Mathematics. toughest areas of the 2018 exam papers. Pearson Edexcel GCSE (9 1) Foundation. New for 2018

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1 New for 08 toughest areas of the 08 exam papers Pearson Edexcel GCSE (9 ) Mathematics Foundation analsis and examples of practical guidance from our intervention workbooks.

2 Top 0 Pearson Edexcel GCSE (9 ) Mathematics Foundation 08 Using data from the ResultsPlus analsis of exam papers, this booklet presents the top 0 toughest areas of the 08 Pearson Edexcel GCSE (9 ) Mathematics Foundation tier exams. This booklet: l delivers specific guidance for ou to work through with our students l provides full worked through exam questions taken from the 08 series l supports students in areas the found most challenging in the 08 exams l identifies how our Target intervention workbooks (see page ) can improve these skills and help students appl them in future exams. The eas-to-follow laout of this booklet demonstrates how relevant pages of Target workbooks can address the ke skills required for each exam question shown. In some cases we have included a page from the Foundation Student Book to address this skill. The Top 0 topics. Rearranging formulae.... Finding graphical solutions to quadratic equations Simplifing expressions with indices Solving linear equations Finding the equation of a straight line Using the line of best fit on a scatter diagram Finding the volume of a prism Mutuall exclusive outcomes Simplifing b collecting like terms Using ratio and scale factor to find lengths in similar figures...

3 Rearranging formulae Pearson Edexcel specification point A5 understand and use standard mathematical formulae; rearrange formulae to change the subject Examiner report 08 Mathematics Foundation Paper (Calculator) question 8 Onl % of students successfull answered this question to gain all marks. Sometimes a string of errors led coincidentall to the correct answer, but no marks could be awarded without the correct method. 8 Make g the subject of the formula T = g + 6 method mark for making the first step in rearranging the formula to make g the subject. method mark for continuing to rearrange the formula. T = g + 6 T = g + 6 g = T 6 The first stage would be to square both sides. Another method is multipling both sides b. Remember, the inverse of is square. accurac mark for the correct answer. To get the second method mark ou need to make sure that ou gain the first method mark. x = 8, x = [ marks] The second stage would be to multipl b. Pearson Edexcel GCSE (9 ) Mathematics Foundation For more practice, including worked examples, see Lesson 0.5 in the: - Foundation Student Book - Foundation Practice Reasoning and Problem-solving books - ActiveLearn Student and Teaching resources.

4 Skills boost Changing the subject of a more complex formula The question required three steps to be taken in order to rearrange a formula, and man students made at least one error. This Skills Boost page from Target Grade 5 Number and Algebra Workbook will show ou how to rearrange a formula. Identif the operations used on the variable: +,, or. Use the inverse operations to change the subject. Guided practice Make t the subject of the formula d = s t Take the reciprocal of both sides. d = d = t s t s Multipl both sides b s. s d s t = s s d = t To get t on the top of the fraction. s s = Worked exam question Draw function machines with the new subject as the input. t s d Work backwards with inverse operations. s d s d 7 a Make Make x the V the subject subject of of Hint D = Take m the square b Make A the subject of P = F V a x = 5 + a root of both sides. b x = d 6 A a c x Make I the subject of V = IR b Make d the subject of s = d = v + u d x = m n t 8 Make t the subject of Make h the subject of the formula A = bh a t = m + r Make b the subject of A = b t + k = x Hint bh Get t on its own first. a c t Make x F the subject of P= F = A d b t Make A the subject of P = F s = n A Hint Take the reciprocal first P = A F Exam-stle 5 Make t the question subject of q = p t + x Hint Get the term with t on its own on one side 9 Make u the subject of the formula v = u + as of the equals sign. 0 Make the subject of a = x Hint The inverse of _ is square. q x = p t Then take the reciprocals. q x = b = t ( marks) Reflect What is the inverse operation of squaring? Unit Formulae 9 ( ) This page is taken from

5 Finding graphical solutions to quadratic equations Pearson Edexcel specification point A identif and interpret roots, intercepts, turning points of quadratic functions graphicall 08 Mathematics Foundation Paper (Calculator) question (c) 7 Examiner report Onl % of students successfull answered this question to gain marks. Man scripts were blank. method mark for marking the line = on the graph. 6 5 O x Tring to calculate a solution to the equation can also be done but using the graph is much more likel to get ou the correct answer. You could also give coordinates but ou need to give both to get the mark (c) Use our graph to find estimates of the solutions to the equation x x 6 = accurac mark for answers between.5 to.7 and.5 to.7. x =.6 x =.6 The answer doesn t have to be exact as long as it is within the range given in the mark scheme. [ marks] Pearson Edexcel GCSE (9 ) Mathematics Foundation For more practice, including worked examples, see Lesson 6. in the - Foundation Student Book - Foundation Practice Reasoning and Problem-solving books - ActiveLearn Student and Teaching resources. 6

6 Skills boost Finding solutions and turning points from quadratic graphs The turning point of a quadratic graph: with x gives a minimum value of. Minimum with x gives a maximum value of. Unit 9 of Target Grade 5 Number and Algebra Workbook will show ou how to find solutions to equations using quadratic graphs where a function of x is equal to zero. This Skills Boost is an example of a page from the unit. To cover the further step of drawing a line = see p88 of the Student Book. Maximum The solutions of the quadratic equation ax + bx + c = 0 are where the graph of = ax + bx + c intercepts the x-axis. O x Solutions are the x-values where = 0 Guided practice Here is the graph of = x x a Write down the minimum value of. b Write down two solutions of x x = 0 a Read the value of at the turning point. = b Read the values of x when = 0 x = and x = = x x 0 x Hint Solutions are not alwas whole numbers. Read the scale as accuratel as ou can. Use the graph of = x a Write down the minimum value of. = b Write down two solutions of x = 0 x = and x = Exam-stle questions = x x 0 x = x = x x + Use the graph of = x x + a Write down the value of at the turning point. = ( marks) b Write down the solution of x x + = 0 x = ( mark) Use the graph of = x x a Write down the coordinates of the turning point. b Write down approximate solutions to x x = 0 ( marks) ( mark) Reflect Look back at the graphs of quadratic equations ou drew in Skills boost. Which of them have one solution and which have two solutions when = 0? Unit 9 Non-linear graphs 59 This page is taken from

7 Simplifing expressions with indices Pearson Edexcel specification point A simplif and manipulate algebraic expressions b simplifing expressions involving sums, products and power, including the laws of indices Examiner report 08 Mathematics Foundation Paper (Calculator) question 0 (b) Students found part (b) of this question particularl difficult, onl 5% getting it right. 0 (b) Simplif (5np ). accurac marks for the correct answer. 5n p 9 You would still get our marks if ou included multiplication signs. accurac mark can be awarded for out of correct terms. The index needs to be applied to each part of the term: (5np ) = 5 n p You need to make sure all the terms are correct. If ou don t ou will lose marks. [ marks] Pearson Edexcel GCSE (9 ) Mathematics Foundation For more practice, including worked examples, see Unit 8 Lesson 8. in the - Foundation Student Book - Foundation Practice Reasoning and Problem-solving books - ActiveLearn Student and Teaching resources. 8

8 Skills boost Laws of indices for multiplication and division To multipl two powers of the same number, add the powers. To divide two powers of the same number, subtract the powers. Guided practice a Simplif 5 5 b Simplif This page from Unit 6 of Target Grade 5 Number and Algebra Workbook is a starting point to help ou simplif expressions that use indices. This exam question uses indices with algebraic and numeric terms. Worked exam question Write as a single power. a 5 5 = 5 + b = = = = = 5 7 = = = Simplif a 5 b 5 Hint = c 5 Write as a single power. a 7 b 05 0 c Evaluate a b 5 c Hint Simplif to, then work out the value. Simplif a 5 x 5 5 b 7 x 7 7 c x 5 Exam-stle question 5 Write ( ) as a single power. Hint ( ) ( mark) Reflect What do evaluate and simplif mean in indices questions? 0 Unit 6 Indices This page is taken from

9 Solving linear equations Pearson Edexcel specification point A7 solve linear equations in one unknown algebraicall 08 Mathematics Foundation Paper (Calculator) question 5 Examiner report 5 Solve 5 x = x 7 This question was beond the algebraic skills of man students and man did not even attempt it. method mark for the correct first step. method mark for correct second step. 5 x = (x 7) 5 x = x x + x = + 5 5x = 9 x =.8 Be careful when rearranging equations with negatives on both sides. The first step is to multipl both sides b. Then isolate terms involving x. accurac mark for correct answer. x = 8, x = [ marks] Pearson Edexcel GCSE (9 ) Mathematics Foundation For more practice, including worked examples, see Unit 5 Lesson 5. in the - Foundation Student Book - Foundation Practice Reasoning and Problem-solving books - ActiveLearn Student and Teaching resources. 0

10 Skills boost Solving linear equations with fractions This page from Unit of Target Grade 5 Number and Algebra Workbook will help ou solve linear equations involving fractions and multiple steps. When the letter term is a fraction like x or a or c, first get the letter term on its own on one 7 side of the = sign, then multipl b the denominator. Guided practice Solve x 5 = Worked exam question Use inverse operations to get the fraction on its own. x 5 = Add 5 to both sides. x = x so use the inverse operation on both sides. x = x 5 x + Solve a x 7 + = 7 b 7 + a = c b 5 = 6 Solve x = a = b = a w 8 = b x 7 = 5 c + x 5 = w = x = x = Simplif Hint (x + ) a x + ( ) b ( x 5 ) c ( 5d + 7 ) 7 Solve Hint (5x + ), so multipl both sides b. a x + = 5x + b x = x + 5 c 8 t = t +5 Exam-stle question 5 Solve x = 5 6x x = ( marks) Reflect Is x + the same as (x + )? In Qa, wh do ou need to put brackets around (x + )? Unit Equations 5 This page is taken from

11 5 Finding the equation of a straight line Pearson Edexcel specification point A9 plot graphs of equations that correspond to straight-line graphs in the coordinate plane; use the form = mx + c to identif parallel lines; find the equation of the line through two given points or through one point with a given gradient 08 Mathematics Foundation Paper (Calculator) question The line L is shown on the grid. It is useful to draw the horizontal and vertical lines on the diagram to find the gradient. method mark for finding the gradient of the line OR for finding the intercept OR for writing b = m(x a) Find an equation for L. method mark for substituting m and x into = mx + c O c = 6 m = = x 6 L 5 Examiner report This question was not answered well with onl 7% of candidates getting it right and man not even attempting it. accurac mark for correct answer. x = 8, x = [ marks] Don t forget to use the intercept and not the x intercept in our equation. Ringing the intercept will not get ou a mark. You need to write it out, in this case c = 6. The question asks students to find the equation of the line L. L will not appear in the equation the letter L is just used to identif the line. Pearson Edexcel GCSE (9 ) Mathematics Foundation For more practice, including worked examples, see Unit 9 Lesson 9. and 9. in the - Foundation Student Book - Foundation Practice Reasoning and Problem-solving books - ActiveLearn Service Student and Teaching resources.

12 Skills boost Finding the equation of a straight line from its graph This page in Unit 8 of Target Grade 5 Number and Algebra Workbook will help ou find the equation of a straight line using = mx + c. To find the equation of a straight line, = mx + c, find the gradient m and the -intercept c. Guided practice Write down the equation of the line x Worked exam question Find the -intercept. c = Find the gradient. m = Substitute m and c into = mx + c Find c, where the line crosses the -axis. = x + Find m, how much the graph goes up when x increases b x x Write down the equation of each of these straight lines. a = b = c = 5 ba 0 5 x c Write down the equation of each of these straight lines. a = b = c = Exam-stle question Write down the equation of this line. 0 x b a x c Hint A negative gradient is how much the graph goes down when x increases b. ( marks) Reflect Given the equations of three lines, how can ou tell which line is the steepest? 5 Unit 8 The equation of a straight line This page is taken from

13 6 Using the line of best fit on a scatter diagram Pearson Edexcel specification point S6 use and interpret scatter graphs of bivariate data; recognise correlation and know that it does not indicate causation; draw estimated lines of best fit; make predictions; interpolate and extrapolate apparent trends while knowing the dangers of so doing 08 Mathematics Foundation Paper (Calculator) question 9 (b) 9 The scatter diagram shows information about girls. It shows the age of each girl and the best time she takes to run 00 metres. Examiner report Man students attempted to provide an explanation but few considered the point in terms of its distance from the line of best fit. 7 6 Time in seconds Age in ears (a) Write down the tpe of correlation. negative Kristina is ears old. Her best time to run 00 metres is seconds. The point representing this information would be an outlier on the scatter diagram. It is not enough to sa that Kristina was the fastest, the statement has to relate to the other girls and to be identified as an outlier it needs further expansion such as she was much faster than all the other girls. [ mark] communication mark for providing a correct explanation. (b) Explain wh. The point would not be in line with the trend of the Remember to add detail to other points. [ mark] our explanation. Pearson Edexcel GCSE (9 ) Mathematics Foundation For more practice, including worked examples, see Unit Lesson.7 in the - Foundation Student Book - Foundation Practice Reasoning and Problem-solving books - ActiveLearn Service Student and Teaching resources.

14 Using the line of best fit Skills boost To help ou use the line of best fit on a scatter diagram look at this page in Unit 8 of Target Grade 5 Shape and Statistics Workbook. Look at page 75 of the Foundation Student Book to learn more about outliers. Interpolation is using the line of best fit to predict data values within the range of the given data. Extrapolation is using the line of best fit to predict data values outside the range of the given data, so is less reliable and ma give impossible estimates. Guided practice The scatter graph shows the exam results for a group of students. The maximum number of marks on each paper is 60. a Paul got marks on Paper but was absent for Paper. Estimate the mark Paul would have got for Paper. b Katie got the maximum of 60 marks on Paper but was absent for Paper. Estimate the mark Katie would have got on Paper. c Which is the more reliable estimate? Explain our answer. Paper Exam results Paper Worked exam question a Draw a line up from on the Paper axis to the line of best fit, then draw a line across from there to the axis for Paper. b Extend the line of best fit to include 60 marks on Paper. Work out the Paper mark that corresponds to 60 marks on Paper. c Write a sentence. The estimate for part is more reliable because The scatter graph shows the top speeds of cars from one manufacturer, and their CO emissions in grams per kilometre. a The manufacturer designs a car with a top speed of 0 mph. Estimate the CO emissions of this car. b The manufacturer designs another car with a top speed of 0 mph. Estimate the CO emissions of this car. CO emissions (g/km) Top speed and CO emissions c Which is the more reliable estimate, our answer to part a or part b? Explain wh Top speed (mph) Reflect Explain the difference between interpolation and extrapolation. 56 Unit 8 Scatter graphs This page is taken from

15 7 Finding the volume of a prism Pearson Edexcel specification points NG6 know and appl formulae to calculate: area of triangles, parallelograms, trapezia; volume of cuboids and other right prisms (including clinders) G0 know the formulae for: Pthagoras theorem a + b = c, and the trigonometric ratios, opposite sin u = hpotenuse, cos u = adjacent opposite and tan u = ; appl them to find angles and hpotenuse adjacent lengths in right-angled triangles in two-dimensional figures 6 08 Mathematics Foundation Paper (Calculator) question 6 To find the volume of the prism ou need to use the formula V = area of cross section length. 6 Here is a triangular prism. This question requires the use of Pthagoras theorem to work out the area of the triangle. A mark is awarded for a correct Pthagorean statement e.g. x + 7. = 8. process mark for a complete process to find the volume of the prism. 7. cm 8. cm Work out the volume of the prism. Give our answer correct to significant figures (= 8.7) 8.7 =. cm. cm 7. cm = 5.57 cm 5.57 cm 8 cm = 80 cm process mark for a process to find the area of the triangular face dependent on getting the first process mark correct. Pearson Edexcel GCSE (9 ) Mathematics Foundation 8 cm accurac mark for an answer in the range For more practice, including worked examples, see Unit 8 Lesson 8.5 in the - Foundation Student Book - Foundation Practice Reasoning and Problem-solving books - ActiveLearn Student and Teaching resources. Examiner report This question was not answered well with man students just multipling dimensions given. process mark for starting to use Pthagoras to find the missing side. process mark for a complete process to find the missing side of the triangle. Note that it sas to significant figures so an answer has to include onl three digits. 80 cm [5 marks]

16 Surface area and volume of a prism Skills boost This page from Unit of Target Grade 5 Shape and Statistics Workbook will help ou work out how to find the volume of prisms and other D shapes. To find out how to use Pthagoras, refer to Unit in the Foundation Student Book. Guided practice For this triangular prism, work out a the surface area b the volume. 5 cm.7 cm 6 cm 7 cm 8 cm Worked exam question Sketch each different face of the triangular prism. a.7 cm Area = = cm 7 cm 8 cm Area = 7 cm = cm Total surface area = = cm Area = = cm Area = = cm There are two triangular faces and one of each rectangle. b Volume = area of cross-section length = 8 = cm For this clinder, work out a the surface area b the volume. Give our answers to decimal place (d.p.). cm 0 cm Hint The clinder is a tube that ou unroll and flatten. The face is a rectangle. The width of the rectangle is the circumference of the circle. a Draw the different faces of this cuboid. b Work out cm 5 cm 8 cm Hint You should have three different rectangles. i the surface area ii the volume. For each prism, work out i the surface area ii the volume. a i b i 5 cm cm 9 cm cm ii 0 cm 8 cm 5 cm cm ii Exam-stle question For this prism, work out a the surface area b the volume. 6 cm 7 cm 5.5 cm 6 cm 0 cm cm ( marks) ( marks) Reflect Without looking at this page, write the formula for working out the volume of a prism. Unit Volume and surface area 9 This page is taken from

17 8 Mutuall exclusive outcomes Pearson Edexcel specification point P appl the propert that the probabilities of an exhaustive set of outcomes sum to one; appl the propert that the probabilities of an exhaustive set of mutuall exclusive events sum to one 08 Mathematics Foundation Paper (Calculator) question (b) A marble is going to be taken at random from a box of marbles. The probabilit that the marble will be silver is 0.5 There must be an even number of marbles in the box. (b) Explain wh. Examiner report The average score for part (b) of this question was 0. out of the mark that could be gained. The most common error was to comment on the splitting of an odd total and incorrectl stating that this was not possible. You cannot have half a marble so the number of marbles in the box must be even. communication mark for a correct explanation. Number of silver marbles total number of marbles = 0.5 = 0.5 multiplied b an odd number will never be a whole number. [ mark] Pearson Edexcel GCSE (9 ) Mathematics Foundation For more practice, including worked examples, see Unit Lesson. in the - Foundation Student Book - Foundation Practice Reasoning and Problem-solving books - ActiveLearn Student and Teaching resources. 8

18 Problem-solve! Get back on track This page from Unit of Target Grade Number and Statistics Workbook will help ou work out problems related to mutuall exclusive events and become confident using probabilit. Exam-stle questions James sas that 7 9 = 5 James is wrong. Explain wh. There are 0 students in the school hall. of the students leave the hall. How man students are still in the hall? There are 0 counters in a bag. The counters are green or ellow or blue. of the counters are green. 5 of the counters are ellow. Work out the number of blue counters in the bag. ABCD is a square. This is an accurate diagram. What fraction of the square ABCD is shaded? A B ( marks) ( marks) ( marks) 5 a Hugh works out that 5 8 = 5 8 = 5 The answer 5 is wrong. Describe one mistake that Hugh has made. D C ( marks) ( mark) b Work out the correct answer to 5 8 Write our answer as a mixed number. ( marks) Now that ou have completed this unit, how confident do ou feel? Mixed numbers and improper fractions Adding and subtracting fractions and mixed numbers Multipling a fraction b an integer Dividing an integer b a fraction 0 Unit Fractions This page is taken from

19 9 Simplifing b collecting like terms Pearson Edexcel specification points A simplif and manipulate algebraic expressions A translate simple situations or procedures into algebraic expressions or formulae; derive an equation, solve the equation(s) and interpret the solution G6 know and appl formulae to calculate; area of triangles, parallelograms, trapezia; volume of cuboids and other right prisms (including clinders) 08 Mathematics Foundation Paper (Calculator) question 7 Examiner report 7 ABC is an isosceles right-angled triangle. Pthagoras won t help ou to solve this problem. A x cm B x cm Ver few students gained full marks on this question, the main error being a failure to use the correct formula for the area of a triangle. Man students used a trial and improvement approach but to be awarded the marks this needed to be completel correct. process mark for a process to set up a complete equation in x. process mark for a process to simplif to x The area of the triangle is 6 cm Work out the value of x. x x = 6 9x = 6 x = 6 9 x = 6 C accurac mark for the correct answer. Tr turning the right-angled triangle into a square to find the solution. If ou use an algebraic method don t forget to find the square root of 6 in the final step. To find the area of a triangle ou use height width the formula Area =. Don t forget to divide b. 6 x =... [ marks] 0 Pearson Edexcel GCSE (9 ) Mathematics Foundation For more practice, including worked examples, see Unit 8 Lesson 8. in the - Foundation Student Book - Foundation Practice Reasoning and Problem-solving books - ActiveLearn Student and Teaching resources.

20 Unit 8 Perimeter, area and volume 5 Calculate the perimeter and area of each shape. All lengths are in centimetres. a 5 5 b You can practice using the formula for the area of a triangle using this page from Unit 8 of the Foundation Student Book Reflect How did ou know which measurements to use in our area calculations? 6 Reasoning a Work out the area of this parallelogram..6 5 cm 8 cm b Trace the parallelogram. Join opposite vertices with a straight line to make two triangles. c What fraction of the parallelogram is each triangle? d Write down the area of one of the triangles. Q6b communication hint Vertices are corners. Q6c hint Are the triangles the same shape and size? Ke point The diagonal splits a parallelogram into two identical triangles. Area of triangles = b h Area of a triangle = b h h h Area of a triangle = bh b b Example Calculate the area of each triangle. b = 7, h = Area = bh = 7 = cm Write down the values of b and h. cm 7 cm Substitute them into the formula for area of a triangle. Write the units with our answer. 7 Calculate the area of each triangle. a b cm 5 cm 9 cm 8 cm c d mm 8 mm 9.8 cm 5 mm.5 cm Q7 hint Find the base first. The height is perpendicular to the base. Q7d hint The base and height measurements are perpendicular to each other. Discussion Is the base measurement ou use alwas along the bottom of the triangle? This page is taken from

21 0 Using ratio and scale factor to find lengths in similar figures Pearson Edexcel specification points R compare lengths, areas and volumes using ratio notation; make links to similarit (including trigonometric ratios) and scale factors G9 appl the concepts of congruence and similarit, including the relationships between lengths, in similar figures 08 Mathematics Foundation Paper (Calculator) question 7 (b) 7 Triangle ABC and triangle DEF are similar. Look carefull these triangles are not the same. A 6. cm 8. cm C (a) Work out the length of DF. D Examiner report This question was attempted b most students but rarel with an success. Those who showed an understanding of scale factors usuall gained full marks..6 cm B F 5 cm E Pthagoras won t help ou to solve this problem. You can also find the scale factor b working out But ou will need to work out and ou ma have to round the number..6 (=.5) cm.5 = 9.6 Find the scale factor (.5) first - this will help ou answer both parts of the question. 9.6 cm [ marks]... (b) Work out the length of CB. Use the same scale factor ou found in part (a) to answer part (b). Finding the difference between the two lengths won t help ou. 5.5 = 0 method mark for an equivalent method to the one shown. accurac mark for the correct answer. 0 cm [ marks]... Pearson Edexcel GCSE (9 ) Mathematics Foundation For more practice, including worked examples, see Unit 9 Lesson 9. in the - Foundation Student Book - Foundation Practice Reasoning and Problem-solving books - ActiveLearn Service.

22 8 Triangle XYZ is similar to triangle ABC. X A 8 cm cm 9 cm B Y Unit 9 Congruence, similarit and vectors This page from Unit 9 in the Foundation Student Book will give ou more practice in questions about scale factor and similarit and enlargement. C cm Z a Which side corresponds to i AB ii XZ iii BC? b What is the scale factor of the enlargement that maps i triangle ABC to triangle XYZ ii triangle XYZ to triangle ABC? c Work out the length of i XZ ii BC d Cop and complete. i ZX = ii XY = iii BC = YZ e f Which angle is the same as i angle CAB ii angle XZY iii angle ABC? Write AB AC Ke point XY as a fraction. Then write as a fraction. What do ou notice? XZ For similar shapes: Corresponding sides are all in the same ratio. Corresponding angles are equal. Q8b hint Compare the lengths of corresponding sides. 9 Triangles ABC and PQR are similar. AC and PR are corresponding sides. a Which side corresponds to BC? A P b Work out the length of PQ..5 cm c Work out the size of B C i angle ACB ii angle ABC. 5 cm Q 5 cm 0 R 0 Communication a Are triangles PQR and UVW similar? Explain our answer. 6 cm Q 0 V R 8 cm 50 W Q0a hint Work out all the angles. P U b Which side corresponds to QR? c Cop and complete. i VW = PQ ii UW = iii QR = This page is taken from 565

23 Next steps Bu now Order online using code 568OTHR to get the schools' price of.9* each: Talk to us Request an appointment to discuss the best package for our school: Download free material Visit our website to download full sample chapters of our Target Grade, 5, 7 and 9 Workbooks: *UK schools price of.9. RRP.99. PEUK Y56a

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