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Name: Sha Tin College Mathematics Department Key Stage 4 CORE Level Course Unit 6 Assignment: Algebra II Total / 47 A: Number Patterns #1(no calc) Fill in the blanks to continue the patterns in this number square. 1 2 4 2 4 8 4 8 16 8 [2] #2(no calc) Four rectangles are outlined in the diagram. The area of the innermost one is 2 cm2, and its perimeter is 6 cm. (a) Working outwards, write down the area and perimeter of the other three rectangles. Sha Tin College Mathematics Department KS 4 CORE ASSIGNMENT Algebra II 1 Rectangle Area (cm2) Perimeter (cm) 1st 1 2 2 2 1 2 6 2nd 3 4 2 3 4 3rd 2 4th 2 [6] (b) Write down the area and perimeter of the next two rectangles in the sequence (not shown in the diagram). Answer (b)(i) 5th rectangle. Area = cm2. Perimeter = cm. cm2. Perimeter = cm. (b)(ii) 6th rectangle. Area = (c) [4] Write down the area and perimeter of the fiftieth rectangle in the sequence Answer (c) 50th rectangle. Area = cm2. Perimeter = cm. [2] Sha Tin College Mathematics Department KS 4 CORE ASSIGNMENT Algebra II 2 #3(no calc) The number triangle below is made up of consecutive odd whole numbers. Row Number triangle Total of row (T) Number of odd numbers in row (R) Average of Row (T R ) 1st 1 1 1 1 2nd 3 5 2 3rd 7 9 11 3 4th 13 15 17 19 (a) 64 4 5th 5 6th 6 16 Fill the fifth and sixth rows of the number triangle. [2] (b) Fill in the blanks in the “Total of row” and “Average of row” columns. [4] (c) Write down the “Total of row” and “Average of row” for the 10th row. Answer (c) Total of 10th row (d) Average of 10th row [2] Write down formulae, in terms of n, for “Total of nth row” and “Average of nth row”. Answer (d) Total of nth row Average of nth row Total for Section A Sha Tin College Mathematics Department KS 4 CORE ASSIGNMENT Algebra II [2] /24 3 B:Linear Sequences #1Calc For the number pattern, fill in the 5th term and then write a general formula to find any term, in terms of n. Term number (n) 1 2 3 4 5 n General Formula : V = Value (V) 5 7 9 11 [3] #2 No calcs Draw an accurate graph of the information in #1 [2] #4 What is the name of the shape of the graph drawn in #2? [1] #5 What kind of function (formula) is V? [1] Total for Section B /7 Sha Tin College Mathematics Department KS 4 CORE ASSIGNMENT Algebra II 4 C: Quadratic Sequences #1Calc (i) a) fill in the 5th term. b) Fill in the 1st difference and the 2nd difference c) What type of general formula links n and V? _______________________________________________________________[1] Term number (n) Value (V) 1st 2nd difference Simultaneous difference Equation 1 8 2 14 3 22 4 32 5 n d) By writing and solving a set of simultaneous equations or otherwise: Write a general formula to find any term, in terms of n. [4] General Formula : V = [2] (ii) a) fill in the 5th term. b) Fill in the 1st difference and the 2nd difference c) What type of general formula links n and V? _______________________________________________________________[1] Term number (n) Value 1 2 3 4 5 n 2 9 22 41 1st difference 2nd difference Simultaneous Equation [4] d) By writing and solving a set of simultaneous equations or otherwise: Write a general formula to find any term, in terms of n. General Formula : V = [2] Sha Tin College Mathematics Department KS 4 CORE ASSIGNMENT Algebra II 5 #2 Draw a sketch of what the graph of the formulae found in #1 would look like. V n [2] #3 What is the name of the shape of the graph drawn in #2? [1] #4 What kind of function (formula) is V? [1] Total for Section C CAN DO STATEMENTS /16 TICK HERE RECAP Continue a sequence of numbers or patterns and find the nth term Investigating – working systematically, making predictions, proving algebraically Investigating – working systematically, looking for patterns, making predictions, generalising RECAP Use a difference method to find the formula for a linear sequence NEW Use a difference method to find the formula for a quadratic sequence Investigating – working systematically, generalizing, proving algebraically Sha Tin College Mathematics Department KS 4 CORE ASSIGNMENT Algebra II 6