# 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 POST**and also check out the questions by topic for the**FOUNDATION 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.

## 0 thoughts on “Surds Revision Questions For Essays”

-->