Home / iGCSE Mathematics (0580) :E2.8 Express direct and inverse proportion in algebraic terms and use this form of expression to find unknown quantities.iGCSE Style Questions Paper 4

iGCSE Mathematics (0580) :E2.8 Express direct and inverse proportion in algebraic terms and use this form of expression to find unknown quantities.iGCSE Style Questions Paper 4

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) Solve the simultaneous equations.

       You must show all your working.[4]

6x+5y = 27
5x-3y = 44

x =
y = 

(b) y is inversely proportional to (x+3)2.

       When x=2, y=8.

       Find y when x=7.

y =  [3]

(c) Solve the inequality.[3]

\(3\left ( x-2 \right )< 7\left ( x+2 \right )\)

Answer/Explanation

Ans:

10(a) correctly equating one set of coefficients

  correct method to eliminate one variable

  x = 7
  y = −3

10(b) 2

10(c) x > −5 final answer

Question

Bernie buys x packets of seeds and y plants for his garden.
He wants to buy more packets of seeds than plants.
The inequality x y 2 shows this information.
He also wants to buy
• less than 10 packets of seeds
• at least 2 plants.
(a) Write down two more inequalities in x or y to show this information.
(b) Each packet of seeds costs $1 and each plant costs $3.
The maximum amount Bernie can spend is $21.
Write down another inequality in x and y to show this information.
(c) The line x = y is drawn on the grid.
Draw three more lines to show your inequalities and shade the unwanted regions.

(d) Bernie buys 8 packets of seeds.
(i) Find the maximum number of plants he can buy.
(ii) Find the total cost of these packets of seeds and plants.
$ ………………………………………….

Answer/Explanation

Answer:

(a) x < 10 oe
\(y \leq 2\) oe
(b) \(x + 3y \leq 21\) oe
(c) ruled broken line x = 10
ruled line y = 2
ruled line from (0, 7) to (21, 0)
correct region indicated cao
(d) (i) 4
(ii) 20

Scroll to Top