Study on the fly ISEE Upper Quantitative ReasoningLinear equations, graphs, and systems

Quantitative Reasoning

Linear equations, graphs, and systems — ISEE Upper practice questions

37 questions on the paper
90 practice questions in the app
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Practice 90 Linear equations, graphs, and systems questions in the app

What this topic is

Linear equations, graphs, and systems on the ISEE Upper Quantitative Reasoning section asks students to find slope from given points, locate intercepts of a line, and solve a system, often from a short sale or quantity story.

A student must use rise over run, set each variable to zero to read intercepts, and add or substitute to isolate the requested unknown. Items are usually direct find-the-value questions whose choices are a fraction, an ordered pair of intercepts, or a whole number.

Traps include reversing slope, swapping intercepts, and answering the other variable.

Sample questions

Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.

Question 1Mid

At a bake sale, the number of cookies sold, $c$ , and the number of brownies sold, $b$ , are related by the equations $c + b = 20$ and $2c - b = 13$ . If $c$ and $b$ are both positive integers, how many brownies were sold?

7✗ Not this one8✗ Not this one9✓ Correct11✗ Not this one

Show answer

Answer: C — 9

Adding the two equations eliminates $b$ : $3c = 33$ , so $c = 11$ . Substituting into $c + b = 20$ gives $b = 9$ .

Question 2Easier

A line passes through the points $(0,4)$ and $(6,1)$ . What is the slope of the line?

-\dfrac{1}{3}

✗ Not this one

\dfrac{1}{2}

✗ Not this one

-\dfrac{1}{2}

✓ Correct

\dfrac{3}{2}

✗ Not this one

Show answer

Answer: C — $-\dfrac{1}{2}$

Slope $=\dfrac{1-4}{6-0}=\dfrac{-3}{6}=-\dfrac{1}{2}$ .

Question 3Easier

What are the intercepts of the line $6x-5y=30$ ?

(5,0)

and

(0,-6)

✓ Correct

(-5,0)

and

(0,6)

✗ Not this one

(6,0)

and

(0,-5)

✗ Not this one

(5,0)

and

(0,6)

✗ Not this one

Show answer

Answer: A — $(5,0)$ and $(0,-6)$

Setting $y=0$ gives $x=5$ , and setting $x=0$ gives $y=-6$ . Thus, the intercepts are $(5,0)$ and $(0,-6)$ .

Every question is picked for where you are right now, wrong answers come back until they stick, and it all works offline.

Practice 90 Linear equations, graphs, and systems questions in the app

Linear equations, graphs, and systems — ISEE Upper practice questions

What this topic is

Sample questions

More ISEE Upper topics

Quantitative Reasoning