Easter Revision 2010 - Wikispacesbentonparkmaths.wikispaces.com/file/view/Getting+a+C+in...answer....

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Name………………….. Easter Revision 2010 GCSE Mathematics

Transcript of Easter Revision 2010 - Wikispacesbentonparkmaths.wikispaces.com/file/view/Getting+a+C+in...answer....

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Name…………………..

Easter Revision

2010

GCSE Mathematics

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Formulae sheet: Higher Tier

Volume of prism = area of cross section × length

length

crosssection

Volume of sphere = 3π3

4r

Surface of sphere = 4r2

r

Volume of cone = hr 2π3

1

Curved surface area of cone = rl l

h

r

In any triangle ABC

Sine rule C

c

B

b

A

a

sinsinsin

A

C

Bc

b a

Cosine rule a2 = b

2 + c

2 – 2bc cos A

Area of triangle = Cabsin2

1

The Quadratic Equation

The solutions of ax2 + bx + c = 0, where a 0, are given by

a

acbbx

2

)4–(– 2

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GCSE Grade C Maths Topics (Number)

Able to estimate the values of calculations involving positive numbers between zero and one

Work out an estimate for 51.0

96.9302

Able to write a number as the product of its prime factors

Express 84 as a product of its prime factors.

Find the LCM of 18 and 24.

Write out the 18 times table: 18, 36, 54, 72 , 90, 108, … .

Write out the 24 times table: 24, 48, 72 , 96, 120,

You can see that 72 is the smallest (least) number in both (common) tables (multiples). Able to work out the LCM and HCF of pairs of numbers

Find the Lowest Common Multiple of 120 and 150.

Find the HCF of 28 and 16. Write out the factors of 28. 1, 2, 4 , 7, 14, 28 Write out the factors of 16. 1, 2, 4 , 8, 16

You can see that 4 is the biggest (highest) number in

both (common) lists (factors).

Able to work out the LCM and HCF of pairs of numbers

Find the Highest Common Factor (HCF) of 84 and 35

a Find approximate answers to

b Use your calculator to find the correct answer. Round off to 3 significant figures Round each value to 1 significant figure

= = b) Using a calculator we find The display should say 349.9285714 which rounds off to 350. This agrees exactly with the estimate.

Able to use a calculator efficiently and know how to give answers to an appropriate degree of accuracy

Use your calculator to work out the value of 2

65.125.20

(a) Write down all the figures on your calculator

display.

...................................

(b) Write your answer to part (a) correct to 1

decimal place.

...................................

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Able to calculate with mixed numbers

Work out 53

2 – 2

4

3

A bank pays 6% compound interest per year on all amounts in a savings account. What is the final amount that Elizabeth will have in her account if she has kept £400 in her bank for three years? The amount in the bank increases by 6% each year, so the multiplier is 1.06, and

after 1 year she will have £400 x1.06 = £424 after 2 years she will have £424 x1.06 = £449.44

after 3 years she will have £449.44 1.06 = £476.41 (rounded) Able to work out compound interest problems

The value of a car depreciates by 35% each year. At the

end of 2007 the value of the car was £5460.

Work out the value of the car at the end of 2006.

Divide 63 cm in the ratio 3 : 4. An alternative method that avoids fractions is to add the parts: 3 + 4 = 7. Divide the original amount by the total: 63 ÷ 7 = 9. Then multiply each portion of the original ratio by the

answer: 3 x9 = 27, 4 x9 = 36. So 63 cm in the ratio 3 : 4 is 27 cm : 36 cm. Solve problems using ratio in appropriate situations

Amy, Beth and Colin share 36 sweets in the ratio 2 : 3 : 4

Work out the number of sweets that each of them receives.

Amy………….sweets Beth………….sweets

Colin…………..sweets

Able to multiply and divide numbers written in index form

(a) Write as a power of 7

(i) 78 ÷ 7

3

......................

(ii) 7

77 32

......................

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GCSE Grade C Maths Topics (Algebra)

Able to expand and simplify expressions

Expand and simplify 3(2x – 1) – 2(2x – 3)

Solve x2 + x = 13.

If x = 3 x2+ x = 32 + 3 = 12

If x = 4 x2+ x = 42 + 4 = 20

Try x = 33 x2+ x = 332 + 33 = 1419

Try x = 32 322 + 32 = 1344

Try x = 31 312 + 31 = 1271

Try x = 315 3152 + 315 = 130725

Try x = 314 3142 + 314 = 129996

x = 314 is a

solution (to two decimal

places) Able to solve equations using trial and improvement

The equation x3 – 2x = 67 has a solution between 4 and 5. Use a

trial and improvement method to find this solution. Give your

answer correct to one decimal place. You must show ALL your

working.

Able to rearrange simple formulae

Make t the subject of the formula v = u + 5t

Able to expand a pair of linear brackets to get a quadratic expression

Expand and simplify (x + 7)(x – 4)

Then plot the x and y coordinates

Able to draw quadratic graphs using a table of values

Complete the table of values for y = x2 + x.

x –3 –2 –1 0 1 2 3

y 6 2 0 6

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Find the nth term of the sequence

3, 7, 11, 15, 19, … The difference between consecutive terms is 4. So the first part of the nth term is 4n. Subtract the difference 4 from the first term 3, which gives 3 – 4 = –1. So the nth term is given by 4n – 1.

Able to give the nth term of a linear sequence

Here are the first 5 terms of an arithmetic sequence.

6, 11, 16, 21, 26

Find an expression, in terms of n, for the nth term of the sequence

Able to solve inequalities

Solve the inequality 6x – 3 < 9

Able to solve inequalities and represent the solution on a number line.

An inequality is shown on the number line.

–4 –3 –2 –1 0 1 2 3 4 (a) Write down the inequality.

(b) Solve 4x – 3 < 7 and draw the solution on a

number line.

Solve 2(y – 3) = 8

Solve 4x + 1 = 2x +12

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Able to solve linear equations GCSE Grade C Maths Topics (Geometry)

Able to find interior angles and exterior angles in polygons

Diagram NOT accurately drawn

The diagram shows part of a regular 10-sided polygon.

Work out the size of the angle marked x.

c= 65⁰ (Alternate angle) d= 65 (Vertically opposite angle) Able to use properties of intersecting and parallel lines.

D E F G

A B C

38º

xº yº

ABC is parallel to DEFG. BE = EF. Angle ABE = 38°.

Find the value of x. x = .............................

Work out the value of y. y = .............................

Able to solve problems in 2-D using Pythagoras’ theorem

ABC is a right-angled triangle. AC = 6 cm. BC = 9 cm.

Work out the length of AB. Give your answer correct to 3

significant figures. Diagram NOT accurately drawn

B

9 cm

A C6 cm

.

x

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Calculate the circumference of the circle.

Give your answer to three significant figures.

C = πd = π x5 cm = 15.7 cm (to 3 significant figures) Calculate the area of the circle.

Able to find area and circumferences of a circle

Able to calculate areas

The radius of the circle is 9.7 cm. Work out the area and

circumference of the circle. Give your answer to

3 significant figures.

The diagram shows a trapezium of height 3 m.Find the

area of this trapezium. State the units with our answer

2 m

6 m

3 m

Diagram accurately drawn

NOT

Able to calculate the volume of prisms and cylinders

A can of drink is in the shape of a cylinder. The can has a

radius of 4 cm and a height of 15 cm.

Calculate the volume of the cylinder.

Give your answer correct to 3 significant figures.

Enlarge the triangle ABC by scale factor 3 from the centre of enlargement (1, 2).

Able to enlarge a 2-D shape about any point

y

8

7

6

5

4

3

2

1

O 1 2 3 4 5 6 7 8 9 10 x On the grid, enlarge the shaded shape by scale factor of 2,

centre (1,1).

9.7 cm

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Able to enlarge a 2-D shape by a fractional scale factor

5

4

3

2

1

–1

–2

–3

–4

–5

54321–1–2–3–4–5

A

O x

y

On the grid, enlarge triangle A by scale factor 2

1, centre O.

Label your new triangle B. A skip has a mass of 220 kg measured to three significant figures. What are the limits of accuracy of the mass of the skip? The smallest possible value is 219.5 kg. The largest possible value is 220.49999999… kg but we say 220.5 kg is the upper limit. Hence the limits of accuracy are 219.5 kg ≤ mass of skip < 220.5 kg

Upper and lower bounds

The length of a line is 63 centimetres, correct to the nearest

centimetre.

Write down the least possible length of the line.

........................................ centimetres

Write down the greatest possible length of the line.

........................................ centimetres

Able to work out compound measures like speed.

An aeroplane flies from Liverpool to Prague, a distance of

1200 km.

The aeroplane takes 4 hours.

Work out the average speed of the aeroplane.

State the units of your answer.

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Able to calculate the gradient of a straight line and use

this to find speed from a distance–time graph.

Judy drove from her home to the airport. She waited at the

airport. Then she drove home. Here is the distance-time graph

for Judy’s complete journey.

1400 1430 1500 1530 1600 1630

Time of day

50

40

30

20

10

0

Distance

from home

(km)

Work out Judy’s average speed on her journey home

from the airport. Give your answer in kilometres per

hour.

Able to draw and describe the locus of a point from a given rule

Sketch the locus of all points that are exactly 3 cm

from the line PQ.

P Q

Draw the locus of all points which are equidistant from the

points A and B.

BA

To construct a line bisector

Draw arcs as shown below

then

Bisect the line AB.

BA

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To construct an angle bisector

Draw arcs as shown below

1. 2.

3.

Use ruler and compasses to construct an angle of 45 at A.

You must show all construction lines.

A Use vectors to describe the translations of the following triangles

7

6

5

4

3

2

1

–1

–2

–6 1–5 2–4 3–3 4–2 5–1 6

y

xO

Translate the triangle by the vector

3

4

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GCSE Grade C Maths Topics (Handling Data)

A survey was done on the number of people in each car leaving the Meadowhall Shopping Centre, in Sheffield. The results are summarised in the table. Calculate a the mode, b the median, c the mean number of people in a car.

The modal number of people in a car is easy to spot. It is the number with the largest frequency (198). Hence, the modal number of people in a car is 2. The median number of people in a car is found by working out where the middle of the set of numbers is located. First, add up frequencies to get the total number of cars surveyed, which comes to 505. Next, calculate the middle position (505 + 1) ÷ 2 = 253

Hence, the mean number of people in a car is 1446 ÷ 505 = 2.9 (2 significant figures).

Averages from discrete data

Rosie had 10 boxes of drawing pins.

She counted the number of drawing pins in each box.

The table gives information about her results.

(a) Write down the modal number of drawing pins in

a box.

.................................

(b) Work out the range of the number of drawing pins

in a box.

.................................

(c) Work out the mean number of drawing pins in a

box.

.................................

Number of

drawing pins Frequency

29 2

30 5

31 2

32 1

You use the midway value of each group, just as in estimating the mean.

• You plot the ordered pairs of midway values

with frequency, namely, (2.5, 4), (7.5, 13), (12.5, 25), (17.5, 32), (22.5, 17), (27.5, 9)

60 students take a science test.The test is marked out of 50.

This table shows information about the students’ marks.

Science mark 0–10 11–20 21–30 31–40 41–50

Frequency 4 13 17 19 7

On the grid, draw a frequency polygon to show this

information.

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Able to draw a frequency polygon for continuous data.

0 10 20 30 40 50

0

5

10

15

20

Science mark

Frequency

The graphs show the relationship between the temperature and the amount of ice cream sold, and that between the age of people and the amount of ice cream they eat.

a Comment on the correlation of each graph. b What does each graph tell you?

The first graph has positive correlation and tells us that as the temperature increases, the amount of ice cream sold increases. The second graph has negative correlation and tells us that as people get older, they eat less ice cream.

Recognise the different types of correlation.

Here is a scatter graph. One axis is labelled “Height”.

Height

For this graph, state the type of correlation.

From the list below, choose the most appropriate label for the

other axis.

length of hair, number of sisters

length of legs, GCSE French mark

The head of a school carries out a survey to find out how much time students in different year groups spend on their homework during a particular week. He asks a sample of 60 students and fills in a two-way table with headings as follows.

This gives a clearer picture of the amount of homework done in each year group.

Able to design questionnaires and surveys

The manager of a school canteen has made some changes. She

wants to find out what students think of these changes. She

uses this question on a questionnaire.

"How much money do you normally spend in the canteen?"

A lot Not much

Design a better question for the canteen manager to use.

You should include some response boxes.

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A girl took the mathematics test and scored 75 marks, but was ill for the English test. How many marks was she likely to have scored?

By drawing a line up from 75 on the mathematics axis to the line of best fit and then drawing a line across to the English axis. This gives 73, which is the mark she is likely to have scored in the English test.

Able to interpret a line of best fit.

The scatter graph shows the Science mark and the Maths mark

for 15 students.

60

50

40

30

20

10

10 20 30 40 50 60

Science mark

Mathsmark

Draw a line of best fit on the scatter graph Sophie’s Science mark was 42. Use your line of best fit to estimate

Sophie’s Maths mark.

The frequency table shows the speeds of 160 vehicles which pass a radar speed check on a dual carriageway.

a What is the experimental probability that a vehicle is travelling faster than 70 mph? b If 500 vehicles pass the speed check, estimate how many will be travelling faster than 70 mph. a The experimental probability is the relative

frequency, which is

b The number of vehicles travelling faster

than 70 mph will be That is, 500 ÷ 20 = 25 vehicles Able to calculate relative frequency from experimental evidence and compare this with the theoretical probability.

Here is a 4-sided spinner.

The sides of the spinner are labelled 1, 2, 3 and 4.

The spinner is biased.

The probability that the spinner will land on each of the

numbers 2 and 3 is given in the table.

The probability that the spinner will land on 1 is equal to

the probability that it will land on 4.

Number 1 2 3 4

Probability x 0.3 0.2 x

(a) Work out the value of x.

x = ………………….

Sarah is going to spin the spinner 200 times.

(b) Work out an estimate for the number of times it

will land on 2

…………………….

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Where are you ?

Tick the boxes that apply to you

Are you...

Able to estimate the values of calculations involving positive numbers

between zero and one.

Able to write a number as the product of its prime factors.

Able to work out the LCM and HCF of pairs of numbers.

Able to use a calculator efficiently and know how to give answers to an

appropriate degree of accuracy.

Able to calculate with mixed numbers.

Able to work out compound interest problems.

Solve problems using ratio in appropriate situations.

Able to calculate the volume of prisms and cylinders.

Able to expand and simplify expressions.

Able to solve equations using trial and improvement.

Able to rearrange simple formulae.

Able to use Pythagoras’ theorem in right-angled triangles.

Able to solve problems in 2-D using Pythagoras’ theorem.

Able to find interior angles and exterior angles in polygons.

Able to translate a 2-D shape by a vector.

Able to reflect a 2-D shape in the line y = x or y = –x.

Able to rotate a 2-D shape about any point.

Able to enlarge a 2-D shape by a fractional scale factor.

Able to enlarge a 2-D shape about any point.

Able to construct line and angle bisectors.

Able to draw and describe the locus of a point from a given rule.

Able to solve problems using loci.

Able to multiply and divide numbers written in index form.

Able to find an estimate of the mean from a grouped table of continuous

data.

Able to draw a frequency polygon for continuous data.

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Are you...

Able to design questionnaires and surveys.

Able to expand a pair of linear brackets to get a quadratic expression.

Able to calculate the gradient of a straight line and use this to find speed

from a distance–time graph.

Know why two shapes are similar.

Able to work out unknown sides using scale factors and ratios.

Able to draw straight lines using the gradient-intercept method.

Able to draw quadratic graphs using a table of values.

Recognise the different types of correlation.

Able to interpret a line of best fit.

Able to calculate relative frequency from experimental evidence and

compare this with the theoretical probability.

Able to give the nth term of a linear sequence.

Able to give the nth term of a sequence of powers of 2 or 10.

Able to work out a formula for the perimeter, area or volume of complex

shapes.

Able to work out whether an expression or formula is dimensionally

consistent and whether it represents a length, an area or a volume.

Able to solve inequalities such as 3x + 2 < 5 and represent the solution on

a number line.

The topics I need to revise and focus are

1.

2.

3.

4.

5.