Algebra 4a: Mastery Questions
Guidance Notes - To answer each question, click on the letter that corresponds to the correct answer. You then need to click the 'Check' button to see if you are correct. If your answer is incorrect, you will be given a hint on how to get the correct answer. You then need to click the 'Try again' button to attempt the question once more.
1. Find the nth term of this sequence

6, 15, 24, 33, ...

  A  
  B  
  C  
  D  
9n + 3
9n
9n + 6
9n − 3
    
2. Here is a pattern of red and blue tiles.

The nth term for the number of blue tiles is

  A  
  B  
  C  
  D  
n2 + 1
n2 − 1
(n + 1)2 − n
n2 − n
    
3. The nth term of this quadratic sequence is

0, 3, 8, 15, 24, ...

  A  
  B  
  C  
  D  
n2 − 1
2n2 − 2
n2 − n
2n2 − 2n
    
4. Here are the first four terms of a quadratic sequence

86, 78, 68, 56, ...

  A  
  B  
  C  
  D  
44
42
48
40
    
5. The nth term of a sequence is n2 − 4n + 2. What is the 10th term of this sequence?

  A  
  B  
  C  
  D  
142
58
62
38
    
6. The nth term of this quadratic sequence is

-1, 5, 15, 29, 47, ...

  A  
  B  
  C  
  D  
n2 − 2
2n2 − 1
n2 − 2n
2n2 − 3
    
7. Which of these sequences will not have 55 as one of its terms?

  A  
1, 1, 2, 3, 5, ...
  B  
1, 3, 6, 10, ...
  C  
6, 13, 20, 27, ...
  D  
3, 7, 13, 21, ...
    
8. The nth term of a sequence is (n + 2) × (n + 3). What is the 5th term of this sequence?

  A  
  B  
  C  
  D  
15
56
80
88
    
9. Expand (n + 2) × (n + 3)

  A  
  B  
  C  
  D  
n2 + 6
n2 + 6n + 5
n2 + 5n + 6
n2 + 5n + 5
    
10. The first three terms of a sequence are

35, 810, 1517, ...

What is the rule for the nth term of this sequence?

  A  
  B  
  C  
  D  
5n − 25n
n + 2n + 4
n2 − 1n2 + 1
n2 + 2nn2 + 2n + 2
    
For Questions 11 and 12, you will need to answer them using paper and pencil and then click the 'Check' button to see if you have done them correctly.
11. Look at this pattern of red and blue tiles.

a) How many red tiles would there be in (i) shape 10 (ii) shape n
b) How many tiles would there be in i) shape 10 (ii) shape n
c) How many blue tiles would there be in i) shape 10 (ii) shape n 		    
12. Look at this growing pattern

a) What would shape 10 look like?
b) What is the associate sum for shape 10?
c) What is the value of 1 + 2 + 3 + ... + 18 + 19 + 20 + 19 + 18 + ... + 3 + 2 + 1?
d) Can you generalise the result? 		    
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