FOR OFFICIAL USE N5 - SQA

1 *X747750101**X7477501*N5 FOR OFFICIAL USEFill in these boxes and read what is printed of seatTow n MarkFull name of centreForename(s)SurnameScottish candidate numberDate of birthYearDayMonthNationalQuali cations2017 Total marks 40 Attempt ALL may NOT use a credit will be given only to solutions which contain appropriate the units for your answer where your answers clearly in the spaces provided in this booklet. Additional space for answers is provided at the end of this booklet. If you use this space you must clearly identify the question number you are blue or black leaving the examination room you must give this book to the Invigilator; if you do not, you may lose all the marks for this , 5 MAY1:00 PM 2:00 PMA/HTPM athematicsPaper 1 (Non- calculator )*X747750102*Page 02 FORMULAE LISTThe roots of ()2240 are 2 xbbacaxbx ca= ++=Sine rule: sin sin sinabc==ABCC osine rule: cos cos2222222 or2bcaabcbcAAbc+ =+ =Area of a triangle: sin12 AabC=Volume of a sphere: 343Vr=Volume of a cone: 213 Vrh=Volume of a pyramid: 13 VAh=Standard deviation: ()21 xxsn = or ()221 x xnsn = , where n is the sample size.

2 *X747750103*Page 03 MARKSDO NOT WRITE IN THIS MARGINT otal marks 40 Attempt ALL questions 1. Given that ()xfx x=+23, evaluate ()5f . 2. The number of calls received by the police was recorded over 10 results are shown 216 218 230 232 247 248 250 265 267 Find the semi-interquartile range of this data.[Turn over22*X747750104*Page 04 MARKSDO NOT WRITE IN THIS MARGIN 3. Evaluate 5364 your answer in its simplest form. 4. Expand and simplify ()() 223 41x xx++.23*X747750105*Page 05 MARKSDO NOT WRITE IN THIS MARGIN 5. The diagram shows a square-based pyramid placed on top of a cube, relative to the coordinate (6,0,0)zyxCBOThe height of the pyramid is half of the height of the is the point (6,0,0).The point C is directly above the centre of the down the coordinates of B and C.]

3 [Turn over2*X747750106*Page 06 MARKSDO NOT WRITE IN THIS MARGIN 6. The diagram below shows the straight line joining points A and ( 1,6)B (3, 2)OyxFind the equation of the line the equation in its simplest *X747750107*Page 07 MARKSDO NOT WRITE IN THIS MARGIN 7. In triangle DEF: DE = 8 centimetres EF = 12 centimetres sin2E3=DEF12 cm8 cmCalculate the area of triangle DEF.[Turn over2*X747750108*Page 08 MARKSDO NOT WRITE IN THIS MARGIN 8. Solve, algebraically, the inequality()xx+>+ 19 15 3 *X74775010 *Page 09 MARKSDO NOT WRITE IN THIS MARGIN 9. In the diagram shown below: ABE is a tangent to the circle centre O Angle DBE is 58 58 DOCEBAC alculate the size of angle CAB.[Turn over3*X747750110*Page 10 MARKSDO NOT WRITE IN THIS MARGIN 10. Change the subject of the formula 24tbFc+= to b. 11.]]]

4 Express ,2320aaa , as a single fraction in its simplest *X747750111*Page 11 MARKSDO NOT WRITE IN THIS MARGIN 12. Gym members are asked to fill out a questionnaire to rate the quality of service provided. They are asked to give a rating on a scale of 1 to ratings given by five members were as follows:1 4 6 3 6In its simplest form, the standard deviation of these ratings can be written as the values of a and b. [Turn over4*X747750112*Page 12 MARKSDO NOT WRITE IN THIS MARGIN 13. The graph below shows two straight lines with the equations: 32xy = 3 19xy+=3x y = 2yxx + 3y = 19 POThe lines intersect at the point , algebraically, the coordinates of *X747750113*Page 13 MARKSDO NOT WRITE IN THIS MARGIN 14. The graph below shows a parabola with equation of the form ()2y xa b=++.]

5 Y( 3,8)Oxx = 5 The equation of the axis of symmetry of the parabola is x = 5.(a) State the value of point ( 3,8) lies on the parabola.(b) Calculate the value of b.[Turn over for next question12*X747750114*Page 14 MARKSDO NOT WRITE IN THIS MARGIN 15. In the diagram below: TS is parallel to QR TS = 5 centimetres QR = 7 centimetres SR = 2 6 centimetresQTPRS5 cm7 cm2 6 cmx cmThe length of PS is x the value of x.[END OF QUESTION paper ]3*X747750115*Page 15 MARKSDO NOT WRITE IN THIS MARGINADDITIONAL SPACE FOR ANSWERS*X747750116*Page 16 MARKSDO NOT WRITE IN THIS MARGINADDITIONAL SPACE FOR ANSWERS*X747750201**X7477502*N5 FOR OFFICIAL USEFill in these boxes and read what is printed of seatTow n MarkFull name of centreForename(s)SurnameScottish candidate numberDate of birthYearDayMonthNationalQuali cations2017 Total marks 50 Attempt ALL may use a credit will be given only to solutions which contain appropriate the units for your answer where your answers clearly in the spaces provided in this booklet.]

6 Additional space for answers is provided at the end of this booklet. If you use this space you must clearly identify the question number you are blue or black leaving the examination room you must give this book to the Invigilator; if you do not, you may lose all the marks for this , 5 MAY2:20 PM 3:50 PMA/HTPM athematicsPaper 2*X747750202*Page 02 FORMULAE LISTThe roots of ()2240 are 2 xbbacaxbx ca= ++=Sine rule: sin sin sinabc==ABCC osine rule: cos cos2222222 or2bcaabcbcAAbc+ =+ =Area of a triangle: sin12 AabC=Volume of a sphere: 343Vr=Volume of a cone: 213 Vrh=Volume of a pyramid: 13 VAh=Standard deviation: ()21 xxsn = or ()221 x xnsn = , where n is the sample size.*X747750203*Page 03 MARKSDO NOT WRITE IN THIS MARGINT otal marks 50 Attempt ALL questions 1. Find v, the magnitude of vector 18143 = v.

7 2. A necklace is valued at value is expected to increase by 4 5% per year over the next 3 the expected value of the necklace after this your answer to the nearest pound.[Turn over23*X747750204*Page 04 MARKSDO NOT WRITE IN THIS MARGIN 3. A piece of land is in the shape of a triangle as mP180 mR147 PQ = 250 metres PR = 180 metres angle QPR = 147 The owner wishes to build a fence along the side the length of the *X747750205*Page 05 MARKSDO NOT WRITE IN THIS MARGIN 4. Solve the equation 22 5 40xx+ =.Give your answers correct to one decimal place. 5. A theatre group sold 4830 tickets for their was 15% more than they sold last many tickets did they sell last year?[Turn over33*X747750206*Page 06 MARKSDO NOT WRITE IN THIS MARGIN 6. A spherical sweet is made by coating a caramel sphere evenly with cross-section of the sweet is shown mm24 mmThe diameter of the sweet is 24 millimetres and the thickness of the chocolate coating is 3 the volume of the chocolate your answer correct to 3 significant figures.]]

8 5*X747750207*Page 07 MARKSDO NOT WRITE IN THIS MARGIN 7. Triangles A and B are shown cm7 cm7 cm19 cm6 cm16 cmABThe triangles are placed together to form the larger triangle shown this larger triangle right-angled?Justify your answer.[Turn over3*X747750208*Page 08 MARKSDO NOT WRITE IN THIS MARGIN 8. In the diagram below, RQ and PQ represent the vectors c and d (a) Express PR in terms of c and line QP is extended to TP = PQ V is the midpoint of PR(b) Express TV in terms of c and your answer in simplest *X747750209*Page 09 MARKSDO NOT WRITE IN THIS MARGIN 9. (a) Factorise 24 25x .(b) Hence simplify 224 252 10xxx .[Turn over13*X747750210*Page 10 MARKSDO NOT WRITE IN THIS MARGIN 10. In the diagram below D, E and F represent the positions of Dunbridge, Earlsford and Fairtown km126 230 NDEFND unbridge is 15 kilometres west of Dunbridge, the bearing of Fairtown is 126.]]

9 From Earlsford the bearing of Fairtown is 230 .Calculate the distance between Dunbridge and not use a scale *X747750211*Page 11 MARKSDO NOT WRITE IN THIS MARGIN 11. A straight line has equation 3 5 10 0xy =.Find the gradient of this line. 12. Express 31x in the form nx.[Turn over22*X747750212*Page 12 MARKSDO NOT WRITE IN THIS MARGIN 13. Two identical shapes are used to form a logo. Each shape is part of a The circles have centres C1 and C2. The radius of each circle is 14 centimetres. The logo has half-turn symmetry about the mid-point of AB. AB is 48 centimetres the height of the *X747750213*Page 13 MARKSDO NOT WRITE IN THIS MARGIN 14. The diagram below shows part of a circle, centre 4 cmThe radius of the circle is 6 4 arc AB has length 31 5 the size of the reflex angle AOB.]

10 [Turn over3*X747750214*Page 14 MARKSDO NOT WRITE IN THIS MARGIN 15. A wind turbine has three blades as shown below. Blade AThe height, h metres, of the tip of blade A above the ground in each rotation is given by cos hx=+40 23, x <0 360where x is the angle blade A has turned clockwise from its vertical position.(a) Calculate the height of the tip of blade A after it has turned through an angle of 60 .1*X747750215*Page 15 MARKSDO NOT WRITE IN THIS MARGIN 15. (continued)(b) Find the minimum height of the tip of blade A above the ground.(c) Calculate the values of x for which the tip of blade A is 61 metres above the ground. [END OF QUESTION paper ]14*X747750216*Page 16 MARKSDO NOT WRITE IN THIS MARGINADDITIONAL SPACE FOR ANSWERS*X747750217*Page 17 MARKSDO NOT WRITE IN THIS MARGINADDITIONAL SPACE FOR ANSWERS*X747750218*Page 18 MARKSDO NOT WRITE IN THIS MARGINADDITIONAL SPACE FOR ANSWERS*X747750219*Page 19 MARKSDO NOT WRITE IN THIS MARGINADDITIONAL SPACE FOR ANSWERS*X747750220*Page 20 MARKSDO NOT WRITE IN THIS MARGINADDITIONAL SPACE FOR ANSWERS]