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Q1. (a) (i) The nth term of a sequence is 4n + 1 Write down the first three terms of the sequence. ................................................................................................................ ................................................................................................................ ................................................................................................................ Answer ...................., ..................., .................... (2) (ii) Is 122 a term in this sequence? Explain your answer. ................................................................................................................ ................................................................................................................ (1) (b) Tom builds fencing from pieces of wood as shown below. How many of pieces of wood will be in Diagram n? .......................................................................................................................... .......................................................................................................................... .......................................................................................................................... Answer ....................................................... (2) (Total 5 marks) Q2. A stacking chair is 100 cm high and 40 cm wide. Not drawn accurately Page 1 of 12 When a chair is added to a stack it increases the height by 10 cm and the width by 5 cm. Not drawn accurately (a) Find an expression for the height of a stack of n chairs. ......................................................................................................................... ......................................................................................................................... Answer ................................................. (2) (b) A rule for the maximum number of chairs that can be stacked before they fall over is 4n + 35 < 70 What is the maximum number of chairs that can be stacked? ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... Answer ................................................. (3) (Total 5 marks) Page 2 of 12 Q3. (a) The first term of a sequence is –2. The rule for continuing the sequence is Add 7 then Multiply by 4 What is the second term of the sequence? ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... Answer ................................................. (1) (b) This rule is used to continue a different sequence. Multiply by 2 then Add 5 The second term of this sequence is 3. What is the first term? ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... Answer ................................................. (3) (Total 4 marks) Page 3 of 12 Q4. Here are the nth terms of 3 sequences. Sequence 1 Sequence 2 Sequence 3 nth term nth term nth term 4n + 1 3n + 3 3n – 1 For each sequence state whether the numbers in the sequence are A Always multiples of 3 S Sometimes multiples of 3 N Never multiples of 3 .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. Answer Sequence 1 .......................... Sequence 2 .......................... Sequence 3 .......................... (Total 3 marks) Q5. The nth term of a sequence is given by the expression n2– 3 Write down the first three terms of the sequence. .................................................................................................................................. .................................................................................................................................. Answer ................... , .................... , .................... (Total 2 marks) Page 4 of 12 M1. (a) (i) 5, 9, 13 –1 each error or omission B1 for 1, 5, 9 or 9, 13, 17 B2 Page 5 of 12 (ii) no and valid reason eg 121 is in the sequence (all) terms are odd 122 is even 121 ÷ 4 not integer note: “no” can be implied B1 Page 6 of 12 (b) 3n + 1 oe B1 for 3n + c or kn + 1 B1 for n3 + 1 unless notation already penalised ignore fw B2 [5] Page 7 of 12 M2. (a) Evidence of searching for a pattern or 10n eg, 100 110 120 130 140 10 10 10 10 M1 10n + 90 oe A1 Page 8 of 12 (b) 4n = 35 leading to n = 8.75 is M0 unless n given as 8 M1 or 4n = 35 leading to n < 8.75 is M1, A1 A1 A1 [5] Page 9 of 12 M3. (a) 20 B1 (b) 3 – 5 or – 2 M1 (their – 2) ÷ 2 M1 –1 SC2 – 1 × 2 + 5 (=3) A1 [4] Page 10 of 12 M4. S, A, N –1eeoo B3 [3] Page 11 of 12 M5. –2, 1, 6 –1 each error or emission. Ignore extra terms 12 – 3, 22 – 3, 32 – 3 is B1 B2 [2] Page 12 of 12