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ACT Comprehensive Diagnostic Quiz

Ten questions testing English conventions, mathematical problem solving, and scientific reasoning.

10 questões · 덱: ACT Mastery: English, Math, Reading & Science · 감수: Ada

문제 1

An arithmetic sequence begins with $a_1 = 7$ and has common difference $d = 4$. What is the 25th term?

  1. $99$
  2. $103$
  3. $107$
  4. $111$

문제 2

What is the sum of the infinite geometric series $12 + 6 + 3 + 1.5 + \dots$?

  1. $20$
  2. $22.5$
  3. $24$
  4. $36$

문제 3

What is the determinant of the matrix $\begin{pmatrix} 5 & 3 \\ 2 & 4 \end{pmatrix}$?

  1. $14$
  2. $20$
  3. $26$
  4. $2$

문제 4

If $\sin(\theta) = \frac{3}{5}$ and $\theta$ is an acute angle, what is the value of $\sec(\theta)$?

  1. $\frac{5}{4}$
  2. $\frac{4}{5}$
  3. $\frac{5}{3}$
  4. $\frac{4}{3}$

문제 5

Which choice correctly punctuates the sentence using a colon?

  1. Elena purchased: notebooks, pens, and highlighters for the term.
  2. Elena purchased three essential supplies: notebooks, pens, and highlighters.
  3. Elena purchased supplies including: notebooks, pens, and highlighters.
  4. Elena purchased such as: notebooks, pens, and highlighters.

문제 6

A raffle game awards $100 with probability $0.05$ and $0 with probability $0.95$. What is the expected payout of a ticket?

  1. $0.50
  2. $5.00
  3. $10.00
  4. $50.00

문제 7

What is the distance between the points $(1, -2)$ and $(4, 2)$ in the coordinate plane?

  1. $3$
  2. $4$
  3. $5$
  4. $7$

문제 8

A triangle has side lengths $a = 5$ and $b = 8$ with included angle $C = 60^\circ$. What is the length of side $c$?

  1. $\sqrt{49} = 7$
  2. $\sqrt{89}$
  3. $\sqrt{40}$
  4. $9$

문제 9

Which sentence avoids a comma splice error?

  1. The experiment concluded at dusk, the scientists logged their observations.
  2. The experiment concluded at dusk; the scientists logged their observations.
  3. The experiment concluded at dusk, however the scientists logged their observations.
  4. The experiment concluded at dusk, therefore the scientists logged their observations.

문제 10

How many different 4-person committees can be chosen from a club of 8 members?

  1. $32$
  2. $56$
  3. $70$
  4. $1680$