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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 - Data Handling & Statistics-2

Answer the following

The stem and leaf diagram shows a sample of 50 scores in a boy’s golf tournament.

a) Write down the median golf score.

b) Calculate the interquartile range & semi-interquartile range for these scores

2. The histogram shows information about the time, t minutes, spent in a shop by each of 80 people.

Complete the frequency table

3. The time taken for each of 120 students to complete a cooking challenge is shown in the table.

(i) Write down the modal time interval.

(ii) Calculate an estimate of the mean time.

(iii)Complete the cumulative frequency table.

(iv)On the grid, draw a cumulative frequency diagram to show this information.

(v) Find the median time. ......................................... min
(vi) Find the interquartile range. ......................................... min
(vii) Find the number of students who took more than 37 minutes to complete the cooking challenge
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IGCSE Mathematics Worksheet - Number 3

Answer the following

11. The ratios of teachers : male students : female students in a school are 2 : 17 : 18. The total number of students is 665. Find the number of teachers.

12.A recipe for tomato soup uses tomatoes and onions in the ratio 7 : 2. If 21 kg of tomatoes are used, how many kilograms of onions are needed?

13. The ratio of flour sugar cocoa in a cake recipe is 2 : 1 5 : 0 5

If 10 kg of flour is used, how much: a sugar b cocoa is used?

14. On a particular day, 1 Australian dollar is worth 0:94 US dollars.

How many Australian dollars can be exchanged for $20 US?

15. For her holiday, Alyssa changed 2800 Malaysian Ringgits (MYR) to US dollars ($) when the exchange rate was 1 MYR = $0.325 . At the end of her holiday she had $210 left.
(a)How many dollars did she spend?
(b) She changed the $210 for 750 MYR. What was the exchange rate in dollars for MYR?

16. A train leaves Zurich at 2240 and arrives in Vienna at 0732 the next day. Work out the time taken.

17. A plane took 1 hour and 10 minutes to fly from Riyadh to Jeddah. The plane arrived in Jeddah at 23 05. At what time did the plane depart from Riyadh?

18. 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.

19.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?

20. Alex invests $200 for 2 years at a rate of 2% per year simple interest. Chris invests $200 for 2 years at a rate of 2% per year compound interest. Calculate how much more interest Chris has than Alex.
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IGCSE Mathematics Worksheet - Number 2

Answer the following

1. Find the lowest common multiple (LCM) of 20 and 24.

2. Write 0.00658 (a) in standard form, (b) correct to 2 significant figures.

3. Round 39.748 to the nearest:

a whole number b one decimal place c two decimal places

4. Round:

a 5.371 to 2 significant figures

b 0:0086 to 1 significant figure

c 423 to 1 significant figure

5. The sides of a triangle are 5.2cm, 6.3cm and 9.4cm, each correct to the nearest millimetre. Calculate the lower bound of the perimeter of the triangle

6. The length of a rectangle is 9.3cm, correct to 1 decimal place. Its width is 7.7 cm, correct to 1 decimal place. Write down the lower bound and the upper bound for the area of the rectangle.

7. S = D/T
In an experiment D and T are both measured correct to 2 significant figures.

When D =7.6 and T = 0.23, find the upper bound for S

8. A circle has a radius of 8.5cm correct to the nearest 0.1cm. The lower bound for the area of the circle is pπcm^2. The upper bound for the area of the circle is qπcm^2.

Find the value of p and the value of q.

9. A map is drawn to a scale of 1 : 1000 000. A forest on the map has an area of 4.6cm^2. Calculate the actual area of the forest in square kilometres.

10. The map alongside has a scale of 1 : 500 000, which means that 1 cm on the map represents 500 000 cm in real life.

a If the distance BC = 2:1 cm on the map, find the actual distance between B and C.

b If E and C are 13:5 km apart, find the length of EC on the map.

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IGCSE Mathematics Worksheet - Number 1

Answer the following

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IGCSE Mathematics Worksheet - Similar Shapes-1

Answer the following

1. The two trapezia below are similar. Find the values of x and y.

2. Explain why the two triangles below are similar. Calculate the lengths marked a and b

3. State whether or not the triangles ABC and XYZ are similar. Show working to support
your answer.

4. Show that triangles ABC and APQ are similar and calculate the length of AC and BP

5. AB is parallel to CD.
Lines AD and BC intersect at point O.
AB = 11 cm. AO = 8 cm. OD = 6 cm.

Calculate the length of CD
.

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