OCR GCE A LEVEL 2022 MATHEMATICS A QUESTION PAPER H240-02 PAPER 2-H240/02 Pure Mathematics and Statistics

Arithmetic series S n a l n a2 1 n d n 2 1 2 1 = + ^ ^ h h = + " - , Geometric series S r a r 1 1 n n = - ^ - h S r a 1 = 3 - for r 1 1 Binomial series a b a a C C b a b a C b b n N n n n n n n n r n ...

Arithmetic series S n a l n a2 1 n d n 2 1 2 1 = + ^ ^ h h = + " - , Geometric series S r a r 1 1 n n = - ^ - h S r a 1 = 3 - for r 1 1 Binomial series a b a a C C b a b a C b b n N n n n n n n n r n r r n 1 1 2 + = + + 2 2 + + f f+ + ! - - - ^ ^ h h, where ! ! ! C n r r n r n C n r n r = = = - J L K K ^ N P O O h ! ! x nx , n n x r n n n r 1 1 x x n 2 1 1 1 1 R + =n + + 2 f f r f 1 ! - + + - - + ^ + ^ ^ ^ h ^ h h h h Differentiation tan kx k k sec x 2 sec t x x an cosec x 2 - -cosec c x x ot sec x cot x cosec x f^xh fl^xh Quotient rule y v u = , x y v v x u u x v d d d d d d = 2 - Differentiation from first principles x lim h x h x f f f h 0 = + - " l^ ^ ^ h h h Integration ln x x x x c f f d f = + c l e dd ^ ^ ^ h h h x x x n x c 1 1 f f d f n n 1 = + + + ; l^ h h a ^ k a ^ hk Integration by parts u x v x uv v x u x d d d d d ; ; = - d Small angle approximations sin i i . , cos 1 2 1 2 i i . - , tan i i . where i is measured in radians 3 © OCR 2022 H240/02 Jun22 Turn over Trigonometric identities sin s ^A B ! ! h = inA B cos cosA B sin cos c ^A B ! " h = osA B cos sinA B sin tan tan tan tan tan A B A B A B 1 ! " ! ^ h = A B k 2 1 a ! ! ^ + hrk Numerical methods Trapezium rule: y xd h y y y 2 y y a b 2 n n 1 . 0 1 + + + +2 1 f+ ^ ^ - y " h h,, where h n b a = - The Newton-Raphson iteration for solving f^xh = 0: x x x x f f n n n n 1 = - + l ^ ^ h h Probability P P ^ ^ A B, + h h = + A B P P ^ ^ h h - A B P P ^ ^ A B+ h h = = A B P P ^ A B h ^ hP^A Bh or A B B A B P P P + ^ = ^ ^ h h h Standard deviation n x n x x x 2 2 2 - = - /^ h / or f f x x f fx x 2 2 - = - 2 ^ h / / / / The binomial distribution If X + B^n p, h then P X x n x p p 1 x n x = = - - J L K ^ ^ K N P O h h O , mean of X is np, variance of X is np^1-ph Hypothesis test for the mean of a normal distribution If X N , 2 + ^n v h then X , n N 2 + n v J L K K N P O O and , n X + N 0 1 v -n ^ h Percentage points of the normal distribution If Z has a normal distribution with mean 0 and variance 1 then, for each value of p, the table gives the value of z such that P^Z z G h = p. 0.75 0.90 0.95 0.674 1.282 1.645 0.975 0.99 0.995 1.960 2.326 2.576 0.9975 0.999 0.9995 2.807 3.090 3.291 p z Kinematics Motion in a straight line Motion in two dimensions v u = +at v u = +at s ut at 2 1 2 = + s ut t a2 1 2 = + s u v t 2 1 = + ^ h s u v t 2 1 = + ^ h v u 2as 2 2 = + s vt at 2 1 2 = - s vt t a2 1 2 = - 4 © OCR 2022 H240/02 Jun2