Maths

Mathematics Higher Tier Year 10

Pupils follow a balanced course leading to assessment in 4 attainment targets – Using and Applying Maths, Number and Algebra, Shape, Space and Measures and Handling Data.  The course is assessed by two 2-hour written examination papers.  One paper allows the use of a calculator and one paper does not.

Autumn Term

Changing the Subject

  • Change the subject of formula.

Simultaneous linear equations

  • Solving simultaneous equations both graphically and algebraically.

  • Substitute for one unknown from one equation into the other equation.

  • Use method of elimination to solve equations.

Inequalities and Shading Regions

  • Solve simple linear inequalities and show them on a number line.

  • Plot lines from equations. 

  • Shade regions satisfying inequalities

Recognising, Graphing and Solving Equations

Draw quadratic, cubic graphs by completing tables of data.

Solve quadratic and cubic equations using a given graph or where one has to be drawn.

Recognise, interpret  and sketch

(a) Linear graphs.

(b) Quadratic graphs.

(c) Cubic graphs.

(d) Other graphs including reciprocal curves.

Circle theorems

Know and use angle and tangent properties of a circle including

  1. Perpendicular bisector of a chord passes through centre of circle

  2. Angle between a tangent and a radius is 90 degrees

  3. Tangents drawn from an external point are equal.

  4. Angle in a semi circle is a right angle

  5. Angle at the centre is twice the angle at the circumference

  6. Angles in the same segment are equal

  7. Opposite angles of a cyclic quad are supplementary

  8. Alternate segment theorem

Give reasons for the steps in their solutions.

Spring Term

Transformations

  • Reflection.

  • Rotation of an object about a centre of rotation.  

  • Translation

  • Enlargement by a scale factor from a centre of enlargement.

Transformation of graphs

Sketch the graph of:

  1. y=f(x+a) given the graph of y=f(x)

  2. y=f(x)+a given the graph of y=f(x)

  3. y=f(ax) given the graph of y=f(x)

  4. y=-f(x) given the graph of y=f(x)

Rational and irrational numbers

To identify: 

  • rational numbers   

  • irrational numbers

  • terminating decimals

  • recurring decimals

To show that a recurring decimal is rational.

Simplify surds.

Surds

  • Manipulate and simplify surds.

Probability

  • Estimate probabilities using available information.

  • Calculate probabilities recognising independent events (i.e..P(A and B) = P(A)xP(B)).

  • Calculate probabilities which are mutually exclusive i.e. P(A or B) = P(A)+P(B).

  • Choose and use an appropriate method to calculate probabilities (i.e. sample space, tree diagram)

  • Formalise probability rules of P(A and B) = P(A)xP(B)) and P(A or B) = P(A)+P(B).

Summer Term

Upper and lower bounds

  • Find upper and lower bounds.

  • Apply correct combinations of upper and lower bounds in problems involving compound measures.

Volume and surface area

  • Revise perimeter and area of circle, trapezium etc.

  • Find the surface area and volume of cylinders, prisms, pyramids, cones and spheres.

  • Recognise lines and planes of symmetry.

Bearings

  • Construct a scale diagram given lengths and bearings.

  • Express an angle as a bearing.

  • Calculate missing lengths / bearings using Trigonometry / Pythagoras Theorem.

Charts

  • Interpret presented data including frequency polygons, pie charts and bar charts. 

Averages

  • Find mode, median and range from simple and grouped data.

  • Find mean from discrete data.

  • Find modal class, estimate the mean, median and range of sets of grouped data.

  • Interpret presented data including frequency polygons, pie charts and bar charts.

Variation/ Proportion

  • Write a formula for direct proportion using the constant (k) of proportionality.

  • Extend proportion ideas to squared, cubic, squared root , cubic root  proportion.

  • Extend proportion ideas to INVERSE proportion.

  • Recognise graphical display of given formulae.