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PLC Papers Created For: Calculating with fractions 2 Grade 5 Objective: Calculate exactly with fractions, including solving problems Question 1 Work out 1 1 6 x 2 3 . Give your answer as a fraction in its simplest form. ………………. (2) Question 2 Work out 2 2 3 2 + 3 . Give your answer as a mixed number. 5 ………………. (3) Question 3 Work out 4 1 3 3 - 1 . Give your answer as a mixed number. 4 ………………. (3) PiXL PLC 2017 Certification Question 4 Here are some fractions 2 8 3 10 4 16 5 10 8 24 1 Two of the fractions are not equivalent to . Circle these two fractions. 4 ………………. (2) Total /10 PiXL PLC 2017 Certification Error intervals 2 Objective: Grade 5 Use inequality notation to specify simple error intervals due to truncation or rounding. Question 1. (a) Find the range of numbers that would round to 500 (to one significant figure) …………………….. (2) (b) Find the range of numbers that would round to 5000 (to 1 significant figure) …………………….. (2) (Total 4 marks) Question 2 Use inequality signs to show the range of possible values for (a) � =0.5 (1.d.p) …………………….. (2) PiXL PLC 2017 Certification (b) � =50 (1 s.f0 …………………….. (2) (Total 4 marks) 3. Question 3. Complete the inequality to show the range of values that would round to 0.4 (to 1 decimal place) … . ≤ 0.4 < ⋯ (2) (Total 2 marks) Total /10 PiXL PLC 2017 Certification 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 2 Grade 5 Objective: Calculate with roots and with integer indices Question 1 Simplify i) x7 x x8 ……………………. (1) ii) y8 ÷ y3 ……………………. (1) Question 2 Write as a power of 5 i) 54 x 52 ……………………. (1) ii) 512 ÷ 56 ……………………. (1) iii) 58 ÷ 510 ……………………. (1) PiXL PLC 2017 Certification iv) 55 x 56 (52)4 ……………………. (3) Question 3 Simplify 3x2y x 5 x y8 ……………………. (2) Total /10 PiXL PLC 2017 Certification Limits of accuracy 2 Objective: Grade 5 Apply and Interpret Limits of Accuracy. Question 1. (a) A field measures 500m by 200m when rounded to the nearest 100m. What is the greatest possible area of the field? …………………….. (2) (b) David runs around the edge of the field twice. What is the least possible distance that he would run? …………………….. (4) (Total 6 marks) Question 2 A pen measures 30 cm to the nearest 10cm. 10 pencils are joined together. What is the total greatest and least possible total length of the pencils? Give your answer in centimetres. Greatest Length…………………….. (2) Least Length …………………….. (2) (Total 4 marks) PiXL PLC 2017 Certification 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 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 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: Calculating with fractions 2 Grade 5 Solutions Objective: Calculate exactly with fractions, including solving problems Question 1 1 Work out 1 6 x 2 . Give your answer as a fraction in its simplest form. 3 = 7 x = = 7 (A1) 6 9 2 3 14 18 (M1) ………………. (2) Question 2 2 2 + 3 . Give your answer as a mixed number + 17 (M1) Work out 3 = 8 = 40 + 91 =6 = 3 15 15 2 5 5 51 15 (M1) 1 15 (A1) ………………. (3) Question 3 4 Work out 1 3 3 - 1 . Give your answer as a mixed number 4 = 13 - (M1) = 52 - = 31 =2 3 12 12 7 4 21 12 (M1) 7 12 (A1) ………………. (3) PiXL PLC 2017 Certification Question 4 Here are some fractions 2 8 3 10 4 16 5 10 8 24 1 Two of the fractions are not equivalent to . Circle these two fractions. A1 For each correct answer 4 ………………. (2) Total /10 PiXL PLC 2017 Certification Error intervals 2 Objective: SOLUTIONS Grade 5 Use inequality notation to specify simple error intervals due to truncation or rounding. Question 1. (a) Find the range of numbers that would round to 500 (to one significant figure) 450 … . ≤ 500 < 550 … (A2) …………………….. (2) (b) Find the range of numbers that would round to 5000 (to 1 significant figure) (c) 4500 … . ≤ 5000 < 5500 … (A2) …………………….. (2) (Total 4 marks) Question 2 Use inequality signs to show the range of possible values for (a) � =0.5 (1.d.p) (d) 0.45 … . ≤ 0.5 < 0.55 … (A2) …………………….. (2) PiXL PLC 2017 Certification (b) � =50 (1 s.f0 (e) 45 … . ≤ 50 < 55 … (A2) …………………….. (2) (Total 4 marks) 3. Question 3. Complete the inequality to show the range of values that would round to 0.4 (to 1 decimal place) … . ≤ 0.4 < ⋯ (a) 0.35 … . ≤ 0.4 < 0.45 … (A2) (2) (Total 2 marks) PiXL PLC 2017 Certification Total /10 PiXL PLC 2017 Certification 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 2 Grade 5 Solutions Objective: Calculate with roots and with integer indices Question 1 Simplify i) x7 x x8 x15 (A1) ……………………. (1) ii) y8 ÷ y3 y5 (A1) ……………………. (1) Question 2 Write as a power of 5 i) 54 x 52 56 (A1) ……………………. (1) ii) 512 ÷ 56 56 (A1) ……………………. (1) iii) 58 ÷ 510 5-2 (A1) ……………………. (1) PiXL PLC 2017 Certification iv) 55 x 56 (52)4 55+6 = 511 or 52x4 = 58 seen (M1) 511 ÷ 58 or 511-8 seen (M1) 53 (A1) ……………………. (3) Question 3 Simplify 3x2y x 5 x y8 15x3y9 (M1 for any two correct terms, A1 for fully correct answer) ……………………. (2) Total /10 PiXL PLC 2017 Certification Limits of accuracy 2 Objective: SOLUTIONS Grade 5 Apply and Interpret Limits of Accuracy. Question 1. (a) A field measures 500m by 200m when rounded to the nearest 100m. What is the greatest possible area of the field? 550 X 250= 137500�� (M1) (A1) ………137500�� …………….. (2) (b) David runs around the edge of the field twice. What is the least possible distance that he would run? 2(450 + 150)= 1200m (M1) 1200� (A1) …………1200� ………….. (4) (Total 6 marks) Question 2 A pen measures 30 cm to the nearest 10cm. 10 pencils are joined together. What is the total greatest and least possible total length of the pencils? Give your answer in centimetres. 35 x 10= 350cm 350cm (A1) PiXL PLC 2017 Certification (M1) Greatest Length……350cm……………….. (2) 25 x 10= 250cm 250cm (A1) (M1) Least Length ………250cm …………….. (2) (Total 4 marks) 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 [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 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