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 Hard
An economist modeled the demand Q for a certain product as a linear function of the selling price P. The demand was 20,000 units when the selling price was \($40\) per unit, and the demand was 15,000 units when the selling price was \($60\) per unit. Based on the model, what is the demand, in units, when the selling price is \($55\) per unit?
A. 16,250
B. 16,500
C. 16,750
D. 17,500
▶️Answer/Explanation
Answer: A
Find slope:
\(
m = \frac{15,000 – 20,000}{60 – 40} = \frac{-5000}{20} = -250
\)
Use equation:
\(
Q = -250P + 30,000
\)
Substitute \( P = 55 \):
\(
Q = -250(55) + 30,000 = 16,250
\)
▶️Desmos
Question Hard
The cost of renting a backhoe for up to 10 days is \($270\) for the first day and \($185\) for each additional day. Which of the following equations gives the cost y, in dollars, of renting the backhoe for x days, where x is a positive integer and \(x \leq 10\)?
A.y =270x — 135
B.y=270x+135
C.y =135x + 270
D.y =135x + 135
▶️Answer/Explanation
Answer: D
Fixed cost for the first day = \(\$270\).
Additional cost per day = \(\$135\) for \( x – 1 \) extra days.
Total cost equation:
\(
y = 270 + 135(x – 1)
\)
Expanding:
\(
y = 135x + 270 – 135 = 135x + 135
\)
▶️Desmos
Question Hard
Oil and gas production in a certain area dropped from 4 million barrels in 2000 to 1.9 million barrels in 2013. Assuming that the oil and gas production decreased at a constant rate, which of the following linear functions f best models the production, in millions of barrels, t years after the year 2000?
A\(f(t)=\frac{21}{130}t+4\)
B\(f(t)=\frac{19}{130}t+4\)
C\(f(t)=-\frac{21}{130}t+4\)
D\(f(t)=-\frac{19}{130}t+4\)
▶️Answer/Explanation
Answer: C
Find the slope \( m \):
\(
m = \frac{1.9 – 4}{2013 – 2000} = \frac{-2.1}{13} = -\frac{21}{130}
\)
Find the equation:
Initial production in 2000: \( 4 \) million barrels → y-intercept is 4.
Equation:
\(
f(t) = -\frac{21}{130}t + 4
\)
▶️Desmos
