VICTORIA
INTERNATIONAL SCHOOL
TERM ASSESSMENT
TERM 2 / 2024
Candidate Name
Class
YEAR 10
__________________________________________________
MATHEMATICS
0580/43
Paper 4 (Extended)
2 h 30 min
You must answer on the exam paper
You will need:
Geometrical Instruments
Soft Clean Eraser
Tracing Paper
__________________________________________________
Instructions
Answer all questions.
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Use a black or dark blue pen.
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Write your name, Class details in the boxes at the top of the page.
Write your answer to each question in the space provided.
Do not use an erasable pen or correction fluid.
Do not write on any bar codes.
Dictionaries are not allowed
Information
• The total mark for this paper is 40.
• The number of marks for each question or part question is
shown in brackets [ ]
________________________________________________________________
This document has 15 pages. Any blank pages are indicated.
[Turn over]
FINAL ASSESSMENT/T2-24
2
1.
a. Lucy is painting the doors in her house. She uses ¾
of a tin of paint for each door. Work out the least
number of tins of paints Lucy needs to paint 7 doors.
Answer: ___________ (3 marks)
b. Work out
6.39 ×104
2.45 ×106
Give your answer in standard form.
Answer: _______________ (2 marks)
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2.
a. A dressmaker measures a length of fabric as 600 m,
correct to the nearest 5 metres. He cuts this into dress
length of 9 m, correct to the nearest metre.
Calculate the largest number of complete dress
lengths he could cut.
Answer: _______________ (3 marks)
b. A rectangular picture has length 15 cm and width 10.5
cm, both correct to the nearest 5mm.
Calculate the upper bound for the area of this picture.
Answer: _______________ (2 marks)
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c. The mass, m grams, of a cake is 1250g, correct to the
nearest 10g.
Complete this statement about the value of m.
__________ ≤ m < ______________
(2 marks)
3. The Venn diagram shows two sets, A and B.
a. Use set notation to complete the statements.
i.
d …………….A
(1 mark)
ii.
{f, g} = _____________
(1mark)
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b. Complete the statement
n ( _____________ ) = 6
(1 mark)
4. Louise leaves home at 09 55 and cycles the 5.6 km to the
supermarket at a constant speed. She takes 15 minutes to
Complete the journey.
a. Write down the time she arrives at the supermarket.
Answer: _____________ (1 mark)
b. Calculate Louise’s average speed from her home to
the supermarket
a. In kilometres per hour,
Answer: _____________ (1 mark)
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b. In metres per second, giving your answer correct
to 1 decimal place.
Answer: _______________ (2 marks)
c. Louise stays at the supermarket for 23 minutes.
On the grid, draw the travel graph of her journey from home
and her stay at the supermarket.
(1 marks)
d. Lousie’s mother leaves home at 1007 to meet Louise
at the supermarket. She cycles at a constant speed
of 28km/h.
i. Work out how long she takes for the 5.6 km
journey. Give your answer in minutes.
Answer: ______________ (2 marks)
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ii. On the grid, show her mother’s journey.
(1 marks)
e. They cycle home together at a constant speed and
arrive at 1054.
i. On the grid, show their journey home. (1 mark)
ii. Calculate, in km/h, their constant speed on the
journey home.
Answer: ____________ (2 marks)
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5. The fares for a train journey are shown in the table below.
From London to Marseille
Adult
Child
Standard Fare
$84
$60
Premier Fare
$140
$96
a. For the standard fare, write the ratio of adult fare : child
fare in its simplest form.
__________ : ___________ (1 mark)
b. For an adult, find the percentage increase in the cost of
the standard fare to the premier fare.
Answer: ____________ (3 marks)
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c. For one journey from London to Marseille, the ratio
number of adults : number of children = 11: 2.
There were 220 adults in total on this journey.
All of the children and 70% of the adults paid the standard
fare.
The remaining adults paid the premier fare.
Calculate the total of the fares paid by the adults and the
children.
Answer: ___________ (5 marks)
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6. Klaus buys 𝑥 silver balloons and 𝑦 gold balloons for a party.
He buys
• more gold balloons than silver balloons
• at least 15 silver balloons
• less than 50 gold balloons
• a total of no more than 70 balloons
a. Write down four inequalities, in terms of 𝑥 and/or 𝑦,
to show this information.
Answer:
_____________________
_____________________
_____________________
_____________________
(4 marks)
b. On the grid, show the information from part (a) by
drawing four straight lines and shading the unwanted
regions.
(5 marks)
c. Silver balloons cost $2 and gold balloons cost $3.
Calculate the most that Klaus could spend.
Answer: ___________ (2 marks)
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7. 𝑓(𝑥 ) =
3
𝑥+2
13
, 𝑥 ≠ −2 , 𝑔(𝑥 ) = 8𝑥 − 5 , ℎ(𝑥 ) = 𝑥 2 + 6
1
a. Work out 𝑔 ( ).
4
Answer: ____________ (1 mark)
b. Work out 𝑓𝑓(2).
Answer: ___________ (2 marks)
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c. Find 𝑔𝑔(𝑥 ), give your answer in its simplest form.
Answer: ___________ (2 marks)
d. Find 𝑔−1 (𝑥 ).
Answer: _______________ (2 marks)
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e. Write 𝑔(𝑥 ) − 𝑓(𝑥) as a single fraction in its simplest
form.
Answer: _______________ (3 marks)
f. Solve the following
i. Show that ℎ𝑔(𝑥 ) = 19 simplifies to
16𝑥 2 − 20𝑥 + 3 = 0 .
(3 marks)
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g. Use the quadratic formula to solve
16𝑥 2 − 20𝑥 + 3 = 0
Show all your working and give your answers
correct to 2 decimal places.
x = _________ or x = _________ (4marks)
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8.
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In a sale, a shop reduces all prices by 12%.
a. Dina buys a book which has an original price of $6.50.
Calculate how much Dina pays for the book.
Answer: _______________ (2 marks)
b. Elu pays $11 for a toy.
Calculate the original price of the toy.
Answer: _______________ (2 marks)
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c. Arno buys a student ticket for $43.68.
This is a saving of 16% on the full price of a ticket.
Calculate the full price of a ticket.
Answer: ___________ (2 marks)
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9. The point P has co-ordinates (10, 12) and the point Q has coordinates (2, −4).
Find,
a. the co-ordinates of the mid-point of the line PQ.
Answer: (____ , ____) (2 marks)
b. the gradient of the line PQ.
Answer: __________ (2 marks)
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c. the equation of a line perpendicular to PQ that passes
through the point (2, 3).
Answer: _______________ (3 marks)
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10.
The diagram shows the positions of three points A, B and C in a
field.
a. Show that BC is 118.1m, correct to 1 decimal place.
(3 marks)
b. Calculate angle ABC.
Answer: _____________ (3 marks)
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c. The bearing of C from A is 147°.
Find the bearing of A from B.
Answer: _______________ (3 marks)
d. The bearing of C from A is 147°
Find the bearing of B from C.
Answer: _______________ (2 marks)
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e. Mitchell takes 35 seconds to run from A to C.
Calculate his average running speed in kilometres per
hour.
Answer: _____________ km/h (3 marks)
f. Calculate the shortest distance from point B to AC.
Answer: _______________ m (3 marks)
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11.
The diagram shows a field ABC.
a. Calculate BC.
BC : _________________ (3 marks)
b. Calculate angle ACB.
Angle ACB: ________________(3 marks)
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c. A gate, G, lies on AB at the shortest distance from C. Calculate
AG.
AG = ___________________ (3 marks)
d. A different triangular field PQR has the same area as ABC.
PQ = 90 m and QR = 60 m.
Work out the two possible values of angle PQR.
Angle PQR = __________ or ___________ (5 marks)
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12. the table shows some values of 𝑦 = 𝑥 3 − 3𝑥 2 + 𝑥
a. Complete the table.
(3marks)
b. On the grid, draw the graph of 𝑦 = 𝑥 3 − 3𝑥 2 + 𝑥
-0.75 ≤ x ≤ 2.75.
(4 marks)
c. Use your graph to complete the inequalities in 𝑥 for
which 𝑦 > −1.
_________ < 𝑥 < __________ and 𝑥 > __________
(3 marks)
d. The equation 𝑥 3 − 3𝑥 2 + 2𝑥 − 1 = 0 can be solved by
drawing a straight line on the grid.
i. Write down the equation of this line.
Answer: _______________ (2 marks)
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ii.
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On the grid, draw this line and use it to solve the
equation 𝑥 3 − 3𝑥 2 + 2𝑥 − 1 = 0.
Answer: x = ____________ (3 marks)
e. By drawing a suitable tangent, find an estimate for the
gradient of the graph of 𝑦 = 𝑥 3 − 3𝑥 2 + 𝑥 at x = -0.25.
Answer: _______________ (3 marks)
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13. The scale drawing shows the positions of house A and B.
The scale is 1 centimetre represents 12 metres.
scale: 1cm to 12m
a. Measure the bearing of house A from house B.
Answer: ____________________ (1 mark)
b. Another house, C, is 102 metres from house B on a
bearing of 157°. On the scale drawing, mark the position
of house C.
(3 marks)
END OF QUESTION PAPER
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