GCSE Cheat Sheet Revision, Cheat Sheet of Music

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r Please check the examination details below before entering your candidate information (Candidate surname Other names ] x. Centre Number Candidate Number Practice Paper Level 1/2 GCSE (9-1) ~ ~, [ Grade 7-9 Aimed Paper Morning (Time: 1 hour 30 minutes) Paper reference r s Mathematics PAPER 1 (Non-Calculator) Higher Tier \. ( You must have: Ruler graduated in centimetres and millimetres, Total Marks ) protractor, pair of compasses, pen, HB or B pencil, eraser, Formulae Sheet (enclosed). Tracing paper may be used. ) XM Instructions @ Use black ink or ball-point pen. @ if pencil is used for diagrams/sketches/graphs it must be dark (HB or B). @ Fill in the boxes at the top of this page with your name, centre number and candidate number. @ Answer all questions. ®@ Answer the questions in the spaces provided — there may be more space than you need. @ You must show all your working. ® Diagrams are NOT accurately drawn, unless otherwise indicated. ® Calculators may not be used. Information @ The total mark for this paper is 80 @ The marks for each question are shown in brackets ao — use this as a guide as to how much time to spend on each question. Your Advice GCSE @ Read each question carefully before you start to answer it. MATHS @ Try to answer every question. 7 @ Check your answers if you have time at the end. 10 NOTWRITE INTHIS AREA DO NOTWRITE INTHIS AREA’ = _E 2 le} Zz ry [2] Ql Qo Q3 Q4 Qs Q6 Q7 Qs Qo Q10 Qu Ql2 Qu3 Qld Qus Q16 Qu7 Qs Qug Q20 Q21 Q22 Q23 Qu List of Topics Total for paper: 80 marks Raticomaabisingy sssssscs:ccsssz:scssczecsazssszscstestenesseceasazzecsaaetnezsiszesanssueteeatestisatssscaaasreeeceanes (Q/8)) Area of a Non-Right Angle Triangle .. . (/2) MBSUMRCEL ONS ces sszbesaszcnsscceca cdots tspela erat descdstecedeetce seu reransacss gustan aba sssceazs basal trentets eteeisscoll (PROD) RReetitartn DMC Catrall cscs 5sccasnscasssssedsccssseesccasececusscbsssecocjssadsasss oes:ceessesecsoseesseedaesesall MOM . 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Flistoopreamashsssscss;ssasscscassssssesesseszszsesuss;suszeusznecszscasstanasenspestasasuasssens eesazapsremmams eeeseaset (HAD) Equatini Alpe braic Fractions) 2:.22:::0:sssesteséetssessnssseisseztosa tte) sovasttnssecos desoundonsieszstaasdl (AD) C/A) Hpaeccot) Brey pennt nd cs socecsssestzds ches, enistecs i sesssustzssSevosts soles esmauase, remteoeareees asec ssscsed ND) Transforming Graphs with Vectors (Ti etme Mee etneat tease bales rrteeen tbe crc nebs teenie rt ererczed AUS) Wreration/Ohanee OF Sigiisssissssssssctessstssssssssssssestessessstisainisiaitinsar masini (UZ) Quadratic Sequence (mth Terna)) ssssssssscsssssscassssccossssssesssseescossssstaassssetessssssenmaaniaeesseeee (73) Algebraic Proof sse:ss:c::sississcissiiannininisaiapninimnnisaunanacan (5) Simla) Shapes) e::::cc::s:s:sssetsssecessasszgactectasszsstecsessassesaectetesassseatecteetissnssassrascecasestaees (3) (Gyragnedeitne mnesepeael AE CS We see sseetSaasszeceteteyebc a eat ctceaatenbadheeseaieeea ah veonstatteantentneretatzereel (I) Trigonometry (Cosine Rite) oo... osesccssssssssssccesssnsssessssesensssasessenssseecsesnaserseneceeas (3) Circle Theorems (Fitid! Angle)) ..........css-ssssssesseensessscesssseesasssseccsssesseessnssssseneereeceseneee (JA) Circle Theorems (Proof) ...........ssssssssccnsssossecoseccnesscseeesssecsansssansecenseccnseesssssnenrsseesseee ( JA) Vectors (Coniporicnt Forni) .......:..sces:csesssesccnseccoasscsasescnsesscosstussccesseconsssersacceassecsesess (if ll} Probability (Conditional) jsss:sscs:ssssssssssss;sestesasiccustiasssstisssiseissntiacnamaiecan (IAD) TOPAL) cx:scicssscas: 180 0 000800 0 20 Answer ALL questions. Write your answers in the spaces provided. You must write down all the stages in your working. 1 Rationalise the denominator: 5 243 (Total for Question 1 is 3 marks) ; AN OA Pres is ew O22 4 VaUv. SIH NESLIM LON OG Wau SIKE NISLIUM LON-OG 22 WSN -SIHL NI SLUM LON OG A rectangular metal sheet has length 1.2 m and width 0.75 m. (a) Work out the area of the sheet. (b) The sheet has a thickness of 4 mm. The density of the metal is 7800 kg/m’. Work out the mass of the sheet. wininicisnas HP (@Q) . kg (3) (Total for Question 2 is 5 marks) 2 P75 15 6 A022 4 Wid SIHINISLYM LON OG VauV SIHL NISLIYM LON-OG WAU: SIHL NPALIM LON-OG DONOTWRITEINTHISAREA © = =—~ DONOTWRITEINTHISAREA | DONOTWRITEINTHISAREA = a 4 The functions f and g are defined by f(x) = 3x —2 a(x) =x +1 Find an expression for f(g(x)). Give your answer in its simplest form. (Total for Question 4 is 3 marks) XN } el Prs 15 8 A oO 2 2 4 4 _ DONOTWRITE INTHIS AREA \ The number x is such that a) Show that x = Tr Given that y = 2x + 5. b) Find the value of y. Q) Q) (Total for Question 5 is 4 marks) J Ce 0g 00 040 90 0 5 7 The diagram shows a sector of a circle. Formula for the area of a sector “360° 7 A B where @ is the angle in degrees and r is the radius. 15cm oO Calculate the area of the sector AOB. Give your answer in terms of 7 and in its simplest form. secu (CHE (Total for Question 7 is 4 marks) DONOT WRITE INTHIS ARE: SA J NNN 01 0 8 ’ Once P7515 8 AO 22 4 va 8 The diagram shows the curve y = x° — 2x + 1. The point P (3, 4) lies on the curve. > ae y S a F pu =x = 24+ 1 = yrx E: — uw: = — z PG,4) Bo} = oO a cS > ao 7) bs ed r a Find the equation of the tangent to the curve at the point P (3, 4). pS 5 Give your answer in the form y = mx + c, where m and c are integers or simplified fractions. at = es ae} Ee) 2: ¢< TE cH os a es e = ce a (Total for Question 8 is 4 marks) ) = 0 ao {OORT : ee lik Zam a! ie _ DONOTWRITEINTHISAREA __ 5 a < 2 = -E 2 = & = 3 = A) a _DONOTWRITE INTHIS ARE to complete a test. | 10 The table shows information about the lengths of time, in minutes, taken by students Time (minutes) ry USES Z On the grid, draw a histogram to 10< t = 20 5 represent this information. 20<1< 40 3 2) 40<1<55 1.5 55<1<70 2.5 A 6 5 — lp bensna tosses sscnnseeceeatsnaesneaseccnsendseancas density 3 | 1 sa 10 20 3040 50 60 70 Time (minutes) 11 Solve the equation 2x = 1 " 3 a x+2 x-1 Show all your working. Give your answers as exact values. (4) x= saiaminis OF be! = ysis nammniiasiaisnareTaeH (Total for Question 11 is 4 marks) — = 00008 00 r | 12. The diagram shows triangle ABC on a coordinate grid. 3 The triangle is transformed by the translation i: ) A z= 5 i 2 4 5 4 3 2 NS : 2} 6 2 B x 4 3 2 -1 0 re2 @ 4 35.6 : = : z 2 wy = = 2 “A 1 i Write down the coordinates of the image of each vertex. S AN Geer ctr ee il octet ase anaes) E 2 B'( ) (2) ~ | 13 yis directly proportional to x. When x = 6, y = 15. (a) Find an equation connecting y and x, (2) (b) Use your equation to complete the table of values. x 0 3 6 9 12 be 0 15 a) (Total for Question 13 is 3 marks) |W! 0 0 A uh Onc PT oi 6) 8 A O22 4 15 Show that the equation we-x-4=0 has a solution between x = | and x = 2. Explain how you obtained your answer. (1) Q) 16 Here are the first five terms of a quadratic sequence. 4 13 26 43 Find an expression, in terms of n, for the nth term of this sequence. QB) 14 ! TM me M90 01008 00 0010 0 0 ae 17 Prove that 2n(n + 3) + (n+ 1)? = 3n° + 7a + 1 for all positive integers n. You must show all your working. GB) = lis Triangle ABC is similar to triangle DEF. D A 6cm 9em ign yom 2 12cm c ca 20cm cs (a) Write down the scale factor of enlargement from triangle ABC to triangle DEF. () (b) Find the value of x. qd) (c) Find the area of triangle DEF. Give your answer in cm’, (1) (Total for Question 18 is 3 marks) : 15 _— MONE UO 0 | 21° Inthe diagram, ABCD is a cyclic quadrilateral. A 68° XD (oj Find the size of angle x. Give a reason for your answer. (4) UTS WER I) ecceced stacascdscestestassaetransessacieataiasd In the diagram, AB is a diameter of the circle. Prove that angle x = 90°. You must give a reason for cach stage of your working. DO NOTWRITE INTHIS AR (4) oon 000 00 8 0 0 17 23 In the diagram, OABC is a parallelogram. iC — Write down vector OB in terms of a and b. qd) A bag contains 5 red marbles, 4 blue marbles and 3 green marbles. One marble is taken at random from the bag and not replaced. A second marble is then taken at random from the bag. Find the probability that (a) the first marble is red and the second is blue, Q) (b) the second marble is green. Q) (Total for Question 24 is 4 marks) | _— (N00 0A