Practice Test 1 - ACT Math

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

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1. Given $f(x)=x^2-2x+1$, what is the value of $f(3)$?
2. A temperature conversion is being simplified. If $5x + 2 = 3x + 18$, what is the value of $x$?
3. A pizza shop offers 6 toppings. A customer chooses exactly 2 different toppings. Since the order of toppings does not matter, how many different 2-topping pizzas are possible?
4. A school principal wants to know what percentage of students at the school eat breakfast. She stands at the cafeteria entrance one morning and asks the first 120 students who walk in whether they ate breakfast. Which characteristic makes this sample biased?
5. What is the simplified form of $9b - 4(2 - b)$?
6. When dividing by a complex number, you often use its conjugate. What is the complex conjugate of $-6+13i$?
7. A regular polygon has an exterior angle of $45^\circ$ at each vertex. How many sides does the polygon have?
8. What is the slope of the line through points (1, 2) and (4, 8)?
9. A cube has a surface area of 54 square units. What is the length of each side of the cube?
10. Solve for $x$: $8x - 6 = 2(x + 3)$
11. What is $\tan(0^\circ)$?
12. What is the range of the data set [11, 14, 18, 21, 25]?
13. Which polynomial is equivalent to $3(x^2 - 2x + 1)$?
14. In $\triangle ABC$ and $\triangle DEF$, $\angle A \cong \angle D$ and $\angle B \cong \angle E$. Also, $AB=10$ and $DE=15$. What is the scale factor from $\triangle ABC$ to $\triangle DEF$?
15. Which vector represents the displacement from point $A(2,-1)$ to point $B(-3,5)$?
16. What is the probability of drawing a spade or a club from a standard deck of cards?
17. A scatterplot shows points representing (x, y) pairs for four measurements. The plotted points are $(1, 4)$, $(2, 6)$, $(3, 5)$, and $(4, 7)$. Which point on the graph represents the condition $x=3$?
18. A line represents a constant-rate change in elevation. The line passes through points $(-2,3)$ and $(4,0)$. What is the slope of the line through points $(-2,3)$ and $(4,0)$?
19. Triangles KLM and NOP are similar with a scale factor of $4:3$. If $KL = 12$, what is $NO$?
20. Two triangles have side lengths $AB=6$, $BC=8$, $AC=10$ and $DE=9$, $EF=12$, $DF=15$. Which statement is true about their relationship?

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