← Lesson📄 Worksheet✅ Memo📝 Exam test🗝️ Marking guide
∑ DANEMATHICS
FREE CAPS MATHS RESOURCES
Grade 12 · Patterns & Sequences
Quadratic Number Patterns (Grade 11 & 12)
WORKSHEET
Name: 
Class: 
Date: 
Mark
  / 14

Answer all questions. Show all your working — marks are awarded for method as well as the final answer.

  1. 1
    Show that 3 ; 8 ; 17 ; 30 ; 47 is a quadratic pattern.
    (2)
    38173047591317444Tn1st2ndSecond differences are constant ⇒ quadratic pattern
  2. 2
    Determine Tₙ for 3 ; 8 ; 17 ; 30 ; 47
    (2)
  3. 3
    Which term of 3 ; 8 ; 17 ; 30 ; 47 equals 122?
    (2)
  4. 4
    Determine the general term of the pattern shown in the difference table below.
    (2)
    1511192946810222Tn1st2nd
  5. 5
    1 ; p ; 11 ; … is a quadratic pattern whose first differences are 3 ; 7 ; … Determine p.
    (2)
  6. 6
    The second difference of a quadratic pattern is 6. Determine a.
    (2)
  7. 7
    Calculate T₁₀ if Tₙ = 2n² − n + 2.
    (2)
TOTAL: 14 marks
© Danemathics — free to print and share for classroom use.danemathics.com

Printing this sheet

  1. In the print dialog open More settings and untick “Headers and footers” — that is what prints the date, time and web address in the margin.
  2. Leave Pages per sheet on 1 so learners keep the full writing space.
  3. Choose Save as PDF as the destination to download it instead of printing.