Pythagoas Volume of cone = Theoem c a a + b = c hyp coss section adj b opp length Intenational GCSE MATHEMATICS FORMULAE SHEET HIGHER TIER Cuved suface aea of cone = adj = hyp opp = hyp opp = adj o sin cos tan cos sin tan opp hyp adj hyp opp adj 1 3 h Volume of pism = aea of coss section h Cicumfeence of cicle = Aea of cicle = Volume of cylinde = h Cuved suface aea of cylinde = h l A b a Sine ule: sin A Cosine ule: a b + c bc cos A length Aea of tiangle c C b sin B Aea of a tapezium = a h b a B c sin C ab sin C 1 (a+b)h The Quadatic Equation The solutions of ax + bx + c 0, whee a 0, ae given by x Volume of sphee = b+ b 4ac a 1 4 3 3 l Suface aea of sphee = 4 h In any tiangle ABC *P48406A04*
6 The table gives infomation about the distances, in kilometes, Daen tavelled to delive 100 pacels. 7 Distance tavelled (d km) Fequency 0 d 5 8 5 d 10 10 d 15 0 15 d 0 14 0 d 5 6 Wok out an estimate fo the mean distance Daen tavelled to delive these pacels....km (Total fo Question 6 is 4 maks) Wok out the diffeence between the amount eceived by Rachel and the amount eceived by Sanjit.... (Total fo Question 7 is 3 maks) *P48406A074* 7 Tun ove
8 (a) On the gid, daw the gaph of yx + 4 fo values of x 1 y 7 6 5 4 1 O 1 4 5 6 x 1 4 5 6 7 (b) Show by shading on the gid, the egion defined by all thee of the inequalities y x + 4 y x 1 Label you egion R. (4) (3) (Total fo Question 8 is 7 maks) 8 *P48406A084*
9 Simplify (x xx 5) Give you answe in the fom ax + bx + c 10 In a sale, nomal pices ae educed by 18% Wok out the nomal pice of the umbella.... (Total fo Question 9 is 3 maks)... (Total fo Question 10 is 3 maks) *P48406A094* 9 Tun ove
1 A, B, C and D ae points on a cicle with cente O. Angle ABC = 48 (a) (i) Calculate the size of angle x. A D (ii) Give a eason fo you answe. x O C 48 B Diagam NOT accuately dawn......... () (b) (i) Calculate the size of angle ADC. (ii) Give a eason fo you answe.......... () (Total fo Question 1 is 4 maks) 1 *P48406A014*
13 14 T is diectly popotional to x T = 400 when x = 65 (a) Find a fomula fo T in tems of x. (b) Calculate the value of T when x = 56.5 $... (Total fo Question 13 is 3 maks)... (3)... (1) (Total fo Question 14 is 4 maks) *P48406A0134* 13 Tun ove
16 The diagam shows two mathematically simila pots, A and B. 8 cm A A has a volume of 64 cm B A has a height of 8 cm (a) Wok out the height of pot B. B (b) Wok out the suface aea of pot A. B Diagam NOT accuately dawn...cm ()...cm () (Total fo Question 16 is 4 maks) *P48406A0154* 15 Tun ove
17 Solve the equation 5x + 8x Show you woking clealy. 18 The cuve with equation y = 10x x + 5 has a minimum at point A. Find the coodinates of A. Show you woking clealy.... (Total fo Question 17 is 3 maks) (...,...) (Total fo Question 18 is 4 maks) 16 *P48406A0164*
1 The Venn diagam shows a univesal set E and sets A, B and C epesent numbes of elements. (a) Find n(a B) E (b) Find n((a C) B) 4 A 6 (c) On the Venn diagam, shade the egion that epesents the set (A B) C 5 8 C 7 B... (1)... (1) (1) (Total fo Question 1 is 3 maks) 18 *P48406A0184*
75 The diagam shows a secto OAB of a cicle, cente O. Angle AOB = 75 Length of ac AB = 7. cm Calculate the aea of the secto. O A 7. cm B Diagam NOT accuately dawn...cm (Total fo Question is 4 maks) *P48406A0194* 19 Tun ove
3 Solve the simultaneous equations Show clea algebaic woking. x + y = 5 x + y = 8... (Total fo Question 3 is 6 maks) 0 *P48406A004*
4 The diagam shows thee boxes containing beads. Box A Box B Box C Tim takes at andom a bead fom box A and puts it into box B. He then takes at andom a bead fom box B and puts it into box C. Finally, he takes at andom a bead fom box C and puts it into box A. the thee boxes.... (Total fo Question 4 is 3 maks) TOTAL FOR PAPER IS 100 MARKS *P48406A014* 1