Download Math: If I flip n fair coins, what is the probability of getting all tails

Math:
If I flip n fair coins, what is the probability of getting all tails?
Games:
Calculate
a. -7 -9 =
b. -8 + 5 =
Number:
Write the missing numbers and the next 3 numbers in each sequence.
Data:
This bar line chart shows number of minutes students spend to get to school.
What number of minutes is the mode?
How many students in total?
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Algebra:
Write the next two terms of the Fibonacci sequence:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, . . .
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Measures:
What units would you use to measure:
a. The length of your classroom
b. The mass of your body
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Interesting questions:
Why do the recurring decimals occur?
Why do we need to study angles?
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Data:
1. On average, for every 7 sedans, 4 sports cars are sold by a car shop. The shop
predicts that it will sell 28 sports cars next month. How many sedans does it
expect to sell?
Number:
2. Jane needs to replace a light bulb, which is 10 cm bellow the ceiling. The
ceiling is 2.4 meters above the floor. Jane is 1.5 meters tall and can reach 46 cm
above the top of her head. Standing on a chair, she can just reach the light bulb.
What is the height of the chair?
3. How many whole numbers between 1 and 1000 do not contain the digit 1?
4. Order these numbers from the smallest to the largest. 108, 512 and 224.
Geometry:
5. Which of the following shapes has the largest number of symmetry lines:
a. equilateral triangle
b. non-square rhombus
c. non-square rectangle
d. isosceles trapezium
e. square
6. The length of a rectangle is increased by 10% and the width decreased by
10%. What fraction is the new area of the old area?
Number:
Here are multiplication tables written in a code. The tables are not in the correct
order. Find the digit, represented by each letter.
a x f = jc
b x f = he
g x f =f
h x f = ai
c x f = ge
f x f = ea
j x f = ca
d x f = bc
e x f = af
i x g = bf
f x g = de
a x g = ec
d x g = ei
cxg=g
h x g = fa
g x g = dh
e x g = cd
b x g = ab
s x q = lp
p x q = no
k x q = om
n x q = os
mxq=q
r x q = pk
q x q = nr
o x q = mn
l x q = kl
Number:
1. Write these numbers in words.
a. 7495
b. 4362
2. Multiply.
a. 7 x 9
b. 8 x 6
3. Even or odd?
a. 678
b. 543
Geometry:
4. Draw parallel lines and perpendicular lines. Give examples of parallel and
perpendicular around you.
5. Draw right-angled, isosceles, equilateral and scalene triangles.
Measures:
6. Write in miles.
a. 320 km
b. 480 km
Number:
1. Write the floor where each lift ends its journey.
a. starts at ground floor, goes down one floor
b. starts at 4, goes down 10 floors
2. Write the difference between:
a. 10 and -4
b. 6 and – 3
3. Calculate:
a. 18 x 8 =
b. 6 x 17 =
c. 4 x 9.3 =
4. Work out:
a. 4083 – 3298 =
b. 3115 – 1551 =
5. Calculate:
a. 5.71 + 2.46 =
b. 4.36 + 5.39 =
6. Write these percentages as two different fractions.
a. 90%
b. 75%
7. Calculate:
a. 73% of $80
b. 61% of $120
8. Complete:
a. 02 =
b. 92 =
9. Which of these numbers are square numbers?
a. 86
b. 36
c. 50
d. 81
Probability:
10. Write one of the words (impossible, unlikely, likely or certain) beside each
statement.
a. I will find a four-leaf clover today.
b. I will walk more than ten steps today.
c. I will land on Mars tonight.
11. A coin is flipped 10 times. Write impossible, unlikely, likely or certain for
each statement.
a. Six throws were tails.
b. We had 6 tails and 6 heads.
12. Write one of these categories (no chance, poor chance, even chance, good
chance or certain) for each statement.
a. I will use a computer today.
b. I will see a dragon tomorrow.
c. I will walk twenty miles this year.
13. True or false?
a. If you drop a piece of toast there is a good chance that it will land butter side
down.
b. If you spin a coin twice, you have a good chance of getting heads twice.
c. It is impossible to get 6 sixes in a row when you throw a 1 – 6 dice.
Geometry:
14. Draw these angles.
a. 141o
b. 38o
15. Two angles make a right angle. If this is the size of one, write the size of the
other.
a. 63o
b. 57o
16. Three angles make a right angle. If these are the sizes of the first two, write
the size of the third angle.
a. 42o, 17o
b. 8o, 69o
17. Two angles make a right angle. What are the angles if one is as follows?
a. five times the other
b. four times the other
18. Jane turns clockwise. What type of angle (acute, obtuse or reflex) does she
move if she goes from:
a. East to South-West
b. North to North-West
19. True or false?
a. The angles of a regular hexagon are all obtuse angles.
b. A triangle cannot have more than one obtuse angle
20. Draw these polygons.
a. a quadrilateral with one reflex angle
b. a triangle with two acute and one obtuse angle
Number:
1. True or false?
a. 10 x 101 is the same as 100 x 11
b. 10 lots of 50 pounds and 5 pence 55 pounds
Measures:
2. Write these in liters
a. 3500 ml
b. 679000 ml
3. Write as kilograms
a. 12000 g
b. 4500 g
4. Write as tones.
a. 5600 kg
b. 48000 kg
5. Write as meters.
a. 4 km
b. 7 km
Number:
1. Write < or > between each pair of numbers.
a. –6 … –12
b. -15 … 1
2. Write 10% of each amount.
a. $76
b. $ 39
3. Multiply.
a. 9 x 3.87 =
b. 4 x 8.64 =
4. Add.
a. 6.73 + 3.84 =
b. 3.67 + 2.25 =
5. Subtract.
a. 7269 – 3542 =
b. 7636 – 2172 =
6. The ratio of blue to orange tiles is 3:5. Write the number of the orange tiles in
the set of:
a. 56 tiles
b. 40 tiles
7. At a bird table, the ratio of robins to blue-tits is 1:4, if there are 24 blue-tits,
how many robins?
8. In a mug of tea the ratio of tea to milk is 7:2. If a mug holds 270 ml, how much
milk and how much tea?
9. How many prime numbers are between 30 and 40?
10. Which of these numbers are prime?
76, 43, 2, 7, 65
Geometry:
11. What is the perimeter of square with the side length of 7cm?
12. Draw a non-square rectangle. Draw it after the rotation 90 degrees clockwise
around one if its vertices.
Measures:
13. Calculate number of hours in these time periods.
a. 1 April 2012 to 30 April 2012
b. 1 October 2012 to 31 December 2012
14. Write each quantity in liters.
a. 300 ml
b. 90 cl
15. Write < or > between each pair of length of times.
a. 1 week … 161 hours
b. 1 fortnight … 20 days
16. True or false?
a. there are twice as many minutes in 5 hours as in 900 seconds
b. There are more fortnights in a year than days in a month
17. Write the number of days in each month.
a. January
b. February
c. April
18. Write the number of days between.
a. 20 July 2012 and 4 September 2012
b. 25 September 2012 and 24 November 2012
Data:
19. True or false?
a. the probability of throwing a 6 on a fair dice is less than the probability of
throwing a 1.
b. it is less likely to draw a black card than a red card from a pack of ordinary
cards.
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Number:
1. Write each of these recurring decimals as fractions in their lowest terms.
a. 0.111111111… =
b. 0.222222222… =
c. 0.333333333… =
d. 0.44444444… =
e. 0.55555555… =
f. 0.66666666… =
g. 0.0909090909… =
2. What is the next square number after 36?
3. Can I get from 24 to 27 by keeping adding 0.4?
Algebra:
4. Find the million-th square number and the million-th triangular number.
Square numbers are the following: 1, 4, 9, 16,…
Triangular numbers are the following: 1, 3, 6, 10,…
5. What are the LCM and HCF for 4 and 6?
Geometry:
6. Draw supplementary, complementary, corresponding, alternate, interior,
exterior and reflex angles.
Statistics:
7. What is primary data and what is secondary data?
8. What is a biased sample and how to avoid it?
9. Write impossible, unlikely, even chances, likely or certain:
a. you will fly to the Moon this week
b. there will be a sunset tomorrow
Algebra:
1. A computer is programmed to start at 5 and count on in steps of 3.
a. Write the first four terms of this sequence.
b. Is this sequence finite or infinite?
2. Calculate the first five terms of each of these sequences.
a. first term 3, term-to-term rule x4 + 1
b. first term 1, term-to-term rule x3 + 4
3. Is this sequence arithmetic? Why yes or why not? 2, 5, 7, 10, 12, 15, . . .
4. Calculate the first five terms of the sequence with position-to-term rule
(2 x position number) + 10
5. What is the term-to-term rule for the sequence with position-to-term rule
(2 x position number) + 10
6. What are the connections between the term-to-term rule and the position-toterm rule for the sequence?
(2 x position number) + 10
7. Calculate the values of these expressions.
a. (9 + 11) x 3
b. 3 + 4 x 5
8. Simplify these expressions.
a. 4f + 6f
b. 9p – 2p
Number:
9. Write the value, in words, of the seven in each of these numbers.
a. 3.708
b. 37.665
10. True or false?
a. 4.25 x 100 = 425
b. 3.2 x 10 = 0.32
11. Calculate both square roots of these numbers.
a. 49
b. 121
12. True or false?
a. 421 x 6 = 5226
b. 47 x 5 = 235
Geometry:
13. 18 cm is a perimeter of a regular hexagon. Find the length of one of the sides
of the hexagon.
14. Two equilateral triangles have all sides 4.4 cm. These two equilateral
triangles are joined along one side to make a rhombus. What is the perimeter of
this rhombus? Calculate the sides lengths of squares, which have the same
perimeter as the triangle and the rhombus, respectively.
Measures:
15. Draw lines, measuring
a. 49 mm
b. 5.5cm
16. Mass of each fruit is 140 g. A box contains 20 of such fruits. What is the mass
of the fruits in the box?
17. A garden is 60m long. Using a scale of 1:1000, draw a line to represent this
length.
Probability:
18. These are the numbers of DVDs bought by different people last year.
11 13 11 20 14 8 14 8 11
Calculate the range and the mode of this dataset.
19. 16, 14, 18, 15, 19, 18, 21, 15, 18, these are times in seconds, taken by ten kids
to run 100 m. Calculate the median and the mean of this dataset.
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Number:
1. Write each of these recurring decimals as fractions in their lowest terms.
a. 0.111111111… =
b. 0.222222222… =
c. 0.333333333… =
d. 0.44444444… =
e. 0.55555555… =
f. 0.66666666… =
g. 0.0909090909… =
h. 0.08333333333… =
Algebra:
2. Find inverse functions to these functions.
a. y = 2 – x
b. y = 7x + 5
3. Find the million-th square number and the million-th triangular number.
Square numbers are the following: 1, 4, 9, 16,…
Triangular numbers are the following: 1, 3, 6, 10,…
4. What are the LCM and HCF for 4 and 6?
Geometry:
5. Draw supplementary, complementary, corresponding, alternate, interior,
exterior and reflex angles.
Statistics:
6. What is primary data and what is secondary data?
7. What is a biased sample and how to avoid it?
8. Write impossible, unlikely, even chances, likely or certain:
a. you will fly to the Moon this week
b. there will be a sunset tomorrow
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Used this for the test paper:
1. Calculate approximate gravity acceleration at the planet where a pendulum of
length L = 1 meter swings back and forth once in 1 second (T = 1 second). Take 
= 3.
Thus, L = 1,  = 3 and T = 1.
Here is the formula: g 
-
4 2 L
T2

Number:
1. Calculate.
a. -6 + 2
b. -2 – 7 + 11
2. Calculate.
a. 6 x -4
b. 2 x -14
3. Calculate these by evaluating the bracket first:
a. -7(-9 + 2)
b. -5(8 - 4)
4. Calculate these by expanding the bracket first:
a. -9(-8 + 10)
b. -6(2 - 5)
5. Convert these percentages into fractions.
a. 62%
b. 15%
Algebra:
6. For each sequence write the next 3 terms and the term-to-term rule.
a. 13, 9, 5, 1, . . .
b. 13, 16, 19, 22, . . .
7. The first term of a sequence is 5. The term-to-term rule is: multiply by 4, then
subtract 10.
What are the next 3 terms of the sequence?
8. True or false?
a. 5, 10, 20, 40, . . . is an arithmetic sequence
b. 5, 8, 11, 14, . . . is an arithmetic sequence
9. Write the next 3 terms of these sequences.
a. 100, 81, 64, 49, . . .
b. 4, 7, 12, 19, . . .
Geometry:
10. Using compasses draw two circles of radius 4 cm that overlap. Join the center
points with the points where the circles overlap. What is the name of the
quadrilateral that you have just drawn?
11. Draw a straight line of 9cm length. Using only a ruler and compasses,
construct the perpendicular bisector to this line.
12. Draw angle of 78 degrees size. Using only a ruler and compasses, construct
the bisector of this angle.
13. The interior angle of a regular polygon is 170 degrees. How many sides does
the polygon have? Calculate the size of the exterior angle.
Measures:
14. True or false?
a. seven liters are about the same as three pints
b. two pounds are about the same as one kilogram.
15. Convert these speeds into kilometers per hour.
a. a sprinter can run at a speed of 10 m/s
b. a bullet can fly at a speed of 1000 m/s
16. Put these volumes in order from smallest to largest.
9.5 cm3, 0.01m3, 950mm3
Statistics:
17. How likely it is to get all 10 heads after flipping a fair coin 10 times? Is it
possible in real life to get all 10 heads like this? Is it almost impossible?
18. Draw a frequency table and record the outcomes of flipping a fair coin and
rolling an eight-sided fair dice. What is the probability of getting a head and an
even number?
19. Choose positive, negative or no correlation to describe the relationship
between:
a. time it takes a girl to run 400 m and to run 800 m
b. the distance a boy can jump in the long jump and time it takes him to run 100
m
Algebra:
1. True or false?
a. the third term of the sequence 4n + 2 is 14
b. the tenth term on the sequence 2 – n is 8
2. Draw a coordinate grid on square paper with x-axis going from -2 to 4 and yaxis going from -10 to 10. Create a table of values for the function y = 2x – 5 from
x = -2 to 4. Plot a graph of the function.
3. Put these equations in order, starting with the steepest.
y = 2x – 3
y = 5x – 10
y = 3x + 5
4. John goes on holiday by car. He drives at an average speed of 60 mph for 1.5
hours and then stops for a rest for half an hour. He then continues his journey at
an average speed of 50 mph for another 1.5 hours. Draw a distance-time graph to
show his journey.
5. Write an expression for each of the following.
a. add u to v, then halve the result
b. square n
6. True or false?
a. the value of 2n when n = 9 is 18.
b. the value of 2n when is 6 is 26
Number:
7. There are 64000 spectators at a soccer match. Out of all the spectators, 0.125
are girls, 0.15 are boys, 0.38 are men and the rest are women. Calculate the
numbers of girls, boys, men and women watching the soccer match.
8. Calculate 3501.75 – 25.9 + 147.3845 =
9. A mass of fully loaded a track is 31.62 tones. Three crates are unloaded. The
masses of the crates are 1.75 ton, 1.86 ton and 0.0275 ton. Calculate the mass of
the track and its remaining load.
Geometry:
10. True or false?
a. the angles 98 degrees and 92 degrees are supplementary angles
b. if two of the angles in a triangle are 47 degrees and 105 degrees, then the third
angle must be 28 degrees.
11. Decide whether each statement is a definition, a convention or a derived
property.
a. an equilateral triangle has 3 equal sides and 3 equal angles.
b. a right angle is represented on a diagram using a small square
c. the interior angles of a pentagon sum to 540 degrees.
12. Write down formulas you can use to find the circumference of a circle. Write
down the formula to find the area of a circle.
13. A basketball hoop is a circle with a diameter of 46 cm. Find the circumference
of the basketball hoop. A basketball has the largest radius of 12 cm. Find the
largest circumference of the basketball.
14. Find the areas of a circle with a diameter of 46 cm and a circle with a radius
of 12 cm.
15. The London Eye has a circumference of 424 m. Calculate the radius of the
London Eye.
16. A ball covers a distance of 8.8 meters in one complete roll. What is the
diameter of the ball?
17. A square has an area of 100 square cm. What is the perimeter of the square?
18. A full oil tank in the shape of a cube contains 3375 liters of oil. Calculate the
length of the side of the oil tank.
19. A disc has diameter 12 cm and thickness 0.8 mm. Calculate the volume of a
stack of 28 discs.
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Number:
1. Work out
-3 + 10 – 2 =
12 x – 6 =
2. Rewrite using index notation
3x3x3x3=
3. Find all the factor pairs for these numbers.
48
72.
Algebra:
4. For each sequence, identify the term-to-term rule and write the next two
terms.
200, 100, 50, 25, . . .
19, 16, 13, 10, . . .
5. What is an arithmetic sequence?
6. Multiply out these brackets.
5(2m + 3)
4(6 + y)
7. Multiply out each bracket and simplify the expression.
-3(2 – y + z)
9(7x - 2) + 8x(3 + x + 2y)
Geometry:
8. Prove that all interior angles in a triangle add up to 180 degrees. Use the
definitions of alternate, corresponding, complementary, supplementary, vertical
and straight angles.
9. Prove that all interior angles in a quadrilateral add up to 360 degrees.
10. Construct an equilateral triangle with the side length of 5cm using only rulers
and compasses.
11. Draw a circle. Show radius, center of circle, diameter and circumference.
12. Calculate the length of a circumference for each of the following radiuses:
1m
20cm
30mm.
Measures:
13. List metric and imperial units.
14. Convert the speed of each animal to kilometers per hour (km/h).
racehorse 20m/s
cheetah 25m/s
sea lion 10m/s
antelope 15m/s
15. Convert these amounts to the units shown.
10 pints (liters)
2 gallons (liters)
16. The volumes of some containers are 1.01cm3 and 1000mm3. Which one is
larger?
Statistics:
17. If I flip 5 fair coins, what is the probability of getting all heads up?
18. What is estimated probability?
19. What is theoretical probability?
20. What is the probability of getting 7 in total by rolling two regular fair sixsided dice?
Project:
21. Describe your math project for this semester.
Number:
1. Convert these decimals to fractions. Give your answers in their simplest form,
as the lowest term.
0.725
0.46
3.2
0.602
2. Write these as fractions.
0.2222222... =
0.8888888... =
0.5555555… =
0.6666666… =
0.7777777… =
3. Convert each percentage into a fraction in its simplest form.
98%
55%
17%
19%
35%
4. There was a 20% discount in a sale. If a coat had a sale price of $38, what was
the original selling price?
Geometry:
5. Calculate the surface area of a cylinder with the height of 20cm and with the
radius of the base 5cm.
6. Calculate the volume of a cylinder with the height of 20cm and with the radius
of the base 5cm.
7. Which quadrilaterals could you make by putting these shapes together?
a. two congruent right-angled triangles
b. two congruent isosceles triangles
8. Define enlargement, reflection, rotation, translation and congruence.
9. Draw a pair of axes from 0 to 10. Draw the triangle with vertices (2, 3), (4, 3)
and (4, 6). Draw an enlargement of the triangle with scale factor 2 and center of
enlargement (3, 4).
10. An object has vertices at (3, 2), (6, 2), (4, 4) and (7, 4). The image given by an
enlargement has vertices at (2, 1), (8, 1), (4, 5) and (10, 5).
Draw the shape on suitable axes.
Identify the shape.
Work out the scale factor.
Find the center of enlargement.
11. An object has vertices at (1, 1), (1, 3), (4, 1) and (4, 3). The image given by an
enlargement has vertices at (-3, -3), (-3, 3), (6, -3) and (6, 3).
Draw the shape on suitable axes.
Identify the shape.
Work out the scale factor.
Find the center of enlargement.
12. An object has vertices at (-1, -1), (-1, -4) and (-5, -1). The image given by an
enlargement has vertices at (2, 5), (10, 5) and (2, 11).
Draw the shape on suitable axes.
Identify the shape.
Work out the scale factor.
Find the center of enlargement.
13. John draws a triangle on a set of axes and enlarges it with scale factor -1 and
with the center of enlargement (0, 0). Find and describe another transformation
that would have exactly the same effect.
Algebra:
14. Simplify these expressions by collecting like terms:
12a + 18b + 4a – 8b =
12a + 18b – 4a + 8b =
13a + 10b + 8a + 3b =
15. Work out each of these expressions.
8–4x5=
80 – 3 x 7 =
3+4x5=
16. Work out each of these expressions when a = 3 and b = 5.
7 – 8b =
7(2a + b) =
3 + 5b =
2a(3 – 2b) =
17. Work out these expressions.
(a + b)2 – c, when a = 5, b = 2 and c = 1
3a2b, when a = 3 and b = 4
18. Write an expression in terms of x for each of these descriptions.
a. 5 less than one third of x
b. 7 more than half of x
19. Alison is x years old. Jane is two years older than Alison.
Write an expression for the age of Jane.
If the sum of their ages is 24, write an equation in terms of x.
Solve your equation to find the age of Alison.
20. Solve each equation.
7x – 5 = 44
3 + 5x = 68
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Algebra:
1. Find the turning points of these functions:
y = 3x2 – 12x – 10
y = - 2x2 + x + 8
2. Solve these equations:
3x2 – 12x – 10 = 0
- 2x2 + x + 8 = 0
3. Calculate the Schwarzschild radiuses for your chair, desk, pen and pencil.
Number:
4. What is a rational number?
5. What is an irrational number?
Theories:
6. What is Game theory?
7. What is Dilemma of a Prisoner in Game theory?
8. What is Chaos theory?
9. What is Fractal?
10. What is self-similarity?
11. What is Cryptography?
12. What is Econometrics?
13. What is Knot theory?
14. What is Second Law of Kepler?
Statistics:
15. A rare disease is breaking out in a town. If nothing is done, 600 people will
die. There are two possible options. Option A will save 200 people. Option B will
either save everyone or no one. It has a 1/3 probability of saving everyone.
What is the probability that option B will save no one?
Which option would you choose? Why?
16. There is a test for disease A that is 98% accurate. One out of 200 people have
disease A, and 10 000 tests are performed.
In the sample of 10 000 people, how many are likely to have disease A?
How many of the people with disease A will test positive?
How many people without disease A will test positive?
John receives a positive test result. What is the probability that he has disease A?
17. Two people make a hexagonal spinner labeled 1 to 6. Each adds up their
scores from two spins. Make up 3 pairs of rules, which give them both the same
chance of winning.
18. The sweets in one bag (A) are equal numbers of sour grapes, flying saucers,
strawberry laces and sherbet lemons. In another bag (B) there are equal
numbers of flying saucers, sour grapes and sherbet lemons. Nathan says that
there is more chance of picking a sherbet lemon from bag A than bag B. Is he
right or not? Why?
19. During one year, 0.7% of a hospital admissions were for broken legs. 70% of
these people were male and 30% were female. 0.4% of the hospital admissions
were for broken arms. These were divided equally between men and women.
The hospital has at total of 10 000 admissions annually.
How many are for women with a broken leg?
How many are for men with a broken arm?
How many are for women with a broken arm and a broken leg? Why?
20. John and Sharon play a game. A fair, six-sided spinner is marked with the
letters of the name of Sharon. If it lands on a vowel, Sharon gets 3 points. If it
lands on a consonant, John gets 2 points. It is spun twice and the points totaled.
Is it a fair game or not? Why?
If it is unfair, suggest a way of making it fair.
Statistics:
1. An airline calculates that the probability of a passenger being disabled is 0.01.
Each plane carries 300 people, and 4 seats are allocated to disabled people. Is
this likely to be sufficient or not? Why?
The airline carries 2.4 x 106 passengers per year. How many of these are likely to
be disabled?
2. Explain why these statements cannot be quite true.
My train has been delayed three days in a row. It cannot possibly be late again
today.
There is a 50% chance that the next baby born in our city will be male.
3. Work out the probability that a person chosen at random from each of these
groups of Internet users did not log on during the past week.
a. In a group of 36 people under the age of 30, 28 people did log on.
b. In a group of 750 people between the age of 30 and 75, 575 did log on.
c. In a group of over-75s, 72 out of 240 people did log on.
4. In a clinical trial, medicine A was compared with medicine B. Patients with a
certain illness were given either medicine A or medicine B at random.
20 out of the 60 patients given medicine A showed a noticeable improvement.
20 out of the 70 patients given medicine B showed a noticeable improvement.
Which medicine seems to be more effective? Why?
In a second trial, only 50 patients were given medicine B, and 20 of these
patients again showed a noticeable improvement. Which seems to be the more
effective medicine now?
5. Doctors wanted to see, which method worked better for giving up smoking:
nicotine patches (P) or nicotine chewing gum (G). Of 360 people given patches,
240 managed to stop smoking by the end of a month. Of 500 people given gum,
320 manage to stop smoking by the end of a month.
Write the probability of success with each method. Compare the probabilities
and say, which method was more effective.
Algebra:
6. Each of these expressions can be written in the form (x + a)2, where a is a
whole number that is either positive or negative. Find a for each expression.
a. x2 – 8x + 16
b. x2 – 26x + 169
c. x2 + 20x + 100
7. Factorize each of these expressions.
a. x2 + 10x + 21
b. x2 + 8x + 16
8. Each of these expressions can be written in the form (x + a)(x - a), where a is a
positive whole number. Find a for each expression.
a. x2 – 64
b. x2 – 9
c. x2 - 144
9. Solve the equation 3x + 4 = 25. Write what you did to both sides to solve it.
10. ax + 4 = bx + c. This formula has x on both sides.
Rearrange it by copying and completing the following: . . . . . . = c – 4.
Factorize the left hand side.
Make x the subject of the formula.
11. The sum of two consecutive integers is 91. What are the values of these
integers?
12. The sum of two consecutive even numbers is 102. What are the values of
these integers?
Number:
13. Does squaring numbers always make them bigger or not? Why?
14. A three-digit number is multiplied by a two-digit number. What are the
minimum and the maximum numbers of digits that the answer could have? Why?
Geometry:
15. Find four different triangles that have whole-number side lengths, at least
two equal sides and a perimeter of 18cm.
By putting your answers in order, or otherwise, prove that there are no any
other triangles that fit all of these conditions.
16. There is a mathematical theorem, which states that any triangle, formed by
drawing lines from any point on the circumference of a circle to the two ends of a
diameter, is right angled.
Draw a circle and check this theorem for yourself. Try three different triangles.
Have you created a practical demonstration or a proof?
17. M is the mid-point of the line AB. Find the coordinates of M for these lines.
a. A(1, -6), B(7, -6)
b. A(4, 7), B(-4, 5)
18. The mid-point of the line segment made by joining the points (-3, 5) and (x, y)
is (3, 0). Find the values of x and y.
19. A 32-inch widescreen TV has a width of 27.89 inches and a diagonal of 32
inches. Work out its viewable area in square centimeters.
Measures:
20. Convert each of these to liters.
a. 37000cm3
b. 7000cm3
-
Algebra:
1. Use these term-to-term rules to find the first five terms of each sequence.
a. Start at 50, divide by 2, then subtract 3.
b. Start at -5, add 2, then multiply by 2.
2. Write the first 4 terms of each sequence.
a. T(n) = 1 – 4n
b. T(n) = 4n – 1
3. Use the pattern of first differences to generate the next term in each sequence.
a. -4, 0, 6, 14, . . .
b. 7, 8, 10, 13, . . .
4. Generate the first 4 terms of each sequence.
a. T(n) = (n2 - 1)/2
b. T(n) = n2 + 10
5. n-th term of a sequence is given by: T(n) = (n + 1)(n+ 2) + n
Write the first 5 terms.
6. For each sequence work out the n-th term using the pattern of differences.
a. 0, 10, 20, 30, 40, . . .
b. 4, 14, 24, 34, 44, . . .
c. 70, 60, 50, 40, 30, . . .
7. Design your own pattern sequence. Work out the n-th term and explain it by
reference to the physical pattern.
8. Find 5 consecutive terms for each of these expressions.
a. n2
b. 10n2
c. n(n + 2)
d. n2 + n + 1
9. Work out the difference pattern for each of these expressions.
a. n2
b. 10n2
c. n(n + 2)
d. n2 + n + 1
10. Each of these quadratic sequences has its n-th term in the form T(n) = an2.
Use the pattern of differences to find the n-th term.
a. 2, 8, 18, 32, 50, . . .
b. 4, 16, 36, 64, 100, . . .
11. Each of these quadratic sequences has its n-th term in the form T(n) = an2 +
b.
Use the pattern of differences to find the n-th term.
a. 11, 14, 19, 26, 35, . . .
b. -1, 5, 15, 29, 47, . . .
12. Each of these quadratic sequences has its n-th term in the form T(n) = an2 +
bx + c.
Use the pattern of differences to find the n-th term.
a. 6, 13, 24, 39, 58, . . .
b. -4, -3, 0, 5, 12, . . .
13. Draw a mapping diagram for each function for x = 0 to x = 5.
a. x  2x – 3
b. x  3 – 2x
14. Using suitable positive and negative values of x, plot the graph of each
function.
a. x  3x
b. x  2x – 3
15. Find the inverse of each function.
a. x  3x
b. x  2x – 3
16. Expand these.
a. 4x(3x + 6y)
b. 2x2(3y – 4x)
17. Expand and simplify these.
a. p(2p + 3d -1) + 4p(5d – 3 + 2w)
b. b2(3b + 2c2 + 4f) – 2b(b2 – 5bc2 + bf)
18. Solve these equations.
a. 6x + 4 = 3x + 13
b. 9x – 5 = 7x + 5
c. x + 14 = 22 – 3x
d. 8 – 4x = 4x - 8
19. Which of these three equations gives the odd solution out?
A. 3(x + 5) = x + 25
B. 3(2x - 5) = 2(x + 6) – 5
C. 4(x - 2) = 3(9 - x)
20. Solve these equations.
a. 2(4x - 1) = 7x – 5(x + 4)
b. 6 – 3(4 – 2x) = 7(x - 3)
c. 5 + 2(2x + 3) = 23 – 4(3x - 5)
Algebra:
1. Use trial and improvement to find the solution to the equation x3 = 780 to one
decimal place.
2. A solution to the equation x3 + 3x2 – 750 = 0 lies between 8 and 9. Use trial and
improvement to find a solution to the equation to two decimal places.
3. Solve each pair of simultaneous equations.
a. x + 3y = 22 and x + y = 10
b. x – 2y = 1 and x + 2y = 13
c. 4x + 3y = 32 and – x – 3y = - 26
d. 2x + 7y = 24 and 5x + 7y = 39
4. Solve each pair of simultaneous equations.
a. 3x + y = 10 and 2x + 5y = 24
b. 3x – y = 21 and x + 5y = 23
c. -2x +3y = 7 and -5x + y = - 28
d. 4x + 3y = 5 and 2x + 7y = 19
Number:
5. Write these numbers in descending order.
-6.09, -6.7, -5.99, -5.75, -6.52, -5.9
Which of these numbers are greater than -6.5?
6. Write true or false for each of these.
a. 3.566 > 3.656
b. 6.77 < 6.599
c. 0.03389 > 0.0337
d. 28.989 > 28.99
7. Put the correct inequality sign between each pair of temperatures.
a. – 12.55
7.95
b. -3.57
-3.75
c. -8.82
-8.9
8. Write each of these ratios in its simplest form.
a. 4cm : 5m
b. 25c : $6
c. 15 hours : 2 days
d. 8 months : 3 years
9. Work out
a. 33 – 7 x 2 =
b. 53 – 52 – 5 =
c. (62 – 2 x 17)3 =
10. Calculate:
a. 62 x 0.1 =
b. 62 x 0.01 =
c. 3.8 x 0.1 =
d. 38 x 0.01 =
e. 120 x 0.01 =
f. 0.5 x 0.01 =
g. 369 x 0.1 =
h. 12 000 x 0.01 =
11. Calculate:
a. 0.6 x 0.4 =
b. 0.02 x 0.3 =
c. 0.15 x 0.02 =
d. 1.2 x 0.9 =
Geometry:
12. Explain how to find the size of the exterior angle of a regular octagon.
13. Calculate the size of the interior angle and the exterior angle of a regular
decagon.
14. The exterior angle of a regular polygon is 12 degrees. How many sides does
the polygon have? Calculate the size of one of the interior angle.
15. True or false?
a. The hypotenuse is the shortest side of a right-angled triangle.
b. The hypotenuse is the side opposite the right angle.
16. True or false?
a. The numbers 5, 12 and 13 are a Pythagorean triple.
b. The numbers 9, 12 and 15 are a Pythagorean triple.
c. The numbers 15, 20 and 30 are a Pythagorean triple.
d. The numbers 25, 60 and 65 are a Pythagorean triple.
17. Draw a straight line of length 10cm. Using only a ruler and compasses, draw
the perpendicular bisector of the line.
18. Use a protractor to draw an angle of 70 degrees. Using only a ruler and
compasses, draw the bisector of this angle.
19. Using only a ruler and compasses, make an accurate drawing of the triangle
with the sides lengths of 5cm, 6cm and 9cm.
20. Draw a circle of 3cm radius. Mark radius, diameter, chord and circumference
on that circle.
Geometry:
1. Draw a circle of radius 5 cm. Mark any three points on the circumference of
the circle and join them up to make a triangle. Construct the perpendicular
bisector of each side of your triangle. Write down what you notice.
Statistics:
2. Jane wants to know, which sport people like to watch most on television. She
asks the members of her athletics club. Give the reasons why her sample could
be biased.
3. Mary is doing a survey on healthy eating. She has written this question.
Do you agree that take-away food is bad for you?
The options for the answers are:
agree
do not know
Write down things that are wrong with her question.
4. Nathan is doing a survey on public transport. He has written his question.
Do you think there are enough buses running during the rush-hour?
What is wrong with his question? Write better question to find out views of
people on the number of buses running during the rush-hour.
5. There are four numbers. One of them is five. The range of the numbers is 6.
The mode of the numbers is 8. What are the missing numbers?
6. There are five unknown numbers. The median of the numbers is 9. The mode
of the numbers is 3. The range of the numbers is 10. The mean of the numbers is
8. What are the numbers?
7. Which of these outcomes are mutually exclusive?
A. a boy or a girl
B. a rugby player or a basketball player
C. someone who likes math or who likes science
D. someone who is the same height as you or is taller than you?
Measures:
8. Convert each of these areas to square centimeters.
a. 15 m2
b. 0.1 m2
c. 15 mm2
d. 15000 mm2
9. True or false?
a. 5 cm3 = 50 mm3
b. 0.55 cm3 = 55 mm3
c. 500 cm3 = 0.0005m3
d. 5000000 cm3 = 5 m3
10. Convert 3500 cm3 to liters.
Number:
11. True or false?
a. 0.2222222. . . = 22/100
b. 0.6363636363… = 7/11
c. 0.3333333… = 3/9
12. Convert into fractions.
a. 0.555555… =
b. 0.52525252… =
c. 0.247247247247… =
13. Convert 0.999999… into a fraction. What do you notice? Explain this.
14. True or false?
a. 0.3 x 0.3 = 0.9
b. 0.02 x 0.5 = 0.01
0.7 x 0.7 = 0.49
15. Work out.
a. 1.73 + 0.173 + 173 + 0.00173 =
b. 17.3 – 0.0173 – 1.73 =
Algebra:
16. Find the highest common factor (HCF) of 12, 60 and 78.
17. Find the lowest common multiple (LCM) of 12, 16 and 36.
18. Use prime factor decomposition to find the HCF and LCM of 15, 35 and 50.
19. Simplify each expression. Leave your answer as power.
a. 23 x 25 =
b. 35 x 37 =
20. Simplify each expression. Leave your answer as power.
a. c93 x c7 =
b. a3 x a2 =
Algebra:
1. True or false?
a. b3 x b3 = 2(b3)
b. c3 x c3 = c9
2. Work out the value of each expression.
a. 30 =
b. 1000 x 32 =
3. Simplify each expression. Leave your answer as power.
a. (23)4 =
b. (24)3 =
4. Find the value of each expression. Give your answer as a fraction.
a. 2-1 =
b. 10-6 =
c. 5-3 =
d. 9-2 =
5. Which of these points lie on the line y = 3x -2?
A (2, 4)
B (4, 2)
C (3, 7)
D (0, -2)
E (-2, -8)
6. Plot these straight-line graphs on a coordinate grid with x values from –4 to +4
and y values from -10 to +10.
a. y = 2x + 1
b. y = -1 -2x
7. Rearrange these equations of straight lines into the form y = mx + c.
a. y + 2 = x
b. y – 2x = 6
c. 2x – 2y = 8
d. 0 = 3 – y - x
Statistics:
8. Alun has two boxes of chocolates.
The probability of getting a hard centered chocolate from box A is 12/20.
The probability of getting a hard centered chocolate from box B is 12/24.
Which box should Alun pick from to have the best chance of getting a hard
centered chocolate? Why?
9. On Halloween Bim and Carol give toffees to children playing Trick or treat.
Bim has 100 toffees, 10 of which have mustard inside!
Carol has 50 toffees, 10 of which have mustard inside!
If you were playing Trick or treat, would you have a higher chance of getting a
mustard toffee from Bim or from Carol?
10. Li has two bags of sweets.
The probability of getting a red sweet from bag A is 6/20.
The probability of getting a red sweet from bag B is 8/25.
Which bag should Li pick from to have the best chance of getting a red sweet?
Why?
11. A group of children are going to race their bikes around a circuit. Which of
these conditions are fair?
A. Everyone sets off at the same time.
B. The youngest child has a two-second head-start.
C. Everyone goes in turn and their time is recorded.
D. If there is a draw, the oldest child wins.
12. Three coins are dropped. Each coin can land either heads (H) or tails (T).
Write all the possible outcomes.
What is the probability of getting exactly two heads?
What is the probability of getting at least two tails?
13. Alice and Joe take it in turns to roll two dice and add the scores.
Write down the possible outcomes and their probabilities.
Before they roll the dice, they guess the total score. What score would you guess?
Why?
14. A box of chocolates contains hard centers, soft centers and liquid centers.
0.25 of the chocolates have a hard center and 0.6 have a soft center. Simon is first
to choose a chocolate. What is the probability that he chooses a chocolate with a
liquid center?
15. Josef has two normal dice. He rolls the two dice and records the number
shown on them.
How many possible outcomes are there?
What is the probability of getting at least one prime number?
What is the probability of getting a total between 8 and 12?
16. A box contains 150 biscuits. The probability of picking a shortbread biscuit is
0.2, a chocolate-chip biscuit is 0.1, a wafer biscuit is 4/15 and a coconut biscuit is
1/6. The rest of the biscuits in the box are custard creams.
What is the probability of picking a custard cream?
How many custard creams are in the box?
17. In a bag there are five 10p coins and five 2p coins. One coin is picket up at
random from the bag and is put back. Another coin is then picket at random from
the bag.
Draw a tree diagram to represent the possible outcomes.
What is the probability of picking two 10p coins?
What is the probability of picking one 10p and one 2p coin?
18. In a bag there are 5 red balls and 3 blue balls. One ball is picked up at random
from the bag and is put back. Another ball is then picket at random from the bag.
Draw a tree diagram to represent the possible outcomes.
What is the probability of picking two red balls?
What is the probability of picking one red and one blue ball?
19. In a survey of 100 dinner ladies, 14 were vegetarians and the rest were not.
Of the vegetarians, 2 wore glasses and 4 wore contact lenses.
Of the non-vegetarians, 6 wore glasses and 25 wore contact lenses.
Draw a tree diagram to represent this information, giving the probabilities on
each branch.
20. A supermarket survey of 100 shoppers found that eight of them only go to
the supermarket on Sundays.
In an average week, the supermarket has 20000 customers.
How many of these customers are likely to go to the supermarket only on
Sundays?
Number:
1. The mass of the Earth is 5.97 x 1024 kg. The mass of the Moon is 7.35 x 1022 kg.
How many times is the Earth more massive than the Moon?
2. John puts his old car for sale for $400. If he does not sell the car, at the start of
each following week he will reduce the price by 10% and then round the new
price to the nearest $10.
At the start of the second week, what is the price of his car?
At the start of the fifth week, what is the price of his car?
He sells the car for $150. During which week did he sell it?
Algebra:
3. Use factors to work out the square root of 784.
4. Use factors to work out the cube root of 729.
5. John has two bulbs, A and B, that turn on and off in a regular pattern. Bulb A
turns on, stays on for 4 s and then terns off and stays off for 4 s. Bulb B turns on,
stays on for 7 s and then terns off and stays off for 7 s. John turns both bulbs on
at the same time. How long will it be before both bulbs turn on again at the same
time?
6. Alun, Bradley and Collister are counting drumbeats. Alun hits a kettledrum
every two beats. Bradley hits a snare every five beats. Collister hits a bass every
eight beats. Alun, Bradley and Collister start hitting their drums at the same time.
How many beats is it before they next hit their drums at the same time?
7. Factorize these expressions completely.
a. 4a2b2 + 8a3b =
b. 9c4d5 + 9c5d4 =
8. Expand each bracket and simplify each expression.
a. 4a2(a2 + b3) + 3b3(2a2 - 3)
b. x3(x2 + y2) – x2(y2 + x3) – x(y2 –x4)
9. Multiply out the brackets for each expression and then simplify.
a. (x + 5)(x + 5)
b. (2x + 5)(2x + 5)
10. Factorize each of these expressions.
a. x2 + 15x + 56
b. x2 + 11x + 30
11. For each mathematical statement write down examples to show that it is not
always true.
a. -2x < 2x
b. x > 1/x
12. Make x the subject of each of these formulas.
a. 0.4x + y = a
b. 5x + 2a = 8p
13. A personal fitness trainer charges her customers $p per hour for gym work
and $r per hour for equipment work. She also charges $s per mile to travel to her
customers. Write a formula for the cost, C, for training a customer who lives m
miles away for x hours of gym work and y hours of equipment work.
Geometry:
14. Draw x- and y- axes from -8 to 8. Draw the shape with vertices (2, 2), (7, 2),
(5, 5) and (3, 5). Label the shape A.
Rotate shape A 90 degrees anticlockwise about the point (0, 1) and then reflect it
in the line y = 2. Label your new image B.
Reflect shape B in the y-axis then translate it one square right and one square up.
Label your new image C.
What single transformation will map shape C into shape A?
15. The volume, V, of a square-based pyramid is given by the formula V = S2h/3,
where S is the side length of the base and h is the height.
Find the volume of a square-based pyramid when S = 10 cm and h = 21 cm.
16. A column is 50 m tall. Man stands 50 m from the base of the. What are the
angles of the triangle made by the point of where man stands and the bottom and
the top of the column?
Statistics:
17. Draw scatter graphs with all possible types of correlation:
a. no correlation
b. very strong positive correlation
c. very strong negative correlation
d. strong positive correlation
e. strong negative correlation
f. weak positive correlation
g. weak negative correlation
18. In a class, 28 of 31 students finished their project. A student was chosen at
random from the class. What is the probability that he or she had not finished his
or her project?
19. A survey about netball was carried out on 100 Year 7 girls. Of the girls
questioned, 3/10 said they preferred to be center, 1/5 said they preferred to be a
defender and 0.25 said they preferred to be an attacker. The rest of the girls had
never played netball, so had no preference. What is the probability of a Year 7
girl never having played netball?
Number:
1. Write each of these recurring decimals as fractions in their lowest terms.
a. 0.111111111… =
b. 0.222222222… =
c. 0.333333333… =
d. 0.44444444… =
e. 0.55555555… =
f. 0.66666666… =
g. 0.0909090909… =
h. 0.08333333333… =
i. 0.076923076923… =
2. What is the role of the digit 9 in establishing a simple link between recurring
decimals and fractions?
3. Which of these represent a proportional weight gain?
a. Gain 20 N of your body weight in two weeks
b. Gain five percent of your body weight in one week
c. Gain 0.1 of your body weight in one month
Algebra:
4. Find inverse functions to these functions.
a. y = 2 – x
b. y = 7x + 5
5. Find the million-th square number and the million-th triangular number.
Square numbers are the following: 1, 4, 9, 16,…
Triangular numbers are the following: 1, 3, 6, 10,…
6. Find the formulas for the first and second differences to this sequence:
T(n) = 0.5n2
Find the formulas for velocity (gradient of the distance) and acceleration
(gradient of the velocity) for this distance-time equation:
d = 0.5t2
What is the velocity? What is the acceleration?
You can draw distance-time graph and speed-time graph to help you.
What do you notice about the differences for the sequence and the gradients to
the distance and velocity?
7. Try to match each term-to-term definition to the correct position-to-term
definition.
a. Start at 2, add 5 each time.
b. Start at 0, add 5 each time.
c. Start at 5, add 2 each time.
A. Multiply the term number by 5, then subtract 3.
B. Multiply the term number by 2, then add 3.
C. Multiply the term number by 5, then subtract 5.
8. How many times larger or smaller will be the height of an astronaut traveling
at the velocity v = 0.8c, according to Einstein? Will the height become larger or
smaller?
hs  h E 1 

v2
c2
Here hE is the height of an astronaut on Earth and hs is the height of an astronaut
in the spaceship traveling with the velocity v.
9. What are the LCM and HCF for 4 and 6?
10. What is the next term in this sequence? 5, 7, 9, …
Geometry:
11. What are the coordinates of turning points of these parabolas and are those
turning points minimums or maximums?
a. y = -2x2 + 7
b. y = 4x2 - 5
12. Draw supplementary, complementary, corresponding, alternate, interior,
exterior and reflex angles.
13. Calculate.
a. sin 0 =
b. cos 0 =
14. The length of a rectangle is increased by f% and the width decreased by the
same f%. What fraction is the new area of the old area?
15. The width (w centimeters) of first rectangle is smaller than its height (h
centimeters). w is increased by d centimeters. h is decreased by the same
number of d centimeters. Thus, there is second rectangle with side lengths of
w+d and h-d with the same perimeter as the first rectangle. Find d through w
and h so that the area of second rectangle is the largest (How much do I need to
increase w and to decrease h so that the area becomes the largest for the same
perimeter?).
Statistics:
16. What is primary data and what is secondary data?
17. What is a biased sample and how to avoid it?
18. Write impossible, unlikely, even chances, likely or certain:
a. you will fly to the Moon this week
b. there will be a sunset tomorrow
-
Geometry:
1. Prove that out of all rectangles with height h, width w and perimeter of 20cm,
the square has the largest area A. Prove this for any perimeter p.
p = 2(h + w)
A = hw
w = 0.5p – h
A = h(0.5p - h) = -h2 + 0.5ph study this parabola and find h for the largest A.
For p = 20 this parabola becomes: A = -h2 + 10h
2. Calculate.
a. sin 90o =
b. cos 60o =
c. sin 30o =
d. tan 45o =
e. tan 90o =
Algebra:
3. If in the year 2212 a velocity v of a spaceship travels is 0.8 of the speed of light
c: v = 0.8c, how many times would a mass of an astronaut traveling on this
spaceship and time to this astronaut change compared to those on the Earth
according to the Special Theory of Relativity?
These are the formulas:
tE
Ts 
v2
1 2
c

Ms 
mE
1

v2
c2
Here Ts and Ms are time and mass of the astronaut in the spaceship and tE and mE
on the Earth, v is the velocity of the spaceship and c is the speed of light.
Number:
4. Capacitors can be joined together in series or parallel.
In series 1/C = 1/C1 + 1/C2
In parallel C = C1 + C2
Calculate the combined capacitance of these capacitors.
1. Calculate the radius r to which you need to compress the soccer ball to make a
black hole out of it. The mass of the soccer ball is m = 0.5 kg.
r

2Gm
c2
m = 0.5
the speed of light c = 3 x 108
gravity constant G = 7 x 10-11
2. Prove Pythagoras theorem.
Prove that H2 = L12 + L22
ABDC and EFGJ are squares.
The side of ABDC is L1 + L2.
 
The side of EFGJ is H.
AFE, FBG, GCJ and JDE are congruent right-angled triangles with hypotenuse H
and with legs L1 and L2.
-
Science:
Best science questions:
Chemistry:
2. Look at this reactivity series. The most active elements are on the left and the
least active elements are on the right.
Mg→Al→Mn→Zn→Cr→Fe→ Co→Ni→
Pb→H→Cu→Hg→Ag→Pd→Pt→Au
Explain possible substitution reactions.
Physics:
Write and explain distance-time and speed-time formulas for a bullet fired at a
given angle of release alpha with the given initial velocity V0. Neglect the air
resistance and neglect rotation of the bullet. Consider the bullet as an infinitely
small material point. Assume that only gravity acts on the bullet after the bullet
was fired. What is the largest height (altitude) of the bullet? At what angle of
release the bullet flies the largest distance and why? Write the expressions
through g, alpha and V0. g is the gravity acceleration.
-
1. What are the applications of gravity surveys? How can they help to predict
earthquakes and tsunamis?
Your pendulum starts oscillating quicker. Does it mean that the gravity became
stronger or weaker? Why?
Note that the larger is the gravity acceleration g, the stronger is the gravity.
Look at this formula for pendulum oscillation to help you:
L
g
Here T is the time taken for the pendulum to swing back and forth,  = 3 is a
constant. L is the length of the pendulum and g is gravity acceleration. On Earth g
= 10 approximately.
T  2

You fly to another planet and you need a gravity survey to know g on that planet.
There for the pendulum of L = 1m, T = 1 second. What is g on that planet? Give
the units.
Physics:
1. Write down and explain the formulas of the Newton Second Law, gravitational
attraction between the objects with given masses and given distance between
their centers of gravity, pressure formula through the force and the area,
moment of force formula through the lever and the force, Law of Ohm and
Kirchhoff Law.
2. Write down and explain the formulas of the gravitational attraction between
the objects with given masses and given distance between their centers of
gravity, pressure formula through the force and the area, and moment of force
formula through the lever and the force.
3. Explain the milk and soap experiment.
4. How do artificial satellites get into and stay in orbit?
5. What are the main types of artificial satellites and their uses?
6. What was the first artificial satellite?
Chemistry:
Used this for paper:
7. What is a chemical reaction?
8. Balance these symbol equations:
a. __H2 + O2  __H2O
b. __C8H18 + __O2  __CO2 + __H2O
c. __Mg + __ TiCl4  __ MgCl2 + __Ti
9. Complete this symbol equation:
__Cr2O3 + __Al  _________ + __Cr
Project:
10. Describe your science project for this semester.
Physics:
1. What is acceleration or deceleration a result of?
2. What does the gradient at the distance-time graph show?
3. What does the slope of the speed-time graph show?
4. What are the main stages of a parachute jump?
5. Why does letting out some air from a vehicle tires help to get out of the mud?
6. Why do structures (such as buildings and bridges) do not collapse?
7. How does a shaduf help to get water out of the river?
8. How can people increase the force using hydraulics?
9. Why can pneumatic tires be used as shock absorbers?
10. What angle of release results in the largest distance?
11. Why does a balloon deflate after being cooled down?
12. Describe the mechanical model of electrical voltage.
13. What are the main methods of power generation today?
14. How was the gravity constant G calculated for the first time?
15. Who was the first to calculate the mass of the Earth? How did this person do
it?
Chemistry:
16. How would you protect the steel parts of your house?
17. Every 10 years you need to renovate your house to protect the steel parts of
your house from the rust. How would you remove the rust?
18. How do people combat the rust and why?
19. What law requires balancing chemical equations?
20. What are the reactivity series?
21. What would you expect to happen when aluminum carbonate is heated?
22. Describe displacement reactions.
23. What is an exothermic reaction?
24. What are the applications of chromatography?
Environment:
25. How would you improve the environment in Sunter?
26. How do you distinguish an acid rain from a non-acid?
27. How do people tackle acid rain?
28. How can acid rain damage your house?
29. What are the impacts of global warming?
Biology:
30. Why may kittens from the same litter be of different colors?
31. Why do we need to stop the decline of number of bees?
Medicine:
32. What diseases are mostly likely to be caused by smoking?
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Physics:
1. Describe the particle model.
2. Describe how you would use the principle of moments to water the plants
using shaduf to get water from the river.
Science:
What force is acting between an object falling in the air and the particles of the
air?
Insulation of houses pays for itself in one year. How would you prove this using
your knowledge about the energy transfers?