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A-level FURTHER MATHEMATICS Paper 1 Time allowed: 2 hours Materials l You must have the AQA Formulae and statistical tables booklet for A‑level Mathematics and A‑level Further Mathematics. l You should have a graphical or scientific calculator that meets the requirements of the specification. Instructions l Use black ink or black ball‑point pen. Pencil should only be used for drawing. l Fill in the boxes at the top of this page. l Answer all questions. l You must answer each q...

AS FURTHER MATHEMATICS Paper 2 Statistics Friday 19 May 2023 Afternoon Time allowed: 1 hour 30 minutes Materials l You must have the AQA Formulae and statistical tables booklet for A‑level Mathematics and A‑level Further Mathematics. l You should have a graphical or scientific calculator that meets the requirements of the specification. l You must ensure you have the other optional Question Paper/Answer Book for which you are entered (either Discrete or Mechanics). You will have 1...

AS FURTHER MATHEMATICS Paper 2 Mechanics Friday 19 May 2023 Afternoon Time allowed: 1 hour 30 minutes Materials l You must have the AQA Formulae and statistical tables booklet for A‑level Mathematics and A‑level Further Mathematics. l You should have a graphical or scientific calculator that meets the requirements of the specification. l You must ensure you have the other optional Question Paper/Answer Book for which you are entered (either Discrete or Statistics). You will have 1...

Answer all questions in the spaces provided. 1 Which expression below is equivalent to tanh x ? Circle your answer. [1 mark] sinh x cosh x sinh x cosh x cosh x sinh x sinh x + cosh x 2 The two vectors a and b are such that a.b = 0 State the angle between the vectors a and b Circle your answer. [1 mark] 0° 45° 90° 180° 3 Do not write outside the box (03) G/Jun23/7366/1 Turn over 8 3 The matrices A and B are given by A = [ 3 1 ] 0 5 B = [ 0 4] 7 1 Calculate AB Circl...

Section A Answer all questions in the spaces provided. 1 The graph of y ¼ f (x) is shown below. O y x One of the four equations listed below is the equation of the graph y ¼ f (x) Identify which one is the correct equation of the graph. Tick (3) one box. [1 mark] y ¼ jx þ 2j þ 3 y ¼ jx þ 2j 3 y ¼ jx 2j þ 3 y ¼ jx 2j 3 Jun23/7357/3 Do not write outside the box (02) 3 2 The trapezium rule is used to estimate the area of the shaded region in each of the graphs bel...

Section A Answer all questions in the spaces provided. 1 The graph of y ¼ f (x) is shown below. O y x One of the four equations listed below is the equation of the graph y ¼ f (x) Identify which one is the correct equation of the graph. Tick (3) one box. [1 mark] y ¼ jx þ 2j þ 3 y ¼ jx þ 2j 3 y ¼ jx 2j þ 3 y ¼ jx 2j 3 Jun23/7357/3 Do not write outside the box (02) 3 2 The trapezium rule is used to estimate the area of the shaded region in each of the graphs bel...

ection A Answer all questions in the spaces provided. 1 The graph of y ¼ ax2 þ bx þ c has roots x ¼ 2 and x ¼ 5 , as shown in the diagram below. O 2 5 y x State the set of values of x which satisfy ax2 þ bx þ c > 0 Tick (3) one box. [1 mark] fx : x < 2g ¨ fx : x > 5g fx : 0 < x < 2g ˙ fx : x > 5g fx : 2 < x < 5g fx : 2 > x > 5g Jun23/7357/2 Do not write outside the box (02) 3 2 It is given that ð6 0 f (x) dx ¼ 20 and ð6 3 f (x) ...

Section A Answer Question 01. Extract A The Crusader States were the result of religious enthusiasm in the West. Many pilgrims rushed to Outremer as soon as the capture of Jerusalem in 1099 became known. Nowhere else were there so many sites so important to Christians, nor was there a better place to end one’s days. They did not come alone because the people who hoped to survive on the charity of pilgrims and the institutions created to help them also went. During the summer, the ports...

Section A Answer Question 01. Source A From the memoirs of Bolshakov, published in Pravda, February 1989. Bolshakov was an intelligence officer in the Soviet Embassy in Havana at the time of the 1962 Cuban Missile Crisis. The events of October 1962 were the first and, fortunately, only nuclear crisis in our history, a moment of fear and illumination. Nikita Khrushchev, John Kennedy, Fidel Castro and the whole of mankind felt that for the first time they were in the same boat at the epic...

Section A Answer Question 01. Source A From the memoirs of Bolshakov, published in Pravda, February 1989. Bolshakov was an intelligence officer in the Soviet Embassy in Havana at the time of the 1962 Cuban Missile Crisis. The events of October 1962 were the first and, fortunately, only nuclear crisis in our history, a moment of fear and illumination. Nikita Khrushchev, John Kennedy, Fidel Castro and the whole of mankind felt that for the first time they were in the same boat at the epic...