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DUNZILLA
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As a Stanford graduate with a background in Economics, I provide targeted academic strategies in Advanced/AP Mathematics, Microeconomics, Macroeconomics, Statistics, Econometrics, and comprehensive test preparation for the ACT (all 4 sections), SAT, and GRE. My teaching philosophy is simple: make learning enjoyable and memorable by turning complex theory into common sense.

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Free ACT Diagnostic Sampler • English & Math

10 Authentic ACT Practice Questions from Official Test Forms. Test your grammar, rhetorical, algebra, and geometry intuition.

0 / 10 Attempted

Part 1: English • Conventions of Standard English & Rhetoric

The passage and corresponding questions remain visible simultaneously below, faithful to the authentic ACT testing experience.

PASSAGE: The Min: A Ship from the Desert

In 2004, a team of archaeologists discovered the remains of an ancient [1]shipyard. In a series of caves at a site named Wadi Gawasis in the [2]Egypt's desert. The team found a wealth of well-preserved planks, anchors, oars, and other sailing equipment. We have long known that ancient Egyptians sailed the freshwater Nile River. However, until Wadi Gawasis was excavated, there had been little evidence that [3]we had also sailed the ocean.

Cheryl Ward drew up plans for building a ship like those the ancient Egyptians had sailed. The completed ship would be named Min of the Desert in honor of the Egyptian god [4]who's likeness adorned many Wadi Gawasis artifacts. Four shipbuilders constructed the Min by using many of the same [5]tools, materials, and techniques, that the shipbuilders of Wadi Gawasis had used.

Question 1 • English Sentence Structure / Fragments
Refer to underlined portion [1]: "...an ancient shipyard. In a series of caves..."
Key: D. The period in the original text creates an incomplete sentence fragment ("In a series of caves at a site named Wadi Gawasis..."). Choice D correctly connects the prepositional phrase to the main independent clause without unnecessary punctuation.
Question 2 • English Usage / Adjective Form
Refer to underlined portion [2]: "...in the Egypt's desert."
Key: J. "Egyptian" serves as the proper descriptive adjective modifying the noun "desert." "Egypt's" is ungrammatical with the preceding definite article "the" ("in the Egypt's desert").
Question 3 • English Pronoun-Antecedent Agreement
Refer to underlined portion [3]: "...there had been little evidence that we had also sailed the ocean."
Key: B. The sentence refers back to the "ancient Egyptians" mentioned in the previous sentence. The pronoun must be third-person plural ("they") rather than first-person ("we").
Question 4 • English Possessive vs. Contraction
Refer to underlined portion [4]: "...in honor of the Egyptian god who's likeness adorned many Wadi Gawasis artifacts."
Key: H. "Who's" is a contraction for "who is." The possessive relative pronoun indicating ownership of the likeness is "whose."
Question 5 • English Punctuation / Unnecessary Commas
Refer to underlined portion [5]: "...using many of the same tools, materials, and techniques, that the shipbuilders..."
Key: H. Items in a series of three or more require commas separating each item, but no comma should be placed after the final list item before the restrictive clause "that...".

Part 2: Mathematics • Core Quantitative Reasoning

Questions 6–10 feature authentic problems from Official ACT Form 73E.

Question 6 • Math Pre-Algebra / Absolute Value
What is |5 − x| when x = 9?
Key: C. Substitute 9 into the expression: |5 − 9| = |−4| = 4. The absolute value of any real quantity represents its non-negative distance from zero.
Question 7 • Math Geometry / Perimeter of Rectangle
The length of a rectangle is 12 feet. The width of the rectangle is 1/2 the length. What is the perimeter of the rectangle, in feet?
Key: J. Length = 12 feet. Width = (1/2)(12) = 6 feet. Perimeter = 2(length + width) = 2(12 + 6) = 2(18) = 36 feet.
Question 8 • Math Elementary Algebra / Combining Expressions
(9m − 4n) − (2n + 5m) is equivalent to:
Key: A. Distribute the negative sign to each term in the second parenthesis: 9m − 4n − 2n − 5m = (9m − 5m) + (−4n − 2n) = 4m − 6n.
Question 9 • Math Intermediate Algebra / Function Evaluation
If g(x) = 2x² − 3x + 4, then g(−3) = ?
Key: E. Evaluate step-by-step: g(−3) = 2(−3)² − 3(−3) + 4 = 2(9) + 9 + 4 = 18 + 9 + 4 = 31.
Question 10 • Math Algebra / System of Inequalities
Given that x ≤ 2 and x + y ≥ 4, what is the LEAST value that y can have?
Key: D. Rearranging the second inequality gives y ≥ 4 − x. To find the minimum boundary for y, we need the maximum possible value for x, which is 2. Thus, y ≥ 4 − 2 = 2.

Diagnostic Results • Score Assessment

Review your accuracy across both ACT English and ACT Math pillars:

0 / 10
Total Score
0 / 5
English Section
0 / 5
Math Section
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