SAT MAth Practice questions – all topics
- Advanced Math Weightage: 35% Questions: 13-15
- Equivalent expressions
- Nonlinear equations in one variable and systems of equations in two variables
- Nonlinear functions
SAT MAth and English – full syllabus practice tests
[calc] Question Easy
$
T=N C
$
For a particular college program, the given equation re lates the cost of tuition \(T\), in dollars, to the number of credits taken, \(N\), and the cost of each credit \(C\), in dollars, where \(N\) and \(C\) are positive numbers. Which equation correctly expresses \(C\) in terms of \(N\) and \(T\) ?
A) \(C=T N\)
B) \(C=T-N\)
C) \(C=\frac{N}{T}\)
D) \(C=\frac{T}{N}\)
▶️Answer/Explanation
Ans: D
Given the equation:
\[ T = N C \]
We need to solve for \( C \) in terms of \( N \) and \( T \).
1. Start with the original equation:
\[ T = N C \]
2. To isolate \( C \), divide both sides by \( N \):
\[ C = \frac{T}{N} \]
So, the correct answer is:
\[ \boxed{D} \]
[Calc] Question Easy
\(1210(x+120)=120\)
Which of the following equations has the same solution as the given equation?
A. \(x+120=12\)
B. \(x+120=130\)
c. \(x+12=12\)
D. \(x+12=120\)
▶️Answer/Explanation
Ans:A
To find an equation with the same solution as \(10(x+120) = 120\), we first need to solve the given equation for \(x\).
\[10(x+120) = 120\]
Divide both sides by \(10\):
\[x + 120 = 12\]
Subtract \(120\) from both sides:
\[x = 12 – 120\]
\[x = -108\]
Now, let’s check which of the given equations has the same solution:
A. \(x + 120 = 12\) -> \(x = -108\)
B. \(x + 120 = 130\) -> \(x = 10\)
C. \(x + 12 = 12\) -> \(x = 0\)
D. \(x + 12 = 120\) -> \(x = 108\)
Among these options, option A has the same solution as the given equation, \(x = -108\).
Therefore, the correct answer is option A: \(x + 120 = 12\).
[Calc] Question Easy
\(2-x^{2}-x^{2}-2\)
Which of the following is equivalent to the given expression?
A. 0
B. 2
C. \(-x^{2}\)
D. \(-2x^{2}\)
▶️Answer/Explanation
Ans: D
We’re given the expression \( 2 – x^2 – x^2 – 2 \), which simplifies to \( -2x^2 \). So, the equivalent expression is \( \text{D. } -2x^2 \).
[Calc] Question Easy
Which expression is equivalent to \(x^4(3x^2 + 9x − 8)\) ?
A)\(x^4 + 3x^2 +9x − 8\)
B)\(3x^6 + 9x^5 − 8x^4\)
C)\(3x^8 + 9x^5 − 8x^4\)
D)\(12x^2 + 36x − 32\)
▶️Answer/Explanation
B)\(3x^6 + 9x^5 − 8x^4\)
We need to find the expression equivalent to \(x^4(3x^2 + 9x – 8)\).
Distribute \(x^4\) to each term inside the parentheses:
\[ x^4(3x^2) + x^4(9x) + x^4(-8) \]
\[ = 3x^6 + 9x^5 – 8x^4 \]
The correct expression is:
B) \(3x^6 + 9x^5 – 8x^4\).
[No calc] Questions Easy
If x > 0, which of the following is equivalent to \(\frac{1}{x}+\frac{1}{2x}\)?
A. 1/x
B. 1/2x
C. 3/2x
D. 2/3x
▶️Answer/Explanation
Ans: C
If \(x>0\), which of the following is equivalent to \(\frac{1}{x}+\frac{1}{2 x}\)?
To simplify \(\frac{1}{x}+\frac{1}{2 x}\), we find a common denominator:
\[\frac{1}{x}+\frac{1}{2x} = \frac{2}{2x} + \frac{1}{2x} = \frac{3}{2x}\]
So, the equivalent expression is C) \(\frac{3}{2x}\).
[Calc] Question Easy
Which expression is equivalent to \(2x^5(x^3 + 5x)\) ?
A) \(3x^8 + 7x^6\)
B) \(3x^{15} + 7x^5\)
C) \(2x^8 + 10x^6\)
D) \(2x^{15} + 10x^5\)
▶️Answer/Explanation
C) \(2x^8 + 10x^6\)
We need to find the expression equivalent to \(2x^5(x^3 + 5x)\).
1. Distribute \(2x^5\):
\[
2x^5 \cdot x^3 + 2x^5 \cdot 5x
\]
\[
= 2x^{5+3} + 10x^{5+1}
\]
\[
= 2x^8 + 10x^6
\]
Thus, the equivalent expression is:
\[ \boxed{2x^8 + 10x^6} \]
[No- Calc] Question Easy
Which expression is equivalent to \(\left(4 x^5+5 x^4\right)-\left(2 x^5+3 x^4\right)\) ?
A) \(2 x^5-2 x^4\)
B) \(2 x^5+2 x^4\)
C) \(6 x^5-8 x^4\)
D) \(6 x^5+8 x^4\)
▶️Answer/Explanation
Ans:B
To find an expression equivalent to \(\left(4 x^5+5 x^4\right)-\left(2 x^5+3 x^4\right)\), we simply distribute the negative sign inside the parentheses and then combine like terms:
\[ \left(4 x^5+5 x^4\right)-\left(2 x^5+3 x^4\right) \]
\[ = 4 x^5 + 5 x^4 – 2 x^5 – 3 x^4 \]
\[ = (4x^5 – 2x^5) + (5x^4 – 3x^4) \]
\[ = 2x^5 + 2x^4 \]
So, the expression equivalent to \(\left(4 x^5+5 x^4\right)-\left(2 x^5+3 x^4\right)\) is:
B) \(2 x^5+2 x^4\)
[Calc] Question Easy
$$
T=0.32 x+0.29 y
$$
Janice raises chickens. She uses the equation shown to estimate the total daily feed intake $\mathrm{T}$, in pounds, for $x$ male and $y$ female chickens that are between 28 and 35 days old.
Which equation estimates the total weekly feed intake $W$, in pounds, for $x$ male and $y$ female chickens that are between 28 and 35 days old?
A) $w=\frac{0.32 x+0.29 y}{7}$
B) $w=\frac{0.32 x}{7}+0.29 y$
C) $w=7(0.32 x)+0.29 y$
D) $\quad w=7(0.32 x+0.29 y)$
▶️Answer/Explanation
D
Question
$\left(2 x^3+3 x\right)\left(x^3-2 x\right)$
Which of the following is equivalent to the expression above?
A. $x^3+5 x$
B. $3 x^3+x$
C. $2 x^6-x^4-6 x^2$
D. $3 x^6-x^4-6 x^2$
▶️Answer/Explanation
Ans: C
Questions
$f(x)=(x+0.25 x)(50-x)$
The function $f$ is defined above. What is the value of $f(20)$ ?
A. 250
B. 500
C. 750
D. 2,000
▶️Answer/Explanation
Ans: C
Question
Which of the following expressions is equivalent to $2(a b-3)+2$ ?
A. $2 a b-1$
B. $2 a b-4$
C. $2 a b-5$
D. $2 a b-8$
▶️Answer/Explanation
Ans: B
Questions
$(2 x+6)+\left(x^2+2 x+1\right)$
Which of the following polynomials is equivalent to the expression given above?
A. $x^2+5$
B. $x^2+7$
C. $4 x^2+7$
D. $x^2+4 x+7$
▶️Answer/Explanation
Ans: D
Questions
An oceanographer uses the equation $s=\frac{3}{2} p$ to model the speed $s$, in knots, of an ocean wave, where $p$ represents the period of the wave, in seconds. Which of the following represents the period of the wave in terms of the speed of the wave?
A. $p=\frac{2}{3} s$
B. $p=\frac{3}{2} s$
C. $p=\frac{2}{3}+s$
D. $p=\frac{3}{2}+s$
▶️Answer/Explanation
Ans: A
Questions
If $y=x+\frac{1}{2}$ and $z=2 x-3$, which of the following is equivalent to $y+y z$ ?
A. $2 x^2-x-1$
B. $2 x^2-x-2$
C. $2 x^2-x-\frac{1}{2}$
D. $2 x^2-2 x-\frac{3}{2}$
▶️Answer/Explanation
Ans: A
Questions
Which of the following equivalent forms of the function $f(x)=4 x^2+4 x-24$ is the most suitable to indicate the $x$-coordinates of the $x$ intercepts of the graph of $y=f(x)$ in the $x y$-plane?
A. $f(x)=4\left(x^2+x-6\right)$
B. $f(x)=4(x-2)(x+3)$
C. $f(x)=2(x-2)(2 x+6)$
D. $f(x)=(2 x-4)(2 x+6)$
▶️Answer/Explanation
Ans: B
Questions
. Which of the following expressions is equivalent to $2 a^2(a+3)$ ?
A. $5 a^3$
B. $8 a^5$
C. $2 a^3+3$
D. $2 a^3+6 a^2$
▶️Answer/Explanation
Ans: D
Question
Which of the following expressions is equivalent to $3 q^2+r^3+5 r-8 q+2\left(q^2+r\right)$ ?
A. $7 r^3-3 q^4$
B. $r^3+5 q^2-q r$
C. $r^3+5 q^2-8 q+6 r$
D. ${ }^3+5 q^2-8 q+7 r$
▶️Answer/Explanation
Ans: D
Question
Which of the following is equivalent to $(2 x+4)^2-4 x^2$ ?
A. $16(x+1)$
B. $8(x+2)$
C. $4(4 x+1)$
D. $2(8 x+1)$
▶️Answer/Explanation
Ans: A
Question
If $3 x-6 y=9 z$, which of the following expressions is equivalent to $x^2-4 x y+4 y^2$ ?
A. $9 z$
B. $3 z^2$
C. $9 z^2$
D. $81 z^2$
▶️Answer/Explanation
Ans: C
Questions
What is the sum of $\left(3 x^5+4 x^2+8\right)$ and $\left(12 x^3-2 x^2+6\right)$ ?
A. $15 x^8+2 x^2+14$
B. $3 x^5+12 x^3+2 x^2+14$
C. $3 x^5+12 x^3+6 x^2+14$
D. $3 x^5+12 x^3+4 x^2-2 x+14$
▶️Answer/Explanation
Ans: B
Questions
$(3 x+2)(2 x+3)$
Which of the following is equivalent to the expression above?
A. $3 x^2+10 x+5$
B. $5 x^2+13 x+5$
C. $6 x^2+13 x+6$
D. $6 x^2+15 x+9$
▶️Answer/Explanation
Ans: C
Questions
Which of the following expressions is equivalent to $x^2+10 x+21$ ?
A. $(x+1)(x+9)+12$
B. $(x+1)(x+9)+12 x$
C. $(x+3)(x+7)+5$
D. $(x+3)(x+7)+5 x$
▶️Answer/Explanation
Ans: A
Questions
$2 x\left(x^2+1\right)+\left(2 x^2-2 x\right)$
Which of the following expressions is equivalent to the expression above?
A. $4 x^2$
B. $2 x^2+2 x$
C. $2 x^3+2 x^2$
D. $2 x^3+2 x^2-4 x$
▶️Answer/Explanation
Ans: C
Questions
If $x+3=2 x-2$, what is the value of $x-4$ ?
A. 9
B. 5
C. 4
D. 1
▶️Answer/Explanation
Ans: D
Question
$5 x^2-3(1-x)-2 x(x+5)$
Which of the following polynomials is equivalent to the expression above?
A. $3 x^2-7 x-3$
B. $3 x^2+7 x-3$
C. $5 x^2-5 x-3$
D. $5 x^2-9 x-3$
▶️Answer/Explanation
Ans: A