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Digital SAT Math: Linear functions -Practice Questions

Digital SAT Math: Linear functions -Practice Questions - New Syllabus

DSAT MAth Practice questions – all topics

  • Algebra Weightage: 35%  Questions: 13-15
    • Linear equations in one variable
    • Linear equations in two variables
    • Linear functions
    • Systems of two linear equations in two variables
    • Linear inequalities in one or two variables

DSAT MAth and English  – full syllabus practice tests

Question   Easy

The line graph shows the number of near-Earth asteroids discovered by the Spacewatch survey from 2003 to 2010.

During which period was the increase in the number of near-Earth asteroids discovered the greatest?
A) From 2003 to 2004
B) From 2004 to 2005
C) From 2005 to 2006
D) From 2007 to 2008

▶️Answer/Explanation

Ans:D

We will compare the increase in the number of near-Earth asteroids discovered from year to year by examining the vertical distances between points on the graph.

1. From 2003 to 2004:
 In 2003, the number of asteroids discovered is approximately 50.8.
 In 2004, the number of asteroids discovered is approximately 70.2.
 Increase: \( 70.2 – 50.8 = 19.4 \).

2. From 2004 to 2005:
 In 2004, the number of asteroids discovered is approximately 70.2.
 In 2005, the number of asteroids discovered is approximately 80.3.
 Increase: \( 80.3 – 70.2 = 10.1 \).

3. From 2005 to 2006:
 In 2005, the number of asteroids discovered is approximately 80.3.
 In 2006, the number of asteroids discovered is approximately 90.9.
Increase: \( 90.9 – 80.3 = 10.6 \).

4. From 2007 to 2008:
In 2007, the number of asteroids discovered is approximately 40.8.
In 2008, the number of asteroids discovered is approximately 80.4.
Increase: \( 80.4 – 40.8 = 39.6 \).

By comparing these increases, we see that the greatest increase occurred from 2007 to 2008.

Question

The line graphed in the xy-plane below models the total cost, in dollars, for a cab ride, y, in a certain city during nonpeak hours based on the number of miles traveled, x.

According to the graph, what is the cost for each additional mile travelled, in dollars, of a cab ride?

A) \$2.00
B) \$2.60
C) \$3.00
D) \$5.00

▶️ Answer/Explanation
Solution
1. Identify two points on the line: (1,5) and (2,7)
2. Calculate the slope (cost per mile):
\(\frac{7-5}{2-1} = 2\)
Answer: A) \$2.00
Question

The linear function \(f\) is defined by \(f(x)=2(x-1)\). What is the value of \(f(4)\)?

A) 1.5
B) 3
C) 6
D) 7

▶️ Answer/Explanation
Solution
1. Substitute \(x = 4\) into the function:
\(f(4) = 2(4 – 1)\)
2. Simplify the expression:
\(f(4) = 2(3) = 6\)
Answer: C) 6
Question

The graph shown models the number of candy bars a certain machine wraps with a label in x seconds.

According to the graph, what is the estimated number of candy bars the machine wraps with a label per second?

A) 2
B) 40
C) 78
D) 80

▶️ Answer/Explanation
Solution
1. Identify two points on the line: (0,0) and (2,80)
2. Calculate the slope (candy bars per second):
\(\frac{80-0}{2-0} = 40\)
Answer: B) 40
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