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UEB Maths and Science Practice Exercises

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B012

2

UEB Maths and Science Practice exercises

Contents

Exercise 1 .................................................................................. 3

Answers .................................................................................... 3

Exercise 2 .................................................................................. 4

Answers .................................................................................... 4

Exercise 3 .................................................................................. 5

Answers .................................................................................... 5

Exercise 4 .................................................................................. 6

Answers .................................................................................... 6

Exercise 5 .................................................................................. 7

Answers .................................................................................... 7

Exercise 6 .................................................................................. 8

Answers .................................................................................... 8

Exercise 7 .................................................................................. 9

Answers .................................................................................... 9

Exercise 8 ................................................................................ 10

Answers .................................................................................. 10

Exercise 9 ................................................................................ 12

Answers .................................................................................. 12

Exercise 10 .............................................................................. 14

Answers .................................................................................. 14

Exercise 11 (Extended practice) .............................................. 16

Answers .................................................................................. 17

Disclaimer ................................................................................... 21

UKAAF contact details ............................................................. 21

UKAAF registered address ...................................................... 21

3

Exercise 1

(a) 3.2 0.4 1.28

(b) There were 20 000 people in the football ground.

(c) 18+=23

(d) 14 - + 3 = 8

(e) 4 7 0.571428

Answers

,ex]cise #a

"<a"> #c4b"8#j4d "7 #a4bh

"<;b"> ,"! 7 #bj"jjj p 9 !

football gr.d4

"<;c"> #ah"6$#d "7 #bc

"<;d"> #ad"-+"6#c "7 #h

"<;e"> #d"/#g

"7 #j4<#egadbh>^4

4

Exercise 2

(a) Work out 1

4 of 48

(b) Work out 1 1

2 3

(c) Work out 2 3

5 23 4

(d) Work out 1 1

12 6

(e) 3 2

Answers

,ex]cise #b

"<a"> ,"w \ #a/d ( #dh

"<;b"> ,"w \ #a/b"/#a/c

"<;c"> ,"w \ #e#b/c"-#b#c/d

"<;d"> ,"w \

#a"-"<#a/b"6#a/f">

"<;e"> "-#c @< #b

5

Exercise 3

a. x

y

b. a b

p q

c. 5 3 13

p 2p 2p

d. 2 1 1

x 1 x 2 2

e. Area 1

(a b)h2

Answers

,ex]cise #c

a4 ;;(x./y)

;b4 ;;(a"6b./p"-q)

;c4 ;;;(#e./p)"6(#c./#bp)

"7 (#ac./#bp);'

;d4 ;;;(#b./x"6#a)

"-(#a./x"6#b) "7 #a/b;'

;e4 ,>ea "7 #a/b"<a"6b">h

6

Exercise 4

a. 1/2 + 3/4 = 5/4

b. 36%

c. 225 15

d. √9 3

e. 25 25

f. 12: 36 1: 3

Answers

,ex]cise #d

a4 #a_/#b"6#c_/#d "7 #e_/#d

;b4 #cf.0

;c4 ;%#bbe+ "7 #ae

;d4 "%#i "7 #c

;e4 #e9#b "7 #be

;f4 #ab3#cf "7 #a3#c

7

Exercise 5

1.

1

416 2

2. 2 2qp q p

3. 2

1h 9

4. 3 125 5

5. 1

6664 64 2

Answers

,ex]cise #e

#a4 #af9#a/d "7 #b

#b4 ;;;p9#bq "7@: p9<#bq>;'

#c4 h;5#a9#b "7 #i

#d4 ;;;%9#c#abe+ "7 #e;'

#e4 ;;;#fd9#a/f "7 %9#f#fd+

"7 #b;'

8

Exercise 6

1. 2 4 8

2. 2

2

13

3

3. 2g 9.8 ms

4. 2.5cm 1

5. Area of a circle = 2r

6. 15 F 9 C

Answers

,ex]cise #f

#a4 ;;;9"-#b"89"-#d

"7 9"6#h;'

#b4 ;;;#c9<"-#b>

"7 (#a./#c9#b);'

#c4 ;;;g ^9 #i4h ms9<"-#b>;'

#d4 #b4e;cm _9 #a77

#e4 ,>ea ( a circle

"7 .pr;9#b

#f4 #ae^j,f ^9 "-#i^j,c

9

Exercise 7

1. tan40

2. secx

3. cosQ

4. 2tanx

5. 2tan50

6. wcost

7.

8. LK t

9. 4

r 1

1 2 3 4 r

Answers

,ex]cise #g

#a4 tan#dj

#b4 sec ;x

#c4 cos,q

#d4 #btan ;x

#e4 #btan#ej

#f4 ;w cos ;t

#g4 .w "7 .?^4

#h4 ;;;<,,lk>^: "7 t,:;'

#i4 ;;;#a"6#b"6#c"6#d

"7 ,.s.5<r"7#a>.9#dr;'

10

Exercise 8

1.

4

PQ 5

6

2. d

dt

3.

333

2

11

x 27 1 26x dx

3 3 3 3

4. a = 2

3

5. 11 4

5 10

6. 1 2 5 6 5 14 6 16 19 22

3 4 7 8 15 28 18 32 43 50

Answers

,ex]cise #h

#a4 ;;;<,,pq>^:

"7 ,"<#d,">

,"<#e,">

,"<#f,">;'

#b4 ;;;.a "7 (d.w./dt)

"7 .?.9<44>;'

11

#c4 ;;;!5#a9#cx9#b;dx

"7 .<(x9#c./#c).>5#a9#c

"7 #bg/c"-#a/c "7 #bf/c;'

#d4 ^2a "7 ,"<"-#b,">

,"< #c,">

#e4 ,"< #aa "-#d ,">

,"<"-#e #aj,">

#f4 ,"<#a #b,">,"<#e #f,">

,"<#c #d,">,"<#g #h,">

"7 ,"<#e"6#ad #f"6#af ,">

,"<#ae"6#bh #ah"6#cb,">

"7 ,"<#ai #bb,">

,"<#dc #ej,">

12

Exercise 9

a. If P {4, 8, 12} and B {even numbers} then A B

b. If D {ford, saab, nissan, renault} then ford D

c. P Q (P Q)

d. xy i iS (x x)(y y)

e. 5

i

i 1

x

f. 6

2

6C

2

Answers

,ex]cise #i

a4 ,if ;,p "7 _<#d1 #h1

#ab_> & ;,b "7 _<ev5 numb]s_>

!n ,a ^< ;,b

;b4 ,if ;,d "7 _<=d1 saab1

nissan1 r5ault_> !n =d ^e ;,d

;c4 ;;;,p7.6,q7

"7 "<,p.8,q">7;'

13

;d4 ;;;,s5<xy>

"7 ,.s"<x5i"-x:">"

"<y5i"-y:">;'

;e4 ;;,.s.5<i"7#a>.9#ex5i

;f4 ;9#f,c5#b "7 "<#f]#b">

14

Exercise 10

1. uncertainty in P = maximum minimumP P

n

2. 11 2 2G 6.67 10 Nm kg

3. Glucose has the molecular formula 6 12 6C H O

4. 2 4 3 2 2N O (g) 2NaOH(aq) NaNO (aq) NaNO (aq) H O(l)

Answers

ex]cise #aj

#a4 unc]ta9ty 9 ;;;,p

"7 (,p5<maximum>

"-,p5<minimum>./n);'

#b4 ;;;,g

"7 #f4fg"8#aj9<"-#aa>

,nm9#bkg9<"-#b>;'

#c4 ,glucose has ! molecul>

=mula ,c;5#f,h5#ab,o5#f

#d4 ;;;,n5#b,o5#d"<g">

"6#b,na,o,h"<aq">

15

\o ,na,n,o5#c"<aq">

"6,na,n,o5#b"<aq">

"6,h5#b,o"<l">;'

16

Exercise 11 (Extended practice)

(a) 8.6 0.2 43

(b) The world's population on 30/01/2014 at 13 14 was

7 209 860 703

(c) 7++3=15

(d) 4 3 1.3

(e) Work out 2 3

45 5

(f) Write 2x 4 1

x 1 x 2 as a single fraction in its simplest form.

(g) Simplify 5 3

2

4y 2y

y

(h) Change $5.20 into pounds if £1 = $1.62.

(i) Find 1

4 %2

of €450.50.

(j) Work out 6 4(3.5 10 ) (5 10 )

(k) Is 4 5 10 2?

(l) Solve (x 2)(2x 5) 4(x 3)

(m) Solve 2 37 x

3 y 2 9

(n) Volume of a sphere = 34r

3

(o) Solve sin sin cos sin 0.53 3

(p) 4 16 2

(q) 1

3327 27 3

(r) 2 2x y 25

17

(s) 2P(g) 2Q(g) R(g) S(g)

(t) n

1

1x x

n

(u) Time for a drink!

Coffee 8 10 4 2C H N O and water

2H O plus milk.

Answers

,ex]cise #aa "<,ext5d$

practice">

"<a"> #h4f"/#j4b "7 #dc

"<;b"> ,! _w's popula;n on

#cj_/#ja_/#bjad at #ac"ad 0

#g"bji"hfj"gjc

"<;c"> #g"6$#d:"6#c "7 #ae

"<;d"> #d"/#c "7 #a4<#c>^4

"<;e"> ,"w \ #d#b/e"-#c/e

18

"<;f"> ,write

;(#bx"6#d./x"-#a)"8(#a./x"6#b)

z a s+le frac;n 9 xs simple/

=m4

"<;g"> ,simplify

;(#dy9#e"6#by9#c./y9#b)

"<;h"> ,*ange @s#e4bj 9to

p.ds if @l#a "7 @s#a4fb4

"<i"> ,f9d #d#a/b.0 (

@e#dej4ej4

"<;j"> ,"w \

"<#c4e"8#aj9<"-#f>">

"/"<#e"8#aj9#d">

"<;k"> ,is #d"8#e

@> #aj"8#b8

19

"<;l"> ,solve

"<x"-#b">"<#bx"6#e">

"7 #d"<x"6#c">

"<;m"> ,solve

,"<"-#b,">"6,"<"-#cg ,">

,"< #c,"> ,"< y"6#b,">

"7 ,"<x ,">

,"<#i,">

"<;n"> ,volume ( a sp"h

"7 #d/c.pr9#c

"<o"> ,solve

;;;sin.?sin"<(.p./#c)">

"6cos.?sin"<(.p./#c)">

"7 #j4e;'

"<;p"> ;;;%9#d#af+ "7 #b;'

20

"<;q"> ;;;#bg9#a/c

"7 %9#c#bg+ "7 #c;'

"<;r"> x;9#b"6y9#b "7 #be

"<;s"> ;;;#b,p"<g">

"6#b,q"<g">

\o ,r"<g">"6,s"<g">;'

"<;t"> ;;;x:

"7 (#a./n),.s.5#a.9nx;'

"<;u"> ,"t = a dr9k6

,c(fee ,c;5#h,h5#aj,n5#d,o5#b

& wat] ,h;5#b,o plus milk6

21

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