Homework on analysing questionnaires – grade C
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The Robert Smyth School Mathematics Faculty Sequences Innovation & excellence HW1 – Grade C Homework on Sequences 1. (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) 2. A pattern using pentagons is made of sticks. The Robert Smyth School 1 The Robert Smyth School Mathematics Faculty Sequences Innovation & excellence (a) Diagram 1 Diagram 2 Diagram 3 5 sticks 9 sticks 13 sticks How many sticks are needed for Diagram 5? ...............…………………………………………………………………………….. ...............…………………………………………………………………………….. Answer ............................................ (2) (b) Write down an expression for the number of sticks in Diagram n. ...............…………………………………………………………………………….. ...............…………………………………………………………………………….. Answer ............................................ (2) 3. Patterns are made from shaded and unshaded squares. 1st pattern (a) 2nd pattern 3rd pattern 4th pattern How many shaded squares are there in the nth pattern? …………..........…............……...................…………….....…………...................... Answer ………………………………….. (1) (b) How many unshaded squares are there in the nth pattern? …………..........…............……...................…………….....…………...................... …………..........…............……...................…………….....…………...................... Answer ………………………………….. (1) (Total 2 marks) The Robert Smyth School 2 The Robert Smyth School Mathematics Faculty Sequences Innovation & excellence 4. The diagrams show a sequence of rectangles. Area = 2 Diagram 1 (a) Area = 6 Diagram 2 Area = 12 Diagram 3 Area = 20 Diagram 4 Write down an expression for the area of Diagram n. ..................................................................................................................................... ..................................................................................................................................... Answer ...................................................................... (2) (b) A rectangle in the sequence has an area of 110 cm2. What is its perimeter? ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... Answer ................................................................ cm (2) (c) Which diagram has a perimeter of 26cm? ...............…………………………………………………………………………….. ...............…………………………………………………………………………….. ...............…………………………………………………………………………….. Answer ............................................ (3) (Total 7 marks) 5. (a) The nth term of a sequence is 4n + 1 (i) Write down the first three terms of the sequence. .......................................................................................................................... .......................................................................................................................... The Robert Smyth School 3 The Robert Smyth School Mathematics Faculty Sequences Innovation & excellence .......................................................................................................................... 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. Diagram 1 4 pieces of wood Diagram 2 7 pieces of wood Diagram 3 10 pieces of wood How many of pieces of wood will be in Diagram n? ...................................................................................................................................... ...................................................................................................................................... ...................................................................................................................................... Answer ....................................................... (2) (Total 5 marks) 6. (a) Write down the first three terms of the sequence whose nth term is given by 5n 4n 7 ..................................................................................................................................... ..................................................................................................................................... Answer .................................................... (2) (b) Which term of the sequence has a value of 1? ..................................................................................................................................... ..................................................................................................................................... The Robert Smyth School 4 The Robert Smyth School Mathematics Faculty Sequences Innovation & excellence ..................................................................................................................................... Answer .................................................... (2) (Total 4 marks) 1. (a) 20 (b) 3–5 B1 M1 or – 2 (their – 2) 2 M1 –1 A1 SC2 – 1 × 2 + 5 (=3) [4] 2. (a) 13 + 4 or diagram 4 drawn oe 21 (b) M1 A1 4n + 1 B2 B1 for 4n + c or n4 + 1 B0 for n4 + c unless notation already penalised in 11(c) fw ignore if numerical term fw deduct B1 if incorrect algebra (c) 4n + 1 = 201 or (201 – 1) ft their (a) for M marks (not n + 4) M1 4n = 200 or 201 4 Accept reasonable attempt at complete build up method for M2 M1 50 A1 [7] 3. (a) 2n or 2nth B1 oe. Accept 2 × n, n × 2 but not n2. Allow x for n but no other letter, unless they explain it (b) n + 1 or nth + 1 oe B1 [2] 4. (a) (b) n² + n or n(n + 1) or n × (n + 1) or (n +1) × n B1 for n² … or brackets omitted B2 42 B2 B1 10 and 11 seen [4] The Robert Smyth School 5 The Robert Smyth School Mathematics Faculty Sequences Innovation & excellence 5. (a) (b) (i) 5, 9, 13 –1 each error or omission B1 for 1, 5, 9 or 9, 13, 17 B2 (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 3n + 1 oe B2 B1 for 3n + c or kn + 1 B1 for n3 + 1 unless notation already penalised ignore fw [5] 6. (a) (b) 5 10 15 , , 11 15 9 B2 – 1ee.oo 7th M1,A1 M1 for 5n = 4n + 7 A1 cao [4] The Robert Smyth School 6
