Practice Test 11 - ACT Math

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

Start practice test

1. A radioactive isotope decays such that its mass, $M(t)$, in grams, after $t$ days is modeled by $M(t) = 50(0.5)^{\frac{t}{8}}$. What is the mass, in grams, of the isotope after 24 days?
2. A sphere has a volume of $288π$ cubic units. What is the radius of the sphere?
3. To rewrite an expression in standard form, compute: What is $(x-7)(x-1)$?
4. A function is defined by $f(x)=\dfrac{x+2}{x-3}$. What is $f(1)$? Show the substitution: $f(x)=\dfrac{x+2}{x-3}$, so $f(1)=\dfrac{1+2}{1-3}$.
5. Which interval contains x = 0 for the function $f(x) = \begin{cases} 5x + 2 & \text{if } x < -2 \\ x^2 & \text{if } -2 \leq x < 1 \\ 3x - 4 & \text{if } x \geq 1 \end{cases}$?
6. A point in the complex plane is represented by $3-4i$. What is the absolute value of $(3-4i)$? Use $|a+bi|=\sqrt{a^2+b^2}$ and simplify.
7. The mean age of 5 people in a room is 30 years. When a 6th person enters the room, the mean age becomes 32 years. How old is the 6th person?
8. What is the mean of the data set [3, 7, 5, 10, 8]?
9. A clothing store buys a jacket for $80. The store increases the price by 50% to determine the retail price. Later, during a sale, the store discounts the retail price by 20%. What is the sale price of the jacket?
10. What is the solution to the equation $4x + 7 = 2x - 9$?
11. What is 30% of 90?
12. A store marks up an item after adding a fixed fee. If $3(x + 4) = 27$, solve for $x$.
13. A neighborhood survey asked 50 people how many pets they currently own. The results are shown in the table below (0 pets \= 10 people; 1 pets \= 20 people; 2 pets \= 15 people; 3 pets \= 5 people). What is the median number of pets owned by the 50 people surveyed?
14. The number of text messages a person received each day for 5 days was: 14, 22, 18, 9, 25. What is the range of the data?​
15. What is $\sin(90^\circ)$?
16. For the function $f(x) = \begin{cases} 2 - x & \text{if } x < 0 \\ 3x + 1 & \text{if } 0 \leq x < 3 \\ x^2 & \text{if } x \geq 3 \end{cases}$, what is f(3)?
17. Simplify: $4(y + 3) - 2y$
18. A function is defined by $f(x)=\dfrac{x-1}{2}$. What is $f(7)$?
19. A line graph shows the number of packages delivered over four days. Based on the graph, what is the measurement at Wednesday?
20. Simplify: $\sqrt{18x^2}$, assuming $x\ge 0$.

Practice tests