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B012
UEB Maths and Science Practice
Exercises
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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
2
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
3
Exercise 2
(a) Work out
1
of 48
4
(b) Work out
1 1
¸
2 3
2
3
(c) Work out 5 - 2
3
4
æ1 1 ö
(d) Work out 1- çç + ÷
÷
÷
çè2 6 ø
(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
4
Exercise 3
a.
x
y
b.
a+ b
p- q
c.
5
3
13
+
=
p 2p 2p
2
1
1
=
x+ 1 x+ 2 2
1
e. Area = (a + b)h
2
d.
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
5
Exercise 4
a. 1/2 + 3/4 = 5/4
b. 36%
c.
225 = 15
d. √ 9 = 3
e. 52 = 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
6
Exercise 5
1
4
1. 16 = 2
2. p2q ¹ p2q
3. h12 = 9
4. 3 125 = 5
1
6
5. 64 =
6
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;'
7
Exercise 6
1. 2´
-
2. 3- 2 =
4= +8
1
32
3. g » 9.8 ms- 2
4. 2.5cm 1¢¢
2
5. Area of a circle = r
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
8
Exercise 7
1. tan 40
2. sec x
3. cosQ
4. 2 tanx
5. 2 tan50
6. w cos t
7.  = 
8. LK = t
4
9. 1+ 2 + 3 + 4 =
å
r
r= 1
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;'
9
Exercise 8
æ4÷
ö
çç ÷
÷
PQ = çç5÷
çç ÷
÷
÷
çè6÷
ø
1.
2.  =
d
= 
dt
3
3.
ò
1
3
éx3 ù 27 1 26
x dx = ê ú =
- =
ê3 ú
3
3
3
ë û1
2
æ4. a = çç
çè
ö
2÷
÷
÷
3÷
ø
æ11 - 4÷
ö
5. çç
÷
çè- 5 10 ÷
÷
ø
æ1 2öæ
ö æ5 + 14 6 + 16 ö
÷
÷
çç5 6÷
ç
6. çç
÷
÷
÷
÷ç7 8ø
÷= èçç15 + 28 18 + 32ø
÷=
çè3 4øè
÷
÷
÷
æ19 22ö
÷
çç
÷
÷
çè43 50ø
÷
Answers
,ex]cise #h
#a4 ;;;<,,pq>^:
"7 ,"<#d,">
,"<#e,">
,"<#f,">;'
#b4 ;;;.a "7 (d.w./dt)
"7 .?.9<44>;'
10
#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,">
,"<
#e4 ,"<
#c,">
#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,">
11
Exercise 9
a. If P = {4, 8, 12} and B = {even numbers} then A Ì B
b. If D = {ford, saab, nissan, renault} then ford Î D
c. P¢È Q¢= (P Ç Q)¢
d. Sxy =
å
(xi - x)(yi - y)
5
e.
å
xi
i= 1
æ6ö
f. 6 C2 = çç ÷
÷
çè2÷
÷
ø
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;'
12
;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">
13
Exercise 10
1. uncertainty in P =
Pmax imum - Pminimum
n
2. G = 6.67 ´ 10- 11 Nm2kg- 2
3. Glucose has the molecular formula C6H12O6
4. N2O4 (g) + 2NaOH(aq) ® NaNO3 (aq) + NaNO2 (aq) + H2O(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">
\o ,na,n,o5#c"<aq">
14
"6,na,n,o5#b"<aq">
"6,h5#b,o"<l">;'
15
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
2 3
(e) Work out 4 5 5
(f) Write
2x + 4
1
´
as a single fraction in its simplest form.
x- 1 x+ 2
4y5 + 2y 3
(g) Simplify
y2
(h) Change $5.20 into pounds if £1 = $1.62.
1
(i) Find 4 % of €450.50.
2
(j) Work out (3.5 ´ 10- 6 ) ¸ (5 ´ 104 )
(k) Is 4 ´ 5 > 10 ´ 2 ?
(l) Solve (x- 2)(2x + 5) = 4(x+ 3)
æ(m) Solve çç
èç
ö
2÷
+
÷
÷
3÷
ø
æ- 37 ö
÷
çç
=
÷
÷
çèy + 2ø
÷
(n) Volume of a sphere =
æxö
çç ÷
÷
÷
÷
èç9ø
4 3
r
3
æ ö
æ ö
çç  ÷
+
cos

sin
(o) Solve sin  sinçç ÷
÷
÷
÷
÷= 0.5
çè3 ø
çè3 ø
(p) 4 16 = 2
1
3
(q) 27 =
3
27 = 3
(r) x2 + y2 = 25
16
(s) 2P(g) + 2Q(g) ® R(g) + S(g)
1 n
(t) x = å x
n 1
(u) Time for a drink!
Coffee C8H10N4O2 and water H2O plus milk.
Answers
,ex]cise #aa "<,ext5d$
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
"<;f"> ,write
17
;(#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
"<;l"> ,solve
"<x"-#b">"<#bx"6#e">
18
"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;'
"<;q"> ;;;#bg9#a/c
"7 %9#c#bg+ "7 #c;'
19
"<;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
20
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21