ISAT Grade 11 Number and Quantity Practice

Number and Quantity skills

Reason quantitatively and use units to solve problems

Perform arithmetic operations with complex numbers

Represent complex numbers and their operations on the complex plane

Standards basis

Idaho Content Standards (Mathematics) — Idaho

How the ISAT reports it

Idaho ISAT is a state assessment administered to grades 3–8 and 11 and reported against Idaho grade-level content standards rather than a separate national testing framework. The public ISAT page points to summative blueprints and math specifications, while the Idaho Content Standards page shows the math program is organized by grade-band/domain progressions aligned to Idaho standards.

Blueprint & weighting

The public Idaho ISAT page references summative blueprints and item specifications, but the accessible official page content did not expose a published domain-by-domain percentage blueprint for math.

Official sources

Idaho Department of Education — Idaho Standards Achievement Test (ISAT)
Idaho Department of Education — Idaho Content Standards

8 free questions · 0/0 correct

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 playmedium

Simplify $(4-i)^{2}$ .

Expand: $(4-i)^{2}=16-8i+i^{2}$ . Since $i^{2}=-1$ , this is $16-8i-1=15-8i\textsf{.}$

Practice playeasy

What is $i^{3}$ ?

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

Practice playeasy

Given $i = \sqrt{-1}$ , what is $\sqrt{64} + \sqrt{-1}$ ?

$\sqrt{64} = 8$ and $\sqrt{-1} = i$ . So $\sqrt{64} + \sqrt{-1} = 8 + i$ .

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 $p = 12$ : $\dfrac{1}{7} \cdot \dfrac{1}{12} = \dfrac{1}{84}$ .

Practice playmedium

A community garden waters the vegetable beds every $10$ days and fertilizes the same beds every $14$ days. Both jobs were done on the same day. In how many days will watering and fertilizing next fall on the same day?

The next day both jobs occur is the least common multiple of $10$ and $14\textsf{.}$ Since the GCF of $10$ and $14$ is $2\textsf{,}$ divide their product by the GCF: $\dfrac{10 \times 14}{2}=70\textsf{.}$ So they coincide again in $70$ days.

Practice playmedium

A drone is flying at a speed of $20$ meters per second. What is the drone's speed in kilometers per hour?
(Note: $1$ kilometer $= 1{,}000$ meters)

Multiply by conversion factors so the old units cancel: $20\,\dfrac{\text{m}}{\text{s}} \times \dfrac{1\,\text{km}}{1{,}000\,\text{m}} \times \dfrac{3{,}600\,\text{s}}{1\,\text{h}} = 72\,\dfrac{\text{km}}{\text{h}}$ .

Practice playeasy

A chess club ordered custom shirts and name tags. Every member received the same number of shirts and the same number of tags. The shipment contained $45$ shirts and $75$ name tags in all. Which could be the number of members in the chess club?

The number of members must divide both totals evenly. The common factors of $45$ and $75$ greater than $1$ are $3$ , $5$ , and $15$ . Only $15$ is listed: $45 \div 15 = 3$ shirts and $75 \div 15 = 5$ tags per member.