Sample Assessment Materials

Edexcel Awards Mathematics Sample Assessment Materials Edexcel Level Award in Algebra (AAL0) Edexcel Level 3 Award in Algebra (AAL30) For first teaching from October 01 Pearson Education Limited is a registered company number 8788 with its registered office at Edinburgh Gate, Harlow, Essex CM0 JE

Contents General Marking guidance... 3 Level... Level Paper... 5 Level Mark scheme... 1 Level 3... Level 3 Paper... 7 Level 3 Mark scheme... 43 EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra 1

EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra

NOTES ON MARKING PRINCIPLES 1 Types of mark M marks: method marks A marks: accuracy marks B marks: unconditional accuracy marks (independent of M marks) Abbreviations cao correct answer only isw ignore subsequent working oe or equivalent (and appropriate) indep - independent ft follow through SC: special case dep dependent 3 No working If no working is shown then correct answers normally score full marks, unless indicated in the mark scheme. If no working is shown then incorrect (even though nearly correct) answers score no marks. 4 With working If there is a wrong answer indicated on the answer line always check the working in the body of the script (and on any diagrams), and award any marks appropriate from the mark scheme. If working is crossed out and still legible, then it should be given any appropriate marks, as long as it has not been replaced by alternative work. If it is clear from the working that the correct answer has been obtained from incorrect working, award 0 marks. If there is no answer on the answer line then check the working for an obvious answer. Any case of suspected misread loses A (and B) marks on that part, but can gain the M marks. If there is a choice of methods shown, then no marks should be awarded, unless the answer on the answer line makes clear the method that has been used. 5 Follow through marks Follow through marks which involve a single stage calculation can be awarded without working since you can check the answer yourself, but if ambiguous do not award. Follow through marks which involve more than one stage of calculation can only be awarded on sight of the relevant working, even if it appears obvious that there is only one way you could get the answer given. EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra 3

6 Ignoring subsequent work It is appropriate to ignore subsequent work when the additional work does not change the answer in a way that is inappropriate for the question: e.g. incorrect cancelling of a fraction that would otherwise be correct It is not appropriate to ignore subsequent work when the additional work essentially makes the answer incorrect e.g. algebra. Transcription errors occur when candidates present a correct answer in working, and write it incorrectly on the answer line; mark the correct answer. 7 Parts of questions Unless allowed by the mark scheme, the marks allocated to one part of the question CANNOT be awarded in another. 8 Use of ranges for answers If an answer is within a range this is inclusive, unless otherwise stated. 4 EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra

Write your name here Surname Other names Edexcel Award Award Algebrain Algebra Level Calculator NOT allowed Centre Number Candidate Number Sample Assessment Material Time: 1 hour 30 minutes Paper Reference AAL0/01 You must have: Ruler graduated in centimetres and millimetres, pen, HB pencil, eraser. Total Marks Instructions Use black ink or ball-point pen. Fill in the boxes at the top of this page with your name, centre number and candidate number. Answer all questions. Answer the questions in the spaces provided there may be more space than you need. Calculators may NOT be used. Information The total mark for this section is 80 The marks for each question are shown in brackets use this as a guide as to how much time to spend on each question. Advice Read each question carefully before you start to answer it. Keep an eye on the time. Try to answer every question. Check your answers if you have time at the end. Turn over S4815A *S4815A0116* 01 Pearson Education Ltd. EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra 5

Answer ALL questions. Write your answers in the spaces provided. You must write down all stages in your working. 1 Pencils are sold in packets of 4 and boxes of 1. Packet of 4 Box of 1 pencils Didi buys p packets of pencils and b boxes of pencils. Write an expression, in terms of p and b, for the number of pencils Didi bought.... (Total for Question 1 is marks) (a) Simplify a + 7b 3 + 5 + 6a 8 b 3 (b) Expand 5(g 3 + 6)... (c) Expand 6k(1 + k k )...... (Total for Question is 6 marks) 6 EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra *S4815A016*

3 The nth term of a sequence is given by the expression 6n 5 (a) Write down the first two terms of the sequence....... Here are the first five terms of another sequence 5 9 13 17 1 (b) Write down an expression, in terms of n, for the nth term of this sequence.... (Total for Question 3 is 4 marks) 4 Here is a formula v = u + at (a) Find the value of v when u = 0, a = 6 and t = 8 (b) Find the value of v when u = 10, a = 5 and t = 3... (c) Find the value of t when v = 0, u = 10 and a =...... (3) (Total for Question 4 is 7 marks) *S4815A0316* EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra 3 7

5 (a) Solve x + 6 = 15 x =... (b) Solve 6p 5 = 3p + 13 p =... (c) Solve 3(t + 5) = 10 x =... (3) (Total for Question 5 is 7 marks) 4 8 EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra *S4815A0416*

6 The line L is shown on the grid. (i) Work out the gradient of the line L.... (ii) Find an equation of the line L.... y 10 L 8 6 4 1 O 1 3 4 5 x 4 6 (Total for Question 6 is 4 marks) *S4815A0516* EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra 5 9

7 (a) Simplify x 4 x 6... (1) (b) Simplify y 8 y 3... (1) (c) Simplify (p ) 4... (1) (d) Simplify 5r 5 s 4 4r 3 s... (e) Expand and simplify 5(a + 3) + (a 4)... (3) (Total for Question 7 is 8 marks) 6 10 EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra *S4815A0616*

8 (a) On the number line below, show the inequality 1 < y 4 3 1 0 1 3 4 5 Here is an inequality, in x, shown on a number line. y 4 3 1 0 1 3 4 5 x (b) Write down the inequality.... (c) 3 n < n is an integer. Write down all the possible values of n.... (d) Solve the inequality 4t 3 > 7... (3) (Total for Question 8 is 9 marks) *S4815A0716* EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra 7 11

9 (a) Complete the table of values for y = x + 4 x 1 0 1 3 4 y y 10 8 6 4 1 O 1 3 4 5 x 4 6 (b) On the grid draw the line with equation y = x + 4 for values of x from 1 to 4 (Total for Question 9 is 4 marks) 8 1 EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra *S4815A0816*

10 Here is a travel graph for Susan s journey from her house to the library and back to her house. 0 18 16 Distance from Susan s house (km) 14 1 10 8 6 4 0 09 00 09 30 10 00 10 30 11 00 11 30 Time Susan stopped at some road works at 09 30 (a) How far is Susan from her house at 09 30? The library is 0 km from Susan s house. (b) (i) At what time did Susan get to the library?... km (1) (ii) How long did Susan stay at the library? (c) At what time did Susan arrive back at her house?...... minutes... (1) (Total for Question 10 is 4 marks) *S4815A0916* EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra 9 13

11 Sketch the graph y = x 4 You must label relevant information on the sketch. (Total for Question 11 is marks) 1 (a) Factorise 6ab 9a... (b) Factorise 1p 18p 3... (Total for Question 1 is 4 marks) 10 14 EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra *S4815A01016*

13 Here is part of a travel graph of Tom s journey from his house to the shops and back. It shows his journey to the shops and how much time he was at the shops. 0 18 16 Distance from Tom s house (km) 14 1 10 8 6 4 O 5 10 15 0 5 30 35 40 45 50 55 60 65 70 75 80 Time in minutes (a) Work out Tom s speed for the first 30 minutes of his journey. Give your answer in km/h. Tom travels back to his house at 60 km/h.... Km/h (b) Complete the travel graph. (Total for Question 13 is 4 marks) *S4815A01116* EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra 11 15

14 The graph shows the cost of using a mobile phone for one month on three different tariffs. 60... 50 Cost ( s) 40 30...... 0 10 0 The three tariffs are 0 0 40 60 80 100 10 Time (minutes) Tariff A Rental 0 every minute costs 0p Tariff B Pay as you go every minute costs 50p Tariff C Rental 5 first 60 minutes free then each minute costs 10p (a) Label each line on the graph with the letter of the tariff. 1 16 EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra *S4815A0116*

Fiona uses her mobile phone for about 60 minutes each month. (b) Explain which tariff would be the cheapest for her to use. You must give the reasons for your answer....... (Total for Question 14 is 4 marks) 15 Make t the subject of the formula p = (u + 5t) t =... (Total for Question 15 is 3 marks) *S4815A01316* EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra 13 17

16 (a) Complete the table of values for y = x + x 3 x 4 3 1 0 1 y 9 1 3 (b) On the grid below, draw the graph of y = x + x 3 for values of x from 4 to y 10 8 6 4 4 3 1 O 1 x 4 5 (c) Use your graph to find estimates for the solutions of x + x 3 = 0... 14 18 EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra *S4815A01416*

(d) Use your graph to find estimates for the solutions of x + x = 7... (Total for Question 16 is 8 marks) ToTAL for PAPer is 80 MArKs *S4815A01516* EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra 15 19

0 EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra

Level (AAL0) mark scheme Award in Algebra AAL0 Question Working Answer Mark Notes 1 4p + 1b B for 4p + 1b oe (B1 for 4p or 1b oe seen) (a) 8a + 6b 3 3 B for 8a + 6b 3 3 (B1 for any two correct from 8a, + 6b 3, 3) (b) 10g 3 + 30 B for 10g 3 + 30 (B1 for 10g 3 or 30) (c) 6k + 1k 6k 3 B for 6k +1k 6k 3 (B1 for any two correct from 6k, 1k or 6k 3 ) 3 (a) 1, 7 B for 1 and 7 (B1 for 1 or 7) (b) 4n + 1 B for 4n + 1 (B1 for a linear expression including 4n) 4 (a) v = 0 + 6 8 48 M1 for V = 0 + 6 8 A1 for 48 (b) v = 10 + 5 3 = 10 15 5 M1 for v = 10 + 5 3 A1 for 5 (c) 0 = 10 + t 0 10 = t t = 10 5 3 M1 for 0 = 10 + t M1 for evidence of 10 or or sight of 0 10 = t or t = 10 or 10 5 = t A1 for 5 EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra 1

Level (AAL0) mark scheme Award in Algebra AAL0 Question Working Answer Mark Notes 5 (a) x = 15 6 x = 9 18 M1 for attempt to subtract 6 from each side or multiply each side by or sight of x = 15 6 or x = 9 oe A1 for 18 (b) 3p = 18 p = 18 3 6 M1 for attempt to collect variables on one side or collect constant terms on one side A1 for 6 (c) 3x + 15 = 10 3x = 10 15 x = 5 3 5 3 3 M1 for expanding bracket or sight of 3x + 15 or divide by 3 or sight of x + 5 = 10 3 M1 for subtracting 15 from both sides or sight of 5 or 10 3 5 A1 for 5 accept 1.6 3 6 (i) 3 M1 for attempt to find difference is y divided by difference in x can be evidenced by drawing a right angled triangle and marking lengths on it A1 for 3 (ii) y = 3x M1 ft for eqn of the form y = mx + c with m = 3 or c = A1 cao EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra

Level (AAL0) mark scheme Award in Algebra AAL0 Question Working Answer Mark Notes 7 (a) x 10 1 B1 cao (b) y 5 1 B1 cao (c) p 8 1 B1 cao (d) 0r 8 s 5 B for 0r 8 s 6 (B1 for two elements correct from 0 or r 8 or s 5 ) (e) 10a + 15 + a 8 1a + 7 3 M1 for 10a + 15 or a 8 A1 for 1a A1 for + 7 8 (a) Correct inequality M1 for a straight line joining 1 to with either an open circle at 1 or a closed circle at A1 for a straight line joining 1 to with an open circle at 1 and a closed circle at Accept appropriate alternative notation where meaning is clear (b) x < 3 B for x < 3 (B1 for x or x < 3) (c) 3,, 1, 0, 1 B cao (B1 for at least 4 correct and not more than one incorrect integer) (d) 4t > 7 + 3 = 10 t > 10 4 t >.5 3 M1 for adding 3 to each side M1 for dividing by 4 A1 for t >.5 EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra 3

Level (AAL0) mark scheme Award in Algebra AAL0 Question Working Answer Mark Notes 9 (a) 6, 4,, 0,, 4 M1 for table of values with values correct A1 for fully correct table of values (b) Correct straight line 4 M1 for plotting all points correctly from their table values or straight line with gradient or line that passes through (0, 4) A1 for a correct line lying between x = 1 and x = 4 10 (a) 10 1 B1 cao (b)(i) 10 00 1 B1 cao (b)(ii) 30 1 B1 cao (c) 11 0 1 B1 cao 11 Graph sketch: includes labelled axes, correct orientation, intersection points with the y- axis labelled (x 4) Sketch of graph B1 for U shaped curve and axes labelled x and y B1 for intersection with y axis labelled at (0, -4) 4 EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra

Level (AAL0) mark scheme Award in Algebra AAL0 Question Working Answer Mark Notes 1 (a) 3a(b 3) M1 for 3 outside a single bracket with linear term in p inside the bracket A1 for 3a(b 3) (b) 6p ( 3p) M1 for partial correct factorisation of the expression using, 3, 6, p, p or any combination used A1 for 6p ( 3p) 13 (a) 0 0.5 = 0 = 40 (b) Line from (45, 0) to (65, 0) M1 for 0 or 0 1 A1 for 40 M1 for drawing a straight line from (45, 0) to time axis A1 if line meets time axis at (65, 0) 14 (a) Correct labels B for lines labelled B, A, C (B1 for labelling one graph correctly) (b) Example explanation: For 60 minutes each month, on Tariff A, Fiona would pay 0 + 60 0. = 3, on B, she would pay 60 0.5 = 30, and on C she would pay 5 only. Correct explanation B for selecting Tariff C supported by explanation using calculations for 60 minutes or for reading correct values from the graph EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra 5

Level (AAL0) mark scheme Award in Algebra AAL0 Question Working Answer Mark Notes 15 p = u + 10t 10t = p u p u 3 M1 for multiplying out bracket or sight of u+ 10t 10 M1 for attempt to take u to other side of formula A1 for p u 10 16 (a) 3, 3, 1, 3 B for all 4 missing values correct (B1 for 1 missing value correct) (b) Correct curve B for plotting all points correctly joined by a curve (B1 for plotting their points correctly) (c) 1.3,.3 B1 for 1.3 ± 0. ft from their line B1 for.3 ± 0. ft from their line (d)., 3.3 M1 for x + x 3 = 4 A1 for to.4 and 3 to 3.4 6 EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra

Write your name here Surname Other names Edexcel Award Award Algebrain Algebra Level 3 Calculator NOT allowed Centre Number Candidate Number Sample Assessment Material Time: hours Paper Reference AAL30/01 You must have: Ruler graduated in centimetres and millimetres, pen, HB pencil, eraser. Total Marks Instructions Use black ink or ball-point pen. Fill in the boxes at the top of this page with your name, centre number and candidate number. Answer all questions. Answer the questions in the spaces provided there may be more space than you need. Calculators are not allowed. Information The total mark for this section is 90 The marks for each question are shown in brackets use this as a guide as to how much time to spend on each question. Advice Read each question carefully before you start to answer it. Keep an eye on the time. Try to answer every question. Check your answers if you have time at the end. Turn over S4816A *S4816A0116* 01 Pearson Education Ltd. EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra 7

Answer ALL questions. Write your answers in the spaces provided. You must write down all stages in your working. 1 (a) Simplify x 4 6 x x 3 (b) Simplify y y 3 1 y 5...... (c) Expand and simplify (x + 5)(x 3)... (d) Factorise 1p q 3 18p 3 q... (Total for Question 1 is 8 marks) 8 EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra *S4816A016*

The straight line L 1 passes through the points A and B with coordinates (1, ) and (4, 4) respectively. (a) Find an equation of L 1 in the form y = mx + c. The line L is perpendicular to the line L 1 and passes through the origin. y =... (3) (b) Find an equation of L... (Total for Question is 5 marks) *S4816A0316* EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra 3 9

3 On the grid, shade the region that satisfies all these inequalities y > 1 x + y < 4 y < 3x + y 10 8 6 4 1 O 1 3 4 5 x 4 6 (Total for Question 3 is 5 marks) 4 30 EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra *S4816A0416*

4 (a) Factorise x 7x + 1... (b) Factorise x + 5x xy 5y... (3) (Total for Question 4 is 5 marks) 5 The equation x 18x + p = 0 has two equal roots. (i) Find the value of p (ii) For this value of p, sketch the graph of y = x 18x + p showing the coordinates of any points at which the graph meets the coordinate axes....... (Total for Question 5 is 5 marks) *S4816A0516* EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra 5 31

6 (a) On the grid below, draw the graph of y = x 3 x 4 for values of x from to +4 (4) (b) Use your graph to find estimates for the solutions of x 3 x = 4... (Total for Question 6 is 6 marks) 6 3 EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra *S4816A0616*

7 Solve the simultaneous equations x y = x y = 7... (Total for Question 7 is 6 marks) *S4816A0716* EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra 7 33

8 Make k the subject of the formula t = k + 1 k k =... (Total for Question 8 is 4 marks) 9 For a quadratic equation the sum of its roots is 3.5 the product of its roots is 1.5 Find the quadratic equation in the form ax + bx + c = 0 where a, b and c are integers.... (Total for Question 9 is 3 marks) 8 34 EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra *S4816A0816*

10 The sum of the first two terms of an arithmetic series is 47. The thirtieth term of this series is 6 (a) Find the first term of the series and the common difference. First term... Common difference... (3) (b) The sum of the first 60 terms of the series.... (Total for Question 10 is 5 marks) 11 Write the quadratic expression x 5x + 3 in the form (x + a) + b where a and b are fractions.... (Total for Question 11 is marks) *S4816A0916* EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra 9 35

1 Here are some sketch graphs. y y y O x O x O x A B C y y O x O x D E The table shows the equations of some graphs. Equation Graph y = 4 x y = x(x 4) y = x 3 x x xy = 8 y = x 4x Match the letter of the graph with its equation. (Total for Question 1 is 3 marks) 10 36 EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra *S4816A01016*

13 Explain why any straight line that passes through the point (1, ) must intersect the curve with equation in exactly two points. x + y = 16 y 5 (1, ) 5 O 5 x 5 (Total for Question 13 is 3 marks) *S4816A01116* EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra 11 37

14 Solve x 4x < 5... (Total for Question 14 is 3 marks) 15 Expand and simplify ( + )(3 + 8) Give your answer in the form a + b where a and b are integers.... (Total for Question 15 is 4 marks) 16 Solve the equation x + 5x 7 = 0... (Total for Question 16 is 3 marks) 1 38 EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra *S4816A0116*

17 Here is a speed time graph that shows Tim s speed between two sets of traffic lights. He travels between the two sets of traffic lights in 9 seconds. 35 30 Speed (m / second) 5 0 15 10 5 0 0 1 3 4 5 6 7 8 9 10 Time (seconds) (a) Work out Tim s acceleration in the first 3 seconds. (b) Work out the distance between the two sets of traffic lights.... metres per second... m (Total for Question 17 is 4 marks) *S4816A01316* EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra 13 39

18 Solve 3 5 x + 1 + x 1 = x 1 x =... (Total for Question 18 is 4 marks) 19 The force, F, between two magnets is inversely proportional to the square of the distance, x, between them. When x = 3, F = 4 (a) Find a formula for F in terms of x. (b) Calculate the value of F when x = F =... (3) (c) Calculate the value of x when F = 64... (1)... (1) (Total for Question 19 is 5 marks) 14 40 EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra *S4816A01416*

0 The graph of y = f(x) is shown on the two grids. (a) On this grid, sketch the graph of y = f(x + ) y 5 5 O 5 x 5 (b) On this grid, sketch the graph of y = f(x) y 5 5 O 5 x 5 (Total for Question 0 is 4 marks) *S4816A01516* EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra 15 41

1 y 10 8 6 4 1 O 1 3 4 5 x 4 6 Use the trapezium rule to find the area of the region under the curve and between x = 0, y = 0 and x = 4 Use 4 strips of equal width.... (Total for Question 1 is 3 marks) TOTAL FOR PAPER IS 90 MARKS 16 4 EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra *S4816A01616*

Level 3 (AAL30) mark scheme Award in Algebra AAL30 Question Working Answer Mark Notes 1 (a) x 7 M1 for either x 4 + 6 or x 4 3 or x 6 3 or x 10 3 A1 cao (b) y 5 B for y 5 5 or y (B1 for sight of y 11/ ) 1 (c) x x 15 M1 for expanding bracket to obtain 4 terms with all 4 correct without considering signs or for 3 terms out of 4 correct with correct signs A1 (d) 6p q (q 3p) M1 for partial correct factorisation of the expression using any two of, 3, 6, p, p, q, q used correctly A1 for 6p q (q 3p) oe (a) Gradient is 4 6 = 4 1 3 y 4 = (x 4) y 4 = x 8 (b) m = 1 m = - 1 = y = x 4 3 3 M1 for attempt to find gradient by using a right angled triangle 6 or using formula or sight of M1 for attempt to use y y1 = m(x x 1) A1 1 y = x M1 for attempt to use mm = 1 A1 EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra 43

Level 3 (AAL30) mark scheme Award in Algebra AAL30 Question Working Answer Mark Notes 3 Correct region shaded 5 M3 for drawing all 3 lines correctly (M for drawing lines correctly) (M1 for drawing one line correctly) A for Correct shading of triangle with vertices ((5, 1); ( 1, 3 1 ); 1, 1) (A1 for correct shading for one inequality) 4 (a) (b) (x 3)(x 4) M1 for (x ± 3)(x ± 4) A1 oe (x + 5)(x y) 3 M1 for x(x + 5) OR y(x + 5) seen M1 for x(x + 5) and y(x + 5) seen A1 oe 44 EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra

Level 3 (AAL30) mark scheme Award in Algebra AAL30 Question Working Answer Mark Notes 5 (i) For equal roots they must both p = 81 5 1 1 M1 for writing that for equal roots they must both be b be b 1 p = ( b) OR b = 4ac 18 = 4p p = 34 4 1 M1 for p = ( b) A1 for 81 OR M1 for writing b = 4ac M1 for substituting 18 = 4p A1 for 81 (ii) Sketch graph M1 for drawing x and y axes with U shaped quadratic graph and for showing the curve touching the positive x axis at one point only A1 for establishing turning point at (9, 0) A1 if curve cuts y axis at (0, 81) 6 (a) Correct curve 4 B1 for drawing suitable axes on grid M1 for calculating points for values of x from x = to +4 A1 for all points correct A1 for drawing smooth curve through their correct points (b) Solution M1 for realisation that solutions lie on y = 0 A1 for x ft from their line EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra 45

Level 3 (AAL30) mark scheme Award in Algebra AAL30 Question Working Answer Mark Notes 7 x = y (y ) y = 7 4y 8y + 4 y = 7 3y 8y 3 = 0 (3y + 1)(y 3) = 0 x = 4, y = 3 x = 3, y = 3 1 6 M1 for rearranging the linear equation in terms of x or y M1 for substituting rearranged linear equation into the quadratic equation M1 for simplifying to get a quadratic in one variable M1 for factorising to obtain (3y + 1)(y 3) = 0 oe y = 3 1 or y = 3 A1 for y = 3 1 or y = 3 x = 3 or x = 4 A1 for x = 3 or x = 4 linked to y values 8 t(k ) = k + 1 tk t = k + 1 tk k = t + 1 k(t ) = t + 1 k = t + 1 t 4 M1 for attempt to multiply LHS by (k ) or sight of t(k ) or tk t (ignore RHS) M1 for attempt to subtract k from LHS or sight of tk k (ignore RHS) or attempt to subtract tk to give t + 1 = k tk (ignore LHS) M1 for attempt to factorise for k e.g. k(t ) or k( t) A1 for t + 1 t 1 or oe t t 46 EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra

Level 3 (AAL30) mark scheme Award in Algebra AAL30 Question Working Answer Mark Notes 9 b x 7x +3 3 b c = 3.5 M1 for establishing = 3.5 and = 1.5 a a a c = 1.5 a b = 7, c = 3 A for x 7x + 3 A1 for x ± 3.5x + 1.5 or x ± 7x + 3 10 (a) a + d = 47 a + 9d = 6 a + d = 47 a + 58d = 14 57d = 171 d = 171 57 a 3 = = 47 a = 50 a = 5 d = 3 3 M1 for establishing a + d = 47 and a + 9d = 6 M1 for solving to find d (or a) A1 for substituting to find a (or d) (b) S = 30 ( 5 + 59 3 ) 3810 M1 for substituting into S = 1 n(a + (n 1)d) A1 11 (x 5 ) 13 B1 for 5 4 B1 for 13 4 1 E, B, A, D, C 3 B3 for all 5 correct B for 3 or 4 correct B1 for 1 or correct EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra 47

Level 3 (AAL30) mark scheme Award in Algebra AAL30 Question Working Answer Mark Notes 13 Explanation given 3 M1 for recognising that the equation is a circle A1 for drawing a circle centre (0, 0) and radius 4 A1 for attempt to draw a straight line through (1, ) so that it passes through the circle in two places with a statement of the line passing through the circle twice or for explanation that the circle is a closed curve and therefore the straight line has infinite length and passes through the circle in two places oe 14 x 4x 5 0 (x 5)(x + 1) 0 1 x 5 3 M1 for factorising (x 5)(x + 1) 0 A1 ft for establishing the critical values A1 15 ( + )(3 + 8) = 6 + 8 + 3 + 8 =10 + 3 + 8 10 + 3 + 8 = 10 + 3 + ( ) 10 + 7 4 M1 3 or 4 of 6, 8, 3, 8 - terms may be simplified and could be in a list A1 for 10 from 6 + 8 B1 8 = 4 OR ( + )(3 + 8) = ( + )(3 + ) =6 + 4 + 3 + 6 + 7 + = 6 + 7 + = A1 10 + 7 cao OR B1 8 = 4 M1 for 3 or 4 terms out of 4 correct in the expansion of ( + )(3 + ) A1 6 + 7 + A1 cao 48 EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra

Level 3 (AAL30) mark scheme Award in Algebra AAL30 Question Working Answer Mark Notes 16 5± 5 4 7 5 ± 5 + 56 4 5± 9 4 Alternative (x + 7)(x 1) x + 7 = 0 or x + 1 = 0 1 or 3.5 3 M1 for correct substitution into quadratic formula or sight of 5± 5 4 7 M1 for method to establish x = A1 for 1 and 3.5 Alternative M1 for (x + 7)(x 1) M1 for x + 7 = 0 or x + 1 = 0 A1 for 1 and 3.5 5± 9 4 17 (a) 30 3 = 10 M1 for 30 3 A1 for 10 (b) 1 (3 + 9) 30 180 M1 for attempt to find the area under the graph A1 for 180 18 (x 1) + 3(x + 1) = 5 5x + 1 = 5 0.8 4 M1 for attempt to multiply one term by a common denominator or sight of (x 1) or 3(x + 1) or 5 M1 for multiplying all terms by a common denominator or sight of (x 1) + 3(x + 1) = 5 M1 for attempt to clear brackets or sight of 5x + 1 = 5 A1 oe 16 EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra 49

Level 3 (AAL30) mark scheme Award in Algebra AAL30 Question Working Answer Mark Notes 19 (a) 1 F 4 = 9 k k = 36 k x x = F = 36 F = x 3 1 M1 for F x k or F = x M1 for method to establish k = 36 or substituting to get 4 = 9 k 36 A1 for F = x (b) 9 1 B1 cao (c) 3 4 1 B1 oe 0 (a) Sketch M1 for a horizontal translation by A1 for translation by to the left (b) Sketch M1 for a reflection in a horizontal line A1 for a reflection in the x axis 1 (½ (8 + 0)+(9 + 8 + 5)) 1 6 sq units 3 1 M1 for (first + last ordinate) or sum of other ordinate values = 4 + M1 for 1 (first + last ordinate) and sum of other ordinate values multiplied by 1 A1 for 6 ± units 50 EA033597 Sample Assessment Materials Edexcel Level and Level 3 Awards in Algebra