Surds Revision Questions For Essays

The below are all the HIGHER TIER questions collated by topic from:

  • AQA – Sample Assessment Material and Practice set 1 and 2 
  • OCR – Sample Assessment Material and Practice set 1
  • Pearson Edexcel – Sample Assessment Material, Specimen set 1 and Specimen set 2.
  • WJEC Eduqas – Sample Assessment Material

Please note that these questions have been copied/retyped from the original sample/specimen assessment materials and whilst every effort has been made to ensure there are no errors, any that do appear are mine and not the exam boards (similarly any errors I have corrected from the originals are also my corrections and not theirs!).

The objective is to provide support to fellow teachers and to give you a flavour of how different topics “could” be examined. They should not be used to form a decision as to which board to use (as if they would .. but it needs to be said!). There is no guarantee that a topic will or won’t appear in the “live” papers from a specific exam board or that examination of a topic will be as shown in these questions.

Please also see my other notes about this resource ON THIS POSTand also check out the questions by topic for theFOUNDATION TIER PAPERS !

PS – The only questions I have excluded , are a few of the questions in relation to scale drawings and bearings due to scaling the pictures.

PPS – Please do not put these papers on your own website – I am still updating them as and when I find mistakes!

PROBABILITY

Probability – H – Venn Diagrams v2

Probability – H – Venn Diagrams v2 – SOLUTIONS v2

Probability – H – Probability 1 v2

Probability – H – Probability 1 v2 – SOLUTIONS v2

Probability – H – Probability 2 v2

Probability – H – Probability 2 v2 – SOLUTIONS v2

Probability – H – Frequency Trees v2

Probability – H – Frequency Trees v2 – SOLUTIONS

GEOMETRY & MEASURES

Geometry – H – Angles in Parallel Lines v2

Geometry H Angles in parallel lines v2 – SOLUTIONS

Geometry – H – Angles in polygons v2

Geometry – H – Angles in polygons v2 – SOLUTIONS

Geometry – H – Area & Perimeter v2

Geometry-H-Area-Perimeter-v2 – SOLUTIONS

Geometry – H – Circle Theorems v2

Geometry – H – Circle Theorems v2 – SOLUTIONS

Geometry – H – Enlargements v2

Geometry H – Enlargements v2 – SOLUTIONS

Geometry – H – Similarity & Congruence v2

Geometry-H-Similarity-Congruence-v2 – SOLUTIONS

Geometry – H – Reflections v2

Geometry – H – Reflections v2 – SOLUTIONS

Geometry – H – Pythagoras Theorem v2

Geometry – H – Pythagoras Theorem v2 – SOLUTIONS

Geometry – H – Exact Value of Trigonometric Ratios v2

Geometry – H – Exact Value of Trigonometric Ratios v2 – SOLUTIONS

Geometry – H – Translations v2

Geometry – H – Translations v2 – SOLUTIONS

Geometry – H – Trigonometry v2

Geometry – H – Trigonometry v2 – SOLUTIONS v2

Geometry – H – Vectors v2

Geometry – H – Vectors v2

Geometry H – Trigonometry 2-v2

Geometry – H – Trigonometry 2 v3 – SOLUTIONS v2

Geometry – H – Rotations v2

Geometry – H – Rotations v2 – SOLUTIONS

Geometry – H – Volume of Prisms, Cones, Pyramids and Spheres v2

Geometry – H – Volume of Prisms, Cones, Pyramids and Spheres v2 – SOLUTIONS

Geometry – H – Plans & Elevations v2

Geometry – H – Plans & Elevations v2 – SOLUTIONS

Geometry – H – Circles Arcs and Sectors v2

Geometry – H – Circles-Arcs-and-Sectors-v2 – SOLUTIONS

Geometry – H – 2D Shapes and 3D Forms v2

Geometry H 2d-shapes and 3D form v2 – SOLUTIONS

ALGEBRA

Algebra – H – Algebraic Fractions v2

Algebra – H – Algebraic Fractions v2 – SOLUTIONS

Algebra – H – Algebraic Proof v2

Algebra – H – Algebraic Proof v2 – SOLUTIONS

Algebra – H – Coordinates v2

Algebra – H – Coordinates v2 – SOLUTIONS v2

Algebra – H – Equation of a Circle v2

Algebra – H – Equation of a Circle v2 – SOLUTIONS

Algebra – H – Equation of a Straight Line v3

Algebra – H – Equation of a Straight Line v2 – SOLUTIONS v2

Algebra – H – Factorising, Expanding, Solving Polynomials v2

Algebra – H – Factorising, Expanding, Solving Polynomials v2 – SOLUTIONS

Algebra – H – Forming & Solving Equations v2

Algebra – H – Forming & Solving Equations v2 – SOLUTIONS

Algebra – H – Functions v2

Algebra – H – Functions v2 – SOLUTIONS

Algebra – H – Inequalities v2

Algebra – H – Inequalities v2 – SOLUTIONS

Algebra – H – Iteration v2

Algebra – H – Iteration v2 – SOLUTIONS

Algebra – H – Quadratic & Cubic Graphs v2

Algebra – H – Quadratic & Cubic Graphs v2 – SOLUTIONS

Algebra – H – Quadratic Formula v2

Algebra – H – Quadratic Formula v2 – SOLUTIONS

Algebra – H – Sequences v2

Algebra – H – Sequences v2 – SOLUTIONS

Algebra – H – Simplify, Expand & Simplify v2

Algebra – H – Simplify, Expand & Simplify v2 – Solutions

Algebra – H – Simultaneous Equations v2

Algebra – H – Simultaneous Equations v2 – SOLUTIONS v3

Algebra – H – Straight Line Graphs v2

Algebra – H – Straight Line Graphs v2 – SOLUTIONS

Algebra – H – Substitution, Solving & Rearranging Equations v2

Algebra – H – Substitution, Solving & Rearranging Equations v2 – SOLUTIONS v2

NUMBER

Number – H – Estimation v2

Number-H-Estimation-v2 – SOLUTIONS 2

Number – H – Factors, Multiples, Primes – Number properties v2

Number – H – Factors, Multiples, Primes – Number properties v2 – SOLUTIONS

Number – H – Fractions v2

Number – H – Fractions v2 – SOLUTIONS

Number – H – Fractions, Decimals & Percentages v2

Number – H – Fractions, Decimals & Percentages v2 – SOLUTIONS v2

Number – H – Multiples in Context v2 

Number – H – Multiples in Context v2 – SOLUTIONS

Number – H – Number Problems v2

Number-H-Number-Problems-v2 – SOLUTIONS

Number – H – Percentages v3

Number – H – Percentages v3 – SOLUTIONS v2

Number – H – Product of Prime Factors, HCF & LCM v2

Number – H – Product of Prime Factors, HCF & LCM v2 – SOLUTIONS

Number – H – Reverse Percentages v2

Number – H – Reverse Percentages v2 – SOLUTIONS

Number – H – Rounding, Bounds and Error Intervals v2

Number – H – Rounding, Bounds and Error Intervals v2 – SOLUTIONS

Number – H – Standard Form v2

Number – H – Standard Form v2 – SOLUTIONS V2

Number – H – Surds v2

Number – H – Surds v2 SOLUTIONS

Number – H – Use of Calculator v2

Number – H – Use of Calculator v2 – SOLUTIONS

Number – H – Decimals including money v2

Number-H-Decimals-including-money-v2 – SOLUTIONS

Number – H – Combinations v2

Number – H – Combinations v2 – SOLUTIONS

Number – H – Bidmas, Powers & Roots v2

Number – H – Bidmas-Powers-Roots-v2 – SOLUTIONS

RATIO & PROPORTION
Ratio – H – Speed, Distance, Time & Rates of Change v2

Ratio – H – Speed, Distance, Time & Rates of Change v2 – SOLUTIONS

Ratio – H – Simple, Compound Interest, Depreciation, Growth & Decay v2

Ratio-H-simple-compound-interest-depreciation-growth-decay-v2-solutions

Ratio – H – Ratio 1 v2

Ratio – H – Ratio 1 v2 -SOLUTIONS

Ratio – H – Proportional Reasoning v2

Ratio-H-Proportional-Reasoning-v2 – SOLUTIONS

Ratio – H – Proportion – Recipes v2

Ratio-H-Proportion-Recipes-v2 – SOLUTIONS

Ratio – H – Direct & Inverse Proportion v2

Ratio – H – Direct & Inverse Proportion v2 – SOLUTIONS

Ratio – H – Currency & Unit Conversion v2

Ratio-H-Currency-Unit-Conversion-v2 – SOLUTIONS

Ratio – H – Conversion Graphs v2

Ratio – H – Conversion graphs v2 – SOLUTIONS

Ratio – H – Compound Measures v2

Ratio – H – Compound Measures v2 – SOLUTIONS

Ratio – H – Best Value v2

Ratio – H -Best-Value v2 – SOLUTIONS

STATISTICS

Statistics – H – Time Series v2

Statistics – H – Scatter Graphs v2

Statistics – H – Scatter Graphs – Solutions

Statistics – H – Sampling v2

Statistics – H – Sampling v2 – Solutions

Statistics – H – Histograms v2

Statistics H – Histograms v2 – SOLUTIONS

Statistics – H – Cumulative Frequency v2

Statistics – H -Cumulative frequency v2 – SOLUTIONS

Statistics – H – Averages v2

Statistics – H – Averages v2 – Solutions

Statistics – H – Box Plots v2

Statistics H – Box Plots v2 – SOLUTIONS

What you need to know:

Surds are defined to be numbers that we leave in root form, \sqrt{2}, rather than decimal form, 1.414213…, so to express their exact value. You may be asked to simplify surds by various applications of the rule \sqrt{ab} = \sqrt{a}\sqrt{b}; this rule is very important for all the work we do surrounding surds, so familiarity with it is necessary.

We say that a number is in surd form when it cannot be simplified any further. For example, \sqrt{3} is in surd form, however \sqrt{27} can be simplified using the above rule as follows:

\sqrt{27} = \sqrt{9 \times 3} = \sqrt{9} \times \sqrt{3} = 3\sqrt{3}

Exam questions often ask that you leave your answers in surd form. In this example, you would likely be deducted a mark if you said that the final answer was \sqrt{27} rather than 3\sqrt{3}.

You are also required to know how to rationalise the denominator of a fraction involving surds. This involves manipulating the fraction so that the bottom of it no longer contains any surds – only whole numbers. You should be able to do this with fractions where the denominator is itself a surd (multiply top and bottom by that surd) as well as with fractions where the denominator is an expression of the form a + \sqrt{b} (multiply top and bottom by a - \sqrt{b}). More than anything else this requires care, so take your time with the arithmetic, especially at the beginning.

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