Samples to Success - QUANTITY - Mathematics High School Number & Number and Quantity

Oct 10, 2026

Samples to Success presents sample ACT-style assessment items for high school Mathematics focused on Number and Quantity. The materials explain how students can demonstrate proficiency by working with real and complex number systems, including integers, rational exponents, vectors, and matrices. The document includes rubric-aligned prompts that emphasize reasoning from numerical quantities in multiple representations, and it highlights how item analysis combined with performance data can guide educators to identify strengths and growth areas through aligned instruction and learning goals.

LanguageEnglish

CategoryExam

FormatPDF

Pages3

Reading Time8 min

AccessFree to download

QUANTITY

Mathematics High School Number & Number and Quantity

Samples to Success Sample items provide valuable insight into how students engage with different texts, tasks, and contexts by highlighting the types of opportunities they need for success in the classroom. These items offer a shared reference point for understanding proficiency expectations, complementing the assessment's role in measuring learning. Analyzing items alongside performance data can enable educators to gain a deeper understanding of students' strengths and areas for growth. Students thrive in environments rich with diverse materials, challenges that vary in task type, and multiple avenues for demonstrating understanding. High-quality instruction, aligned with the learning goals, is the most effective way to support students' growth and prepare them for success. QUANTITY The sample questions included in this rubric are a blend of those typical of the ACT and others that are suitable for classroom instruction, aimed at reinforcing and developing the skills assessed on the ACT. The number and quantity category requires students to demonstrate knowledge of real and complex number systems. Students will show understanding by reasoning with numerical quantities in many forms, including integer and rational exponents, vectors, and matrices. This document contains ACT items and includes excerpts from ACT aligned guides: © ACT Education Corp. MATHEMATICS HIGH SCHOOL NUMBER & Number and Quantity Below Proficient Approaching Proficient Proficient Above Proficient For all nonzero values of 􀜽, the expression 􀯔2􀯔􀯔64 is equal to: A. 0 B. 1 C. 􀜽 D. 􀜽 2 E. 􀜽12 Let 􀝖 = 4 + 5􀝅 and 􀝓 = 3 + 7􀝅 , where 􀝅 is the imaginary unit. What is the value of 2􀝖 + 􀝓 ? A. −28 B. 28􀝅 C. 11 + 12􀝅 D. 11 + 17􀝅 E. 14 + 24􀝅 One of the following values for 􀜽 makes the expression 2􀯔􀯔251 undefined. Which one? A. B. C. D. E. -3 5 − ~~ ~~ 2 -1 0 􀝅 For what positive real value of 􀝇, if any, is the determinant of the matrix [􀝇3 4􀝇] equal to 􀝇? (Note: The determinant of matrix [􀜽􀜿 􀜾􀝀] equals 􀜽􀝀 − 􀜾􀜿 .) A. 3 B. 4 C. 12 D. √12 E. There is no such value of 􀝇 . Number and Quantity Below Proficient Approaching Proficient Proficient Above Proficient Which of the following matrices is equal to 5 [13 24] ? A. [ 53 B. [ 53 C. [ 115 D. [68 24] 220] 104] 79] E. 5 15 1020] 5 [􀜽􀜾] = 14 [2012] What is 􀜽 + 􀜾 ? 41 A. ~~ ~~ 5 148 B. ~~ ~~ 5 C. 448 5 D. 29 191 E. ~~ ~~4 The vector 􀝅 represents 1 mile per hour east, and the vector 􀝆 represents 1 mile per hour north. Maria is jogging south at 12 miles per hour. One of the following vectors represents Maria’s velocity, in miles per hour. Which one? A. −12􀝅 B. −12􀝆 C. 12􀝅 D. 12􀝆 E. 12􀝅 + 12􀝆 Representatives of vectors 􀝑,􀝒, 􀝌 , 􀝍 , and 􀝎 are shown in the standard (􀝔, 􀝕) coordinate plane below. One of the following vectors is equal to the vector 􀝑 + 􀝒 . Which one? A. −􀝎 B. −􀝍 C. −􀝌 D. 􀝌 E. 􀝍 Number and Quantity Below Proficient Approaching Proficient Proficient Above Proficient The lead of a screw is the distance that the screw advances in a straight line when the screw is turned 1 complete turn. If a screw is 2 inches long and has a lead of 18 inch, how many complete turns would get it all the way into a piece of wood? A. 2 B. 8 C. 10 D. 16 E. 28 What is the difference between 1.9 and 1.̅8? (Note: A bar indicates a digit pattern that is repeated.) A. 0.00̅1 B. 0.0̅1 C. 0. ̅1 D. 1.0 E. 10.0 The number 􀜽 is located at-2.5 on the number line below. One of the following number lines shows the location of 􀜽 2 . Which number line is it? If 􀝅 = √−1, then 􀯜􀯜3􀯜2􀯜􀯜3􀯜5 = ? A. -3 B. -1 1 C. ~~ ~~ 2 D. 1 E. 3

FAQs

What skills are students expected to demonstrate in the QUANTITY category?

Students must demonstrate knowledge of real and complex number systems and reason with numerical quantities in multiple forms, including integer and rational exponents, vectors, and matrices.

What kinds of ACT-style prompts are included in this document?

The document includes sample questions blended from typical ACT items and additional questions suitable for classroom instruction, aligned to the proficiency expectations measured by the assessment.

How can educators use the sample items with performance data?

Analyzing the items alongside performance data helps educators better understand students’ strengths and areas for growth, supporting targeted instructional decisions aligned with learning goals.

Oct 10, 2026

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