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
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 Easy
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
Ans: C
The linear function \( f \) is defined by:
\[ f(x) = 2(x-1) \]
We need to find the value of \( f(4) \).
1. Substitute \( x = 4 \) into the function:
\[ f(4) = 2(4-1) \]
2. Simplify inside the parentheses:
\[ f(4) = 2(3) \]
3. Multiply:
\[ f(4) = 6 \]
So, the correct answer is:
\[ \boxed{C} \]
Question Easy
The graph of a linear equation and the graph of a quadratic equation are shown. What is true about the point \((-1,4)\) ?
A) The point satisfies only the quadratic equation
B) The point satisfies only the linear equation.
C) The point satisfies both equations.
D) The point satisfies neither equation.
▶️Answer/Explanation
Ans:C
For the linear equation represented by the straight line: Let’s call this equation y = mx + b, where m is the slope and b is the y-intercept. The point (-1, 4) is on this line, so if I substitute x = -1 and y = 4, it should satisfy the equation. 4 = m(-1) + b Solving for b using the point’s coordinates gives b = 4 + m
For the quadratic equation represented by the parabola: Let’s call this y = ax^2 + bx + c, where a, b, c are constants. Substituting x = -1 and y = 4, we get:
$4 = a(-1)^2 + b(-1) + c$ $
4 = a + (-b) + c$
Therefore, the point (-1, 4) satisfies both the linear and quadratic equations shown.
Question Easy
Jaqueline spent \(\$ 150\) for supplies and gas to start a lawn-mowing service. She charges \$25 for each lawn she mows. In the first week Jaqueline made \(\$ 50\) after the cost of supplies and gas was deducted. Which equation represents this situation, where \(x\) is the number of lawns Jaqueline mowed during the first week?
A) \(25 x-150=50\)
B) \(50-25 x=150\)
C) \(150-25 x=50\)
D) \(25 x+50=150\)
▶️Answer/Explanation
Ans: A
Jaqueline’s earnings can be represented by the equation \(25x – 150 = 50\), where \(x\) is the number of lawns she mowed during the first week. She earns \(\$ 25\) for each lawn mowed, and after deducting the initial cost of \(\$ 150\), she made a profit of \(\$ 50\).
So, the correct equation is:
\[25x – 150 = 50\]
Question Easy
y= 4 − 𝑥
What is the graph of the given equation?
▶️Answer/Explanation
Ans: B
Analyzing the Equation:
1. Slope \((m)\) :
The equation \(y=4-x\) can be rewritten as \(y=-x+4\). Thus, the slope \(m\) is -1 .
2. Y-intercept \((b)\) :
The \(y\)-intercept \(b\) is 4 .
From this graph has negative slope and positive intercept which is only in option – B