Practice Test 9 - ACT Math

20 questions. Answer them in any order, then submit to see your score and every explanation.

Given $i = \sqrt{-1}$ , what is the simplified form of $(4 + 5i) - (1 - 2i)$ ?
A complex number is $-12+5i$ . What is its complex conjugate, used to form a real product with the original number?
Based on the piecewise function $f(x)=\begin{cases} 4x-1, & x<5\\ (x-5)^2, & 5\le x<8\\ 20-x, & x\ge 8 \end{cases}$ what is the value when $x=6$ ?
Two matrices represent consecutive transformations on a vector. Which of the following is the product $AB$ if $ $A=\begin{bmatrix}0 & 2\\ -1 & 3\end{bmatrix},\quad B=\begin{bmatrix}5 & -2\\ 1 & 4\end{bmatrix}?$
If $\frac{7}{x} = \frac{21}{9}$ , what is the value of $x$ ?
Based on the piecewise function $f(x) = \begin{cases} 2x - 3 & \text{if } x < -1 \\ x^2 + 2 & \text{if } -1 \leq x < 2 \\ 5x - 1 & \text{if } x \geq 2 \end{cases}$ , what is f(2)?
If $4x + 2y = 18$ and $2x - y = 1$ , what is the value of $y$ ?
What is $\log_{4}(1)$ ?
A student combines two polynomial expressions while modeling total cost: $(2x^2-3x+1)+(x^2+5x-4)$ . Which polynomial is the result in standard form?
If $2x + 3y = 13$ and $2x - 3y = 1$ , what is the value of $y$ ?
The cost of attending a concert is modeled by the equation $C = 25n + 5$ , where $C$ is the total cost in dollars and $n$ is the number of tickets. What is the cost for 3 tickets?
What is the sum of the interior angles of a decagon?
If $\mathbf{v} = \langle 9, -3 \rangle$ and $\mathbf{w} = \langle -2, 4 \rangle$ , what is $\mathbf{v} + \mathbf{w}$ ?
What is the maximum value of the trigonometric function $y = -3\sin(2x) + 4$ ?
For triangles $\triangle XYZ$ and $\triangle ABC$ , $\triangle XYZ$ has angles $X = 45^\text{o}$ , $Y = 45^\text{o}$ , and $\triangle ABC$ has angles $A = 45^\text{o}$ , $B = 45^\text{o}$ . Are the triangles similar?
A linear model for the number of pages a printer can print is given by $y=\dfrac{1}{2}x-3$ , where $x$ is minutes and $y$ is pages (in tens). Which graph represents the equation $y=\dfrac{1}{2}x-3$ ?
Factor: $4x^2 - 16$
If a salary is increased from $50,000 to $55,000, what is the percent increase?
If $x$ and $y$ are positive integers such that $3^x \cdot 3^y = 81$ , what is the greatest possible value of $x - y$ ?
A hiking trail rises steadily between two marked points on a map. The trail passes through points $(-2, 5)$ and $(4, -1)$ on a coordinate grid, where $x$ is miles east and $y$ is elevation in hundreds of feet. What is the slope of the line through points $(-2,5)$ and $(4,-1)$ ?

Practice tests