SAT 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
SAT MAth and English – full syllabus practice tests
Question Easy
\[
\begin{aligned}
& 5 x+3 y=7 \\
& 2 x+y=2
\end{aligned}
\]
The solution to the given system of equations is \((x, y)\). What is the value of \(7 x+4 y\) ?
A) 2
B) 7
C) 9
D) 23
▶️Answer/Explanation
Ans:C
We need to find the value of \( 7x + 4y \) for the system of equations:
\[
\begin{aligned}
& 5x + 3y = 7 \quad \text{(1)} \\
& 2x + y = 2 \quad \text{(2)}
\end{aligned}
\]
First, solve the system of equations to find \(x\) and \(y\).
Multiply equation (2) by 3 to align the coefficients of \(y\):
\[
3(2x + y) = 3 \cdot 2 \\
6x + 3y = 6 \quad \text{(3)}
\]
Subtract equation (1) from equation (3):
\[
(6x + 3y) – (5x + 3y) = 6 – 7 \\
x = -1
\]
Now substitute \(x = -1\) back into equation (2) to find \(y\):
\[
2(-1) + y = 2 \\
-2 + y = 2 \\
y = 4
\]
Now, we have the solution \( (x, y) = (-1, 4) \).
Next, calculate \(7x + 4y\):
\[
7x + 4y = 7(-1) + 4(4) \\
7x + 4y = -7 + 16 \\
7x + 4y = 9
\]
Question Easy
A company decides to sponsor an employee bowling team. The cost to form the team is \(\$ 180\) per team member plus a onetime \(\$ 25\) team-registration fee. What is the maximum number of team members who can join the team, if the company can spend \(\$ 925\) for the bowling team?
▶️Answer/Explanation
Ans:5
To find the maximum number of team members who can join the bowling team, we need to consider the total cost for the team and the budget available.
Each team member costs \(\$180\) and there is a one-time \(\$25\) team-registration fee. Let \(n\) be the number of team members. Then, the total cost for \(n\) team members is given by:
Total Cost = Cost per team member × Number of team members + Team-registration fee
\[ \text{Total Cost} = 180n + 25 \]
We know that the company can spend \(\$925\) for the bowling team. So, we can set up the equation:
\[ 180n + 25 \leq 925 \]
Now, we solve for \(n\):
\[ 180n \leq 925 – 25 \]
\[ 180n \leq 900 \]
\[ n \leq \frac{900}{180} \]
\[ n \leq 5 \]
So, the maximum number of team members who can join the team is \(5\). Therefore, the correct answer is \(5\).
Question Easy
The mass \(y\), in grams, of juvenile cobia fish \(x\) days after hatching can be modeled by the equation \(y=-324+5.6 x\), where \(60 \leq x \leq 100\). Which graph represents this relationship?
▶️Answer/Explanation
A
For \(\mathrm{x}=60\) :
\(
\begin{aligned}
& y=-324+5.6(60) \\
& y=-324+336 \\
& y=12
\end{aligned}
\)
\(\begin{aligned} & \text { For } x=100: \\ & y=-324+5.6(100) \\ & y=-324+560 \\ & y=236\end{aligned}\)
Question Easy
The shaded region shown represents all solutions to an inequality. Which ordered pair \((x, y)\) is a solution to this inequality?
A) \((5,0)\)
B) \((0,5)\)
C) \((-5,0)\)
D) \((0,-5)\)
▶️Answer/Explanation
A
Option A lie in the Shaded region
Questions Foundation
$
f(x)=-0.5 x+56
$
The given function models the average daily temperature \(f(x)\), in degrees Fahrenheit \(\left({ }^{\circ} \mathrm{F}\right)\), in Chicago \(x\) days after November 1 , for \(0 \leq x \leq 29\). Based on this model, what is the average daily temperature, in \({ }^{\circ} \mathrm{F}\), in Chicago 6 days after November 1 ?
A) 62
B) 60
C) 56
D) 53
▶️Answer/Explanation
Ans:D
To find the average daily temperature \(f(x)\) 6 days after November 1, we need to evaluate the given function \(f(x) = -0.5x + 56\) at \(x = 6\).
Substitute \(x = 6\) into the function:
\[
f(6) = -0.5(6) + 56
\]
\[
f(6) = -3 + 56
\]
\[
f(6) = 53
\]
So, the average daily temperature in Chicago 6 days after November 1 is \(53^\circ \mathrm{F}\).