The graph of g(x) = (x − 3)² + 2 is a transformation of the graph of f(x) = x². Which description is correct?

Shift the graph of f right 3 units and up 2 units.

Shift the graph of f left 3 units and up 2 units.

Shift the graph of f right 3 units and down 2 units.

Shift the graph of f left 3 units and down 2 units.

The comparison in paragraph 4 to checking under a pillow for "the tooth fairy's quarter" mainly suggests that Nadia

hopes for a result while feeling a little foolish for hoping.

expects the starter to change by magic overnight.

misses being a young child with fewer responsibilities.

suspects that someone is secretly tampering with the jar.

In Study 2, which variable did the student intentionally change?

The concentration of sodium hydrogen carbonate in the water

The temperature of the water bath

The number of bubbles produced per minute

Which choice is the best version of the bold portion?

The operators most of them young women, sat

The operators, most of them young women sat

The operators, most of them, young women sat

As it is used in paragraph 2, the word transposes most nearly means

converts from one form into another.

translates into a different language.

shortens by removing words from.

ACT Aspire Early High School

Free ACT Aspire Early High School Practice Questions

10 sample questions for the ACT Aspire Early High School, with the correct answer and an explanation for each. No account needed. Try each one before you open the answer.

Sections covered on the exam: English and Language Usage, Mathematics, Reading, Science.

Question 1 · English and Language Usage
Which choice is the best version of the bold portion?
- A.NO CHANGE
- B.railings it could carry
- C.railings, it was able to carry
- D.railings, but it could carry
Show answer and explanation
Answer: D. railings, but it could carry
The original joins two complete sentences with only a comma, which is a comma splice. Adding the conjunction "but" after the comma correctly joins the clauses and shows the contrast between the simple raft and its large load. "Railings, it was able to carry" only rewords the second clause and is still a comma splice, and "railings it could carry" removes the comma entirely, creating a run-on.
Question 2 · English and Language Usage
Which choice is the best version of the bold portion?
- A.NO CHANGE
- B.it. The staircase
- C.it, then the staircase
- D.it the staircase
Show answer and explanation
Answer: B. it. The staircase
Two complete sentences meet here: one ends with "wax it," and a new one begins with "the staircase glided." A period correctly separates them. "It, then the staircase" is still a comma splice because "then" is not a joining conjunction, and "it the staircase" runs the sentences together with no punctuation.
Question 3 · Mathematics
The graph of g(x) = (x − 3)² + 2 is a transformation of the graph of f(x) = x². Which description is correct?
- A.Shift the graph of f right 3 units and up 2 units.
- B.Shift the graph of f left 3 units and up 2 units.
- C.Shift the graph of f right 3 units and down 2 units.
- D.Shift the graph of f left 3 units and down 2 units.
Show answer and explanation
Answer: A. Shift the graph of f right 3 units and up 2 units.
In (x − h)² + k the graph moves h units horizontally and k units vertically; here h = 3 and k = 2, so the vertex moves from (0, 0) to (3, 2): right 3 and up 2. "Left 3 units and up 2 units" is the common sign error of reading x − 3 as a move to the left.
Question 4 · Reading
The comparison in paragraph 4 to checking under a pillow for "the tooth fairy's quarter" mainly suggests that Nadia
- A.hopes for a result while feeling a little foolish for hoping.
- B.expects the starter to change by magic overnight.
- C.misses being a young child with fewer responsibilities.
- D.suspects that someone is secretly tampering with the jar.
Show answer and explanation
Answer: A. hopes for a result while feeling a little foolish for hoping.
The comparison is followed right away by "half believing and half embarrassed to be believing," which describes hope mixed with self-consciousness. "Expects the starter to change by magic" goes too far, because she only half believes, and the passage says nothing about missing her childhood.
Question 5 · Science
In Study 2, which variable did the student intentionally change?
- A.The concentration of sodium hydrogen carbonate in the water
- B.The light intensity
- C.The temperature of the water bath
- D.The number of bubbles produced per minute
Show answer and explanation
Answer: A. The concentration of sodium hydrogen carbonate in the water
Table 2 lists five different concentrations of sodium hydrogen carbonate, while light was held at 400 µmol/m²/s and temperature at 25 °C. The bubble rate was what the student measured in response, so it is the dependent variable, not the one that was changed.
Question 6 · English and Language Usage
Which choice is the best version of the bold portion?
- A.NO CHANGE
- B.The operators most of them young women, sat
- C.The operators, most of them young women sat
- D.The operators, most of them, young women sat
Show answer and explanation
Answer: A. NO CHANGE
NO CHANGE is correct: "most of them young women" is an interrupting phrase that adds information about the operators, so it is set off by a pair of commas. Dropping either comma leaves the phrase half enclosed, and the comma after "them" splits the phrase in the wrong place.
Question 7 · English and Language Usage
Which choice is the best version of the bold portion?
- A.NO CHANGE
- B.boards' final position
- C.board's final positions'
- D.board's final position
Show answer and explanation
Answer: D. board's final position
The final position belongs to one board, so the singular possessive "board's" is needed. "Boards" without an apostrophe is a plural, not a possessive, "boards'" means more than one board, and "positions'" adds an incorrect plural possessive with nothing following it.
Question 8 · Mathematics
Point P(4, −2) is reflected across the y-axis, and then the image is translated 5 units up. What are the coordinates of the final image?
- A.(−4, 3)
- B.(4, 7)
- C.(−4, −7)
- D.(1, −2)
Show answer and explanation
Answer: A. (−4, 3)
Reflecting across the y-axis changes the sign of the x-coordinate: (4, −2) → (−4, −2). Translating up 5 adds 5 to the y-coordinate: (−4, 3). The choice (4, 7) reflects across the x-axis instead, and (−4, −7) translates down instead of up.
Question 9 · Reading
As it is used in paragraph 2, the word transposes most nearly means
- A.translates into a different language.
- B.reverses the order of.
- C.converts from one form into another.
- D.shortens by removing words from.
Show answer and explanation
Answer: C. converts from one form into another.
Silbo takes spoken Spanish and delivers it "in whistled form," so the words stay Spanish but change form. "Translates into a different language" is tempting, but the same paragraph says Silbo "is not a separate language."
Question 10 · Science
If Spring X continues to behave as it did in Table 1, what would its stretch be with a 400 g mass?
- A.10.0 cm
- B.12.0 cm
- C.14.0 cm
- D.16.0 cm
Show answer and explanation
Answer: D. 16.0 cm
Spring X stretches 2.0 cm per 50 g, which is 0.04 cm per gram, and 0.04 cm/g × 400 g = 16.0 cm. The choice 10.0 cm is the stretch at 250 g, the largest mass in the table, not the extrapolated value.

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