Study Hub
Year 10 Maths Study Guides
Every lesson below links to a pupil-friendly study guide with key notes, vocabulary, common mistakes, and quick questions with answers.
2D and 3D shape: compound shapes
- Area of a sector Study Guide
- Area of compound shapes Study Guide
- Calculating arc length Study Guide
- Checking and securing understanding of area for compound shapes Study Guide
- Checking and securing understanding of area for standard shapes Study Guide
- Checking and securing understanding of circles Study Guide
- Checking and securing understanding of converting between metric and imperial measures Study Guide
- Checking and securing understanding of perimeter for compound shapes Study Guide
- Checking and securing understanding of perimeter for standard shapes Study Guide
- Checking and securing understanding of scales and conversion Study Guide
- Equations from complex shapes Study Guide
- Perimeter and area in a contextual setting Study Guide
- Problem solving with 2D shapes Study Guide
- Problem solving with complex 2D shapes Study Guide
- Shapes on coordinate grids Study Guide
- Shapes within shapes Study Guide
Algebraic manipulation
- Advanced problem solving with algebraic manipulation Study Guide
- Checking and securing understanding of changing the subject Study Guide
- Checking and securing understanding of expanding a single bracket Study Guide
- Checking and securing understanding of factorising Study Guide
- Checking and securing understanding of forming linear equations Study Guide
- Checking and securing understanding of simplifying Study Guide
- Checking and securing understanding of solving and interpreting linear equations Study Guide
- Checking and securing understanding of substitution Study Guide
- Checking and securing understanding of the product of two binomials Study Guide
- Factorising a quadratic expression Study Guide
- Factorising quadratics of the form ax^2 + bx + c Study Guide
- Factorising using the difference of two squares Study Guide
- Further algebraic terminology Study Guide
- Problem solving with algebraic manipulation Study Guide
- Solving complex quadratic equations by completing the square Study Guide
- Solving quadratic equations by completing the square Study Guide
- Solving quadratic equations by factorising Study Guide
- Solving quadratic equations by factorising where rearrangement is required Study Guide
- Solving quadratic equations by using the formula Study Guide
- The product of three binomials Study Guide
Angles
- Checking and securing understanding of advanced angle facts Study Guide
- Checking and securing understanding of angle notation and drawing/measuring angles Study Guide
- Checking and securing understanding of basic angle facts Study Guide
- Checking and securing understanding of exterior angles Study Guide
- Checking and securing understanding of interior angles Study Guide
- Checking and securing understanding of polygons Study Guide
- Checking and securing understanding of properties of shapes Study Guide
- Checking and securing understanding on chains of reasoning with angle facts Study Guide
- Forming equations with angles Study Guide
- Problem solving with angles Study Guide
Arithmetic procedures: index laws
- Advanced problem solving with the laws of indices Study Guide
- Checking and securing understanding of calculating with fractions and decimals Study Guide
- Checking and securing understanding of calculations involving negative numbers Study Guide
- Checking and securing understanding of converting between fractions and decimals Study Guide
- Checking and securing understanding of LCM and HCF Study Guide
- Checking and securing understanding of prime factorisation Study Guide
- Checking and securing understanding of roots and integer indices Study Guide
- Converting any recurring decimal to a fraction Study Guide
- Problem solving with the laws of indices Study Guide
- The laws of indices - division Study Guide
- The laws of indices - fractional exponents Study Guide
- The laws of indices - multiplication Study Guide
- The laws of indices - negative and zero exponents Study Guide
- The laws of indices - raising a power to a power Study Guide
Bearings
Circle theorems
- Checking and securing understanding of the parts of a circle Study Guide
- Identifying which circle theorem to use Study Guide
- Problem solving with circle theorems Study Guide
- The alternate segment theorem Study Guide
- The angle at the centre of the circle is twice the angle at any point on the circumference Study Guide
- The angle in a semicircle is a right angle Study Guide
- The angles in the same segment are equal Study Guide
- The opposite angles of a cyclic quadrilateral sum to 180° Study Guide
- The perpendicular from the centre of a circle to a chord bisects the chord Study Guide
- The tangent at any point on a circle is perpendicular to the radius at that point Study Guide
- The tangents from an external point are equal in length Study Guide
Comparisons of numerical summaries of data
- Calculating summary statistics from a grouped frequency table Study Guide
- Calculating summary statistics from stem and leaf diagrams Study Guide
- Calculating the mean from a grouped frequency table Study Guide
- Checking understanding composite and bar-line charts Study Guide
- Checking understanding of bar charts and pictograms Study Guide
- Checking understanding of measures of central tendency Study Guide
- Checking understanding of pie charts Study Guide
- Checking understanding of summary statistics from a frequency table Study Guide
- Checking understanding of summary statistics from a list Study Guide
- Comparing data sets in context Study Guide
- Comparing various representations of data sets Study Guide
- Constructing stem and leaf diagrams Study Guide
- Problem solving with comparisons of numerical data Study Guide
- Statistical summaries using technology Study Guide
- Weighted means Study Guide
Further transformations
- Advanced problem solving with further transformations Study Guide
- Checking and securing understanding of congruence and similarity Study Guide
- Checking and securing understanding of enlargement with positive fractional scale factors Study Guide
- Checking and securing understanding of enlargement with positive integer scale factors Study Guide
- Checking and securing understanding of reflection Study Guide
- Checking and securing understanding of rotation Study Guide
- Checking and securing understanding of translation Study Guide
- Describing a negative enlargement Study Guide
- Enlargement using a negative scale factor Study Guide
- Identifying multiple transformations Study Guide
- Multiple transformations Study Guide
- Problem solving with further transformations Study Guide
Graphical representations of data: scatter graphs and time series
- Checking understanding of correlation Study Guide
- Checking understanding of scatter graphs Study Guide
- Constructing time series graphs Study Guide
- Estimating from scatter graphs Study Guide
- Interpolation versus extrapolation Study Guide
- Interpreting time series graphs Study Guide
- Outliers in scatter graphs Study Guide
- Problem solving with scatter graphs and time series Study Guide
Linear graphs
- Advanced problem solving with linear graphs Study Guide
- Checking and securing understanding of drawing linear graphs Study Guide
- Checking and securing understanding of drawing vertical and horizontal graphs Study Guide
- Checking and securing understanding of finding the equation of the line from coordinates Study Guide
- Checking and securing understanding of finding the equation of the line from the graph Study Guide
- Checking and understanding graphs showing direct proportion Study Guide
- Graphs showing inverse proportion Study Guide
- Identifying perpendicular linear graphs Study Guide
- Parallel and perpendicular lines on coordinate axes Study Guide
- Parallel linear graphs Study Guide
- Perpendicular linear graphs Study Guide
- Problem solving with linear graphs Study Guide
- Ratios in line segments on coordinate axes Study Guide
Non-linear graphs
- Advanced problem solving with non-linear graphs Study Guide
- Checking and securing understanding of drawing quadratic graphs Study Guide
- Drawing cubic graphs Study Guide
- Drawing exponential graphs Study Guide
- Drawing reciprocal graphs Study Guide
- Drawing the graph for the equation of a circle Study Guide
- Key features of a cubic graph Study Guide
- Key features of a quadratic graph Study Guide
- Key features of a reciprocal graph Study Guide
- Key features of an exponential graph Study Guide
- Problem solving with non-linear graphs Study Guide
Percentages
- Advanced problem solving with percentages Study Guide
- Calculating compound interest rates Study Guide
- Changing compound interest rates Study Guide
- Checking and securing understanding of finding a percentage Study Guide
- Checking and securing understanding of percentage decrease Study Guide
- Checking and securing understanding of percentage increase Study Guide
- Compound interest calculations Study Guide
- Compound interest calculations with technology Study Guide
- Percentage profit and loss Study Guide
- Problem solving with percentages Study Guide
- Simple and compound interest Study Guide
- Simple interest calculations Study Guide
- Simple interest calculations with technology Study Guide
Plans and elevations
Ratio
- Algebraic ratios Study Guide
- Changing ratios Study Guide
- Checking and securing understanding of converting between ratios, percentages and fractions Study Guide
- Checking and securing understanding of equivalent ratios Study Guide
- Checking and securing understanding of real world ratios Study Guide
- Checking and securing understanding of sharing in a ratio Study Guide
- Checking and securing understanding of simplifying and unitising ratios Study Guide
- Combining ratios Study Guide
- Problem solving with algebraic ratios Study Guide
- Problem solving with ratios Study Guide
- Writing equations from ratios Study Guide
Right-angled trigonometry
- Advanced problem solving with right-angled trigonometry Study Guide
- Applying Pythagoras' theorem in 3D Study Guide
- Applying trigonometric ratios in 3D Study Guide
- Applying trigonometric ratios in context Study Guide
- Calculate trigonometric ratios for 0°, 45° and 90° Study Guide
- Calculate trigonometric ratios for 30° and 60° Study Guide
- Calculating the length of a line segment Study Guide
- Checking and further securing understanding of Pythagoras' theorem Study Guide
- Checking and securing understanding of cosine problems Study Guide
- Checking and securing understanding of sine ratio problems Study Guide
- Checking and securing understanding of tangent ratio problems Study Guide
- Checking and securing understanding of the unit circle Study Guide
- Problem solving with right-angled trigonometry Study Guide
- Using Pythagoras' theorem to justify a right-angled triangle Study Guide
Rounding, estimation and bounds
- Advanced problem solving with rounding, estimation and bounds Study Guide
- Checking and securing understanding of estimating through rounding Study Guide
- Checking and securing understanding of rounding and truncating Study Guide
- Problem solving with rounding, estimation and bounds Study Guide
- Upper and lower bounds Study Guide
- Upper and lower bounds in additive calculations Study Guide
- Upper and lower bounds in multiplicative calculations Study Guide
- Using upper and lower bounds practically Study Guide
Sampling
- Advanced problem solving with sampling Study Guide
- Biased questioning Study Guide
- Capture/recapture sampling method Study Guide
- Checking understanding of statistical problems Study Guide
- Data collection Study Guide
- Problem solving with sampling Study Guide
- Sampling limitations Study Guide
- Sampling methods Study Guide
- Stratified sampling Study Guide
- The Statistical Enquiry Cycle Study Guide
- Types of data Study Guide
Similarity
- Checking and securing understanding of congruent triangles (ASA) Study Guide
- Checking and securing understanding of congruent triangles (RHS) Study Guide
- Checking and securing understanding of congruent triangles (SAS) Study Guide
- Checking and securing understanding of congruent triangles (SSS) Study Guide
- Checking and securing understanding of direct proportion in context Study Guide
- Problem solving with advanced similarity knowledge Study Guide
- Problem solving with similarity Study Guide
- The effect of enlargement on the area of a shape Study Guide
- The effect of enlargement on the perimeter of a shape Study Guide
- The effect of enlargement on the volume of a 3D shape Study Guide
- Using the scale factor for enlarging a volume Study Guide
- Using the scale factor for enlarging an area Study Guide
Simultaneous equations: 2 variables
- Checking and securing understanding of interpreting graphs Study Guide
- Combining equations Study Guide
- Forming simultaneous equations Study Guide
- Problem solving with linear and quadratic simultaneous equations Study Guide
- Problem solving with simultaneous equations Study Guide
- Solving a quadratic and linear pair of simultaneous equations graphically Study Guide
- Solving a quadratic and linear pair of simultaneous equations using elimination Study Guide
- Solving a quadratic and linear pair of simultaneous equations using substitution Study Guide
- Solving algebraic simultaneous equations by elimination Study Guide
- Solving more complex simultaneous equations by elimination Study Guide
- Solving simultaneous equations by elimination from a context Study Guide
- Solving simultaneous equations via any method Study Guide
- Solving simultaneous linear equations by substitution Study Guide
- Solving simultaneous linear equations graphically Study Guide
Standard form calculations
- Adding numbers in standard form Study Guide
- Checking and securing understanding of writing large numbers in standard form Study Guide
- Checking and securing understanding of writing small numbers in standard form Study Guide
- Dividing numbers in standard form Study Guide
- Multiplying numbers in standard form Study Guide
- Problem solving with standard form calculations Study Guide
- Subtracting numbers in standard form Study Guide
Surds
- Accuracy of final answers Study Guide
- Addition with surds Study Guide
- Applying the underlying structure of multiplication and division of surds Study Guide
- Identifying square factors to support simplifying surds Study Guide
- Multiplication of surds Study Guide
- Problem solving with surds Study Guide
- Rationalising a single term denominator Study Guide
- Rationalising a two term denominator Study Guide
- Simplifying surds Study Guide
- Solving equations with surds Study Guide
- The distributive law with surds Study Guide
- The distributive law with two or more binomials Study Guide