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Grade& 10:& Revision& Package& Topics&&
&Revision& for&Math& Studies& SL&
1&
!!!!!!!!
Grade 10 Revision for IB DP Math Studies SL
!!!!!Instructions:!Read!carefully!&These& are& the& prior& learning& topics& that& you& should& have&mastered& prior& to& starting&Mathematics&SL/HL.& Please&make& sure& to& show& all& your&working&out.&Write& your& final& answer& in& the& box. &&&&&&&&&&&*Give& all& answers& either& as& an& exact& value& or& correct& to& 3& significant& figures& unless& stated& otherwise. &&&
Grade& 10:& Revision& Package& Topics&&
&Revision& for&Math& Studies& SL&
2&
Numbers& Algebra&•! Forms&of&numbers:&integers,&fractions,&decimals,&
exponents,&absolute&value,&standard&form&(scientific¬ation),&recurring&decimals&and&surds/radicals&
•! The&four&number&operations&(addition,&subtraction,&multiplication&and&division)&using&integers,&decimals&and&fractions,&including&order&of&operations&
•! Simplification&of&expressions&involving&surds&(roots&or&radicals),&including&rationalizing&the&denominator&
•! Calculate&squares,&square&roots,&cubes&and&cube&roots&of&numbers.&&
•! Prime&numbers&and&factors,&including&greatest&common&factor&and&least&common&multiple&
•! Integer,&Fractional&and&Negative&exponents/indices&•! Number&lines&•! Order&quantities&by&magnitude&and&demonstrate&
familiarity&with&the&symbols&=,≈,≤,≥,<,>,&•! Make&estimates&of&numbers,&quantities&and&lengths,&
give&approximations&to&specified&numbers&of&significant&figures&and&decimal&places&and&round&off&answers&to&reasonable&accuracy&in&the&context&of&a&given&problem.&&
•! Units&of&measurement&•! Ratio,&percentage;&direct&and&inverse&proportion&
Sets&and&Numbers&•! Number&systems:&set&of&positive&integers&and&zero&
(N),&integers&(Z),&rational&numbers&(Q),&irrational&numbers&(Q’),&and&real&numbers&(R)&
•! Concept&of¬ation&of&sets,&elements,&universal&(()&(reference&set,&empty&(null)&set,&complement,&subset,&equality&of&sets,&disjoint&sets,&Operations&on&sets;&union&and&intersection.&Communitive,&associative&and&distributive&properties.&&
•! Venn&Diagrams&•! Number&sequences&
•! Addition,&subtraction,&multiplication&and&division&of&algebraic&terms&
•! Manipulation&of&linear&and&quadratic&expressions,&including&factorization,&expansion,&and&the&use&of&the&formula&
•! Linear&functions,&their&graphs,&gradients&and&y]intercept&&•! Algebraic&fractions&&•! Integer&and&fractional&exponents&(including&negative&
number&exponents)&•! Patterns&and&sequences&•! Algorithms&•! Functions&
•! Types&of&functions:&linear,&quadratic,&exponential,&sine&and&cosine&
•! Domain&and&range&•! Transformations&•! Composite&Functions&
•! Equations:&•! Linear&•! Quadratic&•! Simultaneous&
•! Solving&Inequalities&in&one&variable&or&quadratic&equations&•! Arithmetic&and&geometric&series&•! Algebraic&Fractions&•! Simultaneous&Equations&&
Geometry& && Trigonometry& Statistics&and&Probability&•! Geometrical&elements&and&their&classification&•! Perimeter&and&area&of&plane&figures.&Properties&of&triangles&
and&quadrilaterals,&including¶llelograms,&rhombuses,&rectangles,&squares,&kites&and&trapeziums&(trapezoids);&compound&shapes.&&
•! Volumes&of&prisms,&pyramids,&spheres,&cylinders&&&cones.&•! Distance&•! Angle&properties&and&measurement&in°rees.&&•! Compass&directions&and&three&figure&bearings.&&•! Right]angle&trigonometry.&&•! Simple&applications&for&solving&triangles.&&•! Pythagoras’&theorem&and&its&converse.&&•! The&Cartesian&plane&•! Simple&transformations,&translation,&reflection,&rotation,&
enlargement.&&•! Congruence&and&similarity,&including&the&concept&of&scale&
factor&of&an&enlargement.&&•! The&circle,&its¢re&and&radius,&area&and&circumference.&
The&terms&“arc”,&“sector”,&“chord”,&“tangent”&and&“segment”.&&
•! Circle&geometry&•! Three]dimensional&coordinate&geometry&&•! Sine&and&cosine&rules&*&•! The&unit&circle&*&
•! Graphical&analysis&and&representation&(pie&charts,&histograms,&line&graphs,&scatter&plots,&box]and]whisker&plots)&
•! Population&sampling&•! Measures&of¢ral&tendency/location&(mean,&mode,&
median,&quartile,&percentile)&for&discrete&and&continuous&data&
•! Measures&of&dispersion&(range,&interquartile&range)&for&discrete&and&continuous&data&
•! Probability&of&an&event&•! Probability&of&independent,&mutually&exclusive&and&
combined&events&•! Probability&of&successive&trials&•! Standard&deviation&*&•! Conditional&probability&*&
Number& Sense&&
&Revision& for&Math& Studies& SL&
4&
SECTION!1:!Number!Sense!&Calculate:&&1. ! −5 × 5 − (−8) × 2&
&&&&&&&
2. ! 2 + 3(2 − 20 ÷ 24)4 − (54 + 3) ÷ 2&&&&
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Decimals& && Fractions&&3. ! Write& as& decimals. &
&&&
&&&&&&&&4. ! Write& as& fractions. &
&&&
&&&&&&&5. ! Perform& the& following& operations.&Give& the& answer& as& a& decimal& and& a& fraction.&
!
!
Number& Sense&&
&Revision& for&Math& Studies& SL&
5&
50 × 0.1 = 77777777777777777777777777777435 × 0.01 = 77777777777777777777777777777777120.01
= 7777777777777777777777777777771
0.025=&
&&&&&&&&&&&&&&&6. ! &&&&&&&&&7. ! Calculate.&Give& your& answer& as& a& fraction& and& a& decimal.&&
972−43; ×
15=&
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Number& Sense&&
&Revision& for&Math& Studies& SL&
6&
8. ! Nina& scored& 70& out& of& 80& in& a& test,& find& her& score& as& a& percentage.&&&&&&&&&&&&&&&&&9. ! Jeff& bought& a& car& for& $4000& and& sold& it& for& $5000.&What& is& his& percentage& profit?&&&&&&&&&&&&&&&&&10. !John& bought& a& car& for& $4000& and& sold& it& for& $3000.&What& is& his& percentage& loss?&
&&&&&&&&&&&&&
Number& Sense&&
&Revision& for&Math& Studies& SL&
7&
11. !A& school& has& 80& staff.�15%& of& the& staff& wear& glasses.&&Calculate& the& number& of& staff& that& wear& glasses.&&
&&&&&&&&&&&&&&12. !Ayesha& plays& hockey.�Last& year& Ayesha& scored& 8& goals.& This& year& Ayesha& scored& 13& goals.&
Calculate& the& percentage& increase& in& for& the& number& of& goals& scored.&&
&&&&&&&&&&&13. !56%& of& students& in& a& school& are& girls.�There& are& 420& girls& in& the& school.&&
Work& out& the& total& number& of& students& in& the& school.& &&&
&&&&&&&&&&&
Number& Sense&&
&Revision& for&Math& Studies& SL&
8&
14. !Find& the& Lowest& Common&Multiple& (LCM).&& (or& Least& Common&Multiple)& of:&&&&& 60& and& 72&&&&&&&&&&
&&
15. !Find& the& Greatest& Common& Factor& (GCF)& (or& Highest& Common& Factor)& of:&&& 21& and& 35&&&&&&&&&&&&16. !Find& the& Greatest& Common& Factor& (GCF)& (or& Highest& Common& Factor)& of:&&& 21& and& 35&&&&&&&&&&&17. !Find& the& Highest& Common& Factor& and& Lowest& Common&Multiple& of& 168& and& 180.&
&&&&&&&&&&&
Number& Sense&&
&Revision& for&Math& Studies& SL&
9&
18. !Solve.& Leave& your& answer& in& Standard& form.&&&&&&&&&&&&&&&&&&
19. !At& a& school& the& ratio& of& the& number& of& boys& to& number& of& girls& is& 9:11& There& are& 96&more!girls&than& boys.&Work& out& the& total& number& of& students& at& the& school.&&&&&&&&&&&&&&
20.!Water needs to be removed from an underground chamber before work can commence. When the water was at a depth of 3m, five suction pipes were used and emptied the chamber in 4 hours. If the water is now at a depth of 5m (same cross- section), and you want to empty the chamber in 10 hours time, how many pipes need to be used?
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a)&&b) &&c)&
Number& Sense&&
&Revision& for&Math& Studies& SL&
10&
Sets!and!Venn!Diagrams!&21. !&&&&&&&&&&&&22. !Given& the& Universal& set&&ℰ = {odd7numbers7less7than715}7&where&A& and&B& are& subsets& of&ℰ.&&
A = {prime numbers} B = {multiples of 3}
List:�
&&&&&&&&&&&&&&
23.!L = {2, 3, 5, 7, 11}, M = {3, 4, 5, 6}, O = {1, 2, 4, 5, 10, 20}. List:
&&&&&&&&&&&&&&&&&&&&&&&
(a)!L ∩ O& ………………………………………………………………. ..&
(b) !L ∪ O&& ……………………………………………………………. …. &
(c)! M ∪ O& ………………………………………………………………. ..&
(d)!M ∩ O&& ……………………………………………………………. …. &
(e)! Is&5 ∈ L ∩ M7?& …………………………………………………. ..&Explain& your& answer. &&
(a)!A#……………………………………………………………………………. &
(b) !B#……………………………………………………………………………. &
(c)! A’& ……………………………………………………………………………. &
(d)!B’& ……………………………………………………………………………. &
&
Number& Sense&&
&Revision& for&Math& Studies& SL&
11&
24. !Draw& a& Venn& diagram& for& the& following.&&
Universal& Set:& 777(7 = 7 {TUVWXWYZ7 ≤ 710}77And& & & 77[7 = 7 {\]^V_YZ7_\720}77&
&`7 = 7 {abcVTdcWZ7_\73}77
&&&&&&&&&&&&&&25. !&&
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subsets& of&ℇ&
Number& Sense&&
&Revision& for&Math& Studies& SL&
12&
&26. !&
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27. !&&&&
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28. !&&&&&&&&&&
Number&of&students&who&play&tennis&=&&
Number& Sense&&
&Revision& for&Math& Studies& SL&
13&
&29. !&
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30. !&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
Number& Sense&&
&Revision& for&Math& Studies& SL&
14&
31.!Find the 51st
term of the sequence 30, 23, 16, 9, ...
32.!Find the nth term formula of the sequence 7, 11, 15, 19, ...
33.!Find the first three terms of the sequence if un = 7n – 5 &
&&
&&&&&&&34. !&&&&&&&&&&&
Number& Sense&&
&Revision& for&Math& Studies& SL&
15&
35. !Determine& the& value(s)& of& the& 7th& term& in& the& following& geometric& sequences.& Show& your&working& out.& u5& =1,& u8& =27,&& u7& =&&
&&&&&&&&&&&&&&&&&&&&&&&&36. !&&&&
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37. !&
Foundations& of& Algebra&&
&Revision& for&Math& Studies& SL&
16&
SECTION!2:!Foundations!of!Algebra!1. ! Simplify& 5x& +& 4y& +& x& –& 7y&&
&&&&&&&&2. ! Solve& 3(x& –& 2)& =& x& +& 7&&
&&&&&&&&&&
3. ! Solve&4fgh= 1&&
&&&&&&&&&&&
4. ! Solve& 9x–11=5x+7& &&&&&&&&&&&&
Foundations& of& Algebra&&
&Revision& for&Math& Studies& SL&
17&
5. ! Expand& and& simplify:&&a)&& 11& –& 8(a& –& 8)& & & & & b)&& 3a& +& 4(a& –& 3)& &&&&&&&&&&&c)&& 7a& –& 9(8& –& 3a)& & & & & d)&& 4(b& +& 6)& +& 5(b& +& 3)& &&&&&&&&&&&&e)&& 7(4b& –& 3)& –& 9(2b& –& 5)& & & & f)&& c(b& +& 9)& –& b(4c& +& 3b)&
&&&&&&&&&&&&&&&&&&&&&
!
Foundations& of& Algebra&&
&Revision& for&Math& Studies& SL&
18&
6. ! Expand& and& simplify:&&
a)&&(i + 7)(i + 4)& &&&& & b)&(i + 8)(i − 9)&& & & c)&(i − 6)(i − 12)& &&&&&&&&&&d)&(i − 7)4& & & e)&(3i + 8)(2i + 7)& & & f)&(9i − 7)(5i + 11)&
&&&&&&&&&&&&&&&&g)&(12 − 5i)(6i + 7)& & h)&(4i + 9)(4i − 9)&& &&&&&& & &
&&&&&&&&&&&&&&& &
!
!
!
Foundations& of& Algebra&&
&Revision& for&Math& Studies& SL&
19&
7. ! Solve& the& following& by& using& the& GDC:&&
&&&&&&&&& a)&&2i4 + 15i + 7 = 0& & & & & b)&3i4 + 13i + 12 = 0& &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& c)&5i4 − 8i − 21 = 0& & &&&&&&&&&&&&&&&&&&& & d)&2i4 − 13i + 21 = 0&&&&&&&&&&&&&#########e)& 3i4 + 16i − 64 = 07&& & &&&&&&&&&&&&&&&&&&& f)&4i4 + 16i + 15 = 0&&&&&&&&&&&&&&&&&&&
Foundations& of& Algebra&&
&Revision& for&Math& Studies& SL&
20&
Functions!&8. ! Simultaneous& Equations:& You&must& show& your&working& clearly. &&
a)! &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& b)&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& c)&&&&&&&&&&&&&&&&&&
Foundations& of& Algebra&&
&Revision& for&Math& Studies& SL&
21&
Graphing!&&9. !M& is& the& point& (−2,& 4)& and&N& is& the& point& (6,& −8).&&&&! a& & Find& the& coordinates& of& the&midpoint& of& the& line&MN. &&&&&&&&! b& & Find& the& gradient& of& the& line&MN.&! !!! !!!!!!!! c& & Find& the& equation& of& this& line. &!!!!!!!!!! d& & Another& line&PQ& is& parallel& to&MN& and& passes& through& the& point& (1,& 5).&&&&& & Find& the& equation& of&PQ.&&&&&&&&&&&&&
Foundations& of& Algebra&&
&Revision& for&Math& Studies& SL&
22&
&! d& & Another& line&RS& is& perpendicular& to&MN& and& passes& through& the& point& (1,& 5).&&&&& & Find& the& equation& of&RS.&&&&&&&&&&&&&&&&&&&&&
10. !The& point& A& (−3,& 5)& and& the& point& B& (1,& −15)& lie& on& the& line& L.&&a. ! Find& the& equation& of& the& line& L.&&b. ! Find& the& distance& between&A#and& B.&
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Foundations& of& Algebra&&
&Revision& for&Math& Studies& SL&
23&
11. !A& line& has& equation& 6x+2y+9=0& &
(a)& Find& the& gradient& of& the& line.&&
(b)& Find&where& the& line& crosses& the& y]axis& &
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12. !What& is& the& slope,& x]intercept,& and& y]intercept& of& the& equation&5i − 4k = 8& ?&
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ADDITIONAL& CONTENT& FOR& HIGHER& LEVEL&MATHEMATICS&&
&Ticket& to& IB&Mathematics& HL&
24&
SECTION!3:!The!Art!of!Geometry!and!Trigonometry!&1. ! Find& the&missing& angles. &
a& =&
b& =&
c& =&
d& =&
e& =&
f& =&
g& =&
&&&&
ADDITIONAL& CONTENT& FOR& HIGHER& LEVEL&MATHEMATICS&&
&Ticket& to& IB&Mathematics& HL&
25&
2. ! &&&&&&&&&&&&&&&&&&&&&&3. ! Find& the& perimeter& and& area& of& the& following& shape.&
&&&&&&&&
&&&&&&&&&&&&
ADDITIONAL& CONTENT& FOR& HIGHER& LEVEL&MATHEMATICS&&
&Ticket& to& IB&Mathematics& HL&
26&
&4. ! Find& the& volume& and& surface& area& of& the& following&shape. &
&&&&&&&&&&&&&&&&&&&&&&&
5. ! Calculate& the& height& of& a& closed& cylinder&with& a& volume& of& 250& cm3& and& a& radius& of& 5. 5& cm.& Find&the& surface& area& of& the& cylinder. &&&&&&&&&&&&&&&&&&&&&
ADDITIONAL& CONTENT& FOR& HIGHER& LEVEL&MATHEMATICS&&
&Ticket& to& IB&Mathematics& HL&
27&
&6. ! &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&7. ! &&&&&&&&&&&&&&&&&
ADDITIONAL& CONTENT& FOR& HIGHER& LEVEL&MATHEMATICS&&
&Ticket& to& IB&Mathematics& HL&
28&
8. ! &&&&&&&&&&&&&&&&&&&&&&&&&&&&
9. ! &&&&&&&&&&&&&&&&&&&&&&&&&&&&
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&(a)!…………………………………&
&(b) !………………………………...&
ADDITIONAL& CONTENT& FOR& HIGHER& LEVEL&MATHEMATICS&&
&Ticket& to& IB&Mathematics& HL&
29&
&10. !&&&&
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11. !&&&&&&&&&&&&&&&&&&&&&&
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ADDITIONAL& CONTENT& FOR& HIGHER& LEVEL&MATHEMATICS&&
&Ticket& to& IB&Mathematics& HL&
30&
&SECTION!4:!The!Truth!about!Statistics!and!Probability!
!1. ! &&&&
&&&&&&&&&&&&&&&&&&&&
&&&
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a)&
b) &
ADDITIONAL& CONTENT& FOR& HIGHER& LEVEL&MATHEMATICS&&
&Ticket& to& IB&Mathematics& HL&
31&
2. ! &&&&&&&
&&&&&&&&&&&&&&&&&&&&
(b)& i)&Median:& …………………. &
&&&&&& ii)& IQR& …………………………&
&(c)& ………………………………………………………. . …&
………………………………………………………………. &
………………………………………………………………. . &
………………………………………………………………. &
………………………………………………………………. . &
(d)&Median:& …………………………&
ADDITIONAL& CONTENT& FOR& HIGHER& LEVEL&MATHEMATICS&&
&Ticket& to& IB&Mathematics& HL&
32&
3.! Bob asked each of 40 friends how many minutes they took to get to work. The table shows some information about his results.
&&&&&&&&&
(a)!Work out an estimate for the mean time taken.
(b)!State the modal class interval.
(c)!Find the group containing the median.
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ADDITIONAL& CONTENT& FOR& HIGHER& LEVEL&MATHEMATICS&&
&Ticket& to& IB&Mathematics& HL&
33&
4. ! &&&&&&
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5. ! &&&&&&&&&&&
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ADDITIONAL& CONTENT& FOR& HIGHER& LEVEL&MATHEMATICS&&
&Ticket& to& IB&Mathematics& HL&
34&
6. ! &&&&&&&&&&&&&&&&&&&&&&&&&&&&&
7.! 20 students scored goals for the school hockey team last month. The table gives information about the number of goals they scored.
(a) Write down the modal number of goals scored.
(b) Work out the range of the number of goals scored.
(c) Work out the mean number of goals scored.
&& &
&(a)!Median:& ………………………. &&&(b)& IQR:& ………………………………&
&(a)!Modal& Number:& ……………. . &&(a)!Range:& …………………. ………. &&(b)&Mean:& ……………………………&
ADDITIONAL& CONTENT& FOR& HIGHER& LEVEL&MATHEMATICS&&
&Ticket& to& IB&Mathematics& HL&
35&
8. ! The& table& gives& information& about& the& heights,& h&metres,& of& trees& in& a& wood.&&
&
Draw& a& histogram& to& show& this& information.&&
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ADDITIONAL& CONTENT& FOR& HIGHER& LEVEL&MATHEMATICS&&
&Ticket& to& IB&Mathematics& HL&
36&
9. ! The& scatter& graph& shows& information& about& 10& apartments& in& a& city. &The& graph& shows& the& distance& from& the& city& centre& and& the&monthly& rent& of& each& apartment.&&
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The& table& shows& the& distance& from& the& city& centre&and& the&monthly& rent& for& two& other&apartments.&&
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(a)!On& the& scatter& graph,& plot& the& information& from& the& table. &
(b) !Describe& the& relationship& between& the& distance& from& the& city& centre& and& the&monthly& rent.&&&
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&An& apartment& is& 2. 8& km& from& the& city& centre. &
(c)& Find& an& estimate& for& the&monthly& rent& for& this& apartment.&&
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ADDITIONAL& CONTENT& FOR& HIGHER& LEVEL&MATHEMATICS&&
&Ticket& to& IB&Mathematics& HL&
37&
11.!This frequency table gives information about the ages of 60 teachers.
&
(a)!Complete the cumulative frequency table.
&
(b)!On the grid opposite, draw a cumulative frequency graph for this information.
(c)!Use your cumulative frequency graph to find an estimate for the median age.
........................... years
(d)!Use your cumulative frequency graph to find an estimate for the number of teachers older than 55 years.
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ADDITIONAL& CONTENT& FOR& HIGHER& LEVEL&MATHEMATICS&&
&Ticket& to& IB&Mathematics& HL&
39&
12. !Emily& has& a& bag& of& 20& fruit& flavour& sweets.&&
7& of& the& sweets& are& strawberry& flavour,& &11& are& lime& flavour,&2& are& lemon& flavour.&&
Emily& takes& at& random& a& sweet& from& the& bag.&Write& down& the& probability& that& Emily& &
(a)&& takes& a& strawberry& flavour& sweet,& &
(b)&& does& not& take& a& lime& flavour& sweet,& &
(c)&& takes& an& orange& flavour& sweet.&&
& & &(a)!…………………………………….. &&(b) !………. .. …………………. ………. &&(c)& ………………………………………&
ADDITIONAL& CONTENT& FOR& HIGHER& LEVEL&MATHEMATICS&&
&Ticket& to& IB&Mathematics& HL&
40&
13.!Hannah is going to play one badminton match and one tennis match. The probability that she will win the badminton match is l
mn.
The probability that she will win the tennis match is 4h .
(a) Complete the probability tree diagram.&
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(b) Work out the probability that Hannah will win both matches.
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(c) Work out the probability that Hannah will win only one match.
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ADDITIONAL& CONTENT& FOR& HIGHER& LEVEL&MATHEMATICS&&
&Ticket& to& IB&Mathematics& HL&
41&
14. !&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
&(a)!……………………………………………. . &&&(b)& ……………………………………………. . &&&(c)& ………………………………………………&
ADDITIONAL& CONTENT& FOR& HIGHER& LEVEL&MATHEMATICS&&
&Ticket& to& IB&Mathematics& HL&
42&
15. !&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
16. !&&&&&&&&&&&&&&&
&(b) !……………………………………………. . &&&(b)& ……………………………………………. . &&&(c)& ………………………………………………&
&(a)!……………………………………………. . &&&(b)& ……………………………………………. . &&&&
ADDITIONAL& CONTENT& FOR& HIGHER& LEVEL&MATHEMATICS&&
&Ticket& to& IB&Mathematics& HL&
43&
17. !Adam& and& Boris& regularly& play& each& other& at& chess&and& in& 60%& of& their& games& each& player& is&subject& to& a& time& limit.& Adam&wins& 45%& of& the& games& played&with& a& time& limit& but& only& 30%& of&the& games& played&without& a& time& limit.&&&
(a)! Find& the& probability& that& Adam&wins& his& next& game&of& chess& against& Boris.&&
& (b)&Given& that& Adam&wins& a& game,& find& the& probability& that& it& was& played&with& a& time& limit. &&&& &
(a)!……………………………………………. . &&&(b)& ……………………………………………. . &&&&
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