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GCSE Mathematics Worksheet - Probability

Answer the following

1. What is the probability of picking two doubles from a pack of dominoes? [Hint: There are 50 dominoes in a pack. 7 of them are doubles.]

2. John picks a card at random from a pack of 52 cards and throws a dice. What is the probability that he will pick the ace of spades and throw a six?

3. There are 300 seeds in a packet of flower seeds.Each seed will grow into a white flower or a yellow flower or a red flower. The probability of a seed growing into a white flower is 0.62. 45 of the seeds are expected to grow into yellow flowers. One of the seeds is chosen at random from the packet. What is the probability that this seed will grow into a red flower?

4. Martin has a pencil case which contains 4 blue pens and 3 green pens. Martin picks a pen at random from the pencil case. He notes its colour, and then replaces it. He does this two more times. Work out the probability that when Martin takes three pens, exactly two are the same colour.

5. Natalie has 8 socks in a drawer.
5 of the socks are black.
3 of the socks are white.
Natalie takes out a sock at random, writes down its colour and puts it back into
the drawer.Then Natalie takes out a second sock, at random, and writes down its colour. Draw tree diagram and Work out the probability that the two socks are the same colour.

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GCSE Mathematics Worksheet - Compound Measures-1-Notes

Distance-time graphs

In a distance-time graph, the gradient of the line is equal to the speed of the object. The greater the gradient (and the steeper the line) the faster the object is moving.
If an object is accelerating or decelerating, its speed can be calculated at any particular time by:
drawing a tangent to the curve at that time
measuring the gradient of the tangent

Velocity-time graphs

The gradient of the line is equal to the acceleration of the object.
The displacement of an object can be calculated from the area under a velocity-time graph.

Acceleration

Acceleration is the rate of change of velocity. It is the amount that velocity changes per unit time.
The change in velocity can be calculated using the equation:

change in velocity = final velocity - initial velocity

The average acceleration of an object can be calculated using the equation:

This is when:

acceleration (α) is measured in metres per second squared (m/s²)

change in velocity (∆v) is measured in metres per second (m/s)

time taken (t) is measured in seconds (s)

If an object is slowing down, it is decelerating (and its acceleration has a negative value).

Velocity, acceleration and distance

This equation applies to objects in uniform acceleration:

(final velocity)2 - (initial velocity) 2 = 2 × acceleration × distance

This is when:

final velocity (v) is measured in metres per second (m/s)

initial velocity (u) is measured in metres per second (m/s)

acceleration (a) is measured in metres per second squared (m/s2)

displacement (s) is measured in metres (m)

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IGCSE Mathematics Worksheet - Ratio & Proportion-2

Answer the following

1. Melissa is 13 years old. Becky is 12 years old. Daniel is 10 years old. Melissa, Becky and Daniel share £28 in the ratio of their ages. Becky gives a third of her share to her mother. How much should Becky now have?

2. Ann and Bob shared £240 in the ratio 3 : 5 Ann gave a half of her share to Colin. Bob gave a tenth of his share to Colin. What fraction of the £240 did Colin receive?

3. Peter won £75 as a prize. He gave 4/5 of the prize money as a present to Roger and Bethan. Roger and Bethan shared the present in the ratio 2:3 Work out how much they each got.

4. A shop sells CDs and DVDs. In one week the number of CDs sold and the number of DVDs sold were in the ratio 3:5 The total number of CDs and DVDs sold in the week was 728 Work out the number of CDs sold.

5. Rosa prepares the ingredients for pizzas. She uses cheese,topping and dough in the ratio 2 : 3 : 5 Rose uses 70 grams of dough. Work out the number of grams of cheese and the number of grams of topping Rosa uses.

6. Last year Kerry’s take home pay was £15 000 She spent 40% of her take home pay on rent. She used the rest of her take home pay for living expenses, clothes and entertainment in the ratio 3 : 1 : 2 How much did Kerry spend on entertainment last year?

7. Fred has a recipe for 30 biscuits. Here is a list of ingredients for 30 biscuits.

Self-raising flour : 230 g

Butter : 150 g

Caster sugar : 100 g

Eggs : 2

Fred wants to make 45 biscuits.

(a) Complete his new list of ingredients for 45 biscuits

Gill has only 1 kilogram of self-raising flour. She has plenty of the other ingredients.

(b) Work out the maximum number of biscuits that Gill could bake.

8. 4 men can build a shed in 20 hours. Calculate how long the same shed would take to build:
(a) if there was 1 man
(b) if there were 5 men.

9. The yield of wheat from 8 hectares of land is 360 quintals. Find the number of hectares of land required for a yield of 540 quintals?

10. 3 gallons of paint cover 900 square feet. How many gallons will cover 300 square feet?

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IGCSE Mathematics Worksheet - Number 1

Answer the following

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IGCSE Mathematics Worksheet- Sets & Venn Diagrams

Answer the following

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IGCSE Mathematics Important Questions/ Worksheet - Probability

Answer the following

1. Elena has a bag which contains 7 toffees, 4 mints and 2 chocolates.
Elena picks one of these sweets.
What is the probability that she chooses a:
a) mint b) mint or toffee c) mint or chocolate

2. 24 people come for a job interview.

9 of these people wear glasses and 4 of them have contact lenses.

Find the probability that the person chosen for the job:
a) has contact lenses
b) wears glasses
c) does not wear glasses or contact lenses

3. A dice is thrown 120 times.
How many times would you expect to get a:
a) 3 b) 5 c) 4 or 5 d) square number

4. The probability of Anu getting up before 11 a.m. on a Saturday
morning is 1/4. What is the probability of Anu not getting up before
11 a.m. on a Saturday morning?

5. Ahmed has some coins in his pocket. He has 5c, 10c and 50c coins. The
probability of choosing a 5c coin is 0·65. The probability of choosing
a 10c coin is 0·2.
a) What is the probability of choosing a 50c coin?
b) What is the probability of choosing a 10c coin or a 50c coin?

6. A bag contains 8 blue discs and 3 green discs.
One disc is removed at random then replaced.
Another disc is then removed.

a) Copy and complete the tree diagram to show all the outcomes.
Find the probability that:
b) Both discs are blue.
c) Both discs are green.
d) One disc is blue and one disc is green

7. A spinner is spun three times.

a) Copy and complete the tree diagram to show the probability of
getting a ‘two’.

b) Find the probability that the spinner lands on:
i) 3 two’s
ii) no two’s
iii) at least one ‘two’

8. There are 3 males and 5 females in a family of 8 people.

Two of the family members are chosen at random.

a) Copy and complete the tree diagram. Find the probability that:
b) Both people are female.
c) Exactly one person is female.

9. A bag contains 7 green counters and 3 purple counters.

A counter is taken at random and its color noted.

The counter is not returned to the box.

Then a second counter is taken at random and its color noted.

It also is not returned to the box.

Finally a third counter is taken at random, and its color noted.(without replacement)

Work out the probability that

i)all three counters are purple

ii)exactly one of the three counters is purple

iii)at least one of the three counters is purple

10. The probability of John doing more than 2 hours homework on a
Thursday evening is 0·6. If he does more than 2 hours homework, the
probability of seeing friends later that evening is 0·25. If he does 2 hours
or less homework, the probability of seeing friends later that evening is 0·7.

a) Draw a tree diagram to represent the above information.
b) Find the probability that John will see friends later that evening.

Answers for IGCSE Mathematics- Probability
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IGCSE Mathematics Worksheet-Variation -Direct & Inverse

Answer the following

1. If y ∝ x and y = 123 when x = 7.1, find:
a) y when x = 13.2
b) x when y = 391

2. The speed of a falling object is directly proportional to the time it falls. The speed after 5 seconds is 49 m/s.
a What will be the speed of a falling object after 8 seconds?
b How long will it take a falling object to reach a speed of 100 m/s?

3. T is directly proportional to d² and T = 100 when d = 2. Find:
a T when d = 3

b d when T = 200

4. M is directly proportional to the cube of x and when x = 2, M = 24. Find:
a the value of M when x = 3

b the value of x when M = 120

5. When a stone falls freely, the time taken to hit the ground varies in direct proportion to the square root of the distance fallen. If it takes a stone 4 seconds to fall 78.4 m, find how long it would take for a stone to fall 500 m down a mine shaft.

6. If M is inversely proportional to t and M = 200 when t = 3, find:
a M when t = 5
b t when M = 746 (to 2 d.p.)

7. The velocity V of a body travelling a fixed distance is inversely proportional to the time taken t to complete the journey. When the velocity is 40 cm/s, the time taken is 280 seconds.
Find the time when the velocity is 50 cm/s.

8. P varies inversely to the square root of g. When g = 9, P = 20:
a Find P when g = 4.
b Find g when P = 50

9. The time taken to complete a certain job varies inversely to the number of workers doing the task. If 20 workers could do the job in 6 days, find how long it would take 15 workers to do the job.

10. The resistance, R ohms, to the flow of electricity in a wire varies inversely to the area of the cross-section of the wire. When the area is 0.15 cm2, the resistance is 0.24 ohms. Find:
a the resistance when the area is 0.06 cm2
b the area when the resistance is 0.45 ohms.

Answers for IGCSE Maths Variation -Direct & Inverse
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IGCSE Mathematics Worksheet- Circle Theorems

Answer the following

Find the value of unknown

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IGCSE Mathematics - Percentages& Compound interest-Worksheet

Answer the following

1. Alex scored 72% for an examination out of 150 marks. How many marks did Alex score?

2. Petra has a monthly income of $4700. She does not have to pay any tax on the first $2400 she earns, but she has to pay 15% of the remainder as tax.

a How much tax does Petra have to pay?
b How much does Petra have left after tax?
c What percentage of the $4700 does Petra actually pay in tax?

3. A camera is purchased for €650 and is marked up by 20%

Find: a the profit b the selling price

4. Brad bought an old car for $600. He spent $1038 restoring it and sold it for $3500. Find his profit or loss on the sale.

5. Calculate the simple interest on a $4000 loan at a rate of 7% per annum over 3 years. Hence find the total amount to be repaid.

6. What rate of simple interest per annum would need to be charged on a loan of $20 000 if you wanted to earn $ 3000 in interest over 2 years?

7. The value of an old book has increased by 35% to $540. What was its original value?

8. A share trader buys a parcel of shares for $4250 and sells them for $3800.
Calculate the percentage decrease in the investment

9. Increase $3500 by 10% and then decrease the result by 14%

10. $5000 is invested at 8% p.a. compound interest with interest calculated annually.
a What will it amount to after 3 years? b Find the interest earned.

11. After 4 years a tractor purchased for €58 500 has a resale value of €35080.
Find its annual rate of depreciation.

12. Biathlete Jo cycles 60 km at a speed of 30 km/h, and then runs another 15 km at a speed of 10 km/h.
Find: a the total time b the average speed for Jo’s training session.

13. Ahmed earns $20000 each year.In 1991, he paid no tax on the first $3000 of his earnings. He paid 25% of the rest as tax.
Show that he paid $4250 as tax.

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