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SINGLE PURE
Single Pure - Quadratics In Disguise To spot a quadratic in disguise you are looking for an equation where the power on one of the variables is twice that on the other. USE THIS AS A GUIDE AS TO HOW MUCH TIME TO SPEND ON EACH P46710A 5 ©2016 Pearson Education Ltd. 6. A particle P is projected from a fixed origin O with velocity (3i + 4j) m s−1.The particle moves freely under gravity and passes through the point A with position vector λ(i – j) m, where λ is a positiveconstant.
PAPER REFERENCE(S) 6678 EDEXCEL GCE N35391A 2 1. A particle P moves on the x-axis.The acceleration of P at time t seconds, t ≥ 0, is (3t + 5) m s–2 in the positive x-direction.When t = 0, the velocity of P is 2 m s–1 in the positive x-direction.When t = T, the velocity of P is 6 m s–1 in the positive x-direction. Find the value of T. (6) 2. A particle P of mass 0.6 kg is released from rest and slides down a line of PAPER REFERENCE(S) 6683/01 EDEXCEL GCE N29283A 4 3. The histogram in Figure 1 shows the time taken, to the nearest minute, for 140 runners to complete a fun run. Figure 1 Use the histogram to calculate the PAPER REFERENCE(S) 6683/01 EDEXCEL GCE P41805A 5 Turn over 6. A fair blue die has faces numbered 1, 1, 3, 3, 5 and 5. The random variable B represents the score when the blue die is rolled. (a) Write down the probability distribution for B.(2) (b) State the name of this probability distribution.(1) (c) Write down the value of E(B).(1) A second die is red and the random variable R represents the score when the red die is rolled. PAPER REFERENCE(S) 6678/01 EDEXCEL GCE P43997A 2 1. A particle P of mass 2 kg is moving with velocity (i – 4j) m s–1 when it receives an impulse of (3i + 6j) N s. Find the speed of P immediately after the impulse is applied. (5) 2. A particle P of mass 3 kg moves from point A to point B up a line of greatest slope of a fixed rough plane. The plane is inclined at 20° to the horizontal. The coefficient of friction betwee THURSDAY 12 JUNE 2014 Thursday 12 June 2014 – Afternoon AS GCE MATHEMATICS 4728/01 Mechanics 1 QUESTION PAPER *3134014001* INSTRUCTIONS TO CANDIDATES These instructions are the same on the Printed Answer Book and theQuestion Paper.
TUESDAY 21 JUNE 2016 Tuesday 21 June 2016 – Morning A2 GCE MATHEMATICS 4723/01 Core Mathematics 3 QUESTION PAPER *4827937481* INSTRUCTIONS TO CANDIDATES These instructions are the same on the Printed Answer Book and theQuestion Paper.
TUESDAY 16 JUNE 2015 Tuesday 16 June 2015 – Afternoon A2 GCE MATHEMATICS 4724/01 Core Mathematics 4 QUESTION PAPER *3170296828* INSTRUCTIONS TO CANDIDATES These instructions are the same on the Printed Answer Book and theQuestion Paper.
PAPER REFERENCE(S) 6684/01 EDEXCEL GCE P40106A 2 1. A manufacturer produces sweets of length L mm where L has a continuous unifrom distribution with range . (a) Find the probability that a randomly selected sweet has length greater than 24 mm. (2) These sweets are randomly packed in bags of 20 sweets. (b) Find the probability that a randomly selected bag will contain at least 8 sweets with lengthSINGLE PURE
Single Pure - Quadratics In Disguise To spot a quadratic in disguise you are looking for an equation where the power on one of the variables is twice that on the other. USE THIS AS A GUIDE AS TO HOW MUCH TIME TO SPEND ON EACH P46710A 5 ©2016 Pearson Education Ltd. 6. A particle P is projected from a fixed origin O with velocity (3i + 4j) m s−1.The particle moves freely under gravity and passes through the point A with position vector λ(i – j) m, where λ is a positiveconstant.
PAPER REFERENCE(S) 6678 EDEXCEL GCE N35391A 2 1. A particle P moves on the x-axis.The acceleration of P at time t seconds, t ≥ 0, is (3t + 5) m s–2 in the positive x-direction.When t = 0, the velocity of P is 2 m s–1 in the positive x-direction.When t = T, the velocity of P is 6 m s–1 in the positive x-direction. Find the value of T. (6) 2. A particle P of mass 0.6 kg is released from rest and slides down a line of PAPER REFERENCE(S) 6683/01 EDEXCEL GCE N29283A 4 3. The histogram in Figure 1 shows the time taken, to the nearest minute, for 140 runners to complete a fun run. Figure 1 Use the histogram to calculate the PAPER REFERENCE(S) 6683/01 EDEXCEL GCE P41805A 5 Turn over 6. A fair blue die has faces numbered 1, 1, 3, 3, 5 and 5. The random variable B represents the score when the blue die is rolled. (a) Write down the probability distribution for B.(2) (b) State the name of this probability distribution.(1) (c) Write down the value of E(B).(1) A second die is red and the random variable R represents the score when the red die is rolled. PAPER REFERENCE(S) 6678/01 EDEXCEL GCE P43997A 2 1. A particle P of mass 2 kg is moving with velocity (i – 4j) m s–1 when it receives an impulse of (3i + 6j) N s. Find the speed of P immediately after the impulse is applied. (5) 2. A particle P of mass 3 kg moves from point A to point B up a line of greatest slope of a fixed rough plane. The plane is inclined at 20° to the horizontal. The coefficient of friction betwee THURSDAY 12 JUNE 2014 Thursday 12 June 2014 – Afternoon AS GCE MATHEMATICS 4728/01 Mechanics 1 QUESTION PAPER *3134014001* INSTRUCTIONS TO CANDIDATES These instructions are the same on the Printed Answer Book and theQuestion Paper.
TUESDAY 21 JUNE 2016 Tuesday 21 June 2016 – Morning A2 GCE MATHEMATICS 4723/01 Core Mathematics 3 QUESTION PAPER *4827937481* INSTRUCTIONS TO CANDIDATES These instructions are the same on the Printed Answer Book and theQuestion Paper.
TUESDAY 16 JUNE 2015 Tuesday 16 June 2015 – Afternoon A2 GCE MATHEMATICS 4724/01 Core Mathematics 4 QUESTION PAPER *3170296828* INSTRUCTIONS TO CANDIDATES These instructions are the same on the Printed Answer Book and theQuestion Paper.
PAPER REFERENCE(S) 6684/01 EDEXCEL GCE P40106A 2 1. A manufacturer produces sweets of length L mm where L has a continuous unifrom distribution with range . (a) Find the probability that a randomly selected sweet has length greater than 24 mm. (2) These sweets are randomly packed in bags of 20 sweets. (b) Find the probability that a randomly selected bag will contain at least 8 sweets with lengthFURTHER PURE CORE
Further Pure Core - Partial Fractions In single maths you learnt how to split two types of expressions into partial fractions; namely: px +q (ax + b)(cx + d)
USE THIS AS A GUIDE AS TO HOW MUCH TIME TO SPEND ON EACH P46710A 5 ©2016 Pearson Education Ltd. 6. A particle P is projected from a fixed origin O with velocity (3i + 4j) m s−1.The particle moves freely under gravity and passes through the point A with position vector λ(i – j) m, where λ is a positiveconstant.
TUESDAY 16 JUNE 2015 Tuesday 16 June 2015 – Afternoon A2 GCE MATHEMATICS 4724/01 Core Mathematics 4 QUESTION PAPER *3170296828* INSTRUCTIONS TO CANDIDATES These instructions are the same on the Printed Answer Book and theQuestion Paper.
PAPER REFERENCE(S) 6684/01 EDEXCEL GCE P44846A 2 1. In a survey it is found that barn owls occur randomly at a rate of 9 per 1000 km2. (a) Find the probability that in a randomly selected area of 1000 km2 there are at least 10 barn owls. (2) (b) Find the probability that in a randomly selected area of 200 km2 there are exactly 2 barn owls. (3) (c) Using a suitable approximation, find the probability that in a randomly selected area of PAPER REFERENCE(S) 6683/01 EDEXCEL GCE H34279A 5 5. The weight, w grams, and the length, l mm, of 10 randomly selected newborn turtles are given in the table below. l 49.0 52.0 53.0 54.5 54.1 53.4 50.0 51.6 49.5 51.2 w 29 32 34 39 38 35 30 31 29 30 (You may use S ll = 33.381 S wl = 59.99 S ww = 120.1) (a) Find the equation of the regression line of w on l in the form w = a + bl. ADVANCED SUBSIDIARY GCE MATHEMATICS 4728 3 4 An object is projected vertically upwards with speed 7ms−1.Calculate (i) the speed of the object when it is 2.1m above the point of projection, (ii) the greatest height above the point of projection reached by the object, (iii) the time after projection when the object is travelling downwards with speed 5.7ms−1. 5 (i) Q P m kg 0.5 kg 6 m s–1FRIDAY 23 JUNE 2017
*6861537568* Friday 23 June 2017 – Morning A2 GCE MATHEMATICS 4724/01 Core Mathematics 4 QUESTION PAPER INSTRUCTIONS TO CANDIDATES These instructions are the same on the Printed Answer Book and theQuestion Paper.
PAPER REFERENCE(S) 6684/01 EDEXCEL GCE P42035A 3 Turn over 3. An online shop sells a computer game at an average rate of 1 per day. (a) Find the probability that the shop sells more than 10 games in a 7 day period.(3) Once every 7 days the shop has games delivered before it opens. ADVANCED SUBSIDIARY GCE MATHEMATICS 4728 2 1 Two perpendicular forces have magnitudes 8N and 15N. Calculate the magnitude of the resultant force, and the angle which the resultant makes with the larger force. 2 Particles P and Q, of masses 0.45kg and mkg respectively, are attached to the ends of a light inextensible stringwhichpassesover a smallsmoothpulley. WEDNESDAY 8 JUNE 2016 Wednesday 8 June 2016 – Morning AS GCE MATHEMATICS 4732/01 Probability & Statistics 1 QUESTION PAPER *4827193828* INSTRUCTIONS TO CANDIDATES These instructions are the same on the Printed Answer Book and the Question Paper. ADVANCED SUBSIDIARY GCE MATHEMATICS 4728 2 1 A particle P is projected vertically downwards from a fixed point O with initial speed 4.2ms−1, and takes 1.5s to reach the ground. Calculate (i) the speed of P when it reaches the ground, (ii) the height of O above the ground, (iii) the speed of P when it is 5m above the ground. 2 Two horizontal forces of magnitudes 12N and 19N act at a point. Given that the angle between the USE THIS AS A GUIDE AS TO HOW MUCH TIME TO SPEND ON EACH P46710A 5 ©2016 Pearson Education Ltd. 6. A particle P is projected from a fixed origin O with velocity (3i + 4j) m s−1.The particle moves freely under gravity and passes through the point A with position vector λ(i – j) m, where λ is a positiveconstant.
PAPER REFERENCE(S) 6683/01 EDEXCEL GCE N29283A 4 3. The histogram in Figure 1 shows the time taken, to the nearest minute, for 140 runners to complete a fun run. Figure 1 Use the histogram to calculate the PAPER REFERENCE(S) 6678/01 EDEXCEL GCE P43997A 2 1. A particle P of mass 2 kg is moving with velocity (i – 4j) m s–1 when it receives an impulse of (3i + 6j) N s. Find the speed of P immediately after the impulse is applied. (5) 2. A particle P of mass 3 kg moves from point A to point B up a line of greatest slope of a fixed rough plane. The plane is inclined at 20° to the horizontal. The coefficient of friction betwee PAPER REFERENCE(S) 6683/01 EDEXCEL GCE P41805A 5 Turn over 6. A fair blue die has faces numbered 1, 1, 3, 3, 5 and 5. The random variable B represents the score when the blue die is rolled. (a) Write down the probability distribution for B.(2) (b) State the name of this probability distribution.(1) (c) Write down the value of E(B).(1) A second die is red and the random variable R represents the score when the red die is rolled. THURSDAY 12 JUNE 2014 Thursday 12 June 2014 – Afternoon AS GCE MATHEMATICS 4728/01 Mechanics 1 QUESTION PAPER *3134014001* INSTRUCTIONS TO CANDIDATES These instructions are the same on the Printed Answer Book and theQuestion Paper.
PAPER REFERENCE(S) 6678 EDEXCEL GCE N35391A 2 1. A particle P moves on the x-axis.The acceleration of P at time t seconds, t ≥ 0, is (3t + 5) m s–2 in the positive x-direction.When t = 0, the velocity of P is 2 m s–1 in the positive x-direction.When t = T, the velocity of P is 6 m s–1 in the positive x-direction. Find the value of T. (6) 2. A particle P of mass 0.6 kg is released from rest and slides down a line of PAPER REFERENCE(S) 6684/01 EDEXCEL GCE P44846A 5 Turn over 5. Liftsforall claims that the lift they maintain in a block of flats breaks down at random at a mean rate of 4 times per month. To test this, the number of times the lift breaks down in a month is recorded. (a) Using a 5% level of significance, find the critical region for a two-tailed test of the null hypothesis that ‘the mean rate at which the lift breaks down is 4 TUESDAY 16 JUNE 2015 Tuesday 16 June 2015 – Afternoon A2 GCE MATHEMATICS 4724/01 Core Mathematics 4 QUESTION PAPER *3170296828* INSTRUCTIONS TO CANDIDATES These instructions are the same on the Printed Answer Book and theQuestion Paper.
PAPER REFERENCE(S) 6684/01 EDEXCEL GCE P40106A 2 1. A manufacturer produces sweets of length L mm where L has a continuous unifrom distribution with range . (a) Find the probability that a randomly selected sweet has length greater than 24 mm. (2) These sweets are randomly packed in bags of 20 sweets. (b) Find the probability that a randomly selected bag will contain at least 8 sweets with length ADVANCED SUBSIDIARY GCE MATHEMATICS 4728 2 1 A particle P is projected vertically downwards from a fixed point O with initial speed 4.2ms−1, and takes 1.5s to reach the ground. Calculate (i) the speed of P when it reaches the ground, (ii) the height of O above the ground, (iii) the speed of P when it is 5m above the ground. 2 Two horizontal forces of magnitudes 12N and 19N act at a point. Given that the angle between the USE THIS AS A GUIDE AS TO HOW MUCH TIME TO SPEND ON EACH P46710A 5 ©2016 Pearson Education Ltd. 6. A particle P is projected from a fixed origin O with velocity (3i + 4j) m s−1.The particle moves freely under gravity and passes through the point A with position vector λ(i – j) m, where λ is a positiveconstant.
PAPER REFERENCE(S) 6683/01 EDEXCEL GCE N29283A 4 3. The histogram in Figure 1 shows the time taken, to the nearest minute, for 140 runners to complete a fun run. Figure 1 Use the histogram to calculate the PAPER REFERENCE(S) 6678/01 EDEXCEL GCE P43997A 2 1. A particle P of mass 2 kg is moving with velocity (i – 4j) m s–1 when it receives an impulse of (3i + 6j) N s. Find the speed of P immediately after the impulse is applied. (5) 2. A particle P of mass 3 kg moves from point A to point B up a line of greatest slope of a fixed rough plane. The plane is inclined at 20° to the horizontal. The coefficient of friction betwee PAPER REFERENCE(S) 6683/01 EDEXCEL GCE P41805A 5 Turn over 6. A fair blue die has faces numbered 1, 1, 3, 3, 5 and 5. The random variable B represents the score when the blue die is rolled. (a) Write down the probability distribution for B.(2) (b) State the name of this probability distribution.(1) (c) Write down the value of E(B).(1) A second die is red and the random variable R represents the score when the red die is rolled. THURSDAY 12 JUNE 2014 Thursday 12 June 2014 – Afternoon AS GCE MATHEMATICS 4728/01 Mechanics 1 QUESTION PAPER *3134014001* INSTRUCTIONS TO CANDIDATES These instructions are the same on the Printed Answer Book and theQuestion Paper.
PAPER REFERENCE(S) 6678 EDEXCEL GCE N35391A 2 1. A particle P moves on the x-axis.The acceleration of P at time t seconds, t ≥ 0, is (3t + 5) m s–2 in the positive x-direction.When t = 0, the velocity of P is 2 m s–1 in the positive x-direction.When t = T, the velocity of P is 6 m s–1 in the positive x-direction. Find the value of T. (6) 2. A particle P of mass 0.6 kg is released from rest and slides down a line of PAPER REFERENCE(S) 6684/01 EDEXCEL GCE P44846A 5 Turn over 5. Liftsforall claims that the lift they maintain in a block of flats breaks down at random at a mean rate of 4 times per month. To test this, the number of times the lift breaks down in a month is recorded. (a) Using a 5% level of significance, find the critical region for a two-tailed test of the null hypothesis that ‘the mean rate at which the lift breaks down is 4 TUESDAY 16 JUNE 2015 Tuesday 16 June 2015 – Afternoon A2 GCE MATHEMATICS 4724/01 Core Mathematics 4 QUESTION PAPER *3170296828* INSTRUCTIONS TO CANDIDATES These instructions are the same on the Printed Answer Book and theQuestion Paper.
PAPER REFERENCE(S) 6684/01 EDEXCEL GCE P40106A 2 1. A manufacturer produces sweets of length L mm where L has a continuous unifrom distribution with range . (a) Find the probability that a randomly selected sweet has length greater than 24 mm. (2) These sweets are randomly packed in bags of 20 sweets. (b) Find the probability that a randomly selected bag will contain at least 8 sweets with length OXBRIDGE - MATHSHELPER.CO.UK Oxbridge. STEP. STEP is the Sixth Term Entrance Paper, originally used by Cambridge University as an exam sat alongside A Levels. It was usually included in offers given to Mathematics candidates. STEP I 1987 STEP II 1987 STEP III 1987. STEP I 1988 STEP II 1988 STEP III1988. STEP I
PAPER REFERENCE(S) 6683/01 EDEXCEL GCE P41805A 3 Turn over 3. A biologist is comparing the intervals (m seconds) between the mating calls of a certain species of tree frog and the surrounding temperature (t °C).The following results were obtained. t °C 8 13 14 15 15 20 25 30 m secs 6.5 4.5 6 5 4 3 2 1 (Youmay use ¦
USE THIS AS A GUIDE AS TO HOW MUCH TIME TO SPEND ON EACH P46710A 5 ©2016 Pearson Education Ltd. 6. A particle P is projected from a fixed origin O with velocity (3i + 4j) m s−1.The particle moves freely under gravity and passes through the point A with position vector λ(i – j) m, where λ is a positiveconstant.
PAPER REFERENCE(S) 6684/01 EDEXCEL GCE P44846A 2 1. In a survey it is found that barn owls occur randomly at a rate of 9 per 1000 km2. (a) Find the probability that in a randomly selected area of 1000 km2 there are at least 10 barn owls. (2) (b) Find the probability that in a randomly selected area of 200 km2 there are exactly 2 barn owls. (3) (c) Using a suitable approximation, find the probability that in a randomly selected area of PAPER REFERENCE(S) 6684/01 EDEXCEL GCE P42035A 3 Turn over 3. An online shop sells a computer game at an average rate of 1 per day. (a) Find the probability that the shop sells more than 10 games in a 7 day period.(3) Once every 7 days the shop has games delivered before it opens. OXFORD CAMBRIDGE AND RSA WEDNESDAY 20 MAY 2015 4722 Mark Scheme June 2015 Question Answer Marks Guidance 3 (i) sector = 1/ 2 × 8 2 × 1.2 (= 38.4) M1* Attempt area of sector using ½ r2θ, or equiv . Must be correct formula, including ½ M0 if 1.2π used not 1.2. M0 if ½ r2θ used with θ in degrees . Allow equiv method using fractions of a circle PAPER REFERENCE(S) 6686/01 EDEXCEL GCE P35418A 2 1. Find the value of the constant a such that P(a < F8, 10 < 3.07) = 0.94.(2) 2. Two independent random samples , , , and , , , were taken from different normal populations with a common standard deviation σ. The following sample statistics were calculated. WEDNESDAY 8 JUNE 2016 Wednesday 8 June 2016 – Morning AS GCE MATHEMATICS 4732/01 Probability & Statistics 1 QUESTION PAPER *4827193828* INSTRUCTIONS TO CANDIDATES These instructions are the same on the Printed Answer Book and the Question Paper. THURSDAY 24 MAY 2012 Thursday 24 May 2012 – Morning AS GCE MATHEMATICS 4732 Probability and Statistics 1 QUESTION PAPER *4715520612* INSTRUCTIONS TO CANDIDATES These instructions are the same on the Printed Answer Book and the Question Paper. TUESDAY 16 JUNE 2015 Tuesday 16 June 2015 – Afternoon A2 GCE MATHEMATICS 4724/01 Core Mathematics 4 QUESTION PAPER *3170296828* INSTRUCTIONS TO CANDIDATES These instructions are the same on the Printed Answer Book and theQuestion Paper.
ADVANCED SUBSIDIARY GCE MATHEMATICS 4728 2 1 A particle P is projected vertically downwards from a fixed point O with initial speed 4.2ms−1, and takes 1.5s to reach the ground. Calculate (i) the speed of P when it reaches the ground, (ii) the height of O above the ground, (iii) the speed of P when it is 5m above the ground. 2 Two horizontal forces of magnitudes 12N and 19N act at a point. Given that the angle between the USE THIS AS A GUIDE AS TO HOW MUCH TIME TO SPEND ON EACH P46710A 5 ©2016 Pearson Education Ltd. 6. A particle P is projected from a fixed origin O with velocity (3i + 4j) m s−1.The particle moves freely under gravity and passes through the point A with position vector λ(i – j) m, where λ is a positiveconstant.
PAPER REFERENCE(S) 6683/01 EDEXCEL GCE N29283A 4 3. The histogram in Figure 1 shows the time taken, to the nearest minute, for 140 runners to complete a fun run. Figure 1 Use the histogram to calculate the PAPER REFERENCE(S) 6678 EDEXCEL GCE N35391A 2 1. A particle P moves on the x-axis.The acceleration of P at time t seconds, t ≥ 0, is (3t + 5) m s–2 in the positive x-direction.When t = 0, the velocity of P is 2 m s–1 in the positive x-direction.When t = T, the velocity of P is 6 m s–1 in the positive x-direction. Find the value of T. (6) 2. A particle P of mass 0.6 kg is released from rest and slides down a line of PAPER REFERENCE(S) 6683/01 EDEXCEL GCE P41805A 5 Turn over 6. A fair blue die has faces numbered 1, 1, 3, 3, 5 and 5. The random variable B represents the score when the blue die is rolled. (a) Write down the probability distribution for B.(2) (b) State the name of this probability distribution.(1) (c) Write down the value of E(B).(1) A second die is red and the random variable R represents the score when the red die is rolled. PAPER REFERENCE(S) 6678/01 EDEXCEL GCE P43997A 2 1. A particle P of mass 2 kg is moving with velocity (i – 4j) m s–1 when it receives an impulse of (3i + 6j) N s. Find the speed of P immediately after the impulse is applied. (5) 2. A particle P of mass 3 kg moves from point A to point B up a line of greatest slope of a fixed rough plane. The plane is inclined at 20° to the horizontal. The coefficient of friction betwee TUESDAY 16 JUNE 2015 Tuesday 16 June 2015 – Afternoon A2 GCE MATHEMATICS 4724/01 Core Mathematics 4 QUESTION PAPER *3170296828* INSTRUCTIONS TO CANDIDATES These instructions are the same on the Printed Answer Book and theQuestion Paper.
PAPER REFERENCE(S) 6684/01 EDEXCEL GCE P44846A 5 Turn over 5. Liftsforall claims that the lift they maintain in a block of flats breaks down at random at a mean rate of 4 times per month. To test this, the number of times the lift breaks down in a month is recorded. (a) Using a 5% level of significance, find the critical region for a two-tailed test of the null hypothesis that ‘the mean rate at which the lift breaks down is 4 THURSDAY 12 JUNE 2014 Thursday 12 June 2014 – Afternoon AS GCE MATHEMATICS 4728/01 Mechanics 1 QUESTION PAPER *3134014001* INSTRUCTIONS TO CANDIDATES These instructions are the same on the Printed Answer Book and theQuestion Paper.
PAPER REFERENCE(S) 6684/01 EDEXCEL GCE P40106A 2 1. A manufacturer produces sweets of length L mm where L has a continuous unifrom distribution with range . (a) Find the probability that a randomly selected sweet has length greater than 24 mm. (2) These sweets are randomly packed in bags of 20 sweets. (b) Find the probability that a randomly selected bag will contain at least 8 sweets with length ADVANCED SUBSIDIARY GCE MATHEMATICS 4728 2 1 A particle P is projected vertically downwards from a fixed point O with initial speed 4.2ms−1, and takes 1.5s to reach the ground. Calculate (i) the speed of P when it reaches the ground, (ii) the height of O above the ground, (iii) the speed of P when it is 5m above the ground. 2 Two horizontal forces of magnitudes 12N and 19N act at a point. Given that the angle between the USE THIS AS A GUIDE AS TO HOW MUCH TIME TO SPEND ON EACH P46710A 5 ©2016 Pearson Education Ltd. 6. A particle P is projected from a fixed origin O with velocity (3i + 4j) m s−1.The particle moves freely under gravity and passes through the point A with position vector λ(i – j) m, where λ is a positiveconstant.
PAPER REFERENCE(S) 6683/01 EDEXCEL GCE N29283A 4 3. The histogram in Figure 1 shows the time taken, to the nearest minute, for 140 runners to complete a fun run. Figure 1 Use the histogram to calculate the PAPER REFERENCE(S) 6678 EDEXCEL GCE N35391A 2 1. A particle P moves on the x-axis.The acceleration of P at time t seconds, t ≥ 0, is (3t + 5) m s–2 in the positive x-direction.When t = 0, the velocity of P is 2 m s–1 in the positive x-direction.When t = T, the velocity of P is 6 m s–1 in the positive x-direction. Find the value of T. (6) 2. A particle P of mass 0.6 kg is released from rest and slides down a line of PAPER REFERENCE(S) 6683/01 EDEXCEL GCE P41805A 5 Turn over 6. A fair blue die has faces numbered 1, 1, 3, 3, 5 and 5. The random variable B represents the score when the blue die is rolled. (a) Write down the probability distribution for B.(2) (b) State the name of this probability distribution.(1) (c) Write down the value of E(B).(1) A second die is red and the random variable R represents the score when the red die is rolled. PAPER REFERENCE(S) 6678/01 EDEXCEL GCE P43997A 2 1. A particle P of mass 2 kg is moving with velocity (i – 4j) m s–1 when it receives an impulse of (3i + 6j) N s. Find the speed of P immediately after the impulse is applied. (5) 2. A particle P of mass 3 kg moves from point A to point B up a line of greatest slope of a fixed rough plane. The plane is inclined at 20° to the horizontal. The coefficient of friction betwee TUESDAY 16 JUNE 2015 Tuesday 16 June 2015 – Afternoon A2 GCE MATHEMATICS 4724/01 Core Mathematics 4 QUESTION PAPER *3170296828* INSTRUCTIONS TO CANDIDATES These instructions are the same on the Printed Answer Book and theQuestion Paper.
PAPER REFERENCE(S) 6684/01 EDEXCEL GCE P44846A 5 Turn over 5. Liftsforall claims that the lift they maintain in a block of flats breaks down at random at a mean rate of 4 times per month. To test this, the number of times the lift breaks down in a month is recorded. (a) Using a 5% level of significance, find the critical region for a two-tailed test of the null hypothesis that ‘the mean rate at which the lift breaks down is 4 THURSDAY 12 JUNE 2014 Thursday 12 June 2014 – Afternoon AS GCE MATHEMATICS 4728/01 Mechanics 1 QUESTION PAPER *3134014001* INSTRUCTIONS TO CANDIDATES These instructions are the same on the Printed Answer Book and theQuestion Paper.
PAPER REFERENCE(S) 6684/01 EDEXCEL GCE P40106A 2 1. A manufacturer produces sweets of length L mm where L has a continuous unifrom distribution with range . (a) Find the probability that a randomly selected sweet has length greater than 24 mm. (2) These sweets are randomly packed in bags of 20 sweets. (b) Find the probability that a randomly selected bag will contain at least 8 sweets with lengthMATHSHELPER
Welcome to www.mathshelper.co.uk, the 3,457,341st best mathematical website in the world. I hope you will find the content useful. I am absolutely rubbish at web design (no cookies to worry about here); the site is little more than a shell to host the documents that I think are useful. Someone recently described the site as "No frills", and I PAPER REFERENCE(S) 6683/01 EDEXCEL GCE P41805A 3 Turn over 3. A biologist is comparing the intervals (m seconds) between the mating calls of a certain species of tree frog and the surrounding temperature (t °C).The following results were obtained. t °C 8 13 14 15 15 20 25 30 m secs 6.5 4.5 6 5 4 3 2 1 (Youmay use ¦
USE THIS AS A GUIDE AS TO HOW MUCH TIME TO SPEND ON EACH P46710A 5 ©2016 Pearson Education Ltd. 6. A particle P is projected from a fixed origin O with velocity (3i + 4j) m s−1.The particle moves freely under gravity and passes through the point A with position vector λ(i – j) m, where λ is a positiveconstant.
TUESDAY 21 JUNE 2016 Tuesday 21 June 2016 – Morning A2 GCE MATHEMATICS 4723/01 Core Mathematics 3 QUESTION PAPER *4827937481* INSTRUCTIONS TO CANDIDATES These instructions are the same on the Printed Answer Book and theQuestion Paper.
TUESDAY 16 JUNE 2015 Tuesday 16 June 2015 – Afternoon A2 GCE MATHEMATICS 4724/01 Core Mathematics 4 QUESTION PAPER *3170296828* INSTRUCTIONS TO CANDIDATES These instructions are the same on the Printed Answer Book and theQuestion Paper.
ADVANCED SUBSIDIARY GCE MATHEMATICS 4728 3 4 An object is projected vertically upwards with speed 7ms−1.Calculate (i) the speed of the object when it is 2.1m above the point of projection, (ii) the greatest height above the point of projection reached by the object, (iii) the time after projection when the object is travelling downwards with speed 5.7ms−1. 5 (i) Q P m kg 0.5 kg 6 m s–1 PAPER REFERENCE(S) 6684/01 EDEXCEL GCE P42035A 3 Turn over 3. An online shop sells a computer game at an average rate of 1 per day. (a) Find the probability that the shop sells more than 10 games in a 7 day period.(3) Once every 7 days the shop has games delivered before it opens.OCR 4733 JUNE09
2 1 The random variable H has the distribution N(µ, σ2).ItisgiventhatP(H < 105.0)=0.2420 and P(H > 110.0)=0.6915.Find thevalues of µ and σ
FRIDAY 25 JANUARY 2013 4728 Mark Scheme January 2013 5 Question Answer Marks Guidance 1 X = 14 – 5 B1 Or 5 – 14 R2 = (14 – 5)2 + 122 M1 Pythagoras, R as hypotenuse, 3 squared terms R = 15 N A1 tanθ = (14 – 5)/12 M1 Any correct trig, angle between 12 and R targetted. WEDNESDAY 8 JUNE 2016 Wednesday 8 June 2016 – Morning AS GCE MATHEMATICS 4732/01 Probability & Statistics 1 QUESTION PAPER *4827193828* INSTRUCTIONS TO CANDIDATES These instructions are the same on the Printed Answer Book and the Question Paper. PAPER REFERENCE(S) 6683/01 EDEXCEL GCE N29283A 4 3. The histogram in Figure 1 shows the time taken, to the nearest minute, for 140 runners to complete a fun run. Figure 1 Use the histogram to calculate the ADVANCED SUBSIDIARY GCE MATHEMATICS 4728 2 1 A particle P is projected vertically downwards from a fixed point O with initial speed 4.2ms−1, and takes 1.5s to reach the ground. Calculate (i) the speed of P when it reaches the ground, (ii) the height of O above the ground, (iii) the speed of P when it is 5m above the ground. 2 Two horizontal forces of magnitudes 12N and 19N act at a point. Given that the angle between the USE THIS AS A GUIDE AS TO HOW MUCH TIME TO SPEND ON EACH P46710A 5 ©2016 Pearson Education Ltd. 6. A particle P is projected from a fixed origin O with velocity (3i + 4j) m s−1.The particle moves freely under gravity and passes through the point A with position vector λ(i – j) m, where λ is a positiveconstant.
PAPER REFERENCE(S) 6678 EDEXCEL GCE N35391A 2 1. A particle P moves on the x-axis.The acceleration of P at time t seconds, t ≥ 0, is (3t + 5) m s–2 in the positive x-direction.When t = 0, the velocity of P is 2 m s–1 in the positive x-direction.When t = T, the velocity of P is 6 m s–1 in the positive x-direction. Find the value of T. (6) 2. A particle P of mass 0.6 kg is released from rest and slides down a line of PAPER REFERENCE(S) 6678/01 EDEXCEL GCE P43997A 2 1. A particle P of mass 2 kg is moving with velocity (i – 4j) m s–1 when it receives an impulse of (3i + 6j) N s. Find the speed of P immediately after the impulse is applied. (5) 2. A particle P of mass 3 kg moves from point A to point B up a line of greatest slope of a fixed rough plane. The plane is inclined at 20° to the horizontal. The coefficient of friction betwee PAPER REFERENCE(S) 6683/01 EDEXCEL GCE P41805A 5 Turn over 6. A fair blue die has faces numbered 1, 1, 3, 3, 5 and 5. The random variable B represents the score when the blue die is rolled. (a) Write down the probability distribution for B.(2) (b) State the name of this probability distribution.(1) (c) Write down the value of E(B).(1) A second die is red and the random variable R represents the score when the red die is rolled. PAPER REFERENCE(S) 6684/01 EDEXCEL GCE P40106A 2 1. A manufacturer produces sweets of length L mm where L has a continuous unifrom distribution with range . (a) Find the probability that a randomly selected sweet has length greater than 24 mm. (2) These sweets are randomly packed in bags of 20 sweets. (b) Find the probability that a randomly selected bag will contain at least 8 sweets with length TUESDAY 16 JUNE 2015 Tuesday 16 June 2015 – Afternoon A2 GCE MATHEMATICS 4724/01 Core Mathematics 4 QUESTION PAPER *3170296828* INSTRUCTIONS TO CANDIDATES These instructions are the same on the Printed Answer Book and theQuestion Paper.
PAPER REFERENCE(S) 6684/01 EDEXCEL GCE P44846A 5 Turn over 5. Liftsforall claims that the lift they maintain in a block of flats breaks down at random at a mean rate of 4 times per month. To test this, the number of times the lift breaks down in a month is recorded. (a) Using a 5% level of significance, find the critical region for a two-tailed test of the null hypothesis that ‘the mean rate at which the lift breaks down is 4 THURSDAY 12 JUNE 2014 Thursday 12 June 2014 – Afternoon AS GCE MATHEMATICS 4728/01 Mechanics 1 QUESTION PAPER *3134014001* INSTRUCTIONS TO CANDIDATES These instructions are the same on the Printed Answer Book and theQuestion Paper.
PAPER REFERENCE(S) 6683/01 EDEXCEL GCE N29283A 4 3. The histogram in Figure 1 shows the time taken, to the nearest minute, for 140 runners to complete a fun run. Figure 1 Use the histogram to calculate the ADVANCED SUBSIDIARY GCE MATHEMATICS 4728 2 1 A particle P is projected vertically downwards from a fixed point O with initial speed 4.2ms−1, and takes 1.5s to reach the ground. Calculate (i) the speed of P when it reaches the ground, (ii) the height of O above the ground, (iii) the speed of P when it is 5m above the ground. 2 Two horizontal forces of magnitudes 12N and 19N act at a point. Given that the angle between the USE THIS AS A GUIDE AS TO HOW MUCH TIME TO SPEND ON EACH P46710A 5 ©2016 Pearson Education Ltd. 6. A particle P is projected from a fixed origin O with velocity (3i + 4j) m s−1.The particle moves freely under gravity and passes through the point A with position vector λ(i – j) m, where λ is a positiveconstant.
PAPER REFERENCE(S) 6678 EDEXCEL GCE N35391A 2 1. A particle P moves on the x-axis.The acceleration of P at time t seconds, t ≥ 0, is (3t + 5) m s–2 in the positive x-direction.When t = 0, the velocity of P is 2 m s–1 in the positive x-direction.When t = T, the velocity of P is 6 m s–1 in the positive x-direction. Find the value of T. (6) 2. A particle P of mass 0.6 kg is released from rest and slides down a line of PAPER REFERENCE(S) 6678/01 EDEXCEL GCE P43997A 2 1. A particle P of mass 2 kg is moving with velocity (i – 4j) m s–1 when it receives an impulse of (3i + 6j) N s. Find the speed of P immediately after the impulse is applied. (5) 2. A particle P of mass 3 kg moves from point A to point B up a line of greatest slope of a fixed rough plane. The plane is inclined at 20° to the horizontal. The coefficient of friction betwee PAPER REFERENCE(S) 6683/01 EDEXCEL GCE P41805A 5 Turn over 6. A fair blue die has faces numbered 1, 1, 3, 3, 5 and 5. The random variable B represents the score when the blue die is rolled. (a) Write down the probability distribution for B.(2) (b) State the name of this probability distribution.(1) (c) Write down the value of E(B).(1) A second die is red and the random variable R represents the score when the red die is rolled. PAPER REFERENCE(S) 6684/01 EDEXCEL GCE P40106A 2 1. A manufacturer produces sweets of length L mm where L has a continuous unifrom distribution with range . (a) Find the probability that a randomly selected sweet has length greater than 24 mm. (2) These sweets are randomly packed in bags of 20 sweets. (b) Find the probability that a randomly selected bag will contain at least 8 sweets with length TUESDAY 16 JUNE 2015 Tuesday 16 June 2015 – Afternoon A2 GCE MATHEMATICS 4724/01 Core Mathematics 4 QUESTION PAPER *3170296828* INSTRUCTIONS TO CANDIDATES These instructions are the same on the Printed Answer Book and theQuestion Paper.
PAPER REFERENCE(S) 6684/01 EDEXCEL GCE P44846A 5 Turn over 5. Liftsforall claims that the lift they maintain in a block of flats breaks down at random at a mean rate of 4 times per month. To test this, the number of times the lift breaks down in a month is recorded. (a) Using a 5% level of significance, find the critical region for a two-tailed test of the null hypothesis that ‘the mean rate at which the lift breaks down is 4 THURSDAY 12 JUNE 2014 Thursday 12 June 2014 – Afternoon AS GCE MATHEMATICS 4728/01 Mechanics 1 QUESTION PAPER *3134014001* INSTRUCTIONS TO CANDIDATES These instructions are the same on the Printed Answer Book and theQuestion Paper.
OXBRIDGE - MATHSHELPER.CO.UK Oxbridge. STEP. STEP is the Sixth Term Entrance Paper, originally used by Cambridge University as an exam sat alongside A Levels. It was usually included in offers given to Mathematics candidates. STEP I 1987 STEP II 1987 STEP III 1987. STEP I 1988 STEP II 1988 STEP III1988. STEP I
USE THIS AS A GUIDE AS TO HOW MUCH TIME TO SPEND ON EACH P46710A 5 ©2016 Pearson Education Ltd. 6. A particle P is projected from a fixed origin O with velocity (3i + 4j) m s−1.The particle moves freely under gravity and passes through the point A with position vector λ(i – j) m, where λ is a positiveconstant.
LINE INTERSECTIONS
Line Intersections Find the intersection of the following lines. 1. y = 3x 2 and y = x +4. (x; y) = (32; 5 2) 2. y = 5x +1 and y = x 3. (x;y) = (23
TUESDAY 21 JUNE 2016 Tuesday 21 June 2016 – Morning A2 GCE MATHEMATICS 4723/01 Core Mathematics 3 QUESTION PAPER *4827937481* INSTRUCTIONS TO CANDIDATES These instructions are the same on the Printed Answer Book and theQuestion Paper.
PAPER REFERENCE(S) 6684/01 EDEXCEL GCE P42035A 3 Turn over 3. An online shop sells a computer game at an average rate of 1 per day. (a) Find the probability that the shop sells more than 10 games in a 7 day period.(3) Once every 7 days the shop has games delivered before it opens. PAPER REFERENCE(S) 6691/01 EDEXCEL GCE P40472A 3 Turn over 3. (a) Explain what you understand by the Central Limit Theorem.A garage services hire cars on behalf of a hire company. The garage knows that the lifetime of the brake pads has a standard deviation of 5000 miles. TUESDAY 16 JUNE 2015 Tuesday 16 June 2015 – Afternoon A2 GCE MATHEMATICS 4724/01 Core Mathematics 4 QUESTION PAPER *3170296828* INSTRUCTIONS TO CANDIDATES These instructions are the same on the Printed Answer Book and theQuestion Paper.
PAPER REFERENCE(S) 6686/01 EDEXCEL GCE P35418A 2 1. Find the value of the constant a such that P(a < F8, 10 < 3.07) = 0.94.(2) 2. Two independent random samples , , , and , , , were taken from different normal populations with a common standard deviation σ. The following sample statistics were calculated. PAPER REFERENCE(S) 6679 EDEXCEL GCE N29501A 4 4. Figure 3 A uniform solid hemisphere, of radius 6a and centre O, has a solid hemisphere of radius 2a, and centre O, removed to form a bowl B as shown in Figure 3. (a) Show that the centre of mass of B is a from O.(5) Figure 4 The bowl B is fixed to a plane face of a uniform solid cylinder made from the same material as B.The cylinder has radius 2a and height 6a and the combined OXFORD CAMBRIDGE AND RSA WEDNESDAY 20 MAY 2015 4722 Mark Scheme June 2015 Question Answer Marks Guidance 3 (i) sector = 1/ 2 × 8 2 × 1.2 (= 38.4) M1* Attempt area of sector using ½ r2θ, or equiv . Must be correct formula, including ½ M0 if 1.2π used not 1.2. M0 if ½ r2θ used with θ in degrees . Allow equiv method using fractions of a circle MATHSHELPER FOR STUDENTSHOME PAGE
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