Ticket to Studies Grade 10 - isparis.edu · Grade&10:&Revision&Package&Topics& & &...

$: Ticket to Studies Grade 10 - isparis.edu · Grade&10:&Revision&Package&Topics& & & Revision&for&Math&Studies&SL& 2& Numbers& Algebra& •! Forms&of&numbers:&integers,&fractions,&decimals,&$
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. &&&



2&

Numbers& Algebra&•! Forms&of&numbers:&integers,&fractions,&decimals,&

exponents,&absolute&value,&standard&form&(scientific&notation),&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&notation&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&parallelograms,&rhombuses,&rectangles,&squares,&kites&and&trapeziums&(trapezoids);&compound&shapes.&&

•! Volumes&of&prisms,&pyramids,&spheres,&cylinders&&&cones.&•! Distance&•! Angle&properties&and&measurement&in&degrees.&&•! 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&centre&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&central&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&*&



3&

Key!Formulae!!

!

!

!

!

Number& Sense&&


4&

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.&

!

!

Number& Sense&&


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=&

&&&&&&&&&&&&

&&&&&&

Number& Sense&&


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&&


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&&


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&&


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?

&&&

&&&&

&&

a)&&b) &&c)&

Number& Sense&&


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&&


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. !&&

&&&&&&&&&&&&&&&&&&&&&&&&&

&

subsets& of&ℇ&

Number& Sense&&


12&

&26. !&

&&&&&&&&&&&&&&&&&&&&

27. !&&&&

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&&

28. !&&&&&&&&&&

Number&of&students&who&play&tennis&=&&

Number& Sense&&


13&

&29. !&

&&&&&&&&&&&&&&&&&&&&&&&&&&

30. !&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Number& Sense&&


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&&


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. !&&&&

&&&&&&&&&

37. !&

Foundations& of& Algebra&&


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& &&&&&&&&&&&&



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)&

&&&&&&&&&&&&&&&&&&&&&

!



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)&& &&&&&& & &

&&&&&&&&&&&&&&& &

!

!

!



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&&&&&&&&&&&&&&&&&&&



20&

Functions!&8. ! Simultaneous& Equations:& You&must& show& your&working& clearly. &&

a)! &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& b)&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& c)&&&&&&&&&&&&&&&&&&



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.&&&&&&&&&&&&&



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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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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&

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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& =&

&&&&



25&

2. ! &&&&&&&&&&&&&&&&&&&&&&3. ! Find& the& perimeter& and& area& of& the& following& shape.&

&&&&&&&&

&&&&&&&&&&&&



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. &&&&&&&&&&&&&&&&&&&&&



27&

&6. ! &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&7. ! &&&&&&&&&&&&&&&&&



28&

8. ! &&&&&&&&&&&&&&&&&&&&&&&&&&&&

9. ! &&&&&&&&&&&&&&&&&&&&&&&&&&&&

&

&(a)!…………………………………&

&(b) !………………………………...&



29&

&10. !&&&&

&&&&&&&&&&&&&&&&&&&&&&&&&

11. !&&&&&&&&&&&&&&&&&&&&&&

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30&

&SECTION!4:!The!Truth!about!Statistics!and!Probability!

!1. ! &&&&

&&&&&&&&&&&&&&&&&&&&

&&&

&&& &

a)&

b) &



31&

2. ! &&&&&&&

&&&&&&&&&&&&&&&&&&&&

(b)& i)&Median:& …………………. &

&&&&&& ii)& IQR& …………………………&

&(c)& ………………………………………………………. . …&

………………………………………………………………. &

………………………………………………………………. . &

………………………………………………………………. &

………………………………………………………………. . &

(d)&Median:& …………………………&



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.

& &

&

&

&



33&

4. ! &&&&&&

&&&&&&&&

&&

5. ! &&&&&&&&&&&

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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:& ……………………………&



35&

8. ! The& table& gives& information& about& the& heights,& h&metres,& of& trees& in& a& wood.&&

&

Draw& a& histogram& to& show& this& information.&&

&

& &



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.&&

&&

(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.&&

&& &

&



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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38&

&&& &



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)& ………………………………………&



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.&

&&

(b) Work out the probability that Hannah will win both matches.

&&&&&&&

(c) Work out the probability that Hannah will win only one match.

& &

&

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41&

14. !&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

&(a)!……………………………………………. . &&&(b)& ……………………………………………. . &&&(c)& ………………………………………………&



42&

15. !&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

16. !&&&&&&&&&&&&&&&

&(b) !……………………………………………. . &&&(b)& ……………………………………………. . &&&(c)& ………………………………………………&

&(a)!……………………………………………. . &&&(b)& ……………………………………………. . &&&&



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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Transcript of Ticket to Studies Grade 10 - isparis.edu · Grade&10:&Revision&Package&Topics& & &...