plumiFurther numerical methods: OCR MEI A‑Level Further Maths questions
Every OCR MEI A-Level Further Maths exam question on FP.6 Further numerical methods, 2018–2025, with its mark scheme and examiner’s report.
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![June 2025 AS Numerical Methods, question 3: (a) Find the relative error when r is chopped to 3 decimal places. [2] (b) Find the relative error when r is rounded to 3 decimal places. [2] 2 5 2 You are give](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/y41401-jun25-03-qp.webp?v=3)
All 109 questions on Further numerical methods, as a list
- June 2025, Numerical Methods, Q1 (4 marks): The table shows some values of x and the associated values of ( ) f x . x 1.9 2.0 2.1 0.216 92 0.2 0.184 84 f ( )x (a) Determine an estimate of f 2 0 ( . ) usin
- June 2025, Numerical Methods, Q2 (6 marks): The numbers p and q are approximated by P 323 and Q 162 . = = P has been found by rounding p to the nearest whole number. Q has been found by chopping q to the
- June 2025, Numerical Methods, Q3 (5 marks): 3 . y 3 3 Approximations to 1 x d x using the midpoint rule, the trapezium rule and Simpson’s rule + 0 5 . with n = and n 1 2 are shown in the table. The table
- June 2025, Numerical Methods, Q4 (7 marks): The Newton-Raphson method is to be used to find the positive root of the equation 2 tanh x x 4 0 . - + = 2 The diagram shows part of the graph of y tanh x x + .
- June 2025, Numerical Methods, Q5 (10 marks): The diagram shows part of the graph of y sinh x 3 x + . 1 = - y 10 5 x 0 –1 1 2 3 4 –5 The largest positive root, a, of the equation sinh x 3 x 1 0 is to be fou
- June 2025, Numerical Methods, Q6 (7 marks): 1y 6 The midpoint rule is used to find a sequence of approximations to sin x x d . 0 The associated spreadsheet output, together with some further analysis, is
- June 2025, Numerical Methods, Q7 (11 marks): The equation 8 ln x ( 2 ) 3 x 1 0 has a positive root, c, and a negative root, d. + - + = It is proposed that the iterative formula x g ( x ) , where ( ) g x 8
- June 2025, Numerical Methods, Q8 (10 marks): Following an injury an athlete returns to training in preparation for a regional competition. At the end of each week the athlete’s trainer records the time, t
- June 2025, AS Numerical Methods, Q1 (5 marks): The method of interval bisection is used to find a sequence of approximations to one of the roots x 2 of the equation e x 3 x 0 . - - = The table shows the asso
- June 2025, AS Numerical Methods, Q2 (4 marks): The table gives three values of x and the associated values of y. x 2 3 1 - y 0.18 0.45 .3 39 - Use Lagrange’s form of the interpolating polynomial to construct
- June 2025, AS Numerical Methods, Q3 (5 marks): (a) Find the relative error when r is chopped to 3 decimal places. [2] (b) Find the relative error when r is rounded to 3 decimal places. [2] 2 5 2 You are give
- June 2025, AS Numerical Methods, Q4 (8 marks): A student is using a spreadsheet to investigate the curve y f ( ) x at the point where x 2 . Some = = of the spreadsheet output is shown below. Table 4.1 shows
- June 2025, AS Numerical Methods, Q5 (7 marks): 5 . y 5 The spreadsheet output shows a sequence of approximations to f ( )x d x using the trapezium 0 5 . rule and Simpson’s rule, together with some further an
- June 2025, AS Numerical Methods, Q6 (6 marks): 6 The equation . ln x 0 5 x x 2 0 has a root a, such that 1 2 . + - - = 1 1 a A student attempts to find a using the iterative formula 2 x g ( x ) with x 0 = ,
- June 2025, AS Numerical Methods, Q7 (10 marks): A student makes a cup of tea and investigates how long it takes to reach room temperature. The student places the cup of tea on a table in the kitchen and recor
- June 2025, AS Numerical Methods, Q8 (7 marks): Table 8.1 shows some values of x and the associated values of ( )x f . Table 8.1 x 0.5 0.9 1.3 f ( )x 1.414 21 1.099 47 0.711 01 (a) Use the central difference
- June 2025, AS Numerical Methods, Q9 (8 marks): In this question you must show detailed reasoning 4 + The equation . 0 2 x 0 8 . x 0 2 . 0 has a root a such that 0 1 . - = 1 1 a (a) Use the Newton-Raphson met
- June 2024, Numerical Methods, Q1 (4 marks): The table shows some values of x, together with the associated values of a function, ( )x f . x 1.9 2 2.1 0.5842 0.6309 0.6753 f ( )x (a) Use the information in
- June 2024, Numerical Methods, Q2 (6 marks): You are given that a tanh ( ) 1 and b tanh ( ) 2 . = = A is the approximation to a formed by rounding tanh 1 to 1 decimal place. ( ) B is the approximation to b
- June 2024, Numerical Methods, Q3 (6 marks): - 3 The equation x cosh ( x 2 ) 0 has two roots, a and b, such that 1 b . - = a (a) Use the iterative formula x g ( x ) where ( g x ) cosh ( x 2 ) , 1 = = - n n
- June 2024, Numerical Methods, Q4 (10 marks): Between 1946 and 2012 the mean monthly maximum temperature of the water surface of a lake in northern England has been recorded by environmental scientists. Som
- June 2024, Numerical Methods, Q5 (10 marks): The root of the equation ( )x f 0 is being found using the method of interval bisection. Some of = the associated spreadsheet output is shown in the table below
- June 2024, Numerical Methods, Q6 (10 marks): Table 6.1 shows some values of x and the associated values of a function, y f ( ) x . = Table 6.1 x 1.5 1 2 0.840 89 1 1.189 21 f ( )x (a) Explain why it is not
- June 2024, Numerical Methods, Q7 (14 marks): 0y 7 ( )x x A student is using a spreadsheet to find approximations to f d using the midpoint rule, the trapezium rule and Simpson’s rule. Some of the associate
- June 2024, AS Numerical Methods, Q1 (3 marks): The difference table shows some values of x and the associated values of y. x y y 2 3 y y D D D 0 0.8 1 0.7 2 0.1 3 11.3 4 70.5 5 250.6 (a) Complete the copy of
- June 2024, AS Numerical Methods, Q2 (5 marks): A spreadsheet is used to find the approximate value of r + . The output is shown in the table. e A B 1 3.141 593 r 2 e 2.718 282 3 e 5.859 874 r + The formula i
- June 2024, AS Numerical Methods, Q3 (8 marks): Following an injury a professional footballer has to undergo a rehabilitation programme before she can resume playing. As part of the programme she is required
- June 2024, AS Numerical Methods, Q4 (11 marks): The graph shows part of the graph of y f ( ) x . = y 1.5 1 0.5 0 x 2 2.5 3 3.5 4 4.5 -0.5 The equation ( )x f 0 has two positive roots, a and b, where 2 b. = a
- June 2024, AS Numerical Methods, Q5 (10 marks): Table 5.1 shows some values of x and the associated values of ( )x f . Table 5.1 x 5 5.0001 5.001 5.01 5.1 f(x) 12.182 494 12.183 103 12.188 587 12.243 559 12.8
- June 2024, AS Numerical Methods, Q6 (11 marks): The equation log x x 5 0 has two roots, a and b. 3 - = You are given that 1 1 1 2 . a x n (a) Use the iterative formula x x x and x g ( ) , where ( g ) 3 2 , to
- June 2024, AS Numerical Methods, Q7 (12 marks): A student uses the midpoint rule, the trapezium rule and Simpson’s Rule to find a series of 1y approximations to f ( )x d x . The associated spreadsheet output,
- June 2023, Numerical Methods, Q1 (7 marks): You are given that ( x , y ) ( . , . ) 0 9 2 3 and ( x , y ) ( . , . ) 1 1 2 7 . 1 = 2 = 1 2 The values of x1 and x2 have been rounded to 1 decimal place. (a) D
- June 2023, Numerical Methods, Q2 (8 marks): A car tyre has a slow puncture. Initially the tyre is inflated to a pressure of 34.5 psi. The pressure is checked after 3 days and then again after 5 days. The
- June 2023, Numerical Methods, Q3 (6 marks): The diagram shows the graph of y f ( ) x for values of x from 1 to 3.5. = y 2.5 2 1.5 1 0.5 x 0 0.5 1 1.5 2 2.5 3 3.5 The table shows some values of x and the a
- June 2023, Numerical Methods, Q4 (4 marks): by 4 A spreadsheet is used to approximate f ( )x d x using the midpoint rule with 1 strip. a The output is shown in the table below. B C D 3 x f ( )x M1 4 1.5
- June 2023, Numerical Methods, Q5 (6 marks): The equation 3 2 ln x x 0 has a root near x 1 8 . . - - = = A student proposes to use the iterative formula x g ( x ) 3 2 ln x to find this root. 1 = = - n n n
- June 2023, Numerical Methods, Q6 (6 marks): (a) (i) Calculate the relative error when r is chopped to 2 decimal places in approximating 2 r + . 2 [2] (ii) Without doing any calculation, explain whether th
- June 2023, Numerical Methods, Q7 (6 marks): d , when x y 7 y x , is given in Table 7.1. The value of a function, f ( ) , and its gradient function, x 2 = = d Table 7.1 d y x f ( )x d x 2 6 .2 8 - (a) Dete
- June 2023, Numerical Methods, Q8 (8 marks): The graph of y 0 2 . cosh x 0 4 . x for values of x from 0 to 3.32 is shown on the graph below. = - y 1.2 1 0.8 0.6 0.4 0.2 x 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
- June 2023, Numerical Methods, Q9 (9 marks): 1y 3 9 The trapezium rule is used to calculate 3 approximations to sinh x ( ) d x with 1, 2 and 4 strips 0 respectively. The results are shown in Table 9.1. Tab
- June 2023, AS Numerical Methods, Q1 (6 marks): The table shows some spreadsheet output. The values displayed in cells K21 and K22 are exact, but the values displayed in rows 21 and 22 in columns L, M and N h
- June 2023, AS Numerical Methods, Q2 (4 marks): The table gives three values of x and the associated values of y. x 3 5 8 y 9.26 19.3 37.96 Use Lagrange’s method to construct the interpolating polynomial of d
- June 2023, AS Numerical Methods, Q3 (5 marks): You are given that 43 2 . 43 2 . P + and Q = = x y x y - and that x 2 17 . and y 2 14 . . = = The values of x and y have been rounded to 2 decimal places. (a) C
- June 2023, AS Numerical Methods, Q4 (9 marks): It is given that the function ( )x g is continuous and differentiable and that g ( . ) 1 8 0 576 . , correct l = to 3 decimal places. (a) Use this result to det
- June 2023, AS Numerical Methods, Q5 (9 marks): y 5 2 5 The table shows some approximations to x 3 x 2 d x , correct to 8 decimal places, which + + 0 have been found using the midpoint rule and the trapezium
- June 2023, AS Numerical Methods, Q6 (9 marks): After taking his pet dog to the vet for a check-up, a dog owner is advised that the dog is too heavy and must therefore go on a special diet. The owner records
- June 2023, AS Numerical Methods, Q7 (9 marks): 2 7 The equation . 5 39 x 2 17 . x 1 11 . x 0 45 . 0 has a root, a, close to .0 5 . - - + = - (a) Use the Newton-Raphson method with x 0 5 . to determine the va
- June 2023, AS Numerical Methods, Q8 (9 marks): Table 8.1 shows some values of x and the associated values of a function ( )x f . Table 8.1 x 1.2 2 2.8 ( )x 0.9638087 1.3258177 1.4439304 f (a) Use the forward
- June 2022, Numerical Methods, Q1 (4 marks): C 3 7622 . and S 3 6269 . are used to approximate cosh2 and sinh2 respectively. = = (a) Determine whether these approximations are the result of chopping or rou
- June 2022, Numerical Methods, Q2 (7 marks): The table shows some values of x and the associated values of y f ( ) x . = x 2.75 3 3.25 f(x) 0.920799 1 1.072858 d y at x (a) Calculate an estimate of d = usi
- June 2022, Numerical Methods, Q3 (7 marks): 3 The equation ( ) f x sin - ( ) x x 0 1 . 0 has a root a such that 1 1 1 0 . = - + = - a Alex uses an iterative method to find a sequence of approximations to
- June 2022, Numerical Methods, Q4 (8 marks): x 2 4 Fig. 4.1 shows part of the graph of y e x x 1 1 . . = - - - y 3 2 1 x 1 2 3 4 0 –1 Fig. 4.1 x 2 The equation e x x 1 1 . 0 has a root a such that 1 1 1 2
- June 2022, Numerical Methods, Q5 (9 marks): Kai uses the midpoint rule, trapezium rule and Simpson’s rule to find approximations to by f ( ) x d x , where a and b are constants. The associated spreadsheet
- June 2022, Numerical Methods, Q6 (11 marks): Charlie uses fixed point iteration to find a sequence of approximations to the root of the equation 1 2 x x sin - ( ) 1 0 . - + = a k. 2 x x x x Charlie uses th
- June 2022, Numerical Methods, Q7 (14 marks): Sam decided to go on a high-protein diet. Sam’s mass in kg, M, after t days of following the diet is recorded in Fig. 7.1. t 0 10 20 30 M 88.3 80.05 78.7 78.85
- June 2022, AS Numerical Methods, Q1 (7 marks): You are given the following simultaneous equations. 2 x 1 8 . y 5 + = 3 x 2 8 . y 3 + = The constants and the coefficients of x are exact, but the coefficients
- June 2022, AS Numerical Methods, Q2 (6 marks): The table shows some values of x and the associated values of y = f (x). x 1.98 1.99 2 2.01 2.02 f (x) 1.10311648 1.10514069 1.10714872 1.10914075 1.11111695 d
- June 2022, AS Numerical Methods, Q3 (5 marks): Ali uses the trapezium rule with h = 1, h = 0.5 and h = 0.25 to calculate three approximations to 2y f ( )x d x . Ali’s results are shown in the table. 1 h n Tn
- June 2022, AS Numerical Methods, Q4 (12 marks): 2 4 The equation x 3 13 x 11 0 has three roots, a, b and c such that a 1 b 1 c. - + = 5 2 Fig. 4.1 shows part of the graph of y 3 x 13 x 11 . = - + y 10 8 6 4 2
- June 2022, AS Numerical Methods, Q5 (7 marks): - 5 The equation x 3 x 1 0 has two positive roots, a and b, where a 1 b. + = 5 x 1 + n Charlie is using the iterative formula x g ( x ) where ( g x ) to try to
- June 2022, AS Numerical Methods, Q6 (10 marks): Fig. 6.1 shows some values of x and the associated values of f (x). x 1 1.25 1.5 1.75 2 f (x) 0 0.1609640 0.2924813 0.4036775 0.5 Fig. 6.1 2y Sam is using the m
- June 2022, AS Numerical Methods, Q7 (13 marks): Azmi placed a container of liquid in a refrigerator unit in a laboratory. Initially the temperature of the liquid was 22 °C. Azmi recorded the temperature, y °C
- November 2021, Numerical Methods, Q1 (5 marks): (a) (i) Determine the relative error when • 1.414214 is used to approximate 2, • 1.4142142 is used to approximate 2. [3] (ii) Write down the relationship betwee
- November 2021, Numerical Methods, Q2 (6 marks): The table shows some values of x and the associated values of ( )x f . x 1 2 3 4 5 f(x) ‒0.65 ‒0.35 1.77 5.71 11.47 (a) Complete the difference table in the Pri
- November 2021, Numerical Methods, Q3 (7 marks): The method of False Position is used to find a sequence of approximations to the root of an equation. The spreadsheet output showing these approximations, toget
- November 2021, Numerical Methods, Q4 (6 marks): The table shows some values of x and the associated values of ( )x f . x 4 4.0001 4.001 4.01 4.1 4 4.0002386 4.0023871 4.0239468 4.2472072 f ( )x (a) Calculate
- November 2021, Numerical Methods, Q5 (9 marks): When Nina does the weekly grocery shopping she models the total cost by adding up the cost of each item in her head as she goes along. To simplify matters she r
- November 2021, Numerical Methods, Q6 (12 marks): + + 6 The equation . ln x 0 5 x x 1 0 has two roots a and b, such that 0 1 1 1 and 1 1 1 2 . - = a b (a) Use the Newton-Raphson method with x 0 = to obtain b co
- November 2021, Numerical Methods, Q7 (15 marks): y 7 tanh x x Sarah uses the trapezium rule to find a sequence of approximations to ( ) d . 0 Her spreadsheet output is shown in Fig. 7.1. n Tn difference ratio
- November 2021, AS Numerical Methods, Q1 (5 marks): The table shows 3 values of x and the associated values of ( ) f x . x -1 1 2 f x ( ) 0.7 -3.56 -4.94 (a) Use Lagrange’s method to construct the interpolating p
- November 2021, AS Numerical Methods, Q2 (6 marks): The table shows 2 values of x and the associated values of (fx . The values of x are exact and the ) values of ( ) f x have been rounded to 3 decimal places. x
- November 2021, AS Numerical Methods, Q3 (5 marks): The table shows 3 values of x and the associated values of ( ) f x . x 2 2.05 2.1 f x ( ) 1.386294 1.471572 1.558068 (a) Use the forward difference method to fi
- November 2021, AS Numerical Methods, Q4 (13 marks): Fig. 4.1 shows the graph of y ln x 3 x + . 4 = - y 2 1 x –1 0 1 2 3 4 –1 -1 Fig. 4.1 The equation ( ) f x 0 where f ( ) x ln x 3 x 4 has two roots, a and b, whe
- November 2021, AS Numerical Methods, Q5 (10 marks): y 5 f x x A student is trying to find an accurate approximation to ( ) d using the trapezium rule, the 1 midpoint rule and Simpson’s rule. Some of the spreadshe
- November 2021, AS Numerical Methods, Q6 (9 marks): En n to approximate en, and calculates the 6 James is investigating relative error. He uses .2 718 = relative error for various values of n. Some of his results
- November 2021, AS Numerical Methods, Q7 (12 marks): x 2 7 The equation ( ) f x 0 where ( ) f x 0 9 . x - - has a root a, such that x 1 .1 87 . = = . a # x 1 + n Sundip is considering using the iterative formula x
- November 2020, Numerical Methods, Q1 (4 marks): Fig. 1 shows some spreadsheet output. A 1 1E-17 2 1E-17 3 1E-29 Fig. 1 (a) Write the value displayed in cell A3 in standard mathematical notation. [1] The for
- November 2020, Numerical Methods, Q2 (5 marks): Fig. 2 shows 3 values of x and the associated values of a function, ( )x f . x 1 2 5 5 16.6 76.6 f ( )x Fig. 2 Find a polynomial p ( )x of degree 2 to approxima
- November 2020, Numerical Methods, Q3 (7 marks): At Heathwick airport each passenger’s luggage is weighed before being loaded into the hold of the aeroplane. Each weight is displayed digitally in kg to 1 decim
- November 2020, Numerical Methods, Q4 (10 marks): y 3 4 (a) Use the trapezium rule with 1 strip to calculate an estimate of x x 1 d , giving your + [2] answer correct to six decimal places. 1 Fig. 4 shows some
- November 2020, Numerical Methods, Q5 (34 marks): You are given that 3 x x 25 + g ( )x . = 2 Fig. 5.1 shows two values of x and the associated values of ( )x g . x 1.45 1.55 g ( )x 1.49468 1.49949 Fig. 5.1 (a)
- November 2020, AS Numerical Methods, Q1 (9 marks): Fig. 1.1 shows the graph of y f ( ) x for 0 x G . 1 = G y 1.2 1.0 0.8 0.6 0.4 0.2 0 x 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Fig. 1.1 Fig. 1.2 shows three va
- November 2020, AS Numerical Methods, Q2 (8 marks): ex2 2 Fig. 2.1 shows the graph of y f ( ) x where ( )x f for 0 x 1 3 . . = = G G y 7 6 5 4 3 2 1 0 x 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 Fig.
- November 2020, AS Numerical Methods, Q3 (7 marks): Fig. 3 shows three values of x and the associated values of ( )x f . x 1 2 5 2.53 7.71 47.37 f ( )x Fig. 3 (a) Use Lagrange’s method to construct the interpolat
- November 2020, AS Numerical Methods, Q4 (8 marks): A small company leases a machine which they use for scanning, printing and photocopying. The cost of each job completed is displayed in pounds to the nearest te
- November 2020, AS Numerical Methods, Q5 (11 marks): y 5 ( )x x Arthur uses a spreadsheet to approximate f d using the trapezium rule. Some of the output is shown in Fig. 5.1. 0 C D E F 3 x y 4 T 5 0 1.732051 6 1
- November 2020, AS Numerical Methods, Q6 (11 marks): 6 Fig. 6.1 shows the graph of y x 3 x + for 1 2 x 2 . = - - G G y 5 4 3 2 1 x 0 –3 –2 –1 1 2 3 –1 –2 Fig. 6.1 3 - The equation x 3 x 1 0 has three roots, a, b a
- November 2020, AS Numerical Methods, Q7 (6 marks): - 7 The equation x 2 x 1 0 has one root, which is close to x = . 1 - = (a) Use the secant method with x 0 5 . and x 0 8 . to obtain x2, a first approximation to
- June 2019, Numerical Methods, Q1 (6 marks): Fig. 1 shows some spreadsheet output concerning the values of a function, ( )x . f A B C 1 x f ( )x 2 1 0.367879441 0.367879441 3 2 0.018315639 0.38619508 4 3
- June 2019, Numerical Methods, Q2 (8 marks): 2 e x 2 2 Fig. 2.1 shows the graph of y x 5 x 0 5 . . = - + y 2 1 x –1 0 1 –1 Fig. 2.1 2 2 e x 2 x x There are three roots of the equation 5 0 5 . 0 . The roots
- June 2019, Numerical Methods, Q3 (11 marks): In the first week of an outbreak of influenza, 9 patients were diagnosed with the virus at a medical practice in Pencaster. Records were kept of y, the total nu
- June 2019, Numerical Methods, Q4 (13 marks): 4 Fig. 4 shows the graph of y x 6 x + . 4 = - y 6 4 2 x 0 2 4 Fig. 4 5 - There are two roots of the equation x 6 x 4 0 . The roots are a and b, such that b. 1 +
- June 2019, Numerical Methods, Q5 (12 marks): Fig. 5 shows spreadsheet output concerning the estimation of the derivative of a function ( )x f at x 2 using the forward difference method. = A B C D 1 h est
- June 2019, Numerical Methods, Q6 (10 marks): y x 6 The spreadsheet output in Fig. 6 shows approximations to x - d x found using the midpoint 0 rule, denoted by Mn, and the trapezium rule, denoted by Tn. A
- June 2019, AS Numerical Methods, Q1 (8 marks): 2 1 The graph of y 3 15 . x 0 75 . x 5 2 . x 2 2 . is shown in Fig. 1.1. = + - + y 6 5 4 3 2 1 x –2 –1 0 1 2 3 –1 –2 Fig. 1.1 3 2 There are three roots to the e
- June 2019, AS Numerical Methods, Q2 (8 marks): You are given that ( ) f x log ( 2 x 1 ) . = + 10 (a) Calculate the absolute error when ( ) f 5 is used to approximate ( . f 4 98 . ) [2] (b) Hence find an appr
- June 2019, AS Numerical Methods, Q3 (6 marks): Sallysavers Building Society offers a “Bigsaver” account. Interest is payable at the end of each year. The rate of interest is 2.33% per annum. A customer model
- June 2019, AS Numerical Methods, Q4 (5 marks): = ^ h . x 4 Fig. 4.1 shows the graph of y 0 8 . x y 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 x 0 0.5 1 1.5 2 2.5 3 3.5 Fig. 4.1 ^ h for various values x Fig. 4.2 shows som
- June 2019, AS Numerical Methods, Q5 (3 marks): 1 5 (a) Explain what problem may arise in the evaluation of x for large values of x and y. [2] - 10 10 y 10 10 y x 1 1 - (b) Explain why re-writing x as ( may a
- June 2019, AS Numerical Methods, Q6: 8E+14 8E+14 1.0737E+149 1.0737E+149 6.746E+135 1.1529E+298 5.8512E-163
- June 2019, AS Numerical Methods, Q7 (18 marks): 8E+17 8E+17 1.0737E+179 1.0737E+179 0 #NUM! #NUM! Fig. 5 The formulae in cells E2 and F2 are =D2 - C2 and =C2*D2 respectively. Equivalent formulae are entered i
- June 2019, AS Numerical Methods, Q8 (12 marks): ^ h 1 y 8 Fig. 8.1 shows estimates of sin x d x found using the trapezium rule, denoted by Tn, together 0 with some further analysis of these estimates. n Tn di
- June 2018, AS Numerical Methods, Q1 (4 marks): The coordinates of point A are (1.05, 2.71) and the coordinates of point B are (1.07, 3.08). In each case the x and y values have been rounded to two decimal pl
- June 2018, AS Numerical Methods, Q2 (4 marks): The table in Fig. 2 shows some values of log x 3 which are correct to 6 decimal places. x 2 2.25 2.5 2.75 3 log3x 0.630930 0.738140 0.834044 0.920799 1 Fig. 2 3
- June 2018, AS Numerical Methods, Q3 (8 marks): The spreadsheet output in Fig. 3 shows Table 1 and Table 2. A B C D E F G 1 x 2 2.1 2.01 2.001 2.0001 2.00001 2 f(x) 0.64 0.625876972 0.638573473 0.639857204 0.
- June 2018, AS Numerical Methods, Q4 (11 marks): x 2 4 The equation e x x 2 0 has a root a, where 0 1 1 1 and a root b, where 2 1 1 3 . - - = a b (i) Show how to obtain the iterative formula x 2 e x - r r x .
- June 2018, AS Numerical Methods, Q5 (13 marks): The value of shares in Sunfield plc was £2.21 per unit on the first day it came under new management. One week later the value of one unit of shares was £4.00 a
- June 2018, AS Numerical Methods, Q6 (8 marks): - 6 (i) Show that the equation . x x has a root a, where 3 [1] 0 1 2 3 0 1 1 4 . + = a The method of false position is used to find a. The spreadsheet output in
- June 2018, AS Numerical Methods, Q7 (12 marks): x 2 7 Fig. 7.1 shows part of the curve y 2 x + . 3 = - y 6 5 4 3 2 1 0 x 0 1 2 3 4 5 Fig. 7.1 7 ^ h y 4 x 2 (i) State, with a reason, whether using the trapeziu
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