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Set 8.1 – Practice Questions A Name A calculator may be used from Question 10 onwards. 1 Use index notation to write each of the following as the product of its prime factors. a 120 ………………………… b 72 ………………………… (4 marks) 2 Use your results from Question 1 to find a the highest common factor of 120 and 72 ………………………… b the lowest common multiple of 120 and 72 ………………………… (4 marks) 3 Write each of these as a single power. a 73 × 77 ………………………… b 1815 ÷ 183 ………………………… (2 marks) 4 Round each number to the given number of significant figures. a 60 799 (2 s.f.) ………………………… b 0.006 058 7 (3 s.f.) ………………………… (2 marks) © Pearson Education Ltd 2015. Copying permitted for purchasing institution only. This material is not copyright free. Set 8.1 – Practice Questions A 5 Estimate 30.92 ………………………… (2 marks) 6 Fill in each empty box to make the statement true. a 10 + 5(x + 3) ≡ 5(x + b 10 − 3x + 4 ≡ ) + 3(4 − x) (2 marks) 7 Expand and simplify 6x(2x − 4) − 5(2 + x) ………………………… (3 marks) 8 Find the value of each expression when a = 4 and b = −5 a 2 + 3a2 ………………………… b 5 + (15 − 3b)2 ………………………… (3 marks) 9 Solve the equation 20 − 3(2x − 7) = 5(x + 5) − 6 ………………………… (4 marks) © Pearson Education Ltd 2015. Copying permitted for purchasing institution only. This material is not copyright free. Set 8.1 – Practice Questions A 10 A wheel has a diameter of 70cm. Work out its circumference. ….…………………cm2 (2 marks) 11 A circle fits exactly inside a square as shown. The square has sides of length 10cm. a Work out the area of the circle. ……………………cm2 b Work out the area shaded grey. …………………………cm2 (4 marks) 12 A rectangle has length 5cm and width 12cm. Work out the length of the diagonal of the rectangle. …………………………cm (2 marks) © Pearson Education Ltd 2015. Copying permitted for purchasing institution only. This material is not copyright free. Set 8.1 – Practice Questions A 13 The cross-section of a prism is in the shape of a trapezium as shown. The volume of the prism is 630cm 3. Work out its length. ………………………cm (3 marks) 14 A water bottle in the shape of a cylinder holds 1 litre of water when full. Its height is 15cm. Work out the radius of the water bottle. (1 litre = 1000cm3) ………………………cm (3 marks) © Pearson Education Ltd 2015. Copying permitted for purchasing institution only. This material is not copyright free. Set 8.1 – Practice Questions A 15 The graph shows the cost of cleaning a patio for company A and company B. a Quentin uses one company to clean the patio of the hotel that he manages and he uses the other company to clean his small patio at home. Assuming he wants to keep costs low, use the graph to explain which company he uses for the hotel and which for his house. .……………………………………………………………………………………………………………… .……………………………………………………………………………………………………………… .……………………………………………………………………………………………………………… b Work out which company is cheaper, and by how much, to clean a patio with area 50m 2. £………………………… (8 marks) © Pearson Education Ltd 2015. Copying permitted for purchasing institution only. This material is not copyright free. Set 8.1 – Practice Questions A 16 Jan walks 1200 metres in 10 minutes. This would be shown as a straight line on a distance–time graph. Her walking speed varies throughout the 1200 metres. a What does the steepness of the straight line represent? .……………………………………………………………………………………………………………… .……………………………………………………………………………………………………………… b The owners of a holiday house consider three different ways of charging for electricity. Use the graphs to describe the way each option is charged. Option 1:……………………………………..……………………………………………………………… .……………………………………………………………………………………………………………… Option 2:………………………………………..…………………………………………………………… .……………………………………………………………………………………………………………… Option 3:…………………………………………..………………………………………………………… .……………………………………………………………………………………………………………… (6 marks) © Pearson Education Ltd 2015. Copying permitted for purchasing institution only. This material is not copyright free. Set 8.1 – Practice Questions A Answers All answers are worth 1 mark unless otherwise indicated. From Question 12 onwards, deduct no more than 2 marks across the paper for rounding errors. 1 a 23 × 3 × 5 (2) b 23 × 32 (2) 1 mark for any equivalent form, using only the prime factors 2, 3 and 5 1 mark for any equivalent form, using only the prime factors (i.e. 2 and 3) 1 mark for identifying that 23 and 3 are factors of both numbers 2 a 24 (2) b 360 (2) 1 mark for 120 × 72 ÷ 24 or equivalent 3 a 710 b 1812 4 a 61 000 b 0.006 06 5 900 (2) 1 mark for attempting to square 30 6 a 5 b 2 7 12x2 − 29x − 10 (3) 2 marks for 12x2 − 24x – 10 − 5x; or 1 mark for sight of at least two of these four terms 8 a 50 b 905 (2) 1 mark for sight of 900 x = 2 (4) 9 3 marks for 11x = 22 or 41 = 11x + 19; or 1 mark for each side of 20 − 6x + 21 = 5x + 19 10 a 70πcm2 (2) 1 mark for approximation 219.9cm2; accept 3 or more s.f. of 219.911 48 correctly rounded 11 a ≈78.54cm2 (2) accept 3 or more s.f. of 78.539 816 3 correctly rounded b ≈21.46cm2 (2) accept 3 or more s.f. of 78.539 816 3 correctly rounded or (100 − their part a so long as the result is positive; 1 mark for method 12 13cm (2) 1 mark for sight of √52 + 122 or 52 + 122 or 25 + 144 13 15cm (3) 2 marks for sight of 42cm2 or 1 mark for (630 ÷ their 42) 14 ≈4.607cm (3) accept 3 or more s.f. of 4.606 588 66 correctly rounded; 2 marks for 1000 ÷ 15π or for sight of 21.22 or 1 mark for 1000 ÷ 15 15 a company A is cheaper for patios less than 22.5m2 and company B is cheaper for patios more than 22.5m2, so he uses company A for the house and company B for the hotel (2) b company A £162.50 (2) company B £115 (2) 1 mark for correct method (e.g. 130 ÷ 40 × 50) 1 mark for £1.50 or for correct method (e.g. 40 + 60 ÷ 40 × 50) ∴ company B is cheaper by £47.50 (2) 1 mark for sight of 47.5 © Pearson Education Ltd 2015. 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Set 8.1 – Practice Questions A Answers Use the formula for the circumference of a circle Construct and solve equations that involve multiplying out brackets by a negative number and collecting like terms, e.g. 4(2a − 1) = 32 − 3(2a − 2) Substitute positive and negative integers into linear expressions and expressions involving powers Simplify expressions involving brackets and powers, e.g. x(x2 + x + 4), 3(a + 2b) − 2(a + b) Know and understand the meaning of an identity and use the identity sign Use numbers of any size rounded to 1 significant figure to make standardised estimates for calculations with 1 step Recognise graphs showing constant rates of change, average rates of change and variable rates of change Discuss and interpret real-life graphs, e.g. conversion graphs, water filling baths/containers, graphs comparing e.g. mobile phone tariffs – how you can see which tariff is better for different numbers of calls Use and apply Pythagoras’ theorem to solve problems Calculate the lengths, areas and volumes in cylinders Apply the index laws for multiplication and division of small positive integer powers 13 Round numbers to a given number of significant figures Use prime factor decomposition to find the HCF or LCM of 2 numbers Use the formulae for area of a circle, given the radius or diameter / 54 Overall mark: Calculate the lengths and areas given the volumes in right prisms Find the prime factor decomposition of a number Objective 12 Question 10 9 8 7 6 16 15 14 11 Objective accept any way of indicating that charge does not depend on the number of units used (1) b option 1: the charge is constant 5 4 3 2 1 Question 1 marks for speed 16 a her average walking speed (2) option 2: the charge is proportional to the number of units used (1) accept equivalent explanation option 3: the charge per unit decreases with the number of units used until the graph is flat (1) at which point there is no further charge for more units used (1) accept equivalent explanation © Pearson Education Ltd 2015. Copying permitted for purchasing institution only. This material is not copyright free. Set 8.1 – Practice Questions B Name Please use this grid for questions 1–4. 1 Describe the single transformation that moves shape A to shape B. …………………………...……………………………………………………………………………………… (2 marks) 2 Reflect shape A in the line y = −x. Label the image C. Show your answer on the grid. (2 marks) 3 a Rotate shape B 90° anti-clockwise about the point (−1, 1). Label the image D. Show your answer on the grid. b Describe a single transformation that moves shape D to shape C. ……..………………...……………………………………………………………………………………… (4 marks) 4 Enlarge shape A, centre (3, 3), scale factor −2. Label the image E. Show your answer on the grid. (2 marks) © Pearson Education Ltd 2015. Copying permitted for purchasing institution only. This material is not copyright free. Set 8.1 – Practice Questions B 5 Trapezium ABCD is enlarged to produce trapezium EFGH. The perimeter of ABCD is 22cm. a Work out length FG. …………………………cm b Work out the perimeter of trapezium EFGH. ………………………cm (4 marks) 6 A cylinder has radius 4cm, height 5cm and volume 251.33cm 3. It is enlarged using a scale factor of 3. Work out the volume of the enlarged cylinder. Write your answer to the nearest whole number. ………………………cm3 (3 marks) . 7 Work out 0.6 × £24 £………………………… (2 marks) .. 8 Convert 0.37 to a fraction. ………………………… (3 marks) © Pearson Education Ltd 2015. Copying permitted for purchasing institution only. This material is not copyright free. Set 8.1 – Practice Questions B 9 The price of a pair of shoes was £30 The price was reduced to £23.40 Work out the percentage change in price. ………………………% (3 marks) 10 The population of a town is now 200 000 An estimate of the population in the future is worked out by assuming that the population will keep growing at 3% per year. Work out an estimate of the population in 8 years’ time. ………………………… (3 marks) 11 Here is a sketch of a triangle. Use the given side length and angles to make an accurate drawing of the triangle. (3 marks) © Pearson Education Ltd 2015. Copying permitted for purchasing institution only. This material is not copyright free. Set 8.1 – Practice Questions B 12 Construct the perpendicular bisector of this line. Leave in your construction lines. (3 marks) 13 Use a ruler and compasses to construct the bisector of this angle. (3 marks) © Pearson Education Ltd 2015. Copying permitted for purchasing institution only. This material is not copyright free. Set 8.1 – Practice Questions B 14 A council officer is planning a path across a field. The path is to be equidistant from the sports centre, S, and the youth centre, Y. Construct the locus of the points that are equidistant from the two points. (3 marks) 15 A highways architect is planning a new entrance road to a hospital. The road will join South Road to the Accident and Emergency (A&E) entrance of the hospital. The road needs to be placed so that it is the shortest distance possible between South Road and A&E. Use a straight edge and compasses to construct the position of the new road on this plan. (3 marks) © Pearson Education Ltd 2015. Copying permitted for purchasing institution only. This material is not copyright free. Set 8.1 – Practice Questions B Answers All answers are worth 1 mark unless otherwise indicated. Grid for Answers 1–4 1 reflection in the line x = 1 (2) 1 mark for correct transformation; 1 mark for correct line equation 2 correct reflection with vertices of triangle at (−2, −3), (−1, −3), (−1, −5) (2) 1 mark for triangle of correct shape, size and orientation 3 a correct rotation with vertices of triangle at (−2, 1), (−1, 1), (−1, −1) (2) 1 mark for triangle of correct shape, size and orientation b translation ( –04 ) (2) accept follow through from their C and D as long as it is a translation 1 mark for ‘translation’; 1 mark for correct vector 4 correct enlargement with vertices of triangle at (3, 5), (3, 7), (−1, 7) (2) 1 mark for triangle of correct shape, size and orientation 5 a 12cm (2) b 33cm (2) 1 mark for sight of 1.5 1 mark for attempting to multiply 22 by their scale factor 6 6786cm3 (3) 2 marks for 6785.91 or 6785.84; or 1 mark for 27 × 251.33 or π × 12 × 12 × 15 7 £16 (2) 1 mark for sight of 3 37 2 8 99 (3) 1 mark for sight of 100x = 37.373 737 373 7… and a further mark for sight of 100x − x = 37 9 22% (3) 2 marks for 0.22 or for 6.6 ÷ 30 × 100 or equivalent; or 1 mark for 6.6 ÷ 30 10 253 354 (rounding down to whole person at end of eighth year) or 253 352 (with rounding down to whole person at end of each year) (3) if first method, then 2 marks for 1.038 = 1.266 77...; or 1 mark for sight of 200 000 × 1.038 © Pearson Education Ltd 2015. 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Set 8.1 – Practice Questions B Answers 11 triangle correct size with base of 8cm and measured angles of 30°, 40° and 110° (3) 2 marks for 2 correct angles within 1°; 1 mark for 8cm length within 1mm and either 30° or 40° within 1°; or 1 mark for 8cm length correct within 2mm and 2 angles correct within 2° 12 construction arcs evident and angles either side of perpendicular between 89° and 91° (3) 2 marks for angles between 88° and 92° with construction arcs evident; or 1 mark for some evidence of construction arcs; or 1 mark for angles between 89° and 91° without any evidence of construction 13 construction lines and angles either side of the line of bisection are within 1° of each other (3) 2 marks for angles either side of bisection line different by no more than 2°, together with construction lines; or 1 mark for some evidence of correct construction method 14 perpendicular bisector constructed; construction arcs left in and angles either side of bisector between 89° and 91° (3) 2 marks for angles between 88° and 92° with construction arcs evident; or 1 mark for some evidence of construction arcs; or 1 mark for angles between 89° and 91° without any evidence of construction © Pearson Education Ltd 2015. Copying permitted for purchasing institution only. This material is not copyright free. Set 8.1 – Practice Questions B Answers 15 construction arcs evident and angles either side of perpendicular between 89° and 91° (3) 2 marks for angles between 88° and 92° with construction arcs evident; or 1 mark for some evidence of construction arcs; or 1 mark for angles between 89° and 91° without any evidence of construction Convert a recurring decimal to a fraction Learn fractional equivalents to key recurring decimals, e.g. 0.333 333..., 0.666 666 66..., 0.111 11..., and by extension 0.222 222.... Calculate the new volume of a shape after enlargement Understand the implications of enlargement for perimeter Enlarge 2D shapes, given a centre of enlargement outside the shape and a negative whole-number scale factor Recognise and visualise the transformation of 2D shape translation Rotation on a coordinate grid Recognise and use the perpendicular distance from a point to a line as the shortest distance to the line Draw the locus equidistant between 2 points or from a point Use straight edge and compasses to construct the bisector of an angle Use straight edge and compasses to construct the mid-point and perpendicular bisector of a line segment Draw an accurate triangle given two angles and the included side (ASA) Calculate compound interest and repeated percentage change / 43 Overall mark: 15 14 13 12 11 10 9 Question Reflection on a coordinate grid in y = x, y = −x Calculate percentage change, using the formula actual change / original amount × 100 – where formula is recalled Objective Describe a reflection, giving the equation of the line of reflection Objective 8 7 6 5 4 3b 3a 2 1 Question © Pearson Education Ltd 2015. 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