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Selective school test-style practice questions

Five free questions in the style of selective high school placement tests: thinking skills and mathematical reasoning. Tap "Show answer" for the answer and the reasoning.

Name ____________________Date ______________
  1. 1.What number comes next? 2, 6, 12, 20, 30, ?
    36404248
    Show answer
    Answer: 42
    The gaps grow by 2 each time: +4, +6, +8, +10, so the next gap is +12. 30 + 12 = 42.
  2. 2.Every student in the chess club also plays piano. Sam plays piano. Which must be true?
    Sam is in the chess club.Sam is not in the chess club.Sam may or may not be in the chess club.
    Show answer
    Answer: Sam may or may not be in the chess club.
    Chess club members are all piano players, but not every piano player has to be in chess club. So we can't tell.
  3. 3.A train leaves at 9:45 am and the trip takes 2 hours 35 minutes. When does it arrive?
    11:20 am12:10 pm12:20 pm12:35 pm
    Show answer
    Answer: 12:20 pm
    9:45 + 2 hours = 11:45. Add 35 minutes: 11:45 + 15 = 12:00, then 20 more = 12:20 pm.
  4. 4.4 pencils cost $3. How much do 10 pencils cost?
    $6.00$7.00$7.50$12.00
    Show answer
    Answer: $7.50
    One pencil costs $3 ÷ 4 = $0.75. 10 pencils cost 10 × $0.75 = $7.50.
  5. 5.Ann is older than Ben. Ben is older than Cal. Dee is younger than Cal. Who is the youngest?
    AnnBenCalDee
    Show answer
    Answer: Dee
    Oldest to youngest: Ann, Ben, Cal, then Dee (younger than Cal).

Answers: Selective school test-style practice questions

  1. 42. The gaps grow by 2 each time: +4, +6, +8, +10, so the next gap is +12. 30 + 12 = 42.
  2. Sam may or may not be in the chess club.. Chess club members are all piano players, but not every piano player has to be in chess club. So we can't tell.
  3. 12:20 pm. 9:45 + 2 hours = 11:45. Add 35 minutes: 11:45 + 15 = 12:00, then 20 more = 12:20 pm.
  4. $7.50. One pencil costs $3 ÷ 4 = $0.75. 10 pencils cost 10 × $0.75 = $7.50.
  5. Dee. Oldest to youngest: Ann, Ben, Cal, then Dee (younger than Cal).

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StudyHop is not affiliated with or endorsed by ACARA, NESA, the NSW Department of Education or any curriculum or exam authority. Names such as NAPLAN, Selective, OC, HSC and VCE describe the style of practice only. All questions here are original StudyHop questions, not official papers.