SD SBAC High School Concepts and Procedures Practice

SD SBAC High School Concepts and Procedures. Practice it free.

Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency. Content is drawn from the high school clusters listed as targets below (South Dakota administers the high school test in grade 11), with a much greater proportion from clusters the blueprint designates as priority (major) clusters. This High School reporting domain maps to 76 practice skills and 8 representative questions from the playable bank.

High SchoolClaim 176 mapped skills

Concepts and Procedures skills

Target A: Extend the properties of exponents to rational exponents

Target B: Use properties of rational and irrational numbers

Target C: Reason quantitatively and use units to solve problems

Target D: Interpret the structure of expressions

Target E: Write expressions in equivalent forms to solve problems

Target F: Perform arithmetic operations on polynomials

Target G: Create equations that describe numbers or relationships

Target H: Understand solving equations as a process of reasoning and explain the reasoning

Target I: Solve equations and inequalities in one variable

Target J: Represent and solve equations and inequalities graphically

Target K: Understand the concept of a function and use function notation

Target L: Interpret functions that arise in applications in terms of a context

Target M: Analyze functions using different representations

Target N: Build a function that models a relationship between two quantities

Target O: Define trigonometric ratios and solve problems involving right triangles

Target P: Summarize, represent, and interpret data on a single count or measurement variable

Standards basis

South Dakota Mathematics Standards (aligned to the Smarter Balanced/Common Core–style framework used in the SBAC mathematics blueprint) — South Dakota

How the SD SBAC reports it

South Dakota is a Smarter Balanced member state: the South Dakota Math Assessment IS the Smarter Balanced mathematics summative (computer-adaptive, administered every spring in grades 3-8 and 11), reported against South Dakota's math standards. Math is organized into the four Smarter Balanced claims with published assessment targets (Mathematics Content Specifications). Claim 1 (Concepts and Procedures) publishes per-grade assessment targets for grades 3-8 and high school, each a verbatim CCSS-M cluster heading (e.g. grade 3 Target A is cluster 3.OA.A); Claims 2-4 are cross-cutting process claims whose targets are constant across grades and draw on the same grade-level content. On score reports, Claims 2 and 4 are combined into a single reporting category, so three claim scores accompany the overall math score.

Blueprint & weighting

Content Specifications (Reporting Categories section): the total mathematics score is a weighted composite of the four claims — Claim 1 (Concepts and Procedures) contributes roughly 50%, Claim 3 (Communicating Reasoning) roughly 25%, and combined Claims 2 and 4 (Problem Solving / Modeling and Data Analysis) about 25%. The summative blueprint (as of 2018-19) publishes item counts per test event rather than percentages: Claim 1 is 17-20 items in grades 3-5, 16-20 in grades 6-8, and 19-22 in grade 11; the Claim 2/4 and Claim 3 reporting categories are 8-10 items each, totaling 18-20 across the two.

Official sources

South Dakota Department of Education
Smarter Balanced member state: South Dakota
Smarter Balanced Mathematics Content Specifications (July 2015)

8 free questions · 0/0 correct

Practice playhard

If $\dfrac{5x - 2y}{x + 3y} = \dfrac{2}{3}$ , then $\dfrac{x}{y}=$

Cross-multiply to clear the fraction: $3(5x - 2y) = 2(x + 3y)$ , so $15x - 6y = 2x + 6y$ . Collect like terms to get $13x = 12y$ . Divide both sides by $y$ , then by $13$ , to obtain $\dfrac{x}{y} = \dfrac{12}{13}\textsf{.}$

Practice playmedium

If $\dfrac{(x+2)(x-8)}{x+2} = 5$ and $x \neq -2\textsf{,}$ what is the value of $x\textsf{?}$

For $x \neq -2$ , the factor $x+2$ cancels, giving $x-8 = 5$ , so $x = 13\textsf{.}$

Practice playeasy

Which is a factored form of $x^2 - 8x + 15$ ?

Find two numbers with product $15$ and sum $-8$ : $-3$ and $-5$ . So $x^2 - 8x + 15 = (x-3)(x-5)$ .

Practice playmedium

$\begin{cases} x - 2y < -3 \\ x + y > 6 \end{cases}$
The point $(x, y)$ is a solution to the system of inequalities in the coordinate plane. If $y = 5$ , which of the following could be a value of $x$ ?

Substitute $y = 5$ . From $x - 2y < -3$ , $x - 10 < -3$ , so $x < 7$ . From $x + y > 6$ , $x + 5 > 6$ , so $x > 1$ . The value $x = 4$ satisfies $1 < 4 < 7$ .

Practice playeasy

Use completing the square to rewrite the equation in vertex form.

$y = -x^{2} + 6x - 5$

Select the vertex form of the equation.

Factor out $-1$ from the $x$ terms, then complete the square: $y = -(x^{2} - 6x + 9 - 9) - 5 = -((x - 3)^{2} - 9) - 5 = -(x - 3)^{2} + 4\textsf{.}$ The constant $4$ is the maximum value of $y\textsf{.}$

Practice playeasy

The yearbook staff distributed senior photos and lapel pins so that each staff member received the same number of photos and the same number of pins. There were $24$ photos and $36$ pins in all. Which could be the number of staff members?

The number of staff members must divide both $24$ and $36$ . Common factors greater than $1$ include $2$ , $3$ , $4$ , $6$ , and $12$ . Only $12$ appears among the choices: $24 \div 12 = 2$ photos and $36 \div 12 = 3$ pins per person.

Practice playeasy

For what value of $x$ does the graph of $y = -5(x - 11)(x + 4)$ intercept the $x$ -axis?

Set $y = 0$ : $-5(x - 11)(x + 4) = 0$ . The constant $-5 \neq 0$ , so the zeros are $x = 11$ and $x = -4$ . Of the choices, $-4$ is an x-coordinate of an x-intercept.

Practice playmedium

Given that $1 \le m \le 5$ , $3 \le n \le 7$ , and $8 \le p \le 12$ , what is the least possible value of $\dfrac{m}{n} \cdot \dfrac{1}{p}$ ?

Minimize $\dfrac{m}{n}$ with $m = 1$ and $n = 7$ , and minimize $\dfrac{1}{p}$ with $p = 12$ : $\dfrac{1}{7} \cdot \dfrac{1}{12} = \dfrac{1}{84}$ .

SD SBAC High School Concepts and Procedures. Practice it free.

Concepts and Procedures skills

Target A: Extend the properties of exponents to rational exponents

Target B: Use properties of rational and irrational numbers

Target C: Reason quantitatively and use units to solve problems

Target D: Interpret the structure of expressions

Target E: Write expressions in equivalent forms to solve problems

Target F: Perform arithmetic operations on polynomials

Target G: Create equations that describe numbers or relationships

Target H: Understand solving equations as a process of reasoning and explain the reasoning

Target I: Solve equations and inequalities in one variable

Target J: Represent and solve equations and inequalities graphically

Target K: Understand the concept of a function and use function notation

Target L: Interpret functions that arise in applications in terms of a context

Target M: Analyze functions using different representations

Target N: Build a function that models a relationship between two quantities

Target O: Define trigonometric ratios and solve problems involving right triangles

Target P: Summarize, represent, and interpret data on a single count or measurement variable

Topics mapped to this domain

Rational equations — find a ratio (ACT)

Rational equation solving (SAT)

Factoring quadratic expressions (ACT)

Linear inequality system solutions

Standard form to vertex form (ACT/SAT)

Common factor group size (ACT)

Factored polynomial x-intercepts (SAT)

Fraction bounds extreme value (ACT)

Intercepts from general form

LCM word problems (ACT)

Monomial expression multiplication (SAT)

Polynomial combining like terms (ACT/SAT)

8 free questions · 0/0 correct

Turn concepts and procedures into game time.