10TH GRADE STUDY GUIDE 2ND TERM EXAM. HWd BOOK: HIGHER GCSE for AQA SECTION A. LINEAR AND QUADRATIC EQUATION. Find slope, equation of a line, domain and range. Identify y- and x-axis intercepts, solve equation simultaneously by any method, sketch lines, problem solving applications, solve quadratic equations. A2.1 – A2.10. Page 350, 351. A3.4 – A3.9. Page 353 A3.12 – A3-15 Page 354 A4.5 – A4.7 Page 357 SECTION B. LINEAR MODELING. (Line of best fit) S6.3, S6.5, S6.6. Pages 396,397. D3.1 – D3.6 Pages 425, 426, 427, 428, 429. A short sample of exam¸on these topics: Write an equation of the line described 1. The line through A(1, -5) and B(- 2. The line through C(6,4) perpendicular to 3,6) the line 3x+4y=7 3. The line through B (2,-5) parallel to 4. The line through P(3,7) and slope 1 the line 5x-3y=4. 4 5. Write an equation and graph the with x-intercept -3 and y-intercept 5 Graph the following lines. Take note of the domain stated. Use a separate piece of paper. 6. 2x-5y-2=0; Domain: x>1 7. y = -3x-6; Domain: x 0 Find the equation of the following lines: 9. 10. 8. 11. A candle is 30 cm long. When it is lit it burns at the rate of 4 cm per hour. If H cm represents the height of the candle t hours after being lit a) write down the algebraic rule connecting H b) How long does it task for the candle to have its and t 1 height reduced by 5 c) Sketch a graph of H against t d) State the domain and range of the function. e) What is the height of the candle after it has burned for 3 h 15 min? SECTION D. SERIES AND SEQUENCES. Geometric and arithmetic, application problems. A woman deposits $100 into her son’s savings The first four terms of an arithmetic account on his first birthday. On his sequence are shown below. second birthday she deposits $125, $150 on his third birthday, and so on. 1, 5, 9, 13,...... (a) How much money would she (a) Write down the nth term of the deposit into her son’s account on sequence. his 17th birthday? (b) Calculate the 100th term of the (b) How much in total would she have sequence. deposited after her son’s 17th birthday? (c) Find the sum of the first 100 terms of the sequence. The fourth term of an arithmetic sequence is 12 The nth term of an arithmetic sequence is given and the tenth term is 42. by un = 63 – 4n. (a) Given that the first term is u1 and (a) Calculate the values of the first two the common difference is d, write terms of this sequence. down two equations in u1 and d (2) that satisfy this information. (b) Which term of the sequence is –13? (b) Solve the equations to find the (2) values of u1 and d. (c) Two consecutive terms of this sequence, uk and uk + 1, have a sum of 34. Find k. The sixth term of an arithmetic sequence is 24. (a) The first term of an arithmetic sequence is The common difference is 8. –16 and the eleventh term is 39. Calculate the value of the common (a) Calculate the first term of the difference. sequence. (b) The third term of a geometric The sum of the first n terms is 600. sequence is 12 and the fifth term is 16 (b) Calculate the value of n. . 3 All the terms in the sequence are positive. Calculate the value of the common ratio. The fifth term of an arithmetic sequence is 20 The first term of an arithmetic sequence is 0 and and the twelfth term is 41. the common difference is 12. (a) (i) Find the common difference. (a) Find the value of the 96th term of (2) the sequence. (2) (ii) Find the first term of the sequence. The first term of a geometric sequence is (1) 6. The 6th term of the geometric sequence (b) Calculate the eighty-fourth term. is equal to the 17th term of the arithmetic (1) sequence given above. (c) Calculate the sum of the first 200 (b) Write down an equation using this terms. information. (2) (c) Calculate the common ratio of the geometric sequence. The development of this study guide is not compulsory but it will be worth 10 extra points for the second term exam. All processes must be shown. All doubts may be solved any time during the school shift.