1. The document contains a mathematics exam paper with 22 multiple-choice and word problems.
2. It provides instructions for candidates to write their answers in the spaces provided and show all working.
3. The exam covers a range of mathematics topics including algebra, geometry, statistics, and trigonometry.
a handy document for high school and college that my assist in changing our atitudes in study habits and study skills so that we pass examinations and improve our grades and class performance
a handy document for high school and college that my assist in changing our atitudes in study habits and study skills so that we pass examinations and improve our grades and class performance
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
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Biological screening of herbal drugs: Introduction and Need for
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Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
Model Attribute Check Company Auto PropertyCeline George
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Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
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The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
2. 2
*P44613A0224*
International GCSE MATHEMATICS
FORMULAE SHEET – HIGHER TIER
r
Pythagoras’ Volume of cone =
Curved surface area of cone =
Theorem
a2
+ b2
= c2
b
a
c
adj = hyp cos
opp = hyp sin
opp = adj tan
or
opp
tan
adj
adj
cos
hyp
opp
sin
hyp
a
a
Sine rule:
Cosine rule:
Area of triangle
sin A
b
+
sin B
c
sin C
opp
A B
C
b a
c
adj
hyp
Area of a trapezium = (a + b)h1
2
h1 2
2
b2
c 2bc
ab sin C
cos A2
3
b
a
h
a
h
b
Volume of prism = area of cross section length
length
section
cross
Volume of cylinder = r2
h
Curved surface area
The Quadratic Equation
The solutions of ax
where a
x
b b 4ac
2a
0, are given by
bx c 0,+
+
+
of cylinder = 2 rh
h
r
Circumference of circle = 2
Area of circle = r2
2
2
r
r 4 3
3
1
2
r
2
r
Volume of sphere =
r
r
h
l
l Surface area of sphere =
In any triangle ABC
4
r
3. 3
*P44613A0324* Turn over
Answer ALL TWENTY TWO questions.
Write your answers in the spaces provided.
You must write down all the stages in your working.
1
1 euro = 120 yen
£1 = 1.2 euros
Change £50 to yen.
.............................................. yen
(Total for Question 1 is 2 marks)
2 (a) Work out the value of
451 4
14 1 10 3
.
. .+
..............................................
(2)
(b) Work out the value of 7 8 7 22 2
. .−
..............................................
(2)
(Total for Question 2 is 4 marks)
Do NOT write in this space.
4. 4
*P44613A0424*
3 (a) Factorise 14x – 35
..............................................
(1)
(b) Expand and simplify 3(2c – 5) – 2(c – 4)
..............................................
(2)
(c) Simplify (4e3
)2
..............................................
(2)
(d) Expand and simplify (a + 5)(2a – 1)
............................................................
(2)
(Total for Question 3 is 7 marks)
Do NOT write in this space.
5. 5
*P44613A0524* Turn over
4 The diagram shows a shape with one line of symmetry.
Work out the area of the shape.
.............................................. cm2
(Total for Question 4 is 4 marks)
Diagram NOT
accurately drawn
12 cm
15 cm
4 cm
10 cm
6. 6
*P44613A0624*
5 A jar contains coloured beads.
Ajit takes at random a bead from the jar.
The probability that the bead is yellow is 0.08
The probability that the bead is pink is 0.1
The probability that the bead is blue is 0.25
(a) (i) Find the probability that the bead is yellow or blue.
..............................................
(ii) Find the probability that the bead is neither yellow nor pink.
..............................................
(4)
Ajit replaces the first bead in the jar.
He then takes at random a second bead from the jar.
(b) Find the probability that the first bead is yellow and the second bead is blue.
..............................................
(2)
7. 7
*P44613A0724* Turn over
A second jar contains 100 coloured beads.
20 of these beads are brown.
Ajit takes at random a bead from the jar.
He records the colour of the bead and then returns the bead to the jar.
He does this 60 times.
(c) Work out an estimate for the number of times Ajit records a brown bead.
..............................................
(2)
(Total for Question 5 is 8 marks)
6 Solve 4(5y – 1) = 3(6y + 7)
Show clear algebraic working.
y = ..............................................
(Total for Question 6 is 3 marks)
8. 8
*P44613A0824*
7 Eloy’s height was 125 cm when his age was 7 years.
His height was 153 cm when his age was 12 years.
(a) Work out the percentage increase in Eloy’s height between the ages of 7 and 12 years.
..............................................%
(3)
Eloy’s height at the age of 12 years was 85% of his height at the age of 20 years.
(b) Work out Eloy’s height when his age was 20 years.
.............................................. cm
(3)
(Total for Question 7 is 6 marks)
Do NOT write in this space.
9. 9
*P44613A0924* Turn over
8
ABC is a triangle.
The point D lies on AC.
Angle BDC = 90
BD = 10 cm, AB = 15 cm and DC = 12.5 cm.
(a) Calculate the length of AD.
Give your answer correct to 3 significant figures.
.............................................. cm
(3)
(b) Calculate the size of angle BCD.
Give your answer correct to 1 decimal place.
..............................................
(3)
(Total for Question 8 is 6 marks)
Diagram NOT
accurately drawn
A
15 cm
12.5 cm
10 cm
B
CD
10. 10
*P44613A01024*
9 (a) Find the sum of the interior angles of a polygon with 7 sides.
..............................................
(2)
The diagram shows a regular polygon with 7 sides.
(b) Work out the value of x.
Give your answer correct to 1 decimal place.
..............................................
(2)
(Total for Question 9 is 4 marks)
Diagram NOT
accurately drawn
x
11. 11
*P44613A01124* Turn over
10 (a) Find the gradient of the line with equation 3y – 2x = 6
..............................................
(2)
(b) Find an equation of the line with gradient –3 that passes through the point (2, 5).
..............................................
(2)
(Total for Question 10 is 4 marks)
12. 12
*P44613A01224*
11
3780 = 22
× 33
× 5 × 7 3240 = 23
× 34
× 5
(a) Find the highest common factor (HCF) of 3780 and 3240
Give your answer as a product of prime factors.
..............................................
(2)
(b) Find the lowest common multiple (LCM) of 3780 and 3240
Give your answer as a product of prime factors.
..............................................
(2)
(Total for Question 11 is 4 marks)
13. 13
*P44613A01324* Turn over
12 Solve the simultaneous equations
5y – 4x = 8
y + x = 7
Show clear algebraic working.
x = ..............................................
y = ..............................................
(Total for Question 12 is 3 marks)
14. 14
*P44613A01424*
13 The cumulative frequency graph gives information about the intelligence quotients (IQ)
of a random sample of 100 adults.
(a) Use the cumulative frequency graph to find an estimate for the number of adults in
the sample who have an IQ between 85 and 115
..............................................
(2)
(b) Find an estimate for the upper quartile of the IQ of adults in the sample.
..............................................
(2)
(Total for Question 13 is 4 marks)
Cumulative
frequency
100
80
60
40
20
0
60 80 100 120 140
IQ
15. 15
*P44613A01524* Turn over
14
P, Q, R and S are points on a circle, centre O.
QS is a diameter of the circle.
QS and PR intersect at the point T.
OS = 5 cm, QT = 3 cm and TR = 6 cm.
Work out the length of PT.
.............................................. cm
(Total for Question 14 is 3 marks)
Diagram NOT
accurately drawn
O
T
R
P 3 cm
5 cm
6 cm
Q
S
16. 16
*P44613A01624*
15
Zane buys mineral water in large bottles and in small bottles.
The large bottles are mathematically similar to the small bottles.
Large bottles have a height of 32 cm and a volume of 2000 cm3
Small bottles have a volume of 500 cm3
Work out the height of a small bottle.
Give your answer correct to 3 significant figures.
.............................................. cm
(Total for Question 15 is 3 marks)
2000 cm3
500 cm3
Diagram NOT
accurately drawn
32 cm
17. 17
*P44613A01724* Turn over
16 Gemma has 9 counters.
Each counter has a number on it.
1 2 3 4 5 6 7 8 9
Gemma puts the 9 counters into a bag.
She takes at random a counter from the bag and does not replace the counter.
She then takes at random a second counter from the bag.
(a) Work out the probability that the number on each counter is an even number.
..............................................
(2)
(b) Work out the probability that the number on the first counter added to the number on
the second counter gives an odd number.
..............................................
(3)
(Total for Question 16 is 5 marks)
18. 18
*P44613A01824*
17 P is directly proportional to q3
P = 270 when q = 7.5
(a) Find a formula for P in terms of q
..............................................
(3)
(b) Work out the positive value of q when P = q
q = ..............................................
(2)
(Total for Question 17 is 5 marks)
19. 19
*P44613A01924* Turn over
18 y = x3
– 4x2
+ 4x + 3
(a) Find
d
d
y
x
..............................................
(2)
The diagram shows a sketch of the curve with equation y = x3
– 4x2
+ 4x + 3
The point P is a turning point on the curve.
(b) Work out the coordinates of P.
Show clear algebraic working.
(................................ , ................................)
(4)
(c) Write down the range of values of x for which the curve has a negative gradient.
..............................................
(2)
(Total for Question 18 is 8 marks)
y
x
P
O
20. 20
*P44613A02024*
19
The Venn diagram shows all of the elements in sets A, B and E.
(a) Write down the elements in A
..............................................
(1)
(b) Find n(A ∩ B)
..............................................
(1)
(c) Find the elements in (A B) ∪ (A ∪ B)
..............................................
(1)
A ∩ C = Ø
B ∪ C = {5, 6, 7, 8, 9}
n(C) = 3
(d) Write down the elements in C.
..............................................
(1)
(Total for Question 19 is 4 marks)
Do NOT write in this space.
E
A
2 3 8 5
7
1 4
B
10 9 6
21. 21
*P44613A02124* Turn over
20 f:x 2x2
+ 1 g:x
2
1
x
x −
where x 1
(a) Express the composite function gf in the form gf:x ...
Give your answer as simply as possible.
gf:x ..............................................
(2)
(b) Express the inverse function g–1
in the form g–1
:x ...
g–1
:x ..............................................
(3)
(Total for Question 20 is 5 marks)
22. 22
*P44613A02224*
21
A solid cone has a height of 15 cm.
The volume of the cone is 320 cm3
Work out the curved surface area of the cone.
Give your answer correct to 3 significant figures.
.............................................. cm2
(Total for Question 21 is 5 marks)
Diagram NOT
accurately drawn
15 cm
23. 23
*P44613A02324*
22
The diagram shows a triangle ABC.
AB = (2x + 1) cm, AC = (2x – 1) cm and BC = 2 7 cm.
Angle BAC = 60
Work out the value of x.
Show clear algebraic working.
x = .............................................
(Total for Question 22 is 3 marks)
TOTAL FOR PAPER IS 100 MARKS
Diagram NOT
accurately drawn
C
A
60
(2x + 1) cm
(2x – 1) cm 2 7 cm
B