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Quantitative ReasoningFree

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

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.

  • Section: Quantitative Reasoning 37 questions on the paper
  • 90 practice questions in the app

Sample questions

Question 1

At a bake sale, the number of cookies sold, cc, and the number of brownies sold, bb, are related by the equations c+b=20c + b = 20 and 2c−b=132c - b = 13. If cc and bb are both positive integers, how many brownies were sold?

  1. A7
  2. B8
  3. C9
  4. D11
Show answer

Answer: C — 9

Adding the two equations eliminates bb: 3c=333c = 33, so c=11c = 11. Substituting into c+b=20c + b = 20 gives b=9b = 9.

Question 2

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

  1. A−13-\dfrac{1}{3}
  2. B12\dfrac{1}{2}
  3. C−12-\dfrac{1}{2}
  4. D32\dfrac{3}{2}
Show answer

Answer: C — −12-\dfrac{1}{2}

Slope =1−46−0=−36=−12=\dfrac{1-4}{6-0}=\dfrac{-3}{6}=-\dfrac{1}{2}.

Question 3

What are the intercepts of the line 6x−5y=306x-5y=30?

  1. A(5,0)(5,0) and (0,−6)(0,-6)
  2. B(−5,0)(-5,0) and (0,6)(0,6)
  3. C(6,0)(6,0) and (0,−5)(0,-5)
  4. D(5,0)(5,0) and (0,6)(0,6)
Show answer

Answer: A — (5,0)(5,0) and (0,−6)(0,-6)

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

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

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