Quadratic Number Patterns (Grade 11 & 12) — Worksheet & Memo

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Grade 12 · Patterns & Sequences

Quadratic Number Patterns (Grade 11 & 12)

EXAM-STYLE CLASS TEST

Marks

Duration

55 minutes

Questions

Name:

Class:

Date:

Mark

/ 34

Instructions and Information

Answer ALL the questions in this question paper.
Answer QUESTION 1 by circling the letter (A–D) in the answer grid at the end of that section.
Show ALL calculations clearly.
Show all units where applicable.
Number the answers correctly according to the numbering system used in this question paper.
A non-programmable calculator may be used, unless stated otherwise.
Write neatly and legibly.

Question 1

[10 MARKS]

Four options are given as possible answers to the following questions. Choose the correct answer and circle the letter (A–D) in the grid at the end of this section. If you want to change your choice, put a cross through the wrong letter and circle your new choice.

1.1
In a QUADRATIC number pattern, the second difference is …
(1)
A)constant
B)zero
C)increasing
D)equal to the first difference
1.2
For the pattern 204 ; 176 ; 150 ; 126 ; …, the SECOND difference is …
(1)
A)2
B)−28
C)−2
D)−26
1.3
The next TWO terms of 204 ; 176 ; 150 ; 126 ; … are …
(1)
A)104 and 84
B)102 and 78
C)104 and 82
D)100 and 74
1.4
For T_n = an² + bn + c, the value of a is …
(1)
A)half the second difference
B)the second difference itself
C)the first difference
D)the first term
1.5
The general term of 204 ; 176 ; 150 ; 126 ; … is …
(1)
A)T_n = n² − 31n + 234
B)T_n = 2n² − 31n + 234
C)T_n = n² − 28n + 231
D)T_n = n² + 31n + 234
1.6
A quadratic pattern with a > 0 has …
(1)
A)a minimum term
B)a maximum term
C)no turning term
D)a constant first difference
1.7
The general term of 3 ; 8 ; 17 ; 30 ; … is …
(1)
A)T_n = 2n² − n + 2
B)T_n = 4n² − n + 2
C)T_n = 2n² + n + 2
D)T_n = 2n² − n
1.8
For T_n = n² − 31n + 234, the SMALLEST term occurs at …
(1)
A)n = 15 and n = 16, which are equal
B)n = 15,5
C)n = 31
D)n = 1
1.9
For T_n = n² − 31n + 234, the number of NEGATIVE terms is …
(1)
A)4
B)5
C)6
D)2
1.10
The FIRST differences of a quadratic pattern themselves form …
(1)
A)a linear pattern
B)a quadratic pattern
C)a geometric pattern
D)a constant pattern

Answer grid — circle your answers for Question 1

1.1	A	B	C	D
1.2	A	B	C	D
1.3	A	B	C	D
1.4	A	B	C	D
1.5	A	B	C	D
1.6	A	B	C	D
1.7	A	B	C	D
1.8	A	B	C	D
1.9	A	B	C	D
1.10	A	B	C	D

Question 2

[12 MARKS]

A quadratic number pattern T_n = an² + bn + c has these properties:
• T₁ = −2
• the n^th term of the FIRST differences is −6n − 2

2.1
Show that a = −3 and b = 1.
(4)
2.2
Hence determine the general term T_n.
(3)
2.3
Determine whether −19 122 is a term of the sequence. Justify your answer with calculations.
(5)

Question 3

[12 MARKS]

Consider the quadratic pattern 3 ; 8 ; 17 ; 30 ; 47 ; …

3.1
Show that the pattern is quadratic and determine its general term.
(5)
3.2
Determine which term of the pattern is equal to 122.
(4)
3.3
Determine the value of the FIRST difference between T₂₀ and T₂₁.
(3)

TOTAL: 34 marks

This question paper consists of 3 questions.