Try this ACT math practice question on a modified quadratic equation and how the resulting roots are related to the original quadratic equation.

The quadratic equation $ax^2-11x-14=0$ has two real solutions at $-\dfrac{2}{3}$ and $\dfrac{7}{5}$. What are the two solutions of the equation $a(x+1)^2-11(x+1)-14=0$?

1. $\quad -\dfrac{2}{3} \textrm{ and } \dfrac{7}{5}$
2. $\quad -\dfrac{5}{3} \textrm{ and } \dfrac{2}{5}$
3. $\quad -\dfrac{1}{3} \textrm{ and } \dfrac{12}{5}$
4. $\quad -\dfrac{2}{5} \textrm{ and } \dfrac{5}{3}$
5. $\quad -\dfrac{12}{5} \textrm{ and } \dfrac{1}{3}$

Try this ACT math practice question on horizontal and vertical shifts of parabola and the resulting change in their equation:

In the $(x, y)$ coordinate plane, the graph of the parabola $y=-x^2$ is shifted 3 units up and 2 units to the left. Which of the following is an equation of the translated parabola?

1. $\quad y=-(x-2)^2-3$
2. $\quad y= -(x-2)^2 + 3$
3. $\quad y=-(x+2)^2+3$
4. $\quad y=-(x+2)^2-3$
5. $\quad y=-(x+3)^2+2$

Try this ACT math practice question on digits and place value:

If $t$ and $u$ are the tens and units digit of a positive integer $n$, and the number that results after reversing the digits of $n$ is $18$ more than $n$, then which of the following gives $t$ in terms of $u$ ?

1. $\quad 10-u$
2. $\quad u-2$
3. $\quad u-1$
4. $\quad u+1$
5. $\quad u+2$

Try this ACT math practice question on finding terms of a geometric sequence:

The first term of a geometric sequence is $b$, and $r$ is the ratio of the second term to the first term. What is the 100th term of the sequence?

1. $\quad (br)^{99}$
2. $\quad br^{99}$
3. $\quad (br)^{100}$
4. $\quad br^{100}$
5. $\quad br^{101}$

Try this ACT math practice question on factors of a quadratic expression:

The cost of a nylon rope is $p$ dollars per foot. Which of the following expressions gives the cost, in dollars, of $y$ yards and $f$ feet of nylon rope $\textrm{(Note: 1 yard equals 3 feet)}$ ?

1. $\quad p(3y+f)$
2. $\quad p(y+3f)$
3. $\quad p(\dfrac{y}{3} + f)$
4. $\quad p(y+\dfrac{f}{3})$
5. $\quad 3p(y+f)$