WYNBERG BOYS HIGH SCHOOL Department of Mathematics

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WYNBERG BOYS HIGH SCHOOL Department of Mathematics Grade 10 May 00 Time Available hours Marks Available - 110 In Terry Pratchett s

walking on the shell of a giant turtle that is, in turn, swimming randomly through space.

Task 1: Because the Discworlders planet is flat, area is very important to them. Below are the dimensions of a number of their houses.

1 WYNBERG BOYS HIGH SCHOOL Department of Mathematics Grade 10 May 00 Time Available hours Marks Available In Terry Pratchett s Discworld books the characters are absolutely certain of the fact that their world is a flat disc carried on the backs of four elephants walking on the shell of a giant turtle that is, in turn, swimming randomly through space. For some reason you decide a visit to this world will be worthwhile. GOOD LUCK AND ENJOY THE TRIP! Task 1: Because the Discworlders planet is flat, area is very important to them. Below are the dimensions of a number of their houses. In each case find the area, in terms of a, b, c or d. Make sure that your answers are given in expanded form. (Angles that look like right angles may be assumed to be so.) a) b) 3a - 7 b - 1 3a - 7 4b - b + 6 c) d) c + 1 d + 5 5c -

The sum of the x and y values of the intersection point of the straight lines: y x 4 and 3x y 7 () 5. The larger value of h if h 7h 79 () 7.

2 Task : Part of the Discworld community is a group of puzzlers, and because of the flat nature of crosswords they enjoy doing them. Complete the following crossnumber (a copy is attached to the back of this paper ensure your name is on it, please and hand it in with your answer sheets): DOWN: 1. a if 3a The sum of the x and y values of the intersection point of the straight lines: y x 4 and 3x y 7 () 5. The larger value of h if h 7h 79 () 7. The coefficient of x in the expansion of ( 1)( x 5)(x 3) x () ACROSS: 1. The value of 3b 13 if b () 4. The x -coordinate of a point on the graph of y x 5 if the y -coordinate of the point is 659 () 6. The value of d if 3( d ) 5( d 10) 15 (). The value of g if e 3, f 5 e and g 0 f 3e ()

Task 3: On your visit to Discworld, Ericus (a rather tall monk of truth) is rather

boring) test of your mathematical ability. He asks you to complete the following: 1.

3 Task 3: On your visit to Discworld, Ericus (a rather tall monk of truth) is rather suspicious of you and worries about your strange notions of spherical planets and the like. To test whether or not you are mad, he decides to give you a simple (if somewhat boring) test of your mathematical ability. He asks you to complete the following: 1. Factorise: a) a ( b 3c) ( b 3c)a 3( b 3c) b) 4d 3d 15 () c) e ( f 3 g) + h (3 g f ) d) km 15p 3m 5kp 4 t e) (3). Solve for f in the following: a) f 5( f 1) f b) ( f )( f 3) 6 (5) c) 1 (3 f ) ( f 6) (6) d) ( f 5) (3 f ) 6 1 f e) 4 f f 3. Solve the following pair of equations simultaneously: 3p t 1 and p 4t 16 (5)

Task 4: g y C 1. The proof that Discworld is flat is a rather simple matter of interpreting the graphs in the diagram of various objects that have been projected around the planet.

4 Task 4: g y C 1. The proof that Discworld is flat is a rather simple matter of interpreting the graphs in the diagram of various objects that have been projected around the planet. f a) If the equation of the parabola marked h is: A 1,5 B x y x 9 h find the co-ordinates of A, B and C. b) Find the equation of the straight line marked f. () c) If the line marked g is perpendicular to f, then find its equation. (3) d) Give the range of h.. Draw neat, rough sketches of the following graphs on separate sets of axes: a) 4x 3y 4 () b) 9 y x () c) y x 3 (3) d) 16 y x (3) Task 5: An odd system of money is used on parts of Discworld. There are three types of coins, each with the following symbols: You know that you can buy the following number of magical spells with the coins shown: + = = 19 = 7 How many spells could you buy with the following? a) + 4 () b) + (3) c) (3)

Task 6: The Discworlders play around with time and perform complex calculations that shift time from one place to another, but they always have to conserve and balance time, so they make use of

$Now write the rest of the fraction in terms of x. () f) Simplify the fraction to show that the result you found in d) will always be true.$

5 Task 6: The Discworlders play around with time and perform complex calculations that shift time from one place to another, but they always have to conserve and balance time, so they make use of calculations similar to those in the following task. a) Calculate: b) Calculate: c) Calculate: 5 6 (5 7) 37 3 (37 39) ( ) () d) What do you notice? e) Let the numerator be x. Now write the rest of the fraction in terms of x. () f) Simplify the fraction to show that the result you found in d) will always be true. (3) But in all he does, the educator should remember that his aim is not to put into the mind knowledge that was not there before though he may do that within limits but to turn the mind s eye to the light so that it can see for itself; his business, in other words, is not to stick thoughts into his pupils heads but to make them think for themselves. - Plato (in The Republic )

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LHS Algebra Pre-Test

Your Name Teacher Block Grade (please circle): 9 10 11 12 Course level (please circle): Honors Level 1 Instructions LHS Algebra Pre-Test The purpose of this test is to see whether you know Algebra 1 well