MATHSprint Topic List

1,"GCSE: Number",

2,"Integers",

3,"Multiplication tables",

4,"0×","tables.0"

4,"1×","tables.1"

4,"2×","tables.2"

4,"3×","tables.3"

4,"4×","tables.4"

4,"5×","tables.5"

4,"6×","tables.6"

4,"7×","tables.7"

4,"8×","tables.8"

4,"9×","tables.9"

4,"10×","tables.10"

4,"11×","tables.11"

4,"12×","tables.12"

4,"0× to 5×","tables.0/1/2/3/4/5"

4,"6× to 9×","tables.6/7/8/9"

4,"0× to 10×","tables.0/1/2/3/4/5/6/7/8/9/10"

3,"Four operations",

4,"Addition (+ve to 10)","fourops.1"

4,"Subtraction (+ve to 10)","fourops.2"

4,"Multiplication (+ve to 10)","fourops.3"

4,"Division (+ve to 10)","fourops.4"

4,"Addition (±ve to 10)","fourops.5"

4,"Subtraction (±ve to 10)","fourops.6"

4,"Multiplication (±ve to 10)","fourops.7"

4,"Division (±ve to 10)","fourops.8"

4,"Addition (+ve 2-digit)","fourops.11"

4,"Subtraction (+ve 2-digit)","fourops.12"

4,"Multiplication (+ve 2-digit)","fourops.13"

4,"@Division (+ve ?2-digit)","fourops.14"

3,"BIDMAS",

4,"+ve numbers","bidmas.1"

4,"-ve numbers","bidmas.2"

3,"Factors",

4,"List all factors","factors.1"

4,"Express as product of primes","factors.2"

4,"HCF","factors.3"

4,"LCM","factors.4"

2,"Fractions",

3,"Cancelling down fractions",

4,"Easy","cancelfractions.1"

4,"Medium","cancelfractions.2"

4,"Hard","cancelfractions.3"

4,"Misc","cancelfractions.1/2/3"

3,"Equivalent fractions",

4,"Easy","cancelfractions.11"

3,"Converting fractions",

4,"Top-heavy to mixed","cancelfractions.21"

4,"Mixed to top-heavy","cancelfractions.22"

4,"Misc","cancelfractions.21/22"

3,"Fraction arithmetic",

4,"Addition: 3/7 + 2/7","fractions.1"

4,"Subtraction: 3/7 - 2/7","fractions.2"

4,"Add/Sub: 3/7 ± 2/7","fractions.1/2"

4,"Addition: 3/7 + 2/21","fractions.3"

4,"Subtraction: 3/7 - 2/21","fractions.4"

4,"Add/Sub: 3/7 ± 2/21","fractions.3/4"

4,"Addition: 2/5 + 1/6","fractions.5"

4,"Subtraction: 2/5 - 1/6","fractions.6"

4,"Add/Sub: 2/5 ± 1/6","fractions.5/6"

4,"Multiplication: easy","fractions.21"

4,"Division: easy","fractions.22"

4,"Mult/Div: easy","fractions.21/22"

4,"@Combined operations",

2,"Decimals",

3,"Ordering decimals",

4,"@Easy",

3,"Converting",

4,"@Terminating decimal to fraction",

4,"@Recurring decimal to fraction",

2,"Powers and Roots",

3,"Simplifying surds",

4,"Easy square factor","surds.1"

4,"Harder square factor","surds.2"

4,"Rationalise pure surd denominator","surds.3"

4,"Easy square factor, sum","surds.4"

4,"Easy square factor, product","surds.5"

4,"Misc","surds.1/2/3/4/5"

3,"Evaluating",

4,"+ve integer powers","numindices.1"

4,"Exact roots","numindices.2"

4,"-ve and zero integer powers","numindices.3"

4,"±ve and zero integer powers","numindices.1/3"

4,"+ve unit fractional powers","numindices.4"

4,"-ve unit fractional powers","numindices.5"

4,"±ve unit fractional powers","numindices.4/5"

4,"+ve non-unit fractional powers","numindices.6"

4,"-ve non-unit fractional powers","numindices.7"

4,"±ve non-unit fractional powers","numindices.6/7"

4,"Misc powers of integers","numindices.1/3/4/5/6/7"

4,"fraction to +ve integer power","numindices.8"

4,"fraction to -ve integer power","numindices.9"

4,"fraction to ±ve integer power","numindices.8/9"

4,"fraction to +ve fractional power","numindices.10"

4,"fraction to -ve fractional power","numindices.11"

4,"fraction to ±ve fractional power","numindices.10/11"

4,"Misc powers of fractions","numindices.8/9/10/11"

3,"Laws of indices",

4,"Multiplication","numindices.21"

4,"Division","numindices.22"

4,"Brackets","numindices.23"

4,"Misc","numindices.21/22/23"

2,"Sets",

3,"Venn diagrams",

4,"Shade regions (2 sets)","venn.1"

4,"Identify regions (2 sets)","venn.2"

4,"@Shade regions (3 sets)",

4,"@Identify regions (3 sets)",

4,"@Number of elements (2 sets)",

4,"@Number of elements (3 sets)",

3,"Set notation",

4,"Union, Intersection, A'","sets.1"

4,"n(A), n(AUB')","sets.2"

4,"@Element, Subset",

4,"@Misc. combining sets",

4,"@Sets defined algebraically",

4,"@Number of elements",

2,"Percentages",

3,"Converting",

4,"Percentage to decimal","fpdconvert.1"

4,"Decimal to percentage","fpdconvert.2"

4,"Percentage to fraction","fpdconvert.3"

4,"Fraction to percentage","fpdconvert.4"

3,"Find percentage of...",

4,"eg: find 40% of 60","percent.1"

4,"eg: find 32% of 70","percent.2"

4,"eg: find 13.5% of 5.87","percent.3"

3,"Increase/decrease by percentage",

4,"eg: increase 60 by 40%","percent.11"

4,"eg: increase 70 by 32%","percent.12"

4,"eg: increase 5.87 by 13.5%","percent.13"

4,"eg: decrease 60 by 40%","percent.21"

4,"eg: decrease 70 by 32%","percent.22"

4,"eg: decrease 5.87 by 13.5%","percent.23"

4,"eg: increase/decrease 60 by 40%","percent.11/21"

4,"eg: increase/decrease 70 by 32%","percent.12/22"

4,"eg: increase/decrease 5.87 by 13.5%","percent.13/23"

3,"Find percentage increase/decrease",

4,"Find % increase (easy)","percent.31"

4,"Find % increase (medium)","percent.32"

4,"Find % increase (hard)","percent.33"

4,"Find % decrease (easy)","percent.41"

4,"Find % decrease (medium)","percent.42"

4,"Find % decrease (hard)","percent.43"

4,"Find % increase/decrease (easy)","percent.31/41"

4,"Find % increase/decrease (medium)","percent.32/42"

4,"Find % increase/decrease (hard)","percent.33/43"

3,"Compound interest/depreciation",

4,"Compound interest: new value","percent.51"

4,"Compound interest: interest","percent.52"

4,"Compound interest: misc","percent.51/52"

4,"Depreciation: remaining value","percent.53"

4,"Depreciation: loss","percent.54"

4,"Depreciation: misc","percent.53/54"

4,"Compound interest/depreciation","percent.51/52/53/54"

3,"Reverse percentage problem",

4,"Reverse % problem - pre-sale","percent.61"

2,"Ratios",

3,"Manipulation of ratios",

4,"Cancel down a:b","ratios.1"

4,"Cancel down a:b:c","ratios.2"

3,"Using ratios",

4,"Sharing 2 ways","ratios.11"

4,"Sharing 3 ways","ratios.12"

4,"Sharing 2 or 3 ways","ratios.11/12"

4,"Increase","ratios.21"

4,"Decrease","ratios.22"

4,"Increase/decrease","ratios.21/22"

4,"Increase/decrease/share","ratios.11/12/21/22"

2,"Accuracy",

3,"Identifying Accuracy",

4,"Count decimal places","dpsf.1"

4,"Count significant figures","dpsf.2"

3,"Rounding",

4,"Round to decimal places","dpsf.11"

4,"Round to significant figures","dpsf.12"

4,"Round to dec places/sig figs","dpsf.11/12"

4,"@Estimation of calculations",

3,"Upper and lower bounds",

4,"@Identifying",

4,"@Using in calculations",

4,"@Appropriate degree of accuracy",

2,"Standard Form",

3,"Standard form",

4,"Verify","standardform.1"

4,"Convert from","standardform.2"

4,"Convert to","standardform.3"

4,"Multiplication","standardform.11"

4,"Division","standardform.12"

4,"Multiplication/division","standardform.11/12"

4,"Addition","standardform.13"

4,"Subtraction","standardform.14"

4,"Addition/subtraction","standardform.13/14"

4,"Misc. calculations","standardform.11/12/13/14"

2,"Applying Number",

3,"Calculations",

4,"@Using metric units",

4,"@Using time",

4,"@Using money",

4,"@Converting between currencies",

2,"Electronic Calculators",

3,"Evaluating expressions",

4,"@BIDMAS",

1,"GCSE: Algebra",

2,"Use of symbols",

3,"Indices",

4,"Multiplication","indices1.1"

4,"Division","indices1.2"

4,"Brackets","indices1.3"

4,"Misc","indices1.1/2/3"

4,"@Mixed questions",

2,"Algebraic Manipulation",

3,"Collecting like terms",

4,"eg: 3x-5x","collect.1"

4,"eg: 2x+4y-3x+y","collect.2"

3,"Expanding over one bracket",

4,"eg: 2(3x-4)","expand1.1"

4,"eg: 2(3x-4) + 4(-7x+1)","expand1.2"

3,"Taking out a single common factor",

4,"@eg: 6x+4",

4,"@eg: 3x²-9x",

3,"Expanding quadratics",

4,"eg: (x-4)(x+5)","expand2.1"

4,"eg: (x-4)²","expand2.2"

4,"eg: (x-4)(x+4)","expand2.3"

4,"Misc (x±A)(x±B)","expand2.1/2/3"

4,"eg: (3x-7)(-5x+8)","expand2.4"

4,"eg: (3x-7)²","expand2.5"

3,"Factorising quadratics",

4,"eg: x²+4x","factor2.1"

4,"eg: x²+5x+6","factor2.2"

4,"eg: x²-5x+6","factor2.3"

4,"eg: x²±x-6","factor2.4"

4,"eg: x²+10x+25","factor2.5"

4,"eg: x²-25","factor2.6"

4,"Misc x²±Ax±B","factor2.1/2/3/4/5/6"

4,"eg: 3x²-7x+2","factor2.11"

3,"Algebraic fractions",

4,"Cancel common factors","algfractions1.21"

4,"Factorise, then cancel","algfractions1.22"

4,"Multiplication","algfractions1.1"

4,"Division","algfractions1.2"

4,"Mult/Div","algfractions1.1/2"

4,"@Addition/Subtraction",

3,"Completing the square",

4,"@@Complete the square (1)",

4,"@@Complete the square (2)",

4,"@@Find line of symmetry (1)",

4,"@@Find line of symmetry (2)",

4,"@@Find min/max value (1)",

4,"@@Find min/max value (2)",

4,"@@Find co-ordinates of vertex (1)",

4,"@@Find co-ordinates of vertex (2)",

2,"Expressions and Formulae",

3,"Substituting",

4,"@Integers",

4,"@Decimals",

4,"@Fractions",

3,"Rearranging formulae",

4,"@Variable occurs once",

4,"@Variable occurs twice",

2,"Linear Equations",

3,"Solving linear equations (1)",

4,"x ± b = c, (+ve x)","equations1.1"

4,"x ± b = c, (±ve x)","equations1.2"

4,"ax = c, (+ve x)","equations1.3"

4,"ax = c, (±ve x)","equations1.4"

4,"x/d = c, (+ve x)","equations1.5"

4,"x/d = c, (±ve x)","equations1.6"

4,"ax ± b = c, (+ve x)","equations1.11"

4,"ax ± b = c, (±ve x)","equations1.12"

4,"b - ax = c, (+ve x)","equations1.13"

4,"b - ax = c, (±ve x)","equations1.14"

4,"x/d ± b = c, (+ve x)","equations1.15"

4,"x/d ± b = c, (±ve x)","equations1.16"

4,"b - x/d = c, (+ve x)","equations1.17"

4,"b - x/d = c, (±ve x)","equations1.18"

4,"a(x ± b) = c, (+ve x)","equations1.21"

4,"a(x ± b) = c, (±ve x)","equations1.22"

4,"(x ± b)/d = c, (+ve x)","equations1.23"

4,"(x ± b)/d = c, (±ve x)","equations1.24"

4,"Misc (+ve x)","equations1.1/3/5/11/13/15/17/21/23"

4,"Misc (±ve x)","equations1.2/4/6/12/14/16/18/22/24"

3,"Solving linear equations (2)",

4,"ax = cx ± d, (+ve x)","equations1.31"

4,"ax = cx ± d, (±ve x)","equations1.32"

4,"ax ± b = cx ± d, (+ve x)","equations1.33"

4,"ax ± b = cx ± d, (±ve x)","equations1.34"

4,"a(x ± b) = cx ± d, (+ve x)","equations1.35"

4,"a(x ± b) = cx ± d, (±ve x)","equations1.36"

4,"a(x ± b) ± c(x ± d) = e, (+ve x)","equations1.37"

4,"a(x ± b) ± c(x ± d) = e, (±ve x)","equations1.38"

4,"Misc (+ve x)","equations1.31/33/35/37"

4,"Misc (±ve x)","equations1.32/34/36/38"

2,"Proportion",

3,"Finding rule from values",

4,"@Direct proportion","proportion.1"

4,"@Inverse proportion","proportion.2"

4,"@Misc proportion","proportion.1/2"

3,"Finding k",

4,"Direct proportion","proportion.11"

4,"Inverse proportion","proportion.12"

4,"Misc proportion","proportion.11/12"

3,"Finding equation",

4,"Direct proportion","proportion.13"

4,"Inverse proportion","proportion.14"

4,"Misc proportion","proportion.13/14"

3,"Solving",

4,"Direct proportion","proportion.15"

4,"Inverse proportion","proportion.16"

4,"Misc proportion","proportion.15/16"

2,"Linear Simultaneous Equations",

3,"Algebraic solution of simultaneous",

4,"eg: 3x+2y=7, 3x+4y=11 (+ve x,y)","simeqn.1"

4,"eg: 3x+2y=7, 3x+4y=11 (±ve x,y)","simeqn.2"

4,"eg: 3x+2y=7, 6x-y=4 (+ve x,y)","simeqn.3"

4,"eg: 3x+2y=7, 6x-y=4 (±ve x,y)","simeqn.4"

4,"eg: 3x+2y=7, 4x+3y=10 (+ve x,y)","simeqn.5"

4,"eg: 3x+2y=7, 4x+3y=10 (±ve x,y)","simeqn.6"

4,"@Word problems",

3,"Graphical solution of simultaneous",

4,"@Lines plotted",

4,"@Lines not plotted",

2,"Quadratic Equations",

3,"Solving quadratics by factorising",

4,"eg: (x+2)(x+3)=0","quadsolve.1"

4,"eg: x(x+4)=0","quadsolve.2"

4,"eg: x²+4x=0","quadsolve.3"

4,"eg: x²+5x+6=0","quadsolve.4"

4,"eg: x²-5x+6=0","quadsolve.5"

4,"eg: x²±x-6=0","quadsolve.6"

4,"eg: x²+10x+25=0","quadsolve.7"

4,"eg: x²-25=0","quadsolve.8"

4,"Misc x²±Ax±B=0","quadsolve.3/4/5/6/7/8"

4,"@eg: x²±Ax±B=0 rearranged","quadsolve.9"

4,"eg: 3x²-7x+2=0","quadsolve.11"

3,"Solving quadratics by completing the square",

4,"@eg: x²+2x-5=0",

3,"Solving quadratics by formula",

4,"eg: x²+x-5=0","quadsolve.21"

4,"eg: 2x²+x-5=0","quadsolve.22"

4,"@eg: (x+1)(x-4)=3","quadsolve.23"

4,"@eg: 1/x + 1/(x+1) =3","quadsolve.24"

3,"Solving simultaneous linear/quadratic",

4,"eg: y=x², y=2x+3","quadsolve.31"

4,"eg: y=x²+7x+9, y=2x+3","quadsolve.32"

4,"eg: x²+y²=25, 2x+y=1","quadsolve.33"

4,"eg: x²+y²=25, 3x+5y=2","quadsolve.34"

4,"Misc","quadsolve.31/32/33/34"

2,"Numerical Solution",

3,"Trial and Improvement",

4,"@eg: x³+x²-4=0",

2,"Inequalities",

3,"Notation for inequalities",

4,"@understanding <, >, etc.",

4,"@plotting on number line",

4,"@reading off number line",

3,"Solving linear inequalities (+ve a)",

4,"x ± b < c","inequals.1"

4,"ax < c","inequals.3"

4,"ax ± b < c","inequals.5"

4,"a(x ± b) < c","inequals.7"

4,"Misc","inequals.1/3/5/7"

3,"Solving linear inequalities (±ve a)",

4,"ax < c","inequals.4"

4,"ax ± b < c","inequals.6"

4,"a(x ± b) < c","inequals.8"

4,"Misc","inequals.4/6/8"

3,"Listing integer solutions",

4,"@ax ± b < or > m",

4,"@m < x + b < n",

4,"@m < ax < n",

4,"@m < ax ± b < n",

3,"Regions on (x,y) plane",

4,"Shade a region y<>c","regions.1"

4,"Identify an inequality y<>c","regions.2"

4,"Shade a region x<>c","regions.3"

4,"Identify an inequality x<>c","regions.4"

4,"Shade a region y<>mx+c","regions.5"

4,"Identify an inequality y<>mx+c","regions.6"

4,"Misc shade a region","regions.3/5/5/5/5/5"

4,"Misc identify a shaded region","regions.4/6/6/6/6/6"

4,"@Shade several regions","regions.21"

4,"@Identify several inequalities","regions.31"

3,"Quadratic inequalities",

4,"Solve algebraically, eg x² > 4","inequals.81"

4,"Solve algebraically, eg 2x²+4 < 22","inequals.82"

4,"@Show on number line","inequals.84"

4,"List integer solutions, eg x² > 4","inequals.87"

4,"List integer solutions, eg 2x²+4 < 22","inequals.88"

1,"GCSE: Sequences, Functions, Graphs",

2,"Sequences",

3,"Find the next terms",

4,"Linear sequence, +ve terms","sequence.1"

4,"Linear sequence, ±ve terms","sequence.2"

4,"Linear sequence, ±ve decimal terms","sequence.3"

4,"Quadratic sequence, +ve terms","sequence.4"

4,"Quadratic sequence, ±ve terms","sequence.5"

4,"Geometric sequence, integer terms","sequence.6"

4,"Geometric sequence, incl. fractional terms","sequence.7"

4,"Squares, primes, etc.","sequence.8"

4,"Misc","sequence.2/3/5/6/7/8"

3,"Use position-to-term formula",

4,"Linear sequence, +ve terms","sequence.11"

4,"Linear sequence, ±ve terms","sequence.12"

4,"Quadratic sequence, +ve terms","sequence.14"

4,"Quadratic sequence, ±ve terms","sequence.15"

4,"Geometric sequence, integer terms","sequence.16"

4,"Geometric sequence, incl. fractional terms","sequence.17"

4,"Squares, cubes, etc.","sequence.18"

4,"Misc","sequence.12/15/16/17/18"

3,"Solve position-to-term formula",

4,"Linear sequence, +ve terms","sequence.21"

4,"Linear sequence, ±ve terms","sequence.22"

4,"Quadratic sequence, +ve terms","sequence.24"

4,"Quadratic sequence, ±ve terms","sequence.25"

4,"Geometric sequence, integer terms","sequence.26"

4,"Geometric sequence, incl. fractional terms","sequence.27"

4,"Squares, cubes, etc.","sequence.28"

4,"Misc","sequence.22/25/26/27/28"

3,"Use term-to-term formula",

4,"@Simple",

4,"@Harder",

3,"Find the position-to-term formula",

4,"Linear sequence, +ve terms","sequence.31"

4,"Linear sequence, ±ve terms","sequence.32"

4,"Linear sequence, ±ve decimal terms","sequence.33"

4,"Quadratic sequence, +ve terms","sequence.34"

4,"Quadratic sequence, ±ve terms","sequence.35"

4,"Geometric sequence, integer terms","sequence.36"

4,"Geometric sequence, incl. fractional terms","sequence.37"

4,"Squares, cubes, etc.","sequence.38"

4,"Misc","sequence.32/33/35/36/37/38"

2,"Functions",

3,"Functions",

4,"Evaluate f(A)","functions.1"

4,"Solve f(x)=A","functions.2"

4,"Inverse functions (numeric)","functions.3"

4,"Inverse functions (algebraic)","functions.4"

4,"@Composite functions (numeric)","functions.5"

4,"@Composite functions (algebraic)","functions.6"

4,"@Domain and range","functions.7"

2,"Graphs",

3,"Co-ordinates",

4,"@Plotting 2D",

4,"@Identifying 2D",

3,"Straight line graphs",

4,"@Midpoint of a line segment",

4,"@Gradient of a line segment",

4,"@Length of a line segment",

4,"Identify x=... or y=...","lineargraph.13"

4,"Sketch x=... or y=...","lineargraph.14"

4,"@Identify y-intercept",

4,"@Identify gradient",

4,"Identify y=mx+c","lineargraph.11"

4,"Sketch y=mx+c","lineargraph.12"

4,"@Rearrange ax+by=k to y=mx+c",

4,"@Equation of parallel line through point",

4,"@Gradient of perpendicular line",

4,"@Equation of perpendicular line",

3,"Curves",

4,"@Plot from given values y=ax³+bx²+cx+d",

4,"@Plot from given values y=ax³+bx²+cx+d+e/x+f/x²",

4,"@Plot from given values (any)",

4,"@Plot from equation y=ax³+bx²+cx+d",

4,"@Plot from equation y=ax³+bx²+cx+d+e/x+f/x²",

4,"@Plot from equation y=asin/cos(bx)+c",

4,"@Plot from equation (any)",

4,"@Sketch y=x, x², x³",

4,"@Sketch y=1/x, 1/x²",

4,"@Sketch y=sinx, cosx, tanx",

4,"@Sketch (any)",

4,"@Identify y=x, x², x³",

4,"@Identify y=1/x, 1/x²",

4,"@Identify y=sinx, cosx, tanx",

4,"@Identify (any)",

4,"@Sketch circle x²+y²=r²",

4,"@Identify circle x²+y²=r²",

3,"Transformations of graphs",

4,"@Sketch translation in y direction",

4,"@Sketch translation in x direction",

4,"@Sketch stretch in y direction",

4,"@Sketch stretch in x direction",

4,"@Sketch reflection in y=0",

4,"@Sketch reflection in x=0",

4,"@Sketch miscellaneous",

4,"@Identify translation in y direction",

4,"@Identify translation in x direction",

4,"@Identify stretch in y direction",

4,"@Identify stretch in x direction",

4,"@Identify reflection in y=0",

4,"@Identify reflection in x=0",

4,"@Identify miscellaneous",

3,"Interpreting graphs",

4,"@Use conversion graphs",

4,"@Find gradient at a point",

4,"@Find area under graph",

4,"@Graphical solution (1): curve and line",

4,"@Graphical solution (2): choose own y=mx+c",

2,"Calculus",

3,"Differentiation by rule",

4,"eg: y=x³","differ1.1"

4,"eg: y=5x³","differ1.2"

4,"eg: y=6x¯²","differ1.3"

4,"eg: y=7/x³","differ1.4"

4,"eg: y=5x³, y=6x¯² or y=7/x³","differ1.2/3/4"

4,"eg: y=5x³-3x²+6","differ1.11"

4,"eg: y=5x³-3/x²","differ1.12"

4,"@@x^n: n ±ve rational",

3,"Applying differentiation",

4,"Find gradient at a point, eg: y=5x³","differ1.21"

4,"Find gradient at a point, eg: y=4/x","differ1.22"

4,"Find gradient at a point, eg: y=5x³, y=4/x","differ1.21/22"

4,"Find gradient at a point, eg: y=5x³-3x²+6","differ1.23"

4,"Find gradient at a point, eg: y=5x³-3/x²","differ1.24"

4,"Find where gradient = m, eg: y=5x³","differ1.41"

4,"Find where gradient = m, eg: y=4/x","differ1.42"

4,"Find where gradient = m, eg: y=5x³, y=4/x","differ1.41/42"

4,"@Find where gradient = m, eg: y=3x²-4x","differ1.43"

4,"Find maximum/minimum (quadratics)","differ1.31"

4,"Find maximum/minimum (cubics)","differ1.32"

4,"Find maximum/minimum (misc)","differ1.31/32"

4,"@Find maximum/minimum (y=Ax+B/x)","differ1.33"

4,"@Find equation of tangent","differ1.51"

4,"@Find equation of normal","differ1.52"

3,"Kinematics",

4,"Find velocity given x=at³+bt²+ct+d","differ1.61"

4,"Find acceleration given x=at³+bt²+ct+d","differ1.62"

4,"Find acceleration given v=at³+bt²+ct+d","differ1.63"

4,"Find vel or accel given x or v","differ1.61/62/63"

4,"Find vel at t=k given x=at³+bt²+ct+d","differ1.64"

4,"Find accel at t=k given x=at³+bt²+ct+d","differ1.65"

4,"Find accel at t=k given v=at³+bt²+ct+d","differ1.66"

4,"Find vel or accel at t=k given x or v","differ1.64/65/66"

4,"@t^n: Find when v or a = 0",

1,"GCSE: Geometry",

2,"Angles and Triangles",

3,"Angles",

4,"Terminology",

4,"@Estimate size",

4,"@On a straight line",

4,"@At a point",

4,"@Vertically opposite (X)",

4,"@Corresponding (F)",

4,"@Alternate (Z)",

4,"@Interior (C)",

4,"@Misc. properties",

3,"Triangles",

4,"@Types of triangle",

4,"@Angle sum",

4,"@Exterior angle",

2,"Polygons",

3,"Quadrilaterals",

4,"@Types of quadrilateral",

4,"@Angle sum",

3,"Polygons",

4,"@Types of polygon",

4,"@Tessellation",

4,"@Angle sum",

4,"@Angles in regular polygons",

2,"Symmetry",

3,"Line symmetry",

4,"@Find mirror line",

4,"@Construct reflection",

3,"Rotational symmetry",

4,"@Find centre of rotation",

4,"@Find order of symmetry",

2,"Measures",

3,"Bearings",

4,"@Calculate (no trig)",

4,"@Back-bearings",

4,"@Measure",

4,"@Construct",

3,"Compound measures",

4,"@Distance, speed, time",

4,"@Mass, volume, density",

4,"@Volume, area, flow rate",

2,"Construction",

3,"Basic construction",

4,"@Perpendicular bisector",

4,"@Angle bisector",

3,"Other constructions",

4,"@Perpendicular to line at point P",

4,"@Perpendicular from point P to line",

4,"@Equilateral triangle",

4,"@Triangle with given sides",

4,"@Square",

4,"@Hexagon",

3,"Loci",

4,"@Fixed distance from point",

4,"@Fixed distance from line",

4,"@Equidistant from two points",

4,"@Equidistant from two lines",

4,"@Intersecting loci",

4,"@Shading regions",

2,"Circle Properties",

3,"Circle terminology",

4,"@Radius, diameter, circum.",

4,"@Arc, chord, sector, segment",

4,"@Misc",

3,"Circle Theorems",

4,"Isosceles triangles","circle1.11"

4,"Angles in same segment","circle1.12"

4,"Angle at centre","circle1.13"

4,"Angle in a semicircle","circle1.14"

4,"Alternate segment theorem","circle1.15"

4,"Tangent - radius","circle1.16"

4,"Cyclic quadrilaterals","circle1.17"

4,"@Intersecting chords (1)",

4,"@Intersecting chords (2)",

4,"Misc. 1-4","circle1.11/12/13/14"

4,"Misc. 5-7","circle1.15/16/17"

4,"Misc. 1-7","circle1.11/12/13/14/15/16/17"

2,"Geometrical Reasoning",

3,"X",

4,"@x",

2,"Trigonometry and Pythagoras",

3,"Pythagoras",

4,"Integer sides - find hypotenuse","trig1.01"

4,"Integer sides - find shorter side","trig1.02"

4,"Integer sides - find any side","trig1.01/02"

4,"Non-integer sides - find hypotenuse","trig1.06"

4,"Non-integer sides - find shorter side","trig1.07"

4,"Non-integer sides - find any side","trig1.06/07"

4,"@Applied problems (numerical)",

4,"@Applied problems (algebraic)",

3,"Trigonometry - basics",

4,"Names of triangle sides","trig1.20"

4,"Sin ratio from triangle","trig1.21"

4,"Cos ratio from triangle","trig1.22"

4,"Tan ratio from triangle","trig1.23"

4,"Sin/cos/tan ratios from triangle","trig1.21/22/23"

3,"Trigonometry - calculator usage",

4,"Evaluate Sin x","trig1.24"

4,"Evaluate Cos x","trig1.25"

4,"Evaluate Tan x","trig1.26"

4,"Evaluate Sin/Cos/Tan x","trig1.24/25/26"

4,"Evaluate Sin¯¹ x","trig1.27"

4,"Evaluate Cos¯¹ x","trig1.28"

4,"Evaluate Tan¯¹ x","trig1.29"

4,"Evaluate Sin/Cos/Tan¯¹ x","trig1.27/28/29"

3,"Trigonometry - right-angled triangles",

4,"Sin - find Opposite","trig1.31"

4,"Sin - find Hypotenuse","trig1.34"

4,"Sin - find Angle","trig1.37"

4,"Sin - find Misc","trig1.31/34/37"

4,"Cos - find Adjacent","trig1.32"

4,"Cos - find Hypotenuse","trig1.35"

4,"Cos - find Angle","trig1.38"

4,"Cos - find Misc","trig1.32/35/38"

4,"Tan - find Opposite","trig1.33"

4,"Tan - find Adjacent","trig1.36"

4,"Tan - find Angle","trig1.39"

4,"Tan - find Misc","trig1.33/36/39"

4,"Sin/cos/tan - find Numerator Side","trig1.31/32/33"

4,"Sin/cos/tan - find Denominator Side","trig1.34/35/36"

4,"Sin/cos/tan - find Side","trig1.31/32/33/34/35/36"

4,"Sin/cos/tan - find Angle","trig1.37/38/39"

4,"Sin/cos/tan - find Misc","trig1.31/32/33/34/35/36/37/38/39"

4,"@Angle of elevation/depression",

4,"@Bearings",

3,"Trigonometry - non-right-angled triangles",

4,"Sine Rule - find Side","trig1.51"

4,"Sine Rule - find Angle","trig1.52"

4,"Sine Rule - find Misc","trig1.51/52"

4,"Cosine Rule - find Side","trig1.53"

4,"Cosine Rule - find Angle","trig1.54"

4,"Cosine Rule - find Misc","trig1.53/54"

4,"Sine/Cosine Rule - find Side","trig1.51/53"

4,"Sine/Cosine Rule - find Angle","trig1.52/54"

4,"Sine/Cosine Rule - find Misc","trig1.51/52/53/54"

4,"@Calculate bearings",

4,"Find area of triangle","trig1.55"

3,"Trigonometry - mixed questions",

4,"Find misc side or angle (right-angled triangle)","trig1.06/07/31/32/33/34/35/36/37/38/39"

4,"Find misc side or angle (any triangle)","trig1.06/07/31/32/33/34/35/36/37/38/39/51/52/53/54"

3,"3D Geometry",

4,"@Pythagoras",

4,"@Trigonometry - find length",

4,"@Trigonometry - find angle",

4,"@Trig/Pythagoras",

2,"Mensuration",

3,"Mensuration basics",

4,"@Terminology (vertex, edge, etc.)",

4,"@Convert metric units",

4,"@Dimensions of formulae",

3,"2D Mensuration",

4,"@Perimeter of triangle",

4,"@Area of triangle",

4,"@Perimeter of rectangle",

4,"@Area of rectangle",

4,"@Area of parallelogram",

4,"@Area of trapezium",

4,"@Circumference of circle",

4,"@Area of circle",

4,"@Perimeter of ¼,½,¾ circle",

4,"@Area of ¼,½,¾ circle",

4,"@Arc length",

4,"@Perimeter of sector",

4,"@Area of sector",

4,"@Area of segment",

4,"@Perimeter of compound shape (no circles)",

4,"@Area of compound shape (no circles)",

4,"@Perimeter of compound shape (incl. circles)",

4,"@Area of compound shape (incl. circles)",

3,"3D Mensuration",

4,"@Surface area of cuboid",

4,"@Volume of cuboid",

4,"@Surface area of right prism",

4,"@Volume of right prism",

4,"@Volume of pyramid",

4,"@Surface area of cylinder",

4,"@Volume of cylinder",

4,"@Surface area of sphere",

4,"@Volume of sphere",

4,"@Surface area of hemisphere",

4,"@Volume of hemisphere",

4,"@Surface area of cone",

4,"@Volume of cone",

4,"@Misc. surface area",

4,"@Misc. volume",

4,"@Surface area of compound solid",

4,"@Volume of compound solid",

4,"@'Meltdown' problems",

2,"Similarity",

3,"Similar shapes",

4,"Linear scale factor","mensur.91"

4,"Linear to Area scale factor","mensur.92"

4,"Linear to Volume scale factor","mensur.93"

4,"Area to Linear scale factor","mensur.94"

4,"Volume to Linear scale factor","mensur.95"

4,"Area to Volume scale factor","mensur.96"

4,"Volume to Area scale factor","mensur.97"

4,"Misc. scale factor","mensur.91/92/93/94/95/96/97"

3,"Congruent shapes",

4,"@Triangles",

4,"@Other",

1,"GCSE: Vectors and Transformations",

2,"Vectors",

3,"Column vectors",

4,"Addition","vectors1.1"

4,"Subtraction","vectors1.2"

4,"Scalar multiplication","vectors1.3"

4,"Misc","vectors1.1/2/3"

4,"Co-ordinates to vectors","vectors1.4"

4,"Parallel vectors","vectors1.5"

4,"Magnitude","vectors1.6"

3,"Algebraic vectors",

4,"@Expressing using base vectors",

2,"Transformations",

3,"Rotation",

4,"Rotate by 180","transformations.1"

4,"Rotate by 90","transformations.2"

4,"Rotate by 90 or 180","transformations.1/2"

4,"@Find centre of rotation (180)",

4,"@Find centre of rotation (90)",

4,"@Find centre of rotation (90 or 180)",

3,"Reflection",

4,"@Reflect in given line",

4,"@Reflect in x=C or y=C",

4,"@Reflect in y=±x+C",

4,"@Reflect in misc. line",

4,"@Find mirror line (x=C or y=C)",

4,"@Find mirror line (y=±x+C)",

4,"@Find mirror line (misc)",

3,"Translation",

4,"@Translate by column vector (+ve quadrant)",

4,"@Find translation column vector (+ve quadrant)",

4,"@Translate by column vector (four quadrants)",

4,"@Find translation column vector (four quadrants)",

3,"Enlargement",

4,"@Enlarge by +ve scale factor",

4,"@Enlarge by +ve fractional scale factor",

4,"@Enlarge by -ve scale factor",

3,"Misc. transformations",

4,"@Identify (easy)",

4,"@Plot (easy)",

4,"@Identify (harder)",

4,"@Plot (harder)",

1,"GCSE: Statistics",

2,"Presenting Data",

3,"Stem and leaf diagrams",

4,"@Construct",

3,"Box and whisker diagrams",

4,"@Construct",

3,"Scatter diagrams",

4,"@Construct",

4,"@Give correlation",

4,"@Plot best fit line",

4,"@Interpret using best fit",

3,"Frequency polygons",

4,"@Construct",

3,"Pie charts",

4,"@Construct",

4,"@Interpret",

3,"Bar charts",

4,"@Construct",

4,"@Interpret",

3,"Cumulative frequency",

4,"@Fill a table",

4,"@Plot graph from given values",

4,"@Fill a table and plotting graph",

4,"@Interpret graph - median, quartiles",

4,"@Interpret graph - other",

4,"@Interpret graph - misc",

4,"@Fill a table, plot graph and interpret",

3,"Histograms",

4,"Calculate frequency density","freqdensity.1"

4,"Plot histogram from frequency data","freqdensity.2"

4,"Find frequency data from histogram","freqdensity.3"

2,"Statistical Measures",

3,"Average and spread",

4,"Mean (from list)","stat1.1"

4,"Median (from list)","stat1.2"

4,"Mode (from list)","stat1.3"

4,"Range (from list)","stat1.4"

4,"Quartiles (from list)","stat1.5"

4,"IQR (from list)","stat1.6"

4,"@St. Dev. (from list)",

4,"@Mean (from table)",

4,"@Median (from table)",

4,"@Mode (from table)",

4,"@Range (from table)",

4,"@Quartiles (from table)",

4,"@IQR (from table)",

4,"@St. Dev. (from table)",

4,"@Mean (from grouped table)",

4,"@Median (from grouped table)",

4,"@Modal class (from grouped table)",

4,"@Range (from grouped table)",

4,"@St. Dev. (from grouped table)",

4,"@Moving average",

2,"Probability",

3,"Probability basics",

4,"@Probability scale",

4,"@p(not A) = 1 - p(A)",

4,"@Expected frequency",

4,"@p(A or B) = p(A) + p(B) [mutually excl.]",

4,"@p(A and B) = p(A) × p(B) [independent]",

4,"@Test if mutually exclusive",

4,"@Test if independent",

3,"Listing outcomes",

4,"@1 die/spinner",

4,"@2 dice/spinners",

4,"@2 coins/children",

4,"@3 coins/children",

4,"@4 coins/children",

3,"Tree diagrams",

4,"@repeated event, using diagram",

4,"@repeated event, no diagram",

4,"@With replacement, using diagram",

4,"@Without replacement, using diagram",

1,"A LEVEL: Pure/Core",

2,"Sequences & Series",

3,"Arithmetic progression",

4,"nth term",

4,"@@Sum of n terms",

4,"@@Misc problems",

3,"Geometric progression",

4,"@@nth term",

4,"@@Sum of n terms",

4,"@@Sum to infinity",

4,"@@Convergence/divergence",

4,"@@Misc problems",

2,"Polynomials",

3,"Polynomial expressions",

4,"@@Factor theorem",

4,"@@Remainder theorem",

4,"@@Division by linear poly",

2,"Logarithms and Exponentials",

3,"Log laws",

4,"@@logAB = logA + logB",

4,"@@logA/B = logA - logB",

4,"@@logA^N = NlogA",

4,"@@Misc log laws",

3,"Using logarithms",

4,"@@Solve a^x = b",

4,"@@Change of base",

2,"Calculus",

3,"Differentiation (2)",

4,"@@e^x",

4,"@@lnx",

4,"@@Chain rule",

4,"@@Product rule",

4,"@@Quotient rule",

3,"Indefinite integration (1)",

4,"@@x^n: n +ve integer",

4,"@@x^n: n -ve integer, not -1",

4,"@@x^n: n ±ve integer, not -1",

4,"@@x^n: n ±ve rational, not -1",

3,"Indefinite integration (2)",

4,"@@e^x",

4,"@@1/x",

4,"@@Linear substitution",

3,"Definite integration (1)",

4,"@@x^n: n +ve integer",

4,"@@x^n: n -ve integer, not -1",

4,"@@x^n: n ±ve integer, not -1",

4,"@@x^n: n ±ve rational, not -1",

4,"@@x^n: Area between line and curve",

4,"@@x^n: Area between two curves",

4,"@@x^n: Trapezium rule",

4,"@@x^n: Solve dy/dx=f(x)",

3,"Definite integration (2)",

4,"@@e^x",

4,"@@1/x",

4,"@@Linear substitution",

4,"@@Volume of revolution",

2,"Trig algebra",

3,"Trig identities",

4,"@@sin²x+cos²x=1",

4,"@@sinx/cosx=tanx",

4,"@@sec²x=1+tan²x",

4,"@@cosec²x=1+cot²x",

4,"@@sin(A±B)",

4,"@@cos(A±B)",

4,"@@tan(A±B)",

4,"@@sin(2A)",

4,"@@cos(2A)",

4,"@@tan(2A)",

4,"@@Asinx + Bcosx",

3,"Trig equations",

4,"@@Solve sin(kx)=c",

4,"@@Solve cos(kx)=c",

4,"@@Solve tan(kx)=c",

4,"@@Solve sin/cos/tan(kx)=c",

4,"@@Solve trig quadratics",

2,"Graphs",

3,"Curves",

4,"@@Sketch y=ax²+bx+c",

4,"@@Sketch y=(x-a)(x-b)(x-c)",

4,"@@Period of trig graphs",

4,"@@Sketch circle (x-a)²+(y-b)²=r²",

4,"@@Identify circle (x-a)²+(y-b)²=r²",

4,"@@Sketch y=a^x",

4,"@@Sketch y=e^x",

4,"@@Sketch y=lnx",

2,"Trigonometry",

3,"Radians",

4,"@@Radians to degrees",

4,"@@Degrees to radians",

4,"@@Arc length",

4,"@@Sector area",

3,"Trig - exact values",

4,"@@sin 0, 30, 45, 60, 90",

4,"@@cos 0, 30, 45, 60, 90",

4,"@@tan 0, 30, 45, 60, 90",

4,"@@sin/cos/tan 0, 30, 45, 60, 90",

1,"A LEVEL: Mechanics",

1,"A LEVEL: Statistics",

1,"A LEVEL: Discrete & Decision",

2,"Graph Theory",

3,"Definitions",

4,"@@Degree","d1network.1"

4,"@@Eulerian","d1network.2"

2,"Networks",

3,"Minimum Spanning Tree",

4,"Prim","d1network.11"

4,"Kruskal","d1network.12"

4,"Matrix Prim","d1network.13"

3,"Shortest Route",

4,"Dijkstra","d1network.21"

3,"Route Inspection",

4,"Best pairing of 4 odd nodes","d1network.31"

4,"Route Inspection - 4 odd nodes","d1network.32"

3,"Travelling Salesperson",

4,"Nearest neighbour (single)","d1network.41"

4,"Lower bound (single)","d1network.42"

4,"Nearest neighbour (all nodes)","d1network.43"

4,"Lower bound (all nodes)","d1network.44"

2,"Algorithms",

3,"Packing",

4,"First fit","d1packing.01"

4,"First fit decreasing","d1packing.03"

4,"Full bin","d1packing.05"

3,"Sorting",

4,"Bubble sort","d1sorting.01"

4,"Shuttle sort","d1sorting.03"

3,"Order of Algorithms",

4,"Find order from efficiency","d1order.01"

4,"Calculate using order","d1order.03"

2,"Linear Programming",

3,"LP Graphical Solution",

4,"Terminology","d1LP.11"

4,"Definitions","d1LP.12"

4,"@@Setting up inequalities","d1LP.21"

4,"Solving from graph","d1LP.23"

4,"Solving from LP formulation","d1LP.25"

3,"LP Simplex Method",

4,"2-variable simplex","d1simplex.11"

4,"3-variable simplex","d1simplex.12"

A large-scale project such as this is essentially open-ended. There will always be requests for new topics and styles of questions and we invite you to give us your feedback.

Our philosophy is to let you benefit from the hundreds of topics already available and then expand the choice still further over the coming months, taking note of your feedback. Any topics marked ‘@’ or ‘@@’ are not yet coded but will be available in forthcoming updates which can be downloaded for free.