Wallace High School 27/1/11

Transcription

1 Wallace High School 7// Prelim Examination 00/0 MATHEMATICS National Qualifications - Intermediate Maths and Paper (non-calculator) Time allowed - minutes Read carefully. You may NOT use a calculator.. Full credit will e given only where the solution contains appropriate working.. Square-ruled paper is provided.

2 FORMULAE LIST The roots of ax + x + c = 0 are x = ( a ac) Sine rule: a sin A sin B c sin C Cosine rule: a = + c c cos A or cos A = c c a Area of a triangle: Area = ½ a sin C Volume of a sphere: Volume = r Volume of a cone: Volume = r h Volume of a cylinder: Volume = r h Standard deviation: s = ( x n x) x n ( x) / n, where n is the sample size.

3 All questions should e attempted Marks. A line has equation y + 6x = 9. Find its gradient and y-intercept.. The numer of people attending an emergency dental clinic over the course of weeks was recorded (a) Show the aove information in a dot plot. () Comment on the shape of the distriution.. The String section of the Scottish National Orchestra has 6 violinists violists 0 cellists 7 doule ass players. If a player is chosen at random from the String section, what is the proaility that it will e a cellist?. Multiply the rackets and simplify x ( x )(x )

4 . Factorise a 6 6. The diagram shows a cone with radius 0 centimetres and height 0 centimetres. 0 cm Taking π =, calculate the volume 0 cm of the cylinder. 7. Solve, algeraically, the system of equations x + y = x = y + 8. The diagram shows a circle, centre O, with a letter T inside it. The width of the T is 8 cm and the radius of the circle is cm. Calculate the height, h cm, of the T. 8 cm h cm

5 9. A group of S pupils produced the following set of Bleep Test results in PE efore they started their Standard Grade course in August., 0,, 6, 6,,, 0,,, 8, 6, 66, 7, 78, 8, 9, 96, 0,, 6 (a) Write down the lower quartile, median and upper quartile of the data. () Construct a ox plot to illustrate the data. In Decemer, the Bleep Test was repeated and this ox plot drawn (c) Compare the data in August with the data in Decemer. End of question paper

6 Intermediate Paper ~ 00/ Marking Scheme Qu Answer and Marks Examples of Evidence ans : m = ; (0, ) marks a rearranges equation to y = mx + c states gradient states y axis intercept ans : dot plot drawn marks y = x + m = (0, ) suitale scale dots added see end see end [allow two errors] ans: uniform distriution mark correct description ans : 0/ [or /] marks correct numerator correct denominator ans : + x x marks multiplies rackets simplifies answer ans : (a 8)(a + 8) marks recognises diff. of two squares factorises correctly 6 ans : 0 cm marks sus values into formula attempts to simplify efore calculation answer 7 ans : x = ; y = marks sus for x solves for y knows to su solves for x 8 ans : 8 cm marks uniform distriution 0/.../ x [x 8x + x ] x x + 7x + + x x evidence (a 8)(a + 8) V = ⅓ 0² 0 evidence 0 cm (y + ) + y = y = sus for y x = [No need to simplify- do not penalize if simplified] cm assemles facts in RAT knows to use Pythagoras finds missing side answer ( ) cm + = 8 cm cm

7 Qu Answer and Marks Examples of Evidence 9a ans : 9; 8; 88 marks identifies lower quartile identifies median identifies upper quartile Q = 9 Q = 8 Q = 88 ans: ox plot drawn marks scale shown correct ox and whiskers suitale scale diagram drawn c ans: comparison mark compares data any suitale comparison Total 0 marks

8 Wallace High School 7// Prelim Examination 00/0 MATHEMATICS National Qualifications - Intermediate Maths and Paper Time allowed - hour 0 minutes Read carefully. Calculators may e used in this paper.. Full credit will e given only where the solution contains appropriate working.. Square-ruled paper is provided.

9 FORMULAE LIST The roots of ax + x + c = 0 are x = ( a ac) Sine rule: a sin A sin B c sin C Cosine rule: a = + c c cos A or cos A = c c a Area of a triangle: Area = ½ a sin C Volume of a sphere: Volume = r Volume of a cone: Volume = r h Volume of a cylinder: Volume = r h Standard deviation: s = ( x n x) x n ( x) / n, where n is the sample size.

10 All questions should e attempted Marks. In the Garden centre there are types of plants on special offer. This week s specials! Rose ushes and Poppy plants Carly ought Rose ushes and Poppy plants which cost. Steph paid 6.7 for Poppy plants and Rose ushes. How much would Sally pay for a Rose ush and Poppy plants?. Multiply and collect like terms (x )(x + x 6). A Christmas aule is made from a sphere of perspex with a coloured cylinder in the middle. The volume round the cylinder is filled with a thick liquid. The sphere has a diameter of 8 cm. The cylinder has a radius of 6 cm with a height of 6 cm. Calculate the volume of liquid needed to fill the sphere, giving your answer correct to significant figures.. The diagram shows a circle centre O. AB is a diameter and C is a point on the circumference of the circle. A 8 o C Calculate the size of the shaded angle. O B

11 . In Bramley s Toy Shop there are 6 styles of teddy ear. The price of each is shown elow (a) Calculate the mean and standard deviation of these prices. In the same shop the prices of the dolls have a mean of.0 and a standard deviation of.. () Compare the two sets of data making particular reference to the spread of the prices. 6. Two congruent circles overlap to form the symmetrical shape shown elow. Each circle has a diameter of cm and have centres at B and D. A D B C Calculate the area of the shape.

12 7. The pie chart shows the numer of gold medals won y 8 countries in the 00 Winter Olympics. Russia China 8 o 0 o Canada Switzerland 78 o South Korea 8 o o 60 o Germany Norway USA (a) If Norway won 8 gold medals, how many did Canada win? () South Korea and Switzerland won the same numer of gold medals. What percentage of the gold medals did each of these countries win? 8. Marcus invested 000 in a ank which paid % interest per year. (a) Calculate how much money Marcus would have in his account after years. () How long would it take for Marcus money to increase y %? 9. Factorise x 7x

13 Numer of chest infections in last 0 years( I ) 0. In triangle PQR, PR = 0 cm QR = cm. The perimeter of the triangle is cm. R 0 cm Find the size of angle PQR. P cm Q. A group of smokers were asked how many cigarettes they smoked in a day and how many chest infections they had suffered in the last ten years. The results are shown in the scattergraph with the line of est fit drawn Numer of cigarettes smoked in a day ( C ) (a) Comment on the correlation etween the sets of data. () Find the equation of the line of est fit.

14 . In the diagram shown SR = cm, angle SQR = 7 o, angle QPS = o and angle PQS = 68 o. Q P o 68 o 7 o S cm R Calculate the length of PS. End of question paper

15 Intermediate Paper ~ 00/ Marking Scheme Qu Answer and Marks Examples of Evidence ans : 9.7 marks sets up equations strategy for solving equations solves for one variale finds other variale sustitutes values and calculates cost ans: x + 7x 7x + 8 marks starts to multiply rackets completes multiplying rackets simplifies ans : 0 cm marks strategy sus values into formula for sphere sus values into formula for cylinder sutracts to answer correct rounding ans : 8 o marks R + P = ; R + P = 6 7 evidence of scaling equations R = 7 P = = 9 7 x + 0x x.. x x + 8 x + 7x 7x + 8 [must include x term] finding volumes and sutracting V sphere = / π = V cylinder = π 6² 6 = cm a recognises angle in semi-circle uses angle in a triangle uses angle in straight line ans : 0, marks angle ACB = 90 o 80 (8 + 90) = o 80 = 8 o calculates mean squares deviations and adds sustitutes into formula calculates standard deviation 6 = = SD = ( /) ans : appropriate statement mark appropriate comment re spread 6 ans : 0 6 cm marks prices of dolls are less spread out than teddies realises sector of circle uses correct radius finds area of one sector finds area of square finds total area 70/60.. r = 6 cm [could e in formula] π 6 = = cm

16 Qu Answer and Marks Examples of Evidence 7a ans : gold medals marks equates angle to numer of medals finds numer of medals 8 o represents 8 medals; 6 o one medal 78 6 = medals ans : 0% marks 8a finds total of others sutracts and divides ans : 0.67 marks 60 ( ) = = 0% uses correct multiplier knows how to increase answer ans : years marks increases y % strategy answer 9 ans : (x + )(x ) marks first factor correct second factor correct 0 ans : 08 o marks 000 = 60 trial and error [ n ] years (x + ) (x ) Award mark if signs round the wrong way. Signs must e different. a finds missing side knows to use cosine rule sus values into rule finds angle ans : strong positive mark ( + 0) = 8 cm evidence ( ) ( 8) = 0 08 o comment on correlation strong positive correlation ans : I = /7C + marks finds gradient and y intercept states equation of line ans : 0cm marks m = / = /7; c = I = /7C + knows to find QS answer knows to use sine rule sus values answer uses SOH CAH TOA 6 6 cm evidence /sin o = PS/sin68 o ; PS = 6 6..sin68 o /sin o 0cm [ignore premature rounding] Total 0 marks