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) Write as a single fraction in its simplest form
\(\frac{x+3}{x-3}-\frac{x-2}{x+2}\)
(b)\(2^{12}\div 2^{\frac{k}{2}}=32\)
Find the value of k.
k = ………………………………………….
(c) Expand and simplify.
(y+3)(y-4)(2y-1)
………………………………………….
(d) Make x the subject of the formula.
\(x=\frac{3+x}{y}\)
x = ………………………………………….
Answer/Explanation
(a)\(\frac{10x}{(x-3)(x+2)}\) or\( \frac{10x}{x^{2}-x-6}\) final answer
(b) 14
(c) \(2y^{3}-3y^{2}-23y+12 \)final answer
(d)\(x=\frac{3}{y-1}\) final answer
Question
Gaya spends \($48\) to buy books that cost \($x\) each.
(a) Write down an expression, in terms of x, for the number of books Gaya buys.
………………………………………….
(b) Myra spends \($60\) to buy books that cost \($ (x+2)\) each.
Gaya buys 4 more books than Myra.
Show that \(x^{2}+5x-24=0.\)
(c) Solve by factorisation.
\(x^{2}+5x-24=0.\)
x = ……………… or x = ……………….
(d) Find the number of books Myra buys.
………………………………………….
Answer/Explanation
(a)\(\frac{48}{x}\) final answer
(b)\(-\frac{60}{x+2}=4\)
48(x+2)-60x=4x(x+2)
48x + 96 – 60x = 4×2 + 8x oe
leading to\( x^{2}+5x-24=0\)
(c) (x-3)(x+8)
3 and − 8
(d) 12