ACT ASPIRE SAMPLE QUESTIONS: HIGH SCHOOL Math

The ACT Aspire is a Computer-Based Longitudinal Assessment System for College and Career Readiness. The students will face a variety of new technology-enhanced questions as a part of the computer-based tests.

Some of them are Multiple choice-single correct responses, Multiple choice-multiple correct responses, Matching Tables, Drag and Drop, Hot text, Table Fill in, Graphing, Equation/numeric, Extended constructed response, Short answer, and many more.

Today, we will share several sample questions along with practice test links for High School Math that gives you an idea of questions that your students are likely to see on the test. After each sample question, an explanation follows that includes any important aspects of the task that you may need to consider with respect to the skills, processes, and information your students need to know.

Domain: High School >> Real Numbers

Sample Question: Write the following in radical form 27^2/3

1. (√27)³
2. (³√27)²
3. (√27³)
4. 1/²√27²

Answer Explanation: In a problem with a rational exponent, the numerator tells you the power, and the denominator the root. In the problem, ³√27², the denominator is 3 indicating we should take the cube root of 27. The numerator is 2 which means we should square either before or after we take the cube root. So there are two possible correct answers to this problem. One is answer choice B. The other would be 1/²√27².

Standards: HSN.RN.A.1

Click here to practice: Real Numbers Questions on High School

Domain: High School >> Quantities

Sample Question: Evaluate 900^150/300

1. 18
2. 9
3. 3
4. 81

Answer Explanation: 900^150/300 = 9^1/2 = √9 = 3. In a problem with a rational exponent, the numerator tells you the power, and the denominator the root. However, in this problem the exponent can be reduced, so we should reduce that first. The exponent 150/300 = 1/2. So the problem becomes 9 to the 1/5 power.The denominator is 2 so we take the square root of 9 which is 3. The numerator is 1 so we raise 3 to the 1st power and the answer is 3.

Standards: HSN.RN.A.1

Click here to practice: High School Quantities Questions

Domain: High School >> Rotational and line symmetry

Sample Question: Quadrilateral ABCD is a parallelogram. What is the length of BD ?

1. 22
2. 62
3. 44
4. 124

Answer Explanation: The questions states that ABCD is a parallelogram. A property of parallelograms is that the diagonals bisect each other. If a diagonal is bisected, it is divided into two equal parts. Therefore, we can use this property to write and solve an equation to find x: x + 40 = 2x + 18. So, X = 22. Now we can find the length of each segment of DB, which are equal to each other. x + 40 = 22 + 40 = 62; 2(22) + 18 = 62. Add the two parts: 62 + 62 = 124 the length of BD is 124.

Standards: HSG.CO.C.11

Click here to practice: High School Rotational and line symmetry Questions

Domain: High School >> Real Numbers

Sample Question: Evaluate 49^3/2

1. 7
2. 147
3. 21
4. 343

Answer Explanation: 49^3/2 = (√49)³ = (7)³ = 7*7*7 = 343. In a problem with a rational exponent, the numerator tells you the power, and the denominator the root. In this problem 49^3/2, the denominator is 2 so you would take the square root of 49, which equals 7. The numerator is 3 so you would do 7 to the 3rd power (7*7*7) and that equals 343.

Standards: HSN.RN.A.1

Click here to practice: Real Numbers Questions for High School

Domain: High School >> Arithmetic with Polynomials & Rational Expressions

Sample Question: Evaluate the function f(x) = 3x³ – 3x² + 2x + 14 at x = 2 using the Remainder Theorem, with synthetic division.

1. 30
2. 26
3. -30
4. -26

Answer Explanation: The Remainder Theorem is based on synthetic division, which is the process of dividing a polynomial f (x) by a polynomial D(x) and finding the quotient and remainder. This is process evaluates the polynomial f(x) at a value where x = -c if D(x) = x + c. We can divide
(3x³ – 3x² +2x +14)divided by(x-2)
using synthetic division as:

The remainder is the last number in the bottom row of the synthetic division. Therefore, f(2) = 30.

Standards: HSA.APR.B.2

Click here to practice: Arithmetic with Polynomials & Rational Expressions Questions for High School

Looking for online practice tests? Here is the link to practice more of ACT Aspire High School Math questions.