KSA Grade 10 Number and Quantity Practice

Number and Quantity skills

Use properties of rational and irrational numbers

Perform arithmetic with complex numbers

Use units to solve problems

Reason quantitatively and use units to solve problems

Interpret expressions for functions in terms of the situation they model

Standards basis

Kentucky Academic Standards (KAS) for Mathematics — Kentucky

How the KSA reports it

Kentucky KSA is a state summative assessment built on Kentucky Academic Standards (KAS) rather than a separate national framework. For mathematics, the assessed content closely follows Common Core–style grade-band domains in grades 3-8 and uses Kentucky high-school conceptual categories in grade 10.

Blueprint & weighting

KSA uses the Independent / state-specific framework (by grade domains structure).

Official sources

Kentucky Department of Education — Kentucky Summative Assessment
Kentucky Department of Education — Mathematics
Kentucky Department of Education — Kentucky Laws and Regulations

8 free questions · 0/0 correct

Practice playeasy

A package weighs $4$ pounds. What is the weight of the package in ounces?
(Note: $1$ pound $= 16$ ounces)

Multiply by a conversion factor so the old unit cancels: $4\,\text{lb} \times \dfrac{16\,\text{oz}}{1\,\text{lb}} = 64\,\text{oz}$ .

Practice playmedium

A drama club prepared scripts and prop kits for a showcase. Each cast member received the same number of scripts and the same number of prop kits. The club had $54$ scripts and $81$ prop kits in all. Which could be the number of cast members?

The number of cast members must divide both totals. The common factors of $54$ and $81$ greater than $1$ are $3$ , $9$ , and $27$ . Only $9$ appears among the choices: $54 \div 9 = 6$ scripts and $81 \div 9 = 9$ kits per member.

Practice playmedium

What is $(3+2i)^{2}$ ?

Expand: $(3+2i)^{2}=9+12i+4i^{2}$ . Since $i^{2}=-1$ , this is $9+12i-4=5+12i\textsf{.}$

Practice playeasy

What is $i^{6}$ ?

$i^{6} = (i^{2})^{3} = (-1)^{3} = -1$ .

Practice playeasy

Given $i = \sqrt{-1}$ , what is $\sqrt{100} + \sqrt{-49}$ ?

$\sqrt{100} = 10$ and $\sqrt{-49} = 7i$ . So $\sqrt{100} + \sqrt{-49} = 10 + 7i$ .

Practice playmedium

A lab culture starts with $2{,}000$ cells. Each hour, a model estimates that the number of cells triples. Which equation defines this model, where $c(h)$ is the estimated number of cells $h$ hours after the culture begins?

The starting count is $2{,}000$ , and tripling each hour means multiplying by $3$ , so $c(h) = 2{,}000(3)^h$ .

Practice playmedium

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

Maximize $\dfrac{m}{n}$ with $m = 5$ and $n = 3$ , and maximize $\dfrac{1}{p}$ with $p = 8$ : $\dfrac{5}{3} \cdot \dfrac{1}{8} = \dfrac{5}{24}$ .

Practice playeasy

The function $p$ is defined by $p(w) = 1{,}250(1.04)^{w}$ . The function models a savings balance, in dollars, $w$ weeks after an account is opened. Which statement is the best interpretation of $1{,}250$ in this context?

When $w = 0$ , $p(0) = 1{,}250$ . So $\text{\char36}1{,}250$ is the balance when the account is opened.

KSA Grade 10 Number and Quantity. Practice it free.

Number and Quantity skills

Use properties of rational and irrational numbers

Perform arithmetic with complex numbers

Use units to solve problems

Reason quantitatively and use units to solve problems

Interpret expressions for functions in terms of the situation they model

Topics mapped to this domain

Unit conversion word problems (ACT)

Common factor group size (ACT)

Multiplying and squaring complex numbers (ACT)

Complex number operations

Rewriting complex numbers

Writing exponential equations from context (SAT)

Fraction bounds extreme value (ACT)

Interpreting exponential parameters

Interpreting linear parameters

LCM word problems (ACT)

Linear coefficient interpretations (SAT/PSAT 8/9/10)

8 free questions · 0/0 correct

Turn number and quantity into game time.

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