N5 EF1.1 Surds and Indices - Revision

Transcription

1 N EF Surds and Indices - Revision This revision pack covers the skills at Unit Assessment and exam level for Surds and Indices so you can evaluate your learning of this outcome. It is important that you prepare for Unit Assessments but you should also remember that the final exam is considerably more challenging, thus practice of exam content throughout the course is essential for success. The SQA does not currently allow for the creation of practice assessments that mirror the real assessments so you should make sure your knowledge covers the sub skills listed below in order to achieve success in assessments as these revision packs may not cover every possible question that could arise in an assessment. Topic Unit Sub skills Questions Surds EF Simplification of surds - 8 Rationalising the denominator of a surd 9-0 Multiplying and dividing using positive and negative indices including fractions 7 and - Indices EF m ab a b 8 m m m mn n a a 8 m n a n a m 9-0 When attempting a question, this key will give you additional important information. Key Note Question is at unit assessment level, a similar question could appear in a unit assessment or an exam. Question is at exam level, a question of similar difficulty will only appear in an exam. # * The question includes a reasoning element and typically makes a question more challenging. Both the Unit Assessment and exam will have reasoning questions. If a star is placed beside one of the above symbols that indicates the question involves sub skills from previously learned topics. If you struggle with this question you should go back and review that topic, reference to the topic will be in the marking scheme. Question should be completed without a calculator. Question should be completed with a calculator. Questions in this pack will be ordered by sub skill and typically will start off easier and then get more challenging. Some questions may also cover several sub skills from this outcome or even include sub skills from previously learned topics (denoted with a *). Questions are gathered from multiple sources including ones we have created and from past papers. Extra challenge questions are for extension and are not essential for either Unit Assessment or exam preparation. JGHS - N EF Revision

2 FORMULAE LIST The roots of ax bx c 0 are x b b ac a Sine rule: a sin A b sin B c sin osine rule: a b c bccos A or b cos A c a bc Area of a triangle: A absin Volume of a sphere: V r Volume of a cone: V r h Volume of a pyramid: V Ah Standard deviation: s x x n x x n n, where n is the sample size. JGHS - N EF Revision

3 Q Questions Marks 6 Simplify 8 Simplify 7 0 Expand the brackets of 6 Express your answer as a surd in its simplest form Simplify 6 0 Three of the following have the same value. 6 8 Which one has a different value? You must give a reason for your answer The rectangle above has length centimetres and breadth 6 centimetres. alculate the area of the rectangle. Express your answer as a surd in its simplest form. 7 * A B A right angled triangle has dimensions shown above. alculate the length of AB, leaving your answer as a surd in its simplest form. 8 Solve for x, x 8 JGHS - N EF Revision

4 9 Express as a fraction with a rational denominator 0 Simplify. Express your answer as a fraction with a rational denominator Extra hallenge: Rationalise the denominator of Simplify a a y y Simplify y Simplify y y 6 y 7 Expand and simplify a a Expand the brackets and simplify the expression Expand the brackets and simplify the expression 0 Express in its simplest form Evaluate 7 8y, expressing your answer with positive indices y b b a b a a Evaluate 6 8 Each of these large oil containers holds 80 litres of fuel. How many litres are there altogether in the full tanks shown? Give your answer in scientific notation JGHS - N EF Revision

5 The planet Mars is at a distance of 8 0 kilometres from the Sun. The speed of light is 0 0 kilometres per second. How long does it take light from the Sun to reach Mars? Give your answer to the nearest minute A planet takes 88 days to travel round the Sun. The approximate path of the planet round the Sun is a 7 circle with diameter 0 kilometres. Find the speed of the planet as it travels round the sun Give your answer in kilometres per hour, correct to significant figures. The mass of the sun is 0 0 kilograms. The mass of the earth is 97 0 kilograms. Express the mass of the earth as a percentage of the mass of the sun. Give your answer in scientific notation. One atom of gold weighs 7 0 grams. How many atoms will there be in one kilogram of gold? Give your answer in scientific notation correct to significant figures. [END OF REVISION QUESTIONS] [Go to next page for the Marking Scheme] JGHS - N EF Revision

6 Where suitable, you should always follow through an error as you may still gain partial credit. If you are unsure how to do this ask your teacher. Q Simplify 8 Marking Scheme 8 6 Subtract surds Do not accept for Start to simplify surds 6 Fully simplify surds 6 Add and subtract surds 0 orrectly multiply surds Simplify surd and root Any further simplification beyond the correct answer loses Simplify 0 Simplify Subtract surds 9 # Express all surds in a similar form eg 6 6 or 6 6 or 8 6 Answer with valid conclusion 8 is the odd one out since 8 Final mark is only available if comparison is made between odd one out and the other ones. 6 6 Know how to find area and start to simplify Simplify Fully simplify answer 8 6 cm Units required for final mark JGHS - N EF Revision

7 7 * Know to use Pythagoras Simplify to find AB as an unsimplified surd AB AB AB AB Find AB in simplest form AB 9 (cm) This question involves Pythagoras from Relationships. Go back and review that topic if you could not access this question.. Units not required for final mark Simplify 8 Start to simplify x x 9 x x Process for x x Start rationalisation process omplete Rationalise denominator Simplify surd x Simplify fraction Other paths to solution are acceptable as long as they are mathematically correct. Do not accept 6 for Hint: Use conjugate 6 JGHS - N EF Revision

8 6 7 8 multiply a Simplify Numerator Simplify expression 7 y Simplify numerator Simplify numerical component y y Simplify indices y 6 Multiply out first term a Multiply out second term a Express with positive indices a a Multiply out first term b Multiple out second term 0 b Simplify expressions b Write in index form a a a Expand first term a Expand second term a Multiply out brackets 8 8 y y Simplify expression y y y y JGHS - N EF Revision

9 9 0 Write in root form and start to evaluate Evaluate 9 Write with positive index in root form 6 Start to evaluate evaluate 7 7 orrect sum with answer onvert to scientific notation Form correct sum alculate D 0 T S (seconds) 7 onvert to minutes and round minutes 9 Find circumference D onvert Days to hours 88 Evaluate speed Round two significant figures and express in scientific notation D S T km/h JGHS - N EF Revision

10 Express as fraction Express as decimal Express as percentage in scientific notation % 70 % orrect sum Process 08 0 Round answer 0 (gold atoms) [END OF MARKING SHEME] JGHS - N EF Revision