Question
(a) Naga has n marbles.
Panav has three times as many marbles as Naga.
Naga loses 5 marbles and Panav buys 10 marbles.
Together they now have more than 105 marbles.
Write down and solve an inequality in n.
………………………………………….
(b) y is inversely proportional to \(x^{2}.\)
When x = 4, y = 7.5.
Find y when x = 5.
y = ………………………………………….
(c) Find the nth term of each sequence.
(i) 4 2 0 -2 -4 …
………………………………………….
(ii) 1 7 17 31 49 …
………………………………………….
Answer/Explanation
(a) n − 5 + 3n + 10 > 105 or better
n > 25 final answer
(b) 4.8
(c)(i) 6 − 2n final answer
(ii) \(2n^{2}-1\) final answer
Question
(a) The table shows the first five terms of sequence A and sequence B.
(i) Complete the table for the 6th term of each sequence. [2]
(ii) Find the nth term of
(a) sequence A,[2]
(b) sequence B.[2]
(b) The nth term of another sequence is 4n2+n+3.
Find
(i) the 2nd term, [1]
(ii) the value of n when the nth term is 498.
n = [3]
Answer/Explanation
Ans:
11(a)(i) 77 243
11(a)(ii)(a) 2n2+5 oe
11(a)(ii)(b) 3n-1oe
11(b)(i) 21
11(b)(ii) 11
Question
(a) Complete the table for the 5th term and the nth term of each sequence. [11]
(b) 0, 1, 1, 2, 3, 5, 8, 13, 21, …
This sequence is a Fibonacci sequence.
After the first two terms, the rule to find the next term is “add the two previous terms”.
For example, 5+8= 13.
Use this rule to complete each of the following Fibonacci sequences.[3]
2 4 _ _ _
1 _ _ _ 11
_ -1 _ _ 1
(c) \(\frac{1}{3}\), \(\frac{3}{4}\), \(\frac{4}{7}\), \(\frac{7}{11}\), \(\frac{11}{18}\), …
(i) One term of this sequence is \(\frac{p}{q}\).
Find, in terms of p and q, the next term in this sequence.[1]
(ii) Find the 6th term of this sequence.[1]
Answer/Explanation
Ans:
10(a) – 7
13 – 4n oe
36
(n + 1)2oe
125
n3 oe
128
2n + 2 oe
10(b) _, _, 6, 10, 16
_, 3, 4, 7, _
2, _, 1, 0, _
10(c)(i) \(\frac{q}{p+q}\)
10(c)(ii) \(\frac{18}{29}\)