Home / Digital SAT Math Practice Questions – Medium : Nonlinear functions

Digital SAT Math Practice Questions – Medium : Nonlinear functions

Digital SAT Math Practice Questions - Medium : Nonlinear functions - New Syllabus

DSAT MAth Practice questions – all topics

  • Advanced Math Weightage: 35% Questions: 13-15
    • Equivalent expressions
    • Nonlinear equations in one variable and systems of equations in two variables
    • Nonlinear functions

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Question Medium

Cobalt-60 graph

The graph models the mass \( y \), in nanograms, of cobalt-60 (Co-60) remaining in a sample after \( x \) half-lives. The half-life of Co-60 is 5.27 years.

What is the mass, in nanograms, of Co-60 remaining in the sample after 10.54 years?

A) 0.47

B) 1.25

C) 2.00

D) 2.64

▶️ Answer/Explanation
Solution

Answer: B

Half-life = 5.27 years, time = 10.54 years.

Number of half-lives = \( \frac{10.54}{5.27} \approx 2 \).

Mass = \( 5 \times \left(\frac{1}{2}\right)^2 = 5 \times 0.25 = 1.25 \) nanograms.

Alternative method:

Alternative graph

Which is only in option B (because left mass is greater than 1 and less than 2)

Question Medium

Diver height graph

A competitive diver dives from a platform into the water. The graph shown gives the height above the water \( y \), in meters, of the diver \( x \) seconds after diving from the platform. What is the best interpretation of the x-intercept of the graph?

A) The diver reaches a maximum height above the water at 1.6 seconds.

B) The diver hits the water at 1.6 seconds.

C) The diver reaches a maximum height above the water at 0.2 seconds.

D) The diver hits the water at 0.2 seconds.

▶️ Answer/Explanation
Solution

Answer: B

x-intercept is where \( y = 0 \), height is 0 meters.

Graph intersects x-axis around 1.6 seconds.

Best interpretation: diver hits water at 1.6 seconds.

Question  Medium

The graph of the function f is shown. Which of the following is a value of x for which f(x) =0 ?

A. -1

B. 0 

C. 1

D. 4

▶️Answer/Explanation

Ans: C

Values of x  for f(x) = 0 is$-2,1,2.3$

Question Medium

Snow crystal graph

The figure above shows a graph with six regions that correspond to temperature, in degrees Fahrenheit (°F), and humidity conditions, in grams of water vapor per cubic meter of air (g/m³), that will result in different snow crystal shapes when the crystals are grown in a laboratory. Based on the graph, which of the following is a combination of temperature and humidity at which prisms will be formed?

  1. 5°F and 0.15 g/m³
  2. 15°F and 0.18 g/m³
  3. 20°F and 0.02 g/m³
  4. 30°F and 0.08 g/m³
▶️ Answer/Explanation
Solution

Answer: C

Prisms form in the region around 20°F with humidity near 0.02 g/m³.

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