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PLC Papers Created For: Finance 2 Grade 6 Objective: To work with decimals in a financial context, e.g. profit, loss, balance, debit, credit. Question 1 Anna’s bank account was £564.70 in debit before she withdrew £600 to pay her rent. What is her account balance after this transaction? £…………………….. (2) Question 2 What is Anna’s total shopping bill if she buys 2 magazines for £1.65 each 5 bread rolls for 60p each 4 pints of milk for £1.05 per pint. ………….…………………….. (3) Question 3 Charlie is paid £6.20 per hour for her part time job. a) How much will she earn if she works 15 hours ………….…………………….. (2) PiXL PLC 2017 Certification b) How many hours does she need to work to make £310 ………….…………………….. (3) Total /10 PiXL PLC 2017 Certification Index Laws (Negative and Fractional) 2 Grade 7 Objective: Calculate with negative and fractional indices Question 1 Write each expression in negative index form i) 1 4 2 ……………………. (1) ii) 1 12 3 ……………………. iii) 5 7 x (1) ……………………. (1) Question 2 Evaluate i) 2 3 −4 ……………………. (2) PiXL PLC 2017 Certification ii) 64 125 − 1 3 ……………………. (2) iii) 64 −5 6 ……………………. (3) Total /10 PiXL PLC 2017 Certification Powers and Roots 2 Grade 6 Objective: Calculate and estimate powers and roots You will need to use a calculator Question 1 Find the value of i) 2.63 ………………… ii) 1.25 ………………… iii) 5-2 x 73 ………………… (3) Question 2 Evaluate i) √6889 ………………… ii) 3 √0.6 ………………… iii) 4 √625 ………………… (3) Question 3 Work out (6.05)3 - 3√8.4 and give your answer to 3 significant figures. ………………… (2) PiXL PLC 2017 Certification Question 4 Work out 3√5.6 + 4.22 and give your answer to 2 decimal places. ………………… (2) Total /10 PiXL PLC 2017 Certification [Type here] Product Rule 2 Grade 7 Objective: Use the product rule for counting Question 1 James’ teacher gave him the three cards below 5 1 9 She asks him to use the cards to make as many three digit numbers as he can. How many different numbers can James make? …………………….. (2) Question 2 Mr Green owns black, brown and blue shoes and red, green and purple socks. How many combinations of shoes and socks can he wear? …………………… (2) PiXL PLC 2017 Certification [Type here] Question 3 Stephanie has to set a new code for her combination lock. The lock is made up of four parts and each part contains the digits from 0 to 9. a) How many possible codes are there for the lock? …………………… (2) b) Stephanie decides to use even numbers only in her code. How many possible codes are there for the lock now? …………………… (2) c) As well as only using even numbers, Stephanie decides that no digits should be repeated. How many possible codes are there for the lock now? …………………… (2) Total /10 PiXL PLC 2017 Certification [Type here] Product of prime factors 2 Grade 6 Objective: Understand the unique factorisation theorem and perform prime factor decompositions Question 1 Look at the numbers below 11, 13, 15, 17, 19 a) Which number in the list is not prime ……………………….. b) Explain why it is not prime. ………………………………………………………………………………………………… ………………………………………………………………………………………………… (2) Question 2 Write each of the following number as a product of its prime factors i) 44 …………………… (2) ii) 325 …………………… (3) PiXL PLC 2017 Certification [Type here] iii) 840 …………………… (3) Total /10 PiXL PLC 2017 Certification Recurring Decimals 2 Grade 7 Objective: Change recurring decimals into fractions and vice versa. Question1 a) Change 15 24 into a decimal. (2) b) Is the answer from part a recurring decimal or a terminating decimal? Explain your choice below. (2) Question 2 . Change 0.307 into a fraction. (2) Question 3 .. Change 0.047 into a fraction. (2) PiXL PLC 2017 Certification Question 4 .. Convert the recurring decimal 0.78 in to a fraction. (2) Total /10 PiXL PLC 2017 Certification Upper and Lower Bounds 2 Objective: Grade 7 Calculate upper and lower bounds. Question 1. (a) A man weighs 80kg to the nearest kg. Find the greatest possible amount that he could weigh. …………………….. (2) (Total 2 mark) Question 2 Find the upper and lower bounds of xy where � = �� ��� � = �� when both have been rounded to the nearest whole number Upper Bound …………………………... Lower Bound …………………………… (2) (Total 2 marks) Question 3. The following numbers have been rounded to two significant figures. Find the upper and lower bounds for each value. (a) 13 Upper Bound …………………………... Lower Bound …………………………… PiXL PLC 2017 Certification (2) (b) 0.16 Upper Bound …………………………... Lower Bound …………………………… (2) (Total 4 marks) Question 4. Complete the table Value Level of Accuracy 30 Lower Bound Upper Bound 21.5 22.5 1.S.F. Nearest whole number (Total 2 marks) Total /10 PiXL PLC 2017 Certification Using Pi 2 Grade 7 Objective: Understand the value of pi and calculate exactly with it Question 1 If the area of a circle is 49 π cm2, state, with appropriate units, its i) Radius ii) Diameter ………………………….. ……………………….…. iii) Circumference …………………………. (3) Question 2 Simplify the following expressions i) 100 π – 55 5 ……………………….. ii) 6 (8 - 2π) – 8 (4 π – 9) ………………………. (3) PiXL PLC 2017 Certification Question 3 Calculate the circumference of the circle, leaving your answer in terms of π. 11cm ……………….cm (2) Question 4 Calculate the area of the circle, leaving your answer in terms of π. 16cm ……………….cm2 (2) Total /10 PiXL PLC 2017 Certification PLC Papers Created For: Finance 2 Grade 6 Solutions Objective: To work with decimals in a financial context, e.g. profit, loss, balance, debit, credit. Question 1 Anna’s bank account was £564.70 in debit before she withdrew £600 to pay her rent. What is her account balance after this transaction? 564.70 – 600 (M1) -£35.30 (A1) £…………………….. (2) Question 2 What is Anna’s total shopping bill if she buys 2 magazines for £1.65 each 5 bread rolls for 60p each 4 pints of milk for £1.05 per pint. M1 one of (2 x 1.65) = 3.30 or (5 x 0.6) = 3 or (4 x 1.05) = 4.20 M1 for total of their three products A1 for £10.50 ………….…………………….. (3) Question 3 Charlie is paid £6.20 per hour for her part time job. a) How much will she earn if she works 15 hours £6.20 x 15 = (M1) £90 (A1) ………….…………………….. (2) PiXL PLC 2017 Certification b) How many hours does she need to work to make £310 310 ÷ 6.2 or 3100 ÷ 62 or attempt at division with only one error (M2) 50 hours (A1) ………….…………………….. (3) Total /10 PiXL PLC 2017 Certification Index Laws (Negative and Fractional) 2 Grade 7 Solutions Objective: Calculate with negative and fractional indices Question 1 Write each expression in negative index form i) 1 4 2 2-4 (A1) ……………………. (1) i) 1 12 3 12-3 (A1) ……………………. ii) 5 7 x (1) 5x-7 (A1) ……………………. (1) Question 2 Evaluate i) 2 3 −4 2-4 = 1 16 or 3-4 = 81 16 1 81 (M1) (A1) ……………………. (2) PiXL PLC 2017 Certification ii) 64 125 − 1 3 ( 64 ) − 1 3 = 1 4 5 4 or (125 ) 3 = (M1) − 1 (A1) 1 5 ……………………. (2) −5 iii) 64 6 ( 64 ) − 1 6 = 1 2 (M1) 25 = 32 (M1) 1 32 (A1) ……………………. (3) Total /10 PiXL PLC 2017 Certification Powers and Roots 2 Grade 6 Solutions Objective: Calculate and estimate powers and roots You will need to use a calculator Question 1 Find the value of i) 2.63 17.576 (A1) ………………… ii) 1.25 2.48832 (A1) ………………… iii) 5-2 x 73 13.72 (A1) ………………… (3) Question 2 Evaluate i) √6889 83 (A1) ………………… ii) 3 √0.125 0.5 (A1) ………………… iii) 4 √625 5 (A1) ………………… (3) Question 3 Work out (6.05)3 - 3√8.4 and give your answer to 3 significant figures. 219.4123323 (M1) 219 (A1) ………………… (2) PiXL PLC 2017 Certification Question 4 Work out 3√5.6 + 4.22 and give your answer to 2 decimal places. 19.415808 (M1) 19.42 (A1) ………………… (2) Total /10 PiXL PLC 2017 Certification Product Rule 2 Grade 7 Solutions Objective: Use the product rule for counting Question 1 James’ teacher gave him the three cards below 5 1 9 She asks him to use the cards to make as many three digit numbers as he can. How many different numbers can James make? 3 x 2 x 1 or starting to list combinations (M1) 6 (A1) …………………….. (2) Question 2 Mr Green owns black, brown and blue shoes and red, green and purple socks. How many combinations of shoes and socks can he wear? 3 x 3 or starting to list combinations (M1) 9 (A1) …………………… (2) PiXL PLC 2017 Certification Question 3 Stephanie has to set a new code for her combination lock. The lock is made up of four parts and each part contains the digits from 0 to 9. a) How many possible codes are there for the lock? 10 x 10 x 10 x 10 or starting to list combinations (M1) 10000 (A1) …………………… (2) b) Stephanie decides to use even numbers only in her code. How many possible codes are there for the lock now? 5 x 5 x 5 x 5 or starting to list combinations (M1) 625 (A1) …………………… (2) b)As well as only using even numbers, Stephanie decides that no digits should be repeated. How many possible codes are there for the lock now? 5 x 4 x 3 x 2 or starting to list combinations (M1) 120 (A1) …………………… (2) Total /10 PiXL PLC 2017 Certification [Type here] Product of prime factors 2 Grade 6 Solutions Objective: Understand the unique factorisation theorem and perform prime factor decompositions Question 1 Look at the numbers below 11, 13, 15, 17, 19 a) Which number in the list is not prime ……………15………….. b) Explain why it is not prime. 15 has factors other than 1 and itself, such as 5 and 3 (C1) (2) Question 2 Write each of the following number as a product of its prime factors i) 44 M1 for full systematic method of divisions by prime numbers oe factor trees; condone 1 calculation error A1 for 2 x 2 x 11 …………………… (2) ii) 325 M2 for full systematic method of divisions by prime numbers oe factor trees; condone 1 calculation error (M1 for 325 written as a correct product with only one non-prime or equivalent division or a full process with 2 calculation errors.) A1 for 5 x 5 x 13 …………………… (3) PiXL PLC 2017 Certification [Type here] iii) 840 M2 for full systematic method of divisions by prime numbers oe factor trees; condone 1 calculation error (M1 for 840 written as a correct product with only one non-prime or equivalent division or a full process with 2 calculation errors.) A1 for 2 x 2 x 2 x 3 x 5 x 7 …………………… (3) Total /10 PiXL PLC 2017 Certification Recurring Decimals 2 Grade 7 Solutions Objective: Change recurring decimals into fractions and vice versa. Question1 a) Change 15 24 into a decimal. (M1) 0.625 (A1) (2) b) Is the answer from part a recurring decimal or a terminating decimal? Explain your choice below. Terminating, as the decimal doesn’t go on for infinity place values. (A2) (2) Question 2 . Change 0.307 into a fraction. 1000X= 307.7777 100X = 30.777 (2)-(1) -(1) -(2) 900X = 277 (M1) X = 277/900 (A1) (2) PiXL PLC 2017 Certification Question 3 .. Change 0.047 into a fraction. X= 0.0474747 -(1) 100X = 4.7474747 -(2) (2) – (1) 99X = 4.7 (M1) X=47/990 (A1) (2) Question 4 .. Convert the recurring decimal 0.78 in to a fraction. X= 0.78 78 78 -(1) 100X = 78.78 78 78 -(2) (2) – (1) 99 X = 78 X = 26/33 (M1) (A1) (2) Total /10 PiXL PLC 2017 Certification Upper and Lower Bounds 2 Objective: SOLUTIONS Grade 7 Calculate upper and lower bounds. Question 1. (a) A man weighs 80kg to the nearest kg. Find the greatest possible amount that he could weigh. 80.5kg(A2) …………………….. (2) (Total 2 mark) Question 2 Find the upper and lower bounds of xy where � = �� ��� � = �� when both have been rounded to the nearest whole number Upper Bound ………(B1)………12.5X10.5=131.25…………... Lower Bound …9.5X11.5=109.25……(B1)…………………… (2) (Total 2 marks) Question 3. The following numbers have been rounded to two significant figures. Find the upper and lower bounds for each value. (a) 13 Upper Bound ………13.5…………B1………... PiXL PLC 2017 Certification Lower Bound ………12.5…… B1……………… (2) (b) 0.16 Upper Bound……0.165……B1………………... Lower Bound ………0.155 B1…………………… (2) (Total 4 marks) Question 4. Complete the table Value Level of Accuracy 30 22 1.S.F. Nearest whole number Lower Bound 25 Upper Bound 35 B1 21.5 22.5 B1 (Total 2 marks) Total /10 PiXL PLC 2017 Certification Using Pi 2 Grade 7 Solutions Objective: Understand the value of pi and calculate exactly with it Question 1 If the area of a circle is 49 π cm2, state, with appropriate units, its i) Radius 7cm ii) Diameter 14cm ………………………….. iii) Circumference 14 π cm ……………………….…. …………………………. (3) A1 for each correct answer, including units. Question 2 Simplify the following expressions i) 100 π – 55 5 20 π – 11 (A1) ……………………….. ii) 6 (8 - 2π) – 8 (4 π – 9) 48 - 12 π -32 π + 72 (M1 for any three correct terms) 120 - 44 π (A1) ………………………. (3) PiXL PLC 2017 Certification Question 3 Calculate the circumference of the circle, leaving your answer in terms of π. 11cm 2 x π x 11 or π x 22 (M1) 22 π (A1) ……………….cm (2) Question 4 Calculate the area of the circle, leaving your answer in terms of π. 16cm π x 82 or π x 64 (M1) 64 π (A1) ……………….cm2 (2) Total /10 PiXL PLC 2017 Certification