MATHEMATICS REVISION WORKSHEET - 2 YEAR 10 · Page 1 of 13 MATHEMATICS REVISION WORKSHEET - 2 YEAR...

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MATHEMATICS REVISION WORKSHEET - 2

YEAR – 10

1. Each student in a group of 32 students was asked the following question.

“Do you have a desktop computer (D), a laptop (L) or a tablet (T )?”

Their answers showed that

19 students have a desktop computer

17 students have a laptop

16 students have a tablet

9 students have both a desktop computer and a laptop

11 students have both a desktop computer and a tablet

7 students have both a laptop and a tablet

5 students have all three.

(a) Using this information, complete the Venn diagram to show the number of students ineach

appropriate subset.

One of the students with both a desktop computer and a laptop is chosen at random.

(b) Find the probability that this student also has a tablet.

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2.

a) Solve algebraically (Ans correct to 3 s.f )

x2 + y

2 = 28

y = x + 3

b) Solve 3x – 4y = 8

9x + 5y = - 1. 5

3. The diagram below shows a 6-sided shape.

All the corners are right angles.

All measurements are given in centimetres.

The area of the shape is 25 cm2.

Show that 6x2 + 17x – 39 = 0

Solve to find the value of x.

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4. Sameena has a round pencil case and a square pencil case.

There are 4 blue pens and 3 red pens in the round pencil case.

There are 3 blue pens and 5 red pens in the square pencil case.

Sameena takes at random one pen out of each pencil case.

(a) Complete the probability tree diagram.

(b) Work out the probability that the pens Sameena takes are both same colour.

5. AB is a chord of a circle centre O.

The radius of the circle is 30 cm.

Angle AOB = 80°

Work out what percentage of the area of the circle is shaded.

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6. There is a coastguard station at point A and at

point B.

B is due East of A.

The distance from A to B is 12 km.

There is a rowing boat at point R.

R is on a bearing of 160° from A.

R is on a bearing of 220° from B.

There is a speedboat at point T.

T is 5 km due South of A.

Work out the shortest distance from T to R.

Give your answer correct to 1 decimal place.

You must show all your working.

7. The table gives information about the number of students at a school.

Priya is going to survey 60 of the students in the school.

She is going to use a sample stratified by year group.

Work out the number of year 9, year 10 and year 11 students Priya

should have in her sample.

You must show all your working.

8.Clive wants to estimate the number of bees in a beehive.

Clive catches 50 bees from the beehive.

He marks each bee with a dye.

He then lets the bees go.

The next day, Clive catches 40 bees from the beehive.

8 of these bees have been marked with the dye.

a) Work out an estimate for the number of bees in the beehive.

b) Write down any assumptions you have made.

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9. Tom grows tomatoes.

The box plot below shows the distribution of the weights of 15 of Tom’s tomatoes.

(a) Work out the interquartile range.

Jack also grows tomatoes.

Here are the weights, in grams, of 15 of Jack’s tomatoes.

153 155 158 164 166 167 170 170 173 174 175 175 177 179 186

(b) On the grid below, draw a box plot for this information.

(c) Compare the distribution of the weights of Tom’s tomatoes with the distribution of

the weights of Jack’s tomatoes.

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10. Here are two pots.

Pot A and pot B are mathematically similar.

The area of the base of pot B is 160 cm2.

Work out the area of the base of pot A.

11. A model car 24cm long has a volume of 375cm3. What is the length of a similar model

car with a volume of 81cm3

12. In the diagram, PQ is parallel to ST.

PQ = 8 cm, QR = 6 cm and ST = 20 cm

a) Explain why triangles PQR and

TSR are similar.

You must give reasons for any statements you make.

b) Work out the length of SR.

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13. OAB is a triangle.

A is the midpoint of OZ

Y is the midpoint of AB

X is a point on OB

OA

= a OX

= 2b XB

= b

Prove that XYZ is a straight line.

14.

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15.

The diagram shows a farmer’s field ABC.

The farmer decides to grow potatoes in the region of the field which is

• nearer to A than to C and

• nearer to AB than to AC.

Using a straight edge and compasses only,

construct two loci accurately and shade this region on the diagram

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16. a) Complete the table of values for .

x

0 1 2 3 4 5 6 7 8

y

8 18 18 8 0

b) On the grid, draw the graph of for 0 ≤ ≤ 8

d) find the solutions for

= 16

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17. ABCD is a quadrilateral.

Work out the length of DC.

Give your answer correct to 3 significant figures.

18. Mr and Mrs Adams sold their house for £168 000.

They made a profit of 12% on the price they paid for the house.

Calculate how much they paid for the house.

Ivan invests HK$40 000 for 3 years at 2% per year compound interest.

Work out the value of the investment at the end of 3 years.

19. R is inversely proportional to the square of c.

When c = 4, R = 30

(a) Find a formula for R in terms of c.

(b) Calculate the positive value of c when R = 1920.

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19.

ABCDEFGH is a regular octagon.

KLQFP and MNREQ are two identical regular

pentagons.

Work out the size of the angle marked x.

You must show all your working

20.

The radius of a sphere is 3 cm.

The radius of the base of a cone is also 3 cm.

The volume of the sphere is 3 times the volume of the cone.

Work out the curved surface area of the cone.

Give your answer as a multiple of .

Diagram accurately drawn

NOT

3 cm

3 cm

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21.

22. Reflect Triangle A in the line x = - 1

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23.

a) Calculate the acceleration at A, B, C and D on the graph

b) Calculate the distance travelled between time 3 seconds to 8 seconds

MATHEMATICS REVISION WORKSHEET - 2 YEAR 10 · Page 1 of 13 MATHEMATICS REVISION WORKSHEET - 2 YEAR...

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