Grade& 10:& Revision& Package& Topics&
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Grade 10 Revision for IB DP
Math Studies SL
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Instructions:!Read!carefully!
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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.&
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*Give& all& answers& either& as& an& exact& value& or& correct& to& 3& significant& figures& unless& stated& otherwise.&
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1&
Revision& for& Math& Studies& SL&
Grade& 10:& Revision& Package& Topics&
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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&
Geometry& && Trigonometry&
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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&*&
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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&
Statistics&and&Probability&
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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&*&
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2&
Revision& for& Math& Studies& SL&
Grade& 10:& Revision& Package& Topics&
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Key!Formulae!
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Revision& for& Math& Studies& SL&
Number& Sense&
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SECTION!1:!Number!Sense!
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1.! −5 × 5 − (−8) × 2&
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2.! 2 + 3(2 − 20 ÷ 24 )4 − (54 + 3) ÷ 2&
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Decimals& && Fractions&
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3.! Write& as& decimals.&
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4.! Write& as& fractions.&
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5.! !Perform& the& following& operations.& Give& the& answer& as& a& decimal& and& a& fraction.&
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Revision& for& Math& Studies& SL&
Number& Sense&
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50 × 0.1 = 77777777777777777777777777777435 × 0.01 = 77777777777777777777777777777777
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7.! Calculate.& Give& your& answer& as& a& fraction& and& a& decimal.&&
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Revision& for& Math& Studies& SL&
Number& Sense&
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8.! Nina& scored& 70& out& of& 80& in& a& test,& find& her& score& as& a& percentage.&&
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9.! Jeff& bought& a& car& for& $4000& and& sold& it& for& $5000.&What& is& his& percentage& profit?&
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10.!John& bought& a& car& for& $4000& and& sold& it& for& $3000.&What& is& his& percentage& loss?&
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Number& Sense&
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11.!A& school& has& 80& staff. 15%& of& the& staff& wear& glasses.&&
Calculate& the& number& of& staff& that& wear& glasses.&&
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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.&&
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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.&
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Revision& for& Math& Studies& SL&
Number& Sense&
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14.!Find& the& Lowest& Common& Multiple& (LCM).&& (or& Least& Common& Multiple)& of:&&&&& 60& and& 72&
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15.!Find& the& Greatest& Common& Factor& (GCF)& (or& Highest& Common& Factor)& of:&&& 21& and& 35&
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16.!Find& the& Greatest& Common& Factor& (GCF)& (or& Highest& Common& Factor)& of:&&& 21& and& 35&
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17.!Find& the& Highest& Common& Factor& and& Lowest& Common& Multiple& of& 168& and& 180.&
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Number& Sense&
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18.!Solve.& Leave& your& answer& in& Standard& form.&
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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.&&
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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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9&
Revision& for& Math& Studies& SL&
Number& Sense&
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Sets!and!Venn!Diagrams!
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22.!Given& the& Universal& set&&ℰ = {odd7numbers7less7than715}7& where& A& and& B& are& subsets& of&ℰ.&&
A = {prime numbers}
B = {multiples of 3}
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(a)! A# ……………………………………………………………………………. &
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(c)! A’& ……………………………………………………………………………. &
(d)!B’& ……………………………………………………………………………. &
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23.!L = {2, 3, 5, 7, 11}, M = {3, 4, 5, 6}, O = {1, 2, 4, 5, 10, 20}. List:
(a)! L ∩ O& ………………………………………………………………. ..&
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(b)!L ∪ O&& ……………………………………………………………. …. &
(c)! M ∪ O& ………………………………………………………………. ..&
(d)!M ∩ O&& ……………………………………………………………. …. &
(e)! Is&5 ∈ L ∩ M7?& …………………………………………………. ..&
Explain& your& answer.&
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Revision& for& Math& Studies& SL&
Number& Sense&
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24.!Draw& a& Venn& diagram& for& the& following.&
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Universal& Set:&777(7 = 7 {TUVWXWYZ7 ≤ 710}77
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77[7 = 7 {\]^V_YZ7_\720}77&
&`7 = 7 {abcVTdcWZ7_\73}77
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Number& Sense&
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31.!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
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35.!Determine& the& value(s)& of& the& 7th& term& in& the& following& geometric& sequences.& Show& your&
working& out.& u5& =1,& u8& =27,&& u7& =&&
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36.!&&&&
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37.!&
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15&
Revision& for& Math& Studies& SL&
Foundations& of& Algebra&
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SECTION!2:!Foundations!of!Algebra!
1.! Simplify& 5x& +& 4y& +& x& –& 7y&&
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2.! Solve& 3(x& –& 2)& =& x& +& 7&&
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3.! Solve& h = 1&&
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4.! Solve& 9x–11=5x+7&&
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Revision& for& Math& Studies& SL&
Foundations& of& Algebra&
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5.! Expand& and& simplify:&
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a)&& 11& –& 8(a& –& 8)& &
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c)&& 7a& –& 9(8& –& 3a)& &
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e)&& 7(4b& –& 3)& –& 9(2b& –& 5)& &
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b)&& 3a& +& 4(a& –& 3)&
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d)&& 4(b& +& 6)& +& 5(b& +& 3)& &
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f)&& c(b& +& 9)& –& b(4c& +& 3b)&
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Revision& for& Math& Studies& SL&
Foundations& of& Algebra&
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6.! Expand& and& simplify:&
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a)&&(i + 7)(i + 4)&
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d)&(i − 7)4 &
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g)&(12 − 5i)(6i + 7)&
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f)& (9i − 7)(5i + 11)&
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h)&(4i + 9)(4i − 9)&& &&&&&&
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Revision& for& Math& Studies& SL&
Foundations& of& Algebra&
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7.! Solve& the& following& by& using& the& GDC:&
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&&&&&&&&& a)&&2i 4 + 15i + 7 = 0& &
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&&&&&&&&& c)&5i 4 − 8i − 21 = 0& &
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#########e)& 3i 4 + 16i − 64 = 07&&
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b)&3i 4 + 13i + 12 = 0&
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d)&2i 4 − 13i + 21 = 0&
f)&4i 4 + 16i + 15 = 0&
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Revision& for& Math& Studies& SL&
Foundations& of& Algebra&
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Functions!
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8.! Simultaneous& Equations:& You& must& show& your& working& clearly.&
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a)! &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& b)&
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20&
Revision& for& Math& Studies& SL&
Foundations& of& Algebra&
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Graphing!
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9.! M& is& the& point& (−2,& 4)& and& N& is& the& point& (6,& −8).&&&
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! a&& Find& the& coordinates& of& the& midpoint& of& the& line& MN.&
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! b&& Find& the& gradient& of& the& line& MN.&
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! d&& Another& line& PQ& is& parallel& to& MN& and& passes& through& the& point& (1,& 5).&
&&&& & Find& the& equation& of& PQ.&
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Revision& for& Math& Studies& SL&
Foundations& of& Algebra&
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! d&& Another& line& RS& is& perpendicular& to& MN& and& passes& through& the& point& (1,& 5).&
&&&& & Find& the& equation& of& RS.&
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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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Revision& for& Math& Studies& SL&
Foundations& of& Algebra&
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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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23&
Revision& for& Math& Studies& SL&
ADDITIONAL& CONTENT& FOR& HIGHER& LEVEL& MATHEMATICS&
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SECTION!3:!The!Art!of!Geometry!and!Trigonometry!
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1.! Find& the& missing& angles.&
a& =&
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Ticket& to& IB& Mathematics& HL&
ADDITIONAL& CONTENT& FOR& HIGHER& LEVEL& MATHEMATICS&
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3.! Find& the& perimeter& and& area& of& the& following& shape.&
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25&
Ticket& to& IB& Mathematics& HL&
ADDITIONAL& CONTENT& FOR& HIGHER& LEVEL& MATHEMATICS&
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4.! Find& the& volume& and& surface& area& of& the& following&shape. &
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5.! Calculate& the& height& of& a& closed& cylinder& with& a& volume& of& 250& cm3& and& a& radius& of& 5. 5& cm.& Find&
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26&
Ticket& to& IB& Mathematics& HL&
ADDITIONAL& CONTENT& FOR& HIGHER& LEVEL& MATHEMATICS&
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8.! &&&&&
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SECTION!4:!The!Truth!about!Statistics!and!Probability!
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3.! Bob asked each of 40 friends how many minutes they took to get to work. The table shows some
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(b)!State the modal class interval.
(c)! Find the group containing the median.
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6.! &&&&
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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.
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8.! The& table& gives& information& about& the& heights,& h&metres,& of& trees& in& a& wood.&&
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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&
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(b)!Describe& the& relationship& between& the& distance& from& the& city& centre& and& the& monthly& rent.&&
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(c)& Find& an& estimate& for& the& monthly& rent& for& this& apartment.&&
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11.!This frequency table gives information about the ages of 60 teachers.
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(a)! Complete the cumulative frequency table.
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(c)! Use your cumulative frequency graph to find an estimate for the median age.
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(d)!Use your cumulative frequency graph to find an estimate for the number of teachers older
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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.&&
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13.!Hannah is going to play one badminton match and one tennis match. The probability that she will
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14.!&
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15.!&
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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.&&
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(a)! Find& the& probability& that& Adam& wins& his& next& game& of& chess& against& Boris.&
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