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
[No-Calc] Question Easy
What value of x is the solution to the equation x+10=3 ?
A. -13
B. -7
C. 7
D. 13
▶️Answer/Explanation
Ans: B
To solve the equation \(x+10=3\), we need to isolate \(x\) by subtracting 10 from both sides:
\[x + 10 – 10 = 3 – 10\]
\[x = -7\]
So, the solution to the equation is \(x = -7\).
[No-Calc] Question Easy
\(\left | x+3=6 \right |\)
What is the positive solution to the given equation?
A. 2
B. 3
C. 9
D. 18
▶️Answer/Explanation
Ans: B
To find the positive solution to the equation \( |x+3| = 6 \), we consider both the positive and negative cases for the absolute value.
Positive case:
\[ x + 3 = 6 \]
\[ x = 6 – 3 \]
\[ x = 3 \]
Negative case:
\[ -(x + 3) = 6 \]
\[ -x – 3 = 6 \]
\[ -x = 6 + 3 \]
\[ -x = 9 \]
\[ x = -9 \]
Since we’re looking for the positive solution, the answer is \( x = 3 \), which corresponds to option B.
[No-Calc] Question Easy
If 2(x − 4) = x , what value of x makes the equation true?
A) \(\frac{4}{3}\)
B) \(\frac{8}{3}\)
C) 4
D) 8
▶️Answer/Explanation
D) 8
We are given the equation \( 2(x – 4) = x \) and need to find the value of \( x \) that makes the equation true.
Distributing the 2 on the left-hand side:
\[
2(x – 4) = 2x – 8
\]
So, the equation becomes:
\[
2x – 8 = x
\]
Subtract \( x \) from both sides to isolate \( x \):
\[
2x – 8 – x = x – x
\]
\[
x – 8 = 0
\]
Add 8 to both sides to solve for \( x \):
\[
x – 8 + 8 = 0 + 8
\]
\[
x = 8
\]
[Calc] Question Easy
Which equation has the same solution as 8x = 2x + 12?
A) 10x = −12
B) 10x = 12
C) 6x = −12
D) 6x = 12
▶️Answer/Explanation
D) 6x = 12
To find the equation that has the same solution as \(8x = 2x + 12\):
Solve the original equation for \(x\):
\[
8x – 2x = 12
\]
\[
6x = 12
\]
\[
x = 2
\]
Check each option to see which one also has \(x = 2\) as a solution:
Option A: \(10x = -12\)
\[
x = -\frac{12}{10} = -\frac{6}{5}
\]
This does not match \(x = 2\).
Option B: \(10x = 12\)
\[
x = \frac{12}{10} = \frac{6}{5}
\]
This does not match \(x = 2\).
Option C: \(6x = -12\)
\[
x = -2
\]
This does not match \(x = 2\).
Option D: \(6x = 12\)
\[
x = 2
\]
This matches the solution of the original equation.
[Calc] Question Easy
Line segment \(A C\) has a length of 120 and contains point \(B\). If \(A B=5 x+20\) and \(B C=6 x-10\), which equation shows the relationship between the lengths of line segments \(A B, B C\), and \(A C\) ?
A) \(5 x+20=120\)
B) \(6 x-10=120\)
C) \((5 x+20)-(6 x-10)=120\)
D) \((5 x+20)+(6 x-10)=120\)
▶️Answer/Explanation
D
We need to find the equation that represents the relationship between the lengths of the line segments \(AB\), \(BC\), and \(AC\).Since \(AC = AB + BC\):
\[ AC = 120 \]
\[ AB + BC = 120 \]
\[ (5x + 20) + (6x – 10) = 120 \]
Simplifying:
\[ 5x + 20 + 6x – 10 = 120 \]
\[ 11x + 10 = 120 \]
Therefore, the correct equation is:
\[ (5x + 20) + (6x – 10) = 120 \]
So the answer is:
\[ \boxed{D} \]
[Calc] Question Easy
2 |4 – x | + 3 | 4 – x | = 25
What is the positive solution to the given equation ?
▶️Answer/Explanation
9
To find the positive solution to the equation \(2|4-x| + 3|4-x| = 25\), we can simplify and solve it step-by-step.
1. Combine like terms:
\[
(2 + 3)|4-x| = 25
\]
\[
5|4-x| = 25
\]
2. Divide both sides by 5:
\[
|4-x| = 5
\]
3. Solve the absolute value equation:
\[
4-x = 5 \quad \text{or} \quad 4-x = -5
\]
4. Solve each case:
For \(4-x = 5\):
\[
4 – x = 5
\]
\[
-x = 1
\]
\[
x = -1
\]
For \(4-x = -5\):
\[
4 – x = -5
\]
\[
-x = -9
\]
\[
x = 9
\]
Thus, the positive solution is:
\[ \boxed{9} \]
[No-Calc] Question Easy
2p + 6 = 8 + 7p
What value of p satisfies the given equation?
A) \(\frac{-2}{9}\)
B) \(\frac{-2}{5}\)
C) \(\frac{14}{15}\)
D) \(\frac{14}{9}\)
▶️Answer/Explanation
B) \(\frac{-2}{5}\)
We need to solve the equation \( 2p + 6 = 8 + 7p \) for \( p \).
Start with the given equation:
\[
2p + 6 = 8 + 7p
\]
Subtract \( 2p \) from both sides:
\[
6 = 8 + 5p
\]
Subtract 8 from both sides:
\[
6 – 8 = 5p
\]
\[
-2 = 5p
\]
Divide both sides by 5:
\[
p = -\frac{2}{5}
\]
[No-Calc] Question Easy
4(x + 1) = 6 + 2(x + 1)
If x is the solution to the given equation, what is the value of x + 1 ?
A) 1
B) 3
C) 4
D) 6
▶️Answer/Explanation
B) 3
Let’s solve each problem step by step:
\[
4(x+1) = 6+2(x+1)
\]
\[
4x + 4 = 6 + 2x + 2
\]
\[
4x + 4 = 2x + 8
\]
Subtract \(2x\) from both sides:
\[
2x + 4 = 8
\]
Subtract \(4\) from both sides:
\[
2x = 4
\]
divide both sides by \(2\):
\[
x = 2
\]
If \(x = 2\), then \(x+1 = 3\).
So, the correct answer is B) 3.
[Calc] Question Easy
X – 6 = 50
What value of X is the solution to the given equation?
A) -10
B) 44
C) 55
D) 56
▶️Answer/Explanation
D) 56
Solve the equation \(x – 6 = 50\).
1. Isolate \(x\) by adding 6 to both sides of the equation:
\[
x – 6 + 6 = 50 + 6
\]
\[
x = 56
\]
Thus, the value of \(x\) is:
\[ \boxed{56} \]
[Calc] Question Easy
The function g is defined by g(x) = 2x + 1. What is the value of g(x) when x = 1?
A) 3
B) 2
C) 1
D) 0
▶️Answer/Explanation
A) 3
The function \(g(x)\) is defined by \(g(x) = 2x + 1\). What is the value of \(g(x)\) when \(x = 1\)?
1. Substitute \(x = 1\) into the function:
\[
g(1) = 2(1) + 1
\]
\[
g(1) = 2 + 1
\]
\[
g(1) = 3
\]
Thus, the value of \(g(1)\) is:
\[ \boxed{3} \]
[Calc] Question Easy
If 4x + 16 = 24, what is the value of 2x + 8?
A) 14
B) 12
C) 10
D) 8
▶️Answer/Explanation
B) 12
If \(4x + 16 = 24\), we need to determine the value of \(2x + 8\).
1. Solve for \(x\):
\[
4x + 16 = 24
\]
\[
4x = 24 – 16
\]
\[
4x = 8
\]
\[
x = 2
\]
2. Substitute \(x = 2\) into \(2x + 8\):
\[
2x + 8 = 2(2) + 8
\]
\[
= 4 + 8
\]
\[
= 12
\]
Thus, the value of \(2x + 8\) is:
\[ \boxed{12} \]
[Calc] Question Easy
The function $f$ is defined by $f(x)=x+3$. What is the $y$-intercept of the graph of $y=f(x)$ in the $x y$ plane?
A) $(0,-3)$
B) $(0,-1)$
C) $(0,1)$
D) $(0,3)$
▶️Answer/Explanation
D
[Calc] Question Easy
The function $f$ is defined by $f(x)=9 x-16$. What is the value of $f(3)$ ?
A) -39
B) -4
C) 11
D) 27
▶️Answer/Explanation
C
[Calc] Question Easy
$$
6 x-7=12
$$
Which equation has the same solution as the given equation?
A) $6 x=5$
B) $6 x=6$
C) $6 x=18$
D) $6 x=19$
▶️Answer/Explanation
D
[Calc] Question Easy
If $s=4$, what is the value of $20 s-15 s$ ?
A) 4
B) 5
C) 15
D) 20
▶️Answer/Explanation
D
Question
(\(x\)+1)=2(\(x\)+1)
What value of \(x\) satisfies the given equation?
- -1
- 0
- \(\frac{1}{2}\)
- 1
▶️Answer/Explanation
A
Question
3k+2k = 5
What is the solution to the given equation?
- 0
- 1
- 3
- 5
▶️Answer/Explanation
B
Question
What is the solution to the equation $2 x+3=7$ ?
A. 1
B. 1.5
C. 2
D. 4
▶️Answer/Explanation
Ans: C
Questions
If $\frac{1}{2} x-\frac{1}{6} x=1$, what is the value of $x$ ?
A. -4
B. $\frac{1}{3}$
C. 3
D. 6
▶️Answer/Explanation
Ans: C
Questions
$f(x)=2(x-1)+2$
For the function $f$ defined above, what is the value of $f(1)$ ?
A. 3
B. 2
C. 0
D. -1
▶️Answer/Explanation
Ans: B
Questions
$$
5(x-3)=10 x+5
$$
What value of $x$ satisfies the equation above?
A. -4
B. 1
C. 5
D. 15
▶️Answer/Explanation
Ans: A
Questions
If $5 x-7=13$, what is the value of $10 x-14$ ?
A. 4
B. 8
C. 26
D. 65
▶️Answer/Explanation
Ans: C
Question
Lardarius spent a total of $\$ 200$ to lease snowboard equipment at Winter Mountain during his vacation. Each day of his vacation, he purchased a lift ticket for $\$ 44$. If Lardarius purchased $t$ lift tickets, how much money, in dollars, did Lardarius spend during his vacation at Winter Mountain on snowboard equipment and lift tickets?
A. $44 t$
B. $200+11 t$
C. $200+44 t$
D. $200+176 t$
▶️Answer/Explanation
Ans: C
Question
If $10=2 x+14$, which of the following must be true?
A. $4 x=8$
B. $10 x=16$
C. $8 x=-16$
D. $12 x=-144$
▶️Answer/Explanation
Ans: C
Questions
$a x-4=24$
Based on the equation above, what is the value of $2 a x-1$ ?
A. 3
B. 6
C. 8
D. 12
▶️Answer/Explanation
Ans: B
Questions
If $6.2 k=36$, what is the value of $4 k-2$ ?
A. 12
B. 10
C. 6
D. 1
▶️Answer/Explanation
Ans: B
Question
In the $x y$-plane, what is the $y$-intercept of the line with equation $y=4 x-1$ ?
A. 4
B. $\frac{1}{4}$
C. $-\frac{1}{4}$
D. -1
▶️Answer/Explanation
Ans: D
Question
If $m=3$, how much greater is $10 m$ than $6 m$ ?
A. 3
B. 4
C. 12
D. 30
▶️Answer/Explanation
Ans: C