 questions · Deck: Digital SAT Math: Algebra, Advanced Math & Geometry · Curated by Ada

Question 1

Consider the system of linear equations: $$4x + 6y = 12$$ $$2x + ky = 7$$ For what value of $k$ does the system have no solution?

  1. k = 2
  2. k = 3
  3. k = 4
  4. k = 6

Question 2

The height $h(t)$ in feet of a projectile launched into the air after $t$ seconds is modeled by the function $h(t) = -16t^2 + 64t + 80$. What is the maximum height, in feet, reached by the projectile?

  1. 80 feet
  2. 128 feet
  3. 144 feet
  4. 160 feet

Question 3

What is the sum of the solutions to the quadratic equation $3x^2 - 15x + 7 = 0$?

  1. -5
  2. -7/3
  3. 7/3
  4. 5

Question 4

For what value of the constant $c$ does the quadratic equation $x^2 - 8x + c = 0$ have exactly one real solution?

  1. c = 4
  2. c = 8
  3. c = 16
  4. c = 64

Question 5

The population of a town $t$ years after 2020 is modeled by the exponential function $P(t) = 5{,}000(1.07)^t$. By what annual percentage does the town's population increase each year?

  1. 0.07%
  2. 1.07%
  3. 7%
  4. 70%

Question 6

In the xy-plane, what are the coordinates of the center and the length of the radius of the circle defined by $(x - 3)^2 + (y + 5)^2 = 49$?

  1. Center (-3, 5), radius 7
  2. Center (3, -5), radius 7
  3. Center (3, -5), radius 49
  4. Center (-3, 5), radius 49

Question 7

In a circle with center $O$, central angle $\angle AOB$ intercepts arc $AB$ with a measure of $84^\circ$. Point $C$ lies on the circle outside of arc $AB$. What is the measure of the inscribed angle $\angle ACB$?

  1. 21°
  2. 42°
  3. 84°
  4. 168°

Question 8

If $\sin(3x - 10^\circ) = \cos(4x + 9^\circ)$, where both angles are acute, what is the value of $x$ in degrees?

  1. 11
  2. 13
  3. 15
  4. 17

Question 9

What is the slope of a line that is perpendicular to the line with equation $2x - 5y = 10$?

  1. -5/2
  2. -2/5
  3. 2/5
  4. 5/2

Question 10

A teacher adds 5 bonus points to every student's score on a mathematics exam. Which of the following statistical measures of the exam scores remains completely unchanged?

  1. Mean
  2. Median
  3. Standard deviation
  4. Maximum score