Past Paper Example 1
Eduqas Nov 2018 1F Q24 / 1H Q7
7 marks
(a) Use the diagram to solve the simultaneous equations
y - x = 3
x + 2y = 1
Give your answers correct to 1 decimal place.
(b) A theme park sells entrance tickets.
2 adult tickets and 3 child tickets would cost a total of £72.
3 adult tickets and 1 child ticket would cost a total of £66.
A family ticket costs £45 and allows entry for 2 adults and 2 children.
How much cheaper is it to buy a family ticket than it would be to buy 2 adult and 2 child tickets?
y - x = 3
x + 2y = 1
Give your answers correct to 1 decimal place.
(b) A theme park sells entrance tickets.
2 adult tickets and 3 child tickets would cost a total of £72.
3 adult tickets and 1 child ticket would cost a total of £66.
A family ticket costs £45 and allows entry for 2 adults and 2 children.
How much cheaper is it to buy a family ticket than it would be to buy 2 adult and 2 child tickets?
(a) Use the diagram to solve the simultaneous equations
y - x = 3
x + 2y = 1
Give your answers correct to 1 decimal place. [2 marks]
y - x = 3
x + 2y = 1
Give your answers correct to 1 decimal place. [2 marks]
(b) A theme park sells entrance tickets.
2 adult tickets and 3 child tickets would cost a total of £72.
3 adult tickets and 1 child ticket would cost a total of £66.
A family ticket costs £45 and allows entry for 2 adults and 2 children.
How much cheaper is it to buy a family ticket than it would be to buy 2 adult and 2 child tickets? [5 marks]
2 adult tickets and 3 child tickets would cost a total of £72.
3 adult tickets and 1 child ticket would cost a total of £66.
A family ticket costs £45 and allows entry for 2 adults and 2 children.
How much cheaper is it to buy a family ticket than it would be to buy 2 adult and 2 child tickets? [5 marks]
Worked Solution & Mark Scheme (7 marks)
Part (a) Solution:
Locate the intersection of the two straight lines on the graph. M1
x-coordinate is roughly -1.7
y-coordinate is roughly 1.3. A1
x-coordinate is roughly -1.7
y-coordinate is roughly 1.3. A1
Answer (a): x = -1.7, y = 1.3 (accept x = -1.6 to -1.7, y = 1.3 to 1.4)
Part (b) Solution:
Let a = price of adult ticket, c = price of child ticket M1
(1) 2a + 3c = 72 M1
(2) 3a + c = 66 ⇒ c = 66 - 3a
Substitute into (1): 2a + 3(66 - 3a) = 72 ⇒ 2a + 198 - 9a = 72 ⇒ -7a = -126 ⇒ a = 18 M1
Then c = 66 - 3(18) = 66 - 54 = 12 M1
Cost of 2 adult and 2 child tickets = 2(18) + 2(12) = 36 + 24 = £60
Saving with family ticket = 60 - 45 = £15. A1
(1) 2a + 3c = 72 M1
(2) 3a + c = 66 ⇒ c = 66 - 3a
Substitute into (1): 2a + 3(66 - 3a) = 72 ⇒ 2a + 198 - 9a = 72 ⇒ -7a = -126 ⇒ a = 18 M1
Then c = 66 - 3(18) = 66 - 54 = 12 M1
Cost of 2 adult and 2 child tickets = 2(18) + 2(12) = 36 + 24 = £60
Saving with family ticket = 60 - 45 = £15. A1
Answer (b): £ £15 cheaper £