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Grade& 10:& Revision& Package& Topics&&!!!!!!!!Grade 10 Revision for IB DPMath 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.&&&&1&Revision& for& Math& Studies& SL&

Grade& 10:& Revision& Package& Topics&&Numbers&Algebra& s& ! mals&and&fractions,&including&order&of&operations& ! inator& ! ots&of&numbers.&& ! on&factor&and&least&common&multiple& ! & ! Number&lines& ! liarity&with&the&symbols& , , , , , ,& ! iven&problem.&& ! Units&of&measurement& ! ets&and&Numbers& ! l&numbers&(Q’),&and&real&numbers&(R)& ! ociative&and&distributive&properties.&& ! Venn&Diagrams& ! Number&sequences&Geometry& && Trigonometry& ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! rules&*&The&unit&circle&*& ! ! ! ! ! ! ! ! ! ! ! ! equences&Algorithms&Functions& ! ,&sine&and&cosine& ! Domain&and&range& ! Transformations& ! Composite&Functions&Equations:& ! Linear& ! Quadratic& ! atistics&and&Probability& ! ! ! ! ! ! ! ! ty&*&&2&Revision& for& Math& Studies& SL&

Grade& 10:& Revision& Package& Topics&&Key!Formulae!!!!!!&3&Revision& for& Math& Studies& SL&

Number& Sense&&SECTION!1:!Number!Sense!&Calculate:&&1.! 5 5 ( 8) 2&&&&&&&&2.! 2 3(2 20 24 )4 (54 3) 2&&&&&&&&&Decimals& && Fractions&&3.! Write& as& decimals.&&&&&&&&&& !&&4.! Write& as& fractions.&&&&&&&&&&&5.! !Perform& the& following& operations.& Give& the& answer& as& a& decimal& and& a& fraction.&&4&Revision& for& Math& Studies& SL&

Number& Sense&&50 0.1 77777777777777777777777777777435 0.01 77777777777777777777777777777777&&&&&&&&&&&&&&&6.! &&&&&&&&&7.! Calculate.& Give& your& answer& as& a& fraction& and& a& decimal.&&7 419 ; &2 35&&&&&&&&&&&&&&&&&&121 777777777777777777777777777777 &0.010.025&5&Revision& for& Math& Studies& SL&

Number& Sense&&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?&&&&&&&&&&&&&&&6&Revision& for& Math& Studies& SL&

Number& Sense&&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.&&&&&&&&&&&&&&&&7&Revision& for& Math& Studies& SL&

Number& Sense&&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.&&&&&&&&&&&&&8&Revision& for& Math& Studies& SL&

Number& Sense&&18.!Solve.& Leave& your& answer& in& Standard& form.&&&a)&&&&b)&&&&&c)&&&&&&&&&&&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 thewater was at a depth of 3m, five suction pipes were used and emptied the chamber in 4 hours. Ifthe water is now at a depth of 5m (same cross- section), and you want to empty the chamber in10 hours time, how many pipes need to be used?&&&&&&&&&&9&Revision& for& Math& Studies& SL&

Number& !Given& the& Universal& set&&ℰ {odd7numbers7less7than715}7& where& A& and& B& are& subsets& of&ℰ.&&A {prime numbers}B {multiples of 3}List:&&&&&&&&&&&&&&(a)! A# . &(b)!B# . &(c)! A’& . &(d)!B’& . &&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.&&&10&Revision& for& Math& Studies& SL&

Number& Sense&&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.!&&&subsets& of&ℇ&&&&&&&&&&&&&&&&&&&&&&&&&&&11&Revision& for& Math& Studies& SL&

Number& &students&who&play&tennis& &&&&&28.!&&&&&&&&&&&12&Revision& for& Math& Studies& SL&

Number& &&&&&&&&&&&&&&&&&&&&&&&&13&Revision& for& Math& Studies& SL&

Number& Sense&&st31.!Find the 51 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.!&&&&&&&&&&&&14&Revision& for& Math& Studies& SL&

Number& Sense&&35.!Determine& the& value(s)& of& the& 7th& term& in& the& following& geometric& sequences.& Show& your&working& out.& u5& 1,& u8& 27,&& u7& 5&Revision& for& Math& Studies& SL&

Foundations& of& Algebra&&SECTION!2:!Foundations!of!Algebra!1.! Simplify& 5x& & 4y& & x& –& 7y&&&&&&&&&&2.! Solve& 3(x& –& 2)& & x& & 7&&&&&&&&&&&&4fg3.! Solve& h 1&&&&&&&&&&&&&4.! Solve& 9x–11 5x 7&&&&&&&&&&&&&&16&Revision& for& Math& Studies& SL&

Foundations& of& Algebra&&5.! Expand& and& simplify:&&a)&& 11& –& 8(a& –& 8)& &&&&&&&&&&&&c)&& 7a& –& 9(8& –& 3a)& &&&&&&&&&&&&&e)&& 7(4b& –& 3)& –& 9(2b& –& 5)& &&&&&&&&&&&&&&&!&&&&&&&&&b)&& 3a& & 4(a& –& 3)&&&d)&& 4(b& & 6)& & 5(b& & 3)& &&&f)&& c(b& & 9)& –& b(4c& & 3b)&&&17&Revision& for& Math& Studies& SL&

Foundations& of& Algebra&&6.! Expand& and& simplify:&&a)&&(i 7)(i 4)&&&&&&&&&&d)&(i 7)4 &&&&&&&&&&&&&&&&&&g)&(12 5i)(6i 7)&&&&&&&&&&&&&&&&&&&&& b)&(i 8)(i 9)&& &&c)&(i 6)(i 12)& &&e)&(3i 8)(2i 7)& &&f)& (9i 7)(5i 11)&&h)&(4i 9)(4i 9)&& &&&&&&&&&!!!&18&Revision& for& Math& Studies& SL&

Foundations& of& Algebra&&7.! Solve& the& following& by& using& the& GDC:&&&&&&&&&&& a)&&2i 4 15i 7 0& &&&&&&&&&&&&&&&&&&&&&&&&& c)&5i 4 8i 21 0& &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&#########e)& 3i 4 16i 64 07&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&b)&3i 4 13i 12 0&&&&&&&&&&&&&&&&&&d)&2i 4 13i 21 0&f)&4i 4 16i 15 0&&19&Revision& for& Math& Studies& SL&

Foundations& of& Algebra&&Functions!&8.! Simultaneous& Equations:& You& must& show& your& working& clearly.&&a)! &&&&&&&&&&&&&&& b)&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& c)&&&&&&&&&&&&&&&&&&&20&Revision& for& Math& Studies& SL&

Foundations& of& Algebra&&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.&&&&&&&&&&&&&&21&Revision& for& Math& Studies& SL&

Foundations& of& Algebra&&&! 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.&&&&&&&&&&&&&22&Revision& for& Math& Studies& SL&

Foundations& of& Algebra&&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&&&&&&&&&&12.!What& is& the& slope,& x]intercept,& and& y]intercept& of& the& equation& 5i 4k 8& ?&&&&&&&&&&&&&&&23&Revision& for& Math& Studies& SL&

ADDITIONAL& CONTENT& FOR& HIGHER& LEVEL& igonometry!&1.! Find& the& missing& angles.&a& &b& &c& &d& &e& &f& &g& &&&&&&24&Ticket& to& IB& Mathematics& HL&

ADDITIONAL& CONTENT& FOR& HIGHER& LEVEL& MATHEMATICS&&2.! &&&&&&&&&&&&&&&&&&&&&&3.! Find& the& perimeter& and& area& of& the& following& shape.&&&&&&&&&&&&&&&&&&&&&&25&Ticket& to& IB& Mathematics& HL&

ADDITIONAL& CONTENT& FOR& HIGHER& LEVEL& MATHEMATICS&&&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.&&&&&&&&&&&&&&&&&&&&&&26&Ticket& to& IB& Mathematics& HL&

ADDITIONAL& CONTENT& FOR& HIGHER& LEVEL& MATHEMATICS&&&6.! &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&7.! &&&&&&&&&&&&&&&&&&27&Ticket& to& IB& Mathematics& HL&

ADDITIONAL& CONTENT& FOR& HIGHER& LEVEL& MATHEMATICS&&8.! &&&&&&&&&&&&&&&&&&&&&&&&&&&&9.! &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(a)! &&(b)! . .&&28&Ticket& to& IB& Mathematics& HL&

ADDITIONAL& CONTENT& FOR& HIGHER& LEVEL& !&&&&&&&&&&&&&&&&&&&&&&&&&&&&&29&Ticket& to& IB& Mathematics& HL&

ADDITIONAL& CONTENT& FOR& HIGHER& LEVEL& s!and!Probability!!1.! &&&&&&&&&&&&&&&&&&&&&&&&&&&a)&&&&b)&&&30&Ticket& to& IB& Mathematics& HL&

ADDITIONAL& CONTENT& FOR& HIGHER& LEVEL& MATHEMATICS&&2.! &&&&&&&&&&&&&&&&&&&&&&&&&&&(b)& i)& Median:& . &&&&&&&ii)& IQR& &&(c)& . . & . & . . & . & . . &(d)& Median:& &&31&Ticket& to& IB& Mathematics& HL&

ADDITIONAL& CONTENT& FOR& HIGHER& LEVEL& MATHEMATICS&&3.! Bob asked each of 40 friends how many minutes they took to get to work. The table shows someinformation 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.&&&&&&32&Ticket& to& IB& Mathematics& HL&

ADDITIONAL& CONTENT& FOR& HIGHER& LEVEL& MATHEMATICS&&4.! &&&&&&&&&&&&&&&&5.! &&&&&&&&&&&&&&&&33&Ticket& to& IB& Mathematics& HL&

ADDITIONAL& CONTENT& FOR& HIGHER& LEVEL& MATHEMATICS&&6.! &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(a)! Median:& . &&&(b)& IQR:& &7.! 20 students scored goals for the school hockey team last month. The table gives informationabout 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)! Modal& Number:& . . &&(a)! Range:& . . &&(b)& Mean:& &&&34&Ticket& to& IB& Mathematics& HL&

ADDITIONAL& CONTENT& FOR& HIGHER& LEVEL& MATHEMATICS&&8.! The& table& gives& information& about& the& heights,& h&metres,& of& trees& in& a& wood.&&&Draw& a& histogram& to& show& this& information.&&&&&&35&Ticket& to& IB& Mathematics& HL&

ADDITIONAL& CONTENT& FOR& HIGHER& LEVEL& MATHEMATICS&&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.&&&&&&&&&&&&&&The& table& shows& the& distance& from& the& city& centre&and& the& monthly& rent& for& two& other&apartments.&&&&(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.&&&&.&.&&& An& apartment& is& 2. 8& km& from& the& city& centre.&(c)& Find& an& estimate& for& the& monthly& rent& for& this& apartment.&&&&&&&36&Ticket& to& IB& Mathematics& HL&

ADDITIONAL& CONTENT& FOR& HIGHER& LEVEL& MATHEMATICS&&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 olderthan 55 years.&&&&&&&&&&&&&&&&&&&37&Ticket& to& IB& Mathematics& HL&