The only way to learn mathematics is to do mathematics

The only way to learn m

athematics is to do m

athematics

Mathematics Study Pack – All Strands

Useful Websites

https://corbettmaths.com/contents/

https://www.mathsgenie.co.uk/homeschool.html

https://www.mymaths.co.uk/

Number, Ratio and Proportion Page 2

Algebra Page 8

Shapes and Measures 4

Statistics and Probability Page 20

Number, Ratio and Proportion - Answer Page 25

Algebra- Answer Page 26

Shapes and Measures- Answer Page 27

Statistics and Probability - Answer Page 28

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athematics

Number, Ratio and Proportion

+ - x Sig. Fig. Fractions +- Finding % http://www.youtube.com/watch?v=v9J3

VuI8_y0

http://www.youtube.com/watch?v=FzLl

zzIQlDM

http://www.youtube.com/watch?v=eCJ76hz7jPM

http://www.youtube.com/watch?v=52ZlXsFJULI

http://www.youtube.com/watch?v=YWHx0RsRNzI

QUESTION A1 QUESTION B1 QUESTION C1 QUESTION D1 (no calculator)

36 × 28 Round to 1 significant

figure: 19,305,506

Solve 2

+ 6

7 7

Find 30% of 90



figures: 26,935,304

Solve 2

+ 7

9 9

Find 20% of 500



figures: 586,504,620

Solve 2

+ 1

10 5

Find 0.6% of 45



figures: 68,688,586

Solve 8

+ 6

7 14

Find 92.5% of 80



figure: 0.0503205

Solve 2

+ 12

5 15

Find 16.5% of 160


3655 ÷ 15 Round to 2 significant

figures: 3.0566

Solve 2

+ 6

9 7

Find 125% of 125

2

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athematics

Number, Ratio and Proportion

+ - x d.p. Fractions +- Finding % http://www.youtube.com/watch?v=t_bn

lB2KRL4

http://www.youtube.com/watch?v=4Z48

xroNvpA

http://www.youtube.com/watch?v=1Uaj6EUtA7c

http://www.youtube.com/watch?v=52ZlXsFJU

LI

http://www.youtube.com/watch?v=wzbMZZgS

_5U


5775 ÷ 11 Round to 2 d.p.

4.5838304 Solve 2

+ 1

3 3

Find 10% of 920


1212 ÷ 24 Round to 2 d.p.

0.0093459 Solve 2

+ 5

7 7

Find 20% of 650

QUESTION A9 QUESTION B9 QUESTION C9 QUESTION D9 (no calculator) 615384 ÷ 4

Round to 3 d.p. 62.626262

Solve 2

+ 1

3 4

Find 13% of 545

QUESTION A10 QUESTION B10 QUESTION C10 QUESTION D10 (no calculator) 4050 + 3843

Round to 4 d.p. 5803.5832995

Solve 12

+ 1

13 26

Find 110% of 55

QUESTION A11 QUESTION B11 QUESTION C11 QUESTION D11 (no calculator) 20405 − 4737

Round to 2 d.p. 9.99999

Solve 8

+ 3 1

9 3

Find 205% of 60

QUESTION A12 QUESTION B12 QUESTION C12 QUESTION D12 (no calculator) 8049 − 7191

Round to 1 d.p. 0.000991

Solve

2 2

+ 8 4

3 5

Find 0.2% of 5080

3

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athematics

Decimals Negatives Fractions + - + - % http://www.youtube.com/watch?v=w616L

EmrHVE

http://www.youtube.com/watch?v=AcpIO62x2oo

http://www.youtube.com/watch?v=52ZlXsFJU

LI

QUESTION A13 QUESTION B13 QUESTION C13 QUESTION D13 (no calculator) 35.5 + 4.035

Solve −3 + 40

Solve 2

− 1

3 3

Increase 50 by 8%

QUESTION A14 QUESTION B14 QUESTION C14 QUESTION D14 (no calculator) 59.34 + 5.934

Solve −4 + 20

Solve 2

− 1

3 5

Increase 300 by 19%


5.5 − 4.035 Solve

10 − 25

Solve 3

− 1

5 8

Increase 80 by 17.5%

QUESTION A16 QUESTION B16 QUESTION C16 QUESTION D16 (no calculator) 285.44 − 9.999

Solve −3 − 5

Solve 9

− 5

11 33

Decrease 205 by 8%


35.5 ÷ 0.01 Solve

−3 + 9 Solve 25

− 1

28 7

Decrease 60 by 12%

QUESTION A18 QUESTION B18 QUESTION C18 QUESTION D18 (no calculator) 965.960 x 0.01

Solve −3 − 20

Solve 6

− 1

7 4

Decrease 550 by 0.5%

4

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athematics

BIDMAS Negatives Fractions x Number As % http://www.youtube.com/watch?v=fawyx

ROE_ZY

http://www.youtube.com/watch?v=AcpIO62x2oo

http://www.youtube.com/watch?v=rwmFQvrAoNQ

http://www.youtube.com/watch?v=mrsF0IZ17VI

QUESTION E1 QUESTION F1 QUESTION G1 QUESTION H1 8 + 6 × 3 Solve

32 − −3 Solve 3

× 2

4 3

30 as a % of 70

QUESTION E2 QUESTION F2 QUESTION G2 QUESTION H2 12 − 3 × 3 Solve

−19 − −2 Solve 3

× 2

5 9

90 as a % of 250

QUESTION E3 QUESTION F3 QUESTION G3 QUESTION H3 6 × 3! Solve

28 − 40

Solve 3

÷ 2

4 3

32 as a % of 140

QUESTION E4 QUESTION F4 QUESTION G4 QUESTION H4 11 × 2 + (4 ÷ 2) Solve

−5 − 9

Solve 6

÷ 1

7 3

6 as a % of 404

QUESTION E5 QUESTION F5 QUESTION G5 QUESTION H5 20 × 6 ÷ (4 ÷ 2) Solve

−4 2

(H) Solve

3 3

×5 2

4 3

55 as a % of 130

QUESTION E6 QUESTION F6 QUESTION G6 QUESTION H6 2 × (9 − 5) Solve

30

−5

(H) Solve

2 2

÷ 4 1

5 4

44 as a % of 20

5

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athematics

Factors Indices Ratios Finding 100% http://www.youtube.com/watch?v=uE9O

8N5JYB4

http://www.youtube.com/watch?v=od6XjR6H7HI

http://www.youtube.com/watch?v=HpdMJaKaXXc

http://www.youtube.com/watch?v=RJmWJmoZFp

g

QUESTION E7 QUESTION F7 QUESTION G7 QUESTION H7 List the factors of 20 Solve

32 Divide 500 into the

ratio 2:3 If 60% is 300, what is

100%?

QUESTION E8 QUESTION F8 QUESTION G8 QUESTION H8 List the factors of 32 Solve

25 Divide 180 into the

ratio 2:3:4 If 120% is 80, what is

100%?

QUESTION E9 QUESTION F9 QUESTION G9 QUESTION H9 List the common

factors of 40 and 10 Solve 390

Tom and Meg divide £300. If Meg has £20 , write their share ratio

in its lowest form

If 30% is 600, what is 100%?

QUESTION E10 QUESTION F10 QUESTION G10 QUESTION H10 List the common

factors of 55 and 25 Solve 402

Bob and Oli share money at a ratio of 4:3. Bob has £50.

How much does Oli have?

If I add 20% to a number and end with

90, what did I start with?

QUESTION E11 QUESTION F11 QUESTION G11 QUESTION H11 Write 300 as a product

of its prime factors Solve 3431

Amy and Dan share money at a ratio of 5:3. Amy has £30.

How much does Dan have?

If I subtract 5% from a number and end with 190, what did I start

with?

QUESTION E12 QUESTION F12 QUESTION G12 QUESTION H12 Write 420 as a product

of its prime factors Write in index form:

8×8×8×82 Divide £450 into a

ratio of 4:5 If I subtract 90% from a number and finish with 10, what did I

start with?

6

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athematics

Multiples Prime/Square Equivalents % Change http://www.youtube.com/watch?v=vbQ-

sQfxH8M

http://www.youtube.com/watch?v=mIStB5X4U8M

http://www.youtube.com/watch?v=XVVvR2_Jt9s

http://www.youtube.com/watch?v=CLbRHY1Y

PK4

QUESTION E13 QUESTION F13 QUESTION G13 QUESTION H13 Write down a multiple

of 26 What prime numbers are there between 40

and 50?

Write 0.5 as a fraction I start with 80 and finish at 100. What %

increase is this?

QUESTION E14 QUESTION F14 QUESTION G14 QUESTION H14 Write down a multiple

of 9 What prime numbers are there between 60

and 70?

Write 9% as a decimal I start with 50 and finish at 105. What %

increase is this?

QUESTION E15 QUESTION F15 QUESTION G15 QUESTION H15 Find a common

multiple of 9 and 30 Write the number 21 as a product of any

combination of prime numbers

Write 2/3 as a percent I start with 6 and finish at 26. What %

increase is this?

QUESTION E16 QUESTION F16 QUESTION G16 QUESTION H16 Find the lowest

common multiple of 204 and 80

Write down the first 4 square numbers

Order these (ascending):

1 , 0.04, 40%, 30%

3

I start with 120 and finish at 100. What %

decrease is this?



Are square numbers always positive?

Order these (descending):

1

, 0.36, 51%, 0.09 7


decrease is this?



What square numbers are there between 80

and 105?

Which of these are equivalent?

0.2, 2%, 2

, 20

, 2.5 10 100


increase is this?

7

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athematics

Algebra 1

Simplify

Substitute Solve Rearrange

http://qrs.ly/nr2g1xp

http://www.youtube.com/watch?v=o2KZKfbi5hA

http://www.youtube.com/watch?v=QtWreZNO5_8

http://www.youtube.com/watch?v=F1azJEdfx5c

https://www.youtube.com/watch?v=ZudoYJM1ntA

QUESTION A1 QUESTION B1 QUESTION C1 QUESTION D1 Simplify 3a x 2b

If a = 4 & b = 3 Work out the value of

a2 + 2b

Find x if 4x = 10

Make q the subject v = 2k - q

QUESTION A2 QUESTION B2 QUESTION C2 QUESTION D2 Simplify 4a2 x ab

If a = 4 & b = 0 Work out the value of

6a - 2b

Solve 5(x + 6) = 40

Make w the subject p = tw

QUESTION A3 QUESTION B3 QUESTION C3 QUESTION D3 Simplify

10q – 3q + 2q If c = 4 & d = 3

Work out the value of (c + 2d)²

Solve 9(x-2) = 9

Make h the subject m = 5 + h2

QUESTION A4 QUESTION B4 QUESTION C4 QUESTION D4

Simplify 9x + 6 - 5x - 1

If c = 2 & d = 7 Evaluate (3c)² - d

If p - 14 = 8 Find the value of p

Make z the subject t = 2(z – 3)


8p 4p

If a = 7 & b = 2 What is the value of

4(a – b)

Find the value of x if 30 ÷ x = 5

Make h the subject m = ½ (h + 4)


17r – 9r + 3r If a= 4, b= 3, c= 2, e=1

What is the value of 2ae + 6cb

Find x if 14x - 3 = 25

Make b the subject a = y + 2b

8

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athematics

9

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athematics

Simplify Substitute Solve Rearrange

QUESTION A13 QUESTION B13 QUESTION C13 QUESTION D13 Express in its simplest

form 3a x b x 2c²

What is the value of 6a - b

if a = 4 & b = 7?

Solve 10 - x > 3

Make b the subject if a = 5b

QUESTION A14 QUESTION B14 QUESTION C14 QUESTION D14 Simplify 8x +6y - 5x +y

Evaluate 8d + 5c² if c = 4 & d = 3?

Solve 3x - 7 < 17

Make b the subject of a = 2b - 1


18a ÷ 2

What is the value of 3a + 2b

if a = 5 & b = 4?

Solve 5x + 7 < 52

Make b the subject if a = 3 + 2b

QUESTION A16 QUESTION B16 QUESTION C16 QUESTION D16 Express in its simplest

form 3c x 2c²

Evaluate 2c² - 4d if c = 3

& d = 2?

Find x if 4x > 20

Make b the subject if a = 4(b – 7)

QUESTION A17 QUESTION B17 QUESTION C17 QUESTION D17 Simplify 9a - 4a

What is the value of 3a - 8b if a =10

& b = 3?

Solve 2(x + 4) 18

Make b the subject of a = 2(7 + b)


4x +3y +5x +8y

Evaluate 3c3 if c = 10?

Solve 20 - 4x 0

Make t the subject of p = 2t - 4

10

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athematics

Algebra 2

Sequences Factorising Expanding Expressions

https://www.youtube.com/watch?v=V02nV_qR_xQ

https://www.youtube.com/watch?v=ExGagW-EKbs

https://www.youtube.com/watch?v=xbOKyCWPbfc https://www.youtube.com

/watch?v=3s_lroR5_1U

http://www.youtube.com/watch?v=IJ0K8QoVPAE

QUESTION E1 QUESTION F1 QUESTION G1 QUESTION H1 Write down the next

number in this sequence

10, 7, 4 , 1, ?

Factorise 15a + 25

Expand 7(4x - 3)

Write the perimeter



6, 13, 20, 27, ?

Factorise 7x + 21x 2

Expand and simplify 10a + 3a(a - 2)

Write the perimeter



1.3, 1.8 , 2.3, ?

Factorise 4a + 6b

Expand 3(2x + 5)

Write the perimeter



3, 4.5, 6, 7.5, ?

Factorise 9x 2– 12x

Expand and simplify 4a(a + 2) + 3a

Write the perimeter



1, 4, 9, 16, ?

Factorise 15a – 20b

Expand 3(5 + 4x)

Write the perimeter


number in this

sequence

1,,,, …?

Factorise 21x + 3x 2

Expand and simplify 7a - 2(a + 2)

Write the perimeter

3 x

2 x

5 x

2 x x+1

x+1

2 x

½ x

2 x + 1

11

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athematics


QUESTION E7 QUESTION F7 QUESTION G7 QUESTION H7 Find the nth term of this

sequence: 2, 5, 8, 11,

Factorise 6p + 2pq

Expand 2(7x - 3)

Write the perimeter


sequence: 10, 5, 0, −5,

Factorise fully 14x - 35x 2

Expand and simplify 9a - a(a + 4)

Write the perimeter


sequence: 20, 40, 60, 80

Factorise 14 – 7x

Expand -2(4x + 5)

Write the perimeter


sequence: 13, 15, 17, 19

Factorise fully 12x – 15x2

Expand and simplify 3a(2a + 1) - 7a

Write the area

2x


sequence: 10, 7, 4, 1

Factorise: 3𝑥+9 Expand and simplify (𝑥+2)(𝑥+3)

Write the area

x


sequence: 11, 111, 211, 311

Factorise: 18𝑎+24𝑏 Expand and simplify (𝑥+2)(𝑥−3)

Write the area

2 x 2

½ x + 2h

x+3

3 x

3 x

x

12

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athematics


QUESTION E13 QUESTION F13 QUESTION G13 QUESTION H13 Find the 100th term of

this sequence: 17, 20, 23, 26

Factorise: 4𝑥+10𝑥! Expand and simplify (𝑥+4)(𝑥+3)

Write the area



Factorise: 2𝑣!+6𝑣𝑤 Expand and simplify (𝑥−2)(𝑥−3)

Write the area

QUESTION E15 QUESTION F15 QUESTION G15 QUESTION H15

Find the 100th term of this sequence: 55, 60, 65, 70

Factorise: 9𝑝!−9𝑝𝑞 Expand and simplify (𝑥+2)(2𝑥+3)

Write the area



Factorise: 21𝑣!+49𝑣𝑤 Expand and simplify (𝑥+1)(𝑥−1)

Write the area


this sequence: -5, -10, -15, -20

Factorise: 77𝑏!+14𝑏𝑐 Expand and simplify (𝑥+8)(𝑥+3)

Write the area


this sequence: -16, -26, -36, -46

Factorise: 40𝑔!+70𝑔ℎ Expand and simplify 𝑥+5 !

Write the area

2 x

2 x +1

2 x

4 x

2 x

4 x 2

2 x

6 x

4 x 2

13

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athematics

Shape and Measures Perimeter Area Surface Area Volume

http://www.youtube.com/watch?v=sFGW3L0SSnw

http://www.youtube.com/watch?v=IO7SP7CoDHo

http://www.youtube.com/watch?v=FhiY10RgS

NU

http://www.youtube.com/watch?v=o4tOjMT0Hj

M


r = 4cm h = 10cm

r = 4cm h = 10cm


10cm

10cm


7cm

7cm


4cm

3cm 13cm

4cm

3cm 13cm


3cm

1cm 8cm

3cm

1cm 8cm


8cm

6cm

4 cm 5 cm

6 cm

2 cm

6 cm

2 cm

6 cm

2 cm

6 cm

26 cm

13 cm

9 cm 11 cm

5 cm

4 cm

15 cm

5 cm

6 cm

9 cm

4 cm

9 cm

3 cm

3 cm

8 cm

5 cm

3 cm 14

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athematics

Perimeter Area Surface Area Volume

http://www.youtube.com/watch?v=sFGW3L0S

Snw

http://www.youtube.com/watch?v=IO7SP7CoDHo

http://www.youtube.com/watch?v=FhiY10Rg

SNU

http://www.youtube.com/watch?v=HZO5

EIfbKhg




3cm

2cm 10cm


6cm

5cm

3cm 8cm


4cm

2cm

6cm

r = 2cm h = 20cm

r = 2cm h = 20cm


4cm

6cm

7cm

16cm

r = 2.5cm h = 9cm

r = 2.5cm h = 9cm

6 cm 6 cm

7 cm

5 cm

3 cm

3 cm 9 cm

6 cm

3 cm

11 cm

6 cm

5 cm

11 cm

9 cm

4 cm

3 cm

20 cm

8 cm

6 cm

5 cm

4 cm

3 cm

6 cm

16 cm

4 cm

9 cm

4 cm

5 cm

8 cm

16 cm

6 cm

12 cm

6 cm

5 cm

4 cm 2 cm

13 cm 7 cm

15

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athematics

Pythagoras Angles Shapes Transforms

http://www.youtube.com/watch?v=Fx9NV-FrXkM

http://www.youtube.com/watch?v=6HWkX1Nw0n4

http://www.youtube.com/watch?v=RY9Q1RG-h4g


Name this shape


Name this shape


Name this shape


Name this shape

Rotate 90o CW about the point


Name this shape



Name this shape


4 cm

3 cm c 80 o

a

9 cm

5 cm c

120 o

a

10 cm

6 cm c

a

b

5 cm 12 cm

a

b

3 cm 9 cm

100 o

a

b

7 cm 18 cm

48 o

a

16

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athematics

Pythagoras Angles Shapes Transforms

http://www.youtube.com/watch?v=Fx9NV-FrXkM

http://www.youtube.com/watch?v=6HWkX1Nw0n4

http://www.youtube.com/watch?v=RY9Q1RG-h4g

QUESTION E1 QUESTION F1 QUESTION G1 QUESTION H1 A ladder rests against a wall. The ladder is 10m long, and its base is 5m from the wall. How high is the wall?

Name this shape

QUESTION E2 QUESTION F2 QUESTION G2 QUESTION H2 A ladder rests against a wall. The ladder is 15m long, and its base is 7m from the wall. How high is the wall?

Name this shape

QUESTION E3 QUESTION F3 QUESTION G3 QUESTION H3 For a 10cm square, what is the distance

between the diagonal vertices?

Name this shape

Enlarge s.f. 2

QUESTION E4 QUESTION F4 QUESTION G4 QUESTION H4 For a 15m x 22m

rectangle, what is the distance between the

diagonal vertices?

Name this shape

Enlarge s.f. 2

QUESTION E5 QUESTION F5 QUESTION G5 QUESTION H5 The diagonal distance across a field is 40m.

If the length of the shortest side of the

field is 8m, how long is the other side?

Name this shape

Enlarge s.f. 1/2

QUESTION E6 QUESTION F6 QUESTION G6 QUESTION H6 The diagonal distance across a field is 30m.

If the length of the shortest side of the

field is 4m, how long is the other side?

Name this shape

Enlarge s.f. 2

48 o a

52 o a

159 o

a

122 o

a

a

52 o

a

35 o

17

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athematics

Circles Measures Time Bearings

http://www.youtube.com/watch?v=b

Ua3vz7UV6U

http://www.youtube.com/watch?v=1yIgFzSUU

ys

http://www.youtube.com/watch?v=ay0sw2GiB

Zk

http://www.youtube.com/watch?v=_BSZH0EhLS8

QUESTION E7 QUESTION F7 QUESTION G7 QUESTION H7 If r = 2cm, find the area.

Convert 100mm into metres

Write down the

3 figure bearing


If r = 4cm, find the area.

Convert 20cm2 into mm2

Write down the

3 figure bearing


If d = 9cm, find the area.

Convert 12m2 into cm2

Write down the 3 figure bearing


If d = 5cm, find the circumference.

Convert 4 feet into inches

Write down

the 3 figure bearing


If r = 9cm, find the circumference.

How many seconds are there in eleven

minutes and sixteen seconds?

from L


If the circumference is 30cm, find the radius

How many minutes are there in four hours and twenty seconds?

Write down the

3 figure bearing

Find the bearing of S

70 º

145 º

40 º

18

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athematics

Circles Measures Time Nets

http://www.youtube.com/watch?v=b

Ua3vz7UV6U

http://www.youtube.com/watch?v=1yIgFzSUU

ys

http://www.youtube.com/watch?v=ay0sw2Gi

BZk

http://www.youtube.com/watch?v=_BSZH0EhLS8

QUESTION E13 QUESTION F13 QUESTION G13 QUESTION H13 If r = 9cm, find the perimeter.

Convert 100ml into litres

Find the difference between 09:34 and

16:19


If r = 9cm, find the area.

Convert 2500ml into litres

Find the difference between 22:34 and

08:45


If r = 4cm, find the perimeter.

Convert 11mm into metres

Convert 720 seconds into minutes


8cm Find the perimeter.

Convert 30 metres into kilometres

Convert 3.25 hours into minutes


12cm Find the perimeter.

Convert 400kg into grams

Convert 7.5 hours into minutes

QUESTION E18 QUESTION F18 QUESTION G18 QUESTION H18 For H, r = 2cm For K, r = 8cm

Find the area of K.

Convert 1.05 kg into grams

Convert 12 minutes into hours

1 cm

1 cm

H K

19

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athematics

Data Handling and Probability 1

Mode Median Range Mean

http://www.youtube.com/watch?v=YpW4IlN0t_c

QUESTION A1 QUESTION B1 QUESTION C1 QUESTION D1 Find the mode of this

data set: 3,8,6,5,4,3,4,5,5

Find the median of this data set:

3,8,6,5,4,3,4,5,5

Find the range of this data set:

3,8,6,5,4,3,4,5,5

Find the mean of this data set:

3,8,6,5,4,3,4,5,5


data set: 0.2, 0.5, 0.1, 0.1, 0.6,

0.9, 1.4


0.2, 0.5, 0.1, 0.1, 0.6, 0.9, 1.4


0.2, 0.5, 0.1, 0.1, 0.6, 0.9, 1.4


0.2, 0.5, 0.1, 0.1, 0.6, 0.9, 1.4


data set: 11, 11, 11, 11, 12, 12,

12, 12, 13, 13


11, 11, 11, 11, 12, 12, 12, 12, 13, 13


11, 11, 11, 11, 12, 12, 12, 12, 13, 13


11, 11, 11, 11, 12, 12, 12, 12, 13, 13


data set: 1, 2, 3, 4, 5, 6

Find the median of this data set: 1, 2, 3, 4, 5, 6


1, 2, 3, 4, 5, 6


1, 2, 3, 4, 5, 6


data set: 0.09, 0.03, 0.3, 0.45, 0.20, 0.11, 0.03, 0.3


0.09, 0.03, 0.3, 0.45, 0.20, 0.11, 0.03, 0.3


0.09, 0.03, 0.3, 0.45, 0.20, 0.11, 0.03, 0.3


0.09, 0.03, 0.3, 0.45, 0.20, 0.11, 0.03, 0.3


data set: 57, 67, 56, 66, 77, 76,

46, 47, 56


57, 67, 56, 66, 77, 76, 46, 47, 56


57, 67, 56, 66, 77, 76, 46, 47, 56


57, 67, 56, 66, 77, 76, 46, 47, 56

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athematics

Mode Median Range Mean

http://www.youtube.com/watch?v=wEalHXgkd5M

QUESTION A7 QUESTION B7 QUESTION C7 QUESTION D7 Score Frequency Score Frequency Score Frequency Score Frequency 3 10 3 10 3 10 3 10

4 15 4 15 4 15 4 15

5 5 5 5 5 5 5 5

QUESTION A8 QUESTION B8 QUESTION C8 QUESTION D8 Score Frequency Score Frequency Score Frequency Score Frequency 1 10 1 10 1 10 1 10

2 20 2 20 2 20 2 20

3 30 3 30 3 30 3 30

4 40 4 40 4 40 4 40

QUESTION A9 QUESTION B9 QUESTION C9 QUESTION D9 Score Frequency Score Frequency Score Frequency Score Frequency 1-5 4 1-5 4 1-5 4 1-5 4

6-10 6 6-10 6 6-10 6 6-10 6

11-15 1 11-15 1 11-15 1 11-15 1

16-20 7 16-20 7 16-20 7 16-20 7

QUESTION A10 QUESTION B10 QUESTION C10 QUESTION D10 Score Frequency Score Frequency Score Frequency Score Frequency 1-10 9 1-10 9 1-10 9 1-10 9

11-20 2 11-20 2 11-20 2 11-20 2

21-30 6 21-30 6 21-30 6 21-30 6

31-40 13 31-40 13 31-40 13 31-40 13

QUESTION A11 QUESTION B11 QUESTION C11 QUESTION D11 Score f Score f Score f Score f 0 ≤ 𝑥 ≤ 9 22 0 ≤ 𝑥 ≤ 9 22 0 ≤ 𝑥 ≤ 9 22 0 ≤ 𝑥 ≤ 9 22 9 < 𝑥 ≤ 19 40 9 < 𝑥 ≤ 19 40 9 < 𝑥 ≤ 19 40 9 < 𝑥 ≤ 19 40 19 < 𝑥 ≤ 29 44 19 < 𝑥 ≤ 29 44 19 < 𝑥 ≤ 29 44 19 < 𝑥 ≤ 29 44 𝑥 > 29 4 𝑥 > 29 4 𝑥 > 29 4 𝑥 > 29 4

QUESTION A12 QUESTION B12 QUESTION C12 QUESTION D12 Score f Score f Score f Score f 0 ≤ 𝑥 ≤ 9 3 0 ≤ 𝑥 ≤ 9 3 0 ≤ 𝑥 ≤ 9 3 0 ≤ 𝑥 ≤ 9 3 9 < 𝑥 ≤ 19 0 9 < 𝑥 ≤ 19 0 9 < 𝑥 ≤ 19 0 9 < 𝑥 ≤ 19 0 19 < 𝑥 ≤ 29 6 19 < 𝑥 ≤ 29 6 19 < 𝑥 ≤ 29 6 19 < 𝑥 ≤ 29 6 𝑥 > 29 0 𝑥 > 29 0 𝑥 > 29 0 𝑥 > 29 0

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athematics

Distance Time Graphs Questionnaires Gradient

http://www.youtube.com/watch?v=2ux__gfVu9U

http://www.youtube.com/watch?v=7onVHIkS1

YY

http://www.youtube.com/watch?v=ykeC

Km9JqSA


“Are you a criminal?” What’s wrong with this

question?

Find the gradient of y = 3x + 2

QUESTION C14 QUESTION D14 “Are you: A – young, or

B- old?” What’s wrong with this

question?

Find the gradient of y = -2x + 9

QUESTION A15 QUESTION B15 QUESTION C15 QUESTION D15 How far did the

cyclist from the above graph travel?

Using the above graph, how long did the cyclist stop for

altogether?

“Do you think maths is great or just good?”

What’s wrong with this question?

Find the gradient of y + 2x = 2

QUESTION A16 QUESTION B16 QUESTION C16 QUESTION D16 How long did she

take? What was her

average speed excluding stops?

“On a scale of 1-10, how happy are you?”


Find the gradient of the sloped line below:

2

6

QUESTION A17 QUESTION B17 QUESTION C17 QUESTION D17 What was her

average speed in km/h?

How can you tell from the shape of the graph when she travelled fastest?

“What shoe size are you? 1-4, 4-8, 8-12”



3

5

QUESTION A18 QUESTION B18 QUESTION C18 QUESTION D18 How many stops did

she make ? Over which stage did

this happen? “Do you like cheap, nasty chocolate or

expensive chocolate?” What’s wrong with this

question?


2

9

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athematics

Pie Charts Pie Charts Scatter Graph Pictograms

http://www.youtube.com/watch?v=1oShnkmA_ww

http://www.youtube.com/watch?v=IQKJThMqrZY

http://www.youtube.com/watch?v=UKOt

Ggq_wvY

QUESTION E1 QUESTION F1 QUESTION G1 QUESTION H1 If a pie chart is constructed to display results of a survey of 300 people, how many degrees would make up 1 person?

If 90o in a pie chart represents 60 people,

how many are represented overall?

What is the name for

values like these?

If 3 people are represented by ✪, how many are represented

by ✪✪✪✪ ?




Draw a line of best fit


by ✪✪✪ ?

QUESTION E3 QUESTION F3 QUESTION G3 QUESTION H3 If a pie chart is constructed to display results of a survey of 60 people, how many degrees would make up 5 people?



Comment on the

correlation


by ✪✪✪✪✪✪ ?


If 24o in a pie chart represents 116

people, how many are represented overall?

Comment on the correlation

If 12 people are represented by

✪✪✪ how many are represented by ✪?

QUESTION E5 QUESTION F5 QUESTION G5 QUESTION H5 If a pie chart is constructed to display results of a survey of 200 people, how many degrees would make up 100 people?

David says that 12 people on his pie

chart take up a slice with angle 121o. How

do you know he’s wrong?

Predict a WPM score for someone who did 5 weeks of practice

If 70 people are represented by ✪✪ how

many are represented by ✪?

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athematics

Probability 1 Probability 2 Probability 3 Probability 4

http://www.youtube.com/watch?v=dS2p_APpcnI

QUESTION E7 QUESTION F7 QUESTION G7 QUESTION H7 If P(A) = 0.2, find P(A’) E a b c d If P(A) = 2/9, how

many times might event ‘A’ happen out

of 400?

What is the probability of getting an odd

number on a six sided dice?

P 0.4 0.1 0.1

Complete the probability table

QUESTION E8 QUESTION F8 QUESTION G8 QUESTION H8 If P(A) = 0.71, find

P(A’) E a b c d If P(A) = 11/30, how


of 500?

What is the probability of getting tails on a

fair coin? P 0.2 0.6 0.1

Complete the probability table


P(A’) E a b c d If P(A) = 1/3, how


of 100?

What is the probability of drawing a 10 from

a deck of cards at random?

P 0.4 4x 6x 2x Find x




of 700?

What is the probability of drawing a red 10 from a deck of cards

at random?

P 0.7 0.1 0.1 0.1 What is the probability

of event a or b occurring?


P(A’) E a b c d If P(A) = 13/15, how


of 150?

What is the probability of drawing a red 6

from a deck of cards at random?

P 0.3 0.2 0.1 0.4 Find the probability of event c NOT occurring




of 220?

How many ways are there of drawing two cards from a deck

that total ‘5’ at random? (Assume

Aces are ‘1’s)

P 0.4 0.4 0.1 0.1 Find the probability of

either event b or d occurring

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athematics

Answers

Section A Section B Section C Section D

A1 1008 B1 20,000,000 C1 1 and 1/7 D1 27 A2 6880 B2 27,000,000 C2 1 D2 100 A3 21372 B3 587,000,000 C3 2/5 D3 0.27 A4 67932 B4 69,000,000 C4 1 and 4/7 D4 74 A5 55664 B5 0.05 C5 1 and 1/5 D5 26.4 A6 243.67 B6 3.1 C6 1 and 5/63 D6 156.25 A7 525 B7 4.58 C7 1 D7 92 A8 50.5 B8 0.01 C8 1 D8 130 A9 153846 B9 62.626 C9 11/12 D9 70.85 A10 7893 B10 5803.5833 C10 25/26 D10 60.5 A11 15668 B11 10.00 C11 4 and 2/9 D11 123 A12 858 B12 0.0 C12 11 and 7/15 D12 10.16 A13 39.535 B13 37 C13 1/3 D13 54 A14 65.274 B14 16 C14 7/15 D14 357 A15 1.465 B15 −15 C15 19/40 D15 94 A16 275.441 B16 −8 C16 2/3 D16 188.6 A17 3550 B17 6 C17 3/4 D17 52.8 A18 0.6596 B18 −23 C18 17/28 D18 547.25

Section E Section F Section G Section H E1 26 F1 35 G1 1/2 H1 42.9% E2 3 F2 −17 G2 2/15 H2 36% E3 54 F3 −12 G3 1 and 1/8 H3 22.9% E4 24 F4 −14 G4 2 and 4/7 H4 1.5% E5 60 F5 16 G5 21 and 1/4 H5 42.3% E6 8 F6 −6 G6 48/85 H6 220% E7 1,2,4,5,10,20 F7 9 G7 200: 300 H7 500 E8 1,2,4,8,16,32 F8 32 G8 40: 60: 80 H8 66.67% E9 1,2,5,10 F9 1 G9 1: 14 H9 2000 E10 1,5 F10 1600 G10 £37.50 H10 75 E11 2!×3×5! F11 343 G11 £18 H11 200 E12 2!×3×5×7 F12 8! G12 200: 250 H12 100

E13 26,52,78 𝑒𝑡𝑐 F13 41,43,47 G13 1/2 H13 25% E14 9,18,27, 𝑒𝑡𝑐 F14 61,67 G14 0.09 H14 110% E15 90,180 𝑒𝑡𝑐 F15 7×3 G15 66.67% H15 333.33%

E16 4080 F16 1,2,4,9 G16 0.04,30%,1/3,40% H16 16.67% E17 600 F17 𝑦𝑒𝑠 G17 51%,0.36,1/7,0.09 H17 81.5%

E18 80 F18 81,100 G18 0.2, 2/10, 20/100 H18 35.3%

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athematics

Answers

Section A J L A1 6𝑎𝑏 A2 4𝑎!𝑏 A3 9𝑞 A4 4𝑥 + 5 A5 2 A6 11𝑟 A7 −2𝑥 + 3𝑦 A8 30𝑎𝑏 A9 8𝑎𝑏! A10 5𝑥 + 7 A11 −10𝑟 A12 2𝑎 A13 6𝑎𝑏𝑐! A14 3𝑥 + 7𝑦 A15 9𝑎 A16 6𝑐! A17 5𝑎 A18 9𝑥 + 11𝑦 Section E J L E1 −2 E2 34 E3 2.8 E4 9 E5 25 E6 1/16 E7 3𝑛 − 1 E8 −5𝑛 + 15 E9 20𝑛 E10 2𝑛 + 11 E11 −3𝑛 + 13 E12 100𝑛 − 89 E13 314 E14 −157 E15 550 E16 −377 E17 −500 E18 −1006

Section B J L B1 22 B2 24 B3 100 B4 29 B5 20 B6 44 B7 −0.4 B8 1944 B9 −108 B10 20.25 B11 5 B12 126 B13 17 B14 104 B15 23 B16 10 B17 6 B18 3000 Section F J L F1 5(3𝑎 + 5) F2 7𝑥(1+ 3𝑥) F3 2(2𝑎 + 3𝑏) F4 3𝑥(3𝑥 − 4) F5 5(3𝑎 − 4𝑏) F6 3𝑥(7+ 𝑥) F7 2𝑝(3+ 𝑞) F8 7𝑥(2− 5𝑥) F9 7(2− 𝑥) F10 3𝑥(4− 5𝑥) F11 3(𝑥 + 3) F12 6(3𝑎 + 4𝑏) F13 2𝑥(2+ 5𝑥) F14 2𝑣(𝑣 + 3𝑤) F15 9𝑝(𝑝 − 𝑞) F16 7𝑣(3𝑣 + 7𝑤) F17 7𝑏(11𝑏 + 2𝑐) F18 10𝑔(4𝑔 + 7ℎ)

Section C J L C1 𝑥 = 2.5 C2 𝑥 = 2 C3 𝑥 = 3 C4 𝑥 = 2 C5 𝑥 = 6 C6 𝑥 = 2 C7 𝑥 = 0.6 C8 𝑥 = 450 C9 𝑥 = 10 C10 𝑥 = 3 C11 𝑥 = 4.5 C12 𝑥 = 2 C13 𝑥 < 7 C14 𝑥 < 8 C15 𝑥 < 9 C16 𝑥 > 5 C17 𝑥 ≤ 5 C18 𝑥 ≤ 5 Section G J L G1 28𝑥 − 21 G2 3𝑎! + 4𝑎 G3 6𝑥 + 15 G4 4𝑎! + 7𝑎 G5 12𝑥 + 15 G6 5𝑎 − 4 G7 14𝑥 − 6 G8 −𝑎! + 5𝑎 G9 −8𝑥 − 10 G10 6𝑎! − 4𝑎 G11 𝑥! + 5𝑥 + 6 G12 𝑥! − 𝑥 − 6 G13 𝑥! + 7𝑥 + 12 G14 𝑥! − 5𝑥 + 6 G15 2𝑥! + 7𝑥 + 6 G16 𝑥! − 1 G17 𝑥! + 11𝑥 + 24 G18 𝑥! + 10𝑥 + 25

Section D J L D1 𝑞 = 2𝑘 − 𝑣 D2 𝑤 = 𝑝/𝑡 D3 ℎ = 𝑚 − 5 D4 𝑧 = !!!

!

D5 ℎ = 2𝑚 − 4 D6 𝑏 = !!!

!

D7 𝑦 = !!!!!

D8 𝑏 = 𝑚 + ℎ! D9 𝑎 = 𝑐! − 𝑏! D10 𝑔 = 3/𝑘 D11 𝑔 = 𝑦/𝑚 D12 𝑚 = 3𝑘 + 9 D13 𝑏 = 𝑎/5 D14 𝑏 = !!!

!

D15 𝑏 = !!!!

D16 𝑏 = !!!"

!

D17 𝑏 = !!!"!

D18 𝑡 = !!!

!

Section H J L H1 12𝑥 H2 14𝑥 H3 4𝑥 + 2 H4 16𝑥 H5 3.5𝑥 H6 12𝑥 + 6 H7 10𝑥! H8 2𝑥 + 8ℎ H9 4𝑥 + 12 H10 6𝑥! H11 3𝑥! H12 𝑥! H13 2𝑥! + 𝑥 H14 4𝑥! H15 4𝑥! H16 4𝜋𝑥! H17 9𝜋𝑥! H18 4𝜋𝑥!

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athematics

Answers Section A J L A1 16𝑐𝑚 A2 16𝑐𝑚 A3 14𝑐𝑚 A4 45𝑐𝑚 A5 28𝑐𝑚 A6 30𝑐𝑚 A7 24𝑐𝑚 A8 88𝑐𝑚 A9 12𝑐𝑚 A10 36𝑐𝑚 A11 40𝑐𝑚 A12 20𝑐𝑚 A13 5𝑐𝑚 A14 10.3𝑐𝑚 A15 11.7𝑐𝑚 A16 10.9𝑐𝑚 A17 8.5𝑐𝑚 A18 16.6𝑐𝑚 Section E J L E1 8.7𝑚 E2 13.3𝑚 E3 14.1𝑐𝑚 E4 26.6𝑚 E5 39.2𝑚 E6 29.7𝑚 E7 12.6𝑐𝑚! E8 50.3𝑐𝑚! E9 63.6𝑐𝑚! E10 15.7𝑐𝑚 E11 56.5𝑐𝑚 E12 4.8𝑐𝑚 E13 60.4𝑐𝑚 E14 190.9𝑐𝑚! E15 26.8𝑐𝑚 E16 24.0𝑐𝑚 E17 36.6𝑐𝑚 E18 118.5𝑐𝑚!

Section B J L B1 25𝑐𝑚! B2 12𝑐𝑚! B3 169𝑐𝑚! B4 27.5𝑐𝑚! B5 37.5𝑐𝑚! B6 36𝑐𝑚! B7 36𝑐𝑚! B8 15𝑐𝑚! B9 60𝑐𝑚! B10 88𝑐𝑚! B11 16𝑐𝑚! B12 154𝑐𝑚! B13 100! B14 120! B15 108! B16 120! B17 80! B18 132! Section F J L F1 132! F2 52! F3 159! F4 122! F5 76! F6 72.5! F7 0.1𝑚 F8 2000𝑚! F9 120000𝑐𝑚! F10 48 𝑖𝑛𝑐ℎ𝑒𝑠 F11 17!𝐶 F12 68𝑚𝑝ℎ F13 0.1 𝑙 F14 2.5 𝑙 F15 0.011𝑚 F16 0.03𝑘𝑚 F17 400000𝑔 F18 1050𝑔

Section C J L C1 351.9𝑐𝑚! C2 600𝑐𝑚! C3 294𝑐𝑚! C4 206𝑐𝑚! C5 70𝑐𝑚! C6 129𝑐𝑚! C7 100𝑐𝑚! C8 254𝑐𝑚! C9 112𝑐𝑚! C10 158𝑐𝑚! C11 276.5𝑐𝑚! C12 180.6𝑐𝑚! C13 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙𝑜𝑔𝑟𝑎𝑚 C14 𝑒𝑞𝑢𝑖𝑙𝑎𝑡𝑒𝑟𝑎𝑙 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒 C15 𝑟𝑖𝑔ℎ𝑡 − 𝑎𝑛𝑔𝑙𝑒𝑑 𝑡𝑟𝑖. C16 𝑖𝑠𝑜𝑐𝑒𝑙𝑒𝑠 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒 C17 𝑡𝑟𝑎𝑝𝑒𝑧𝑖𝑢𝑚 C18 ℎ𝑒𝑥𝑎𝑔𝑜𝑛 Section G J L G1 𝑜𝑐𝑡𝑎𝑔𝑜𝑛 G2 𝑐𝑢𝑏𝑜𝑖𝑑 G3 𝑠𝑞𝑢𝑎𝑟𝑒 𝑏𝑎𝑠𝑒𝑑 𝑝𝑦𝑟𝑎𝑚𝑖𝑑 G4 𝑐𝑜𝑛𝑒 G5 𝑡𝑟𝑖𝑎𝑛𝑔𝑢𝑙𝑎𝑟 𝑝𝑟𝑖𝑠𝑚 G6 𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟 G7 1:15 G8 11: 56 G9 8:22 G10 1:40 G11 676 seconds G12 240 !

! mins

G13 5ℎ𝑟𝑠 45 𝑚𝑖𝑛𝑠 G14 10ℎ𝑟𝑠 11 𝑚𝑖𝑛𝑠 G15 12 𝑚𝑖𝑛𝑠 G16 195 𝑚𝑖𝑛𝑢𝑡𝑒𝑠 G17 450 𝑚𝑖𝑛𝑢𝑡𝑒𝑠 G18 0.2 ℎ𝑜𝑢𝑟𝑠

Section D J L D1 50.3𝑐𝑚! D2 1000𝑐𝑚! D3 343𝑐𝑚! D4 156𝑐𝑚! D5 24𝑐𝑚! D6 60𝑐𝑚! D7 81𝑐𝑚! D8 480𝑐𝑚! D9 180𝑐𝑚! D10 360𝑐𝑚! D11 251.3𝑐𝑚! D12 176.7𝑐𝑚! D13 𝑠𝑒𝑒 𝑏𝑒𝑙𝑜𝑤 D14 𝑠𝑒𝑒 𝑏𝑒𝑙𝑜𝑤 D15 𝑠𝑒𝑒 𝑏𝑒𝑙𝑜𝑤 D16 𝑠𝑒𝑒 𝑏𝑒𝑙𝑜𝑤 D17 𝑠𝑒𝑒 𝑏𝑒𝑙𝑜𝑤 D18 𝑠𝑒𝑒 𝑏𝑒𝑙𝑜𝑤 Section H J L H1 𝑠𝑒𝑒 𝑏𝑒𝑙𝑜𝑤 H2 𝑠𝑒𝑒 𝑏𝑒𝑙𝑜𝑤 H3 𝑠𝑒𝑒 𝑏𝑒𝑙𝑜𝑤 H4 𝑠𝑒𝑒 𝑏𝑒𝑙𝑜𝑤 H5 𝑠𝑒𝑒 𝑏𝑒𝑙𝑜𝑤 H6 𝑠𝑒𝑒 𝑏𝑒𝑙𝑜𝑤 H7 070! H8 090! H9 145! H10 320! H11 245! H12 270! H13 𝑐𝑢𝑏𝑒 H14 𝑐𝑢𝑏𝑜𝑖𝑑 H15 𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟 H16 𝑡𝑟𝑖𝑎𝑛𝑔𝑢𝑙𝑎𝑟 𝑝𝑟𝑖𝑠𝑚 H17 𝑠𝑞𝑢𝑎𝑟𝑒 𝑏𝑎𝑠𝑒𝑑 𝑝𝑦𝑟𝑎𝑚𝑖𝑑 H18 𝑡𝑒𝑡𝑟𝑎ℎ𝑒𝑑𝑟𝑜𝑛

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athematics

Answers

Section A Section B Section C Section D A1 5 B1 5 C1 5 D1 4.8 (1𝑑𝑝) A2 0.1 B2 0.5 C2 1.3 D2 0.5 (1𝑑𝑝) A3 11 𝑎𝑛𝑑 12 B3 12 C3 2 D3 11.8 A4 𝑛𝑜 𝑚𝑜𝑑𝑒 B4 3.5 C4 5 D4 3.5 A5 0.03 𝑎𝑛𝑑 0.3 B5 0.155 C5 0.42 D5 0.19 (2𝑑𝑝) A6 56 B6 57 C6 31 D6 60.9 (1𝑑𝑝) A7 4 B7 4 C7 2 D7 3.8 (1𝑑𝑝) A8 4 B8 3 C8 3 D8 3 A9 16 − 20 B9 6 − 10 C9 19 D9 11.1 (1𝑑𝑝) A10 31 − 40 B10 21 − 30 C10 39 D10 23.2( 1𝑑𝑝) A11 19 < 𝑥 ≤ 29 B11 9 < 𝑥 ≤ 19 C11 39 D11 16.8 (1𝑑𝑝) A12 19 < 𝑥 ≤ 29 B12 19 < 𝑥 ≤ 29 C12 29 D12 17.5 A13 − B13 − C13 𝑢𝑛𝑟𝑒𝑙𝑖𝑎𝑏𝑙𝑒 D13 3 A14 − B14 − C14 𝑣𝑎𝑔𝑢𝑒 D14 −2 A15 60𝑘𝑚 B15 1.5 ℎ𝑜𝑢𝑟𝑠 C15 𝑡𝑜𝑜 𝑓𝑒𝑤 𝑜𝑝𝑡𝑖𝑜𝑛𝑠 D15 −2 A16 5 ℎ𝑜𝑢𝑟𝑠 B16 17.1 𝑘𝑚/ℎ C16 𝑖𝑠 10 ℎ𝑎𝑝𝑝𝑦? D16 0.33 A17 12 𝑘𝑚/ℎ B17 𝑠𝑡𝑒𝑒𝑝𝑒𝑠𝑡 𝑏𝑖𝑡 C17 𝑖𝑛𝑐𝑜𝑟𝑟𝑒𝑐𝑡 𝑠𝑐𝑎𝑙𝑒 D17 0.6

A18 2 B18 𝐸 𝑡𝑜 𝐹 C18 𝑏𝑖𝑎𝑠𝑒𝑑 D18 0.22

Section E Section F Section G Section H E1 1.2!

F1 240 G1 Outlier 𝑉𝑎𝑙𝑢𝑒 H1 12 E2 18!

F2 198 G2 − H2 39 E3 30!

F3 300 G3 𝑚𝑜𝑑𝑒𝑟𝑎𝑡𝑒 + 𝑣𝑒 H3 144 E4 45!

F4 1740 G4 𝑠𝑡𝑟𝑜𝑛𝑔 + 𝑣𝑒 H4 4 E5 180!

F5 35.702 𝑝𝑒𝑜𝑝𝑙𝑒! G5 58 H5 35 E6 − F6 − G6 − H6 − E7 0.8 F7 0.4 G7 89 H7 0.5 E8 0.29 F8 0.1 G8 183 H8 0.5 E9 0.91 F9 𝑥 = 0.05 G9 33 H9 1/13 E10 0.59 F10 0.8 G10 315 H10 1/26 E11 0.01 F11 0.9 G11 130 H11 1/26 E12 0.68 F12 0.5 G12 31 H12 32 E13 −2,0,2,4 F13 2,4,6,8 G13 2,0,2,8 H13 5,4,5,8 E14 −7,0,7,14 F14 −12, −3,6,15 G14 3,0,3,12 H14 10,9,10,13 E15 3,0, −3, −6 F15 −12, −10, −8, −6 G15 −1,0, −1, −4 H15 0, −2,0,6 E16 6,0, −6, −12 F16 5, −2, −9, −16 G16 4,0,4,16 H16 2,0,4,14 E17 7,7,7,7 F17 −2, −3, −4, −5 G17 0.5,0,0.5,2 H17 7,4,5,10 E18 1,0, −1, −2 F18 2.5,3,3.5,4 G18 1.5,0,1.5,6 H18 −1,4,5,2

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The only way to learn mathematics is to do mathematics

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