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UKAAF Logo UK Association for Accessible Formats
UEB Maths and Science Practice Exercises
Copyright © 2016 UK Association for Accessible Formats
(UKAAF).
Not for re-sale. You may reproduce in whole or in part with
acknowledgement to UKAAF.
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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