Prel Examination 005 / 06 MATHEMATICS National Qualifications - Intermediate Maths Units and Paper (non-calculator) Time allowed - 35 minutes Fill in these oxes and read carefully what is printed elow Full name of centre Town Forename(s) Surname Date of irth Day Month Year Candidate numer Seat numer. You may NOT use a calculator.. Write your working in the spaces provided. 3. Full credit will e given only where the solution contains appropriate working.
FORMULAE LIST Circumference of a circle: C = d Area of a circle: A = r Theorem of Pythagoras: c a + = c a Trigonometric ratios in a right angled triangle: hypotenuse x o adjacent opposite tan x sin x o cos x o o opposite adjacent opposite hypotenuse adjacent hypotenuse
All questions should e attempted. (a) Find 3 5 7. () Find 3 of 6m (c) Find 6 ( 5) (d) Find 4 38 6. When a plane left Glasgow at Christmas to go to Lapland the temperature was 3 o C. By the time it landed in Lapland the temperature had fallen y o C. What was the temperature in Lapland?
3. In London s theatreland a group of people were asked to say what their favourite musical was and this pie chart was drawn. CATS THE LION KING 5% 0% 5% MAMA MIA 30% MARY CHITTY POPPINS CHITTY BANG BANG If 50 people were asked altogether, how many people said that Mary Poppins was their favourite musical? 3 4. Andrew, the window cleaner, takes minutes to clean the 8 windows in my neighour s house. Working at the same rate, how long will it take him to clean the 8 windows in my house? 3
5. (a) On the coordinate diagram elow plot the points: K(-6, -4), L(-6, 5) and M(4, 5) y 5-5 O 5 x -5 () The 3 points aove are the corners of a rectangle. On the same diagram plot the point N which is the fourth corner of the rectangle. (c) Write down the coordinates of N. 6. At a printers the following prices are charged for printing flyers. Up to 5000 copies: 35 per 000 0 000 copies: 3 per 000 5 000 copies: 7 per 000 0 000 copies: per 000 How much would Lorraine e charged for printing 9000 copies? 3
7. The Anderson Family have just uilt a sun room onto their house. The side wall is glass and is in the shape of a rectangle and a right angled triangle. m 3 m 4m Calculate the area of glass needed to construct the side wall. 4 8. A letter is chosen from the word: SCOTTISH What is the proaility that it will e a T? Give your answer in its simplest form.
9. The tale elow shows the profit made y a large manufacturing company over 5 years. Year Profit (nearest 0 000) 998 0000 999 55000 000 35000 00 60000 00 75000 Draw a ar graph, on the grid elow, to illustrate the information. 3
0. When Helen went to Canada the exchange rate was 5 dollars to the pound. How many dollars did she get for 300?. A us leaves town A at 40 and arrives in town B at 075 the next morning. How long did the journey take? END OF QUESTION PAPER
Prelim Examination 005 / 06 MATHEMATICS National Qualifications - Intermediate Maths Units and Paper Time allowed - 55 minutes Fill in these oxes and read carefully what is printed elow Full name of centre Town Forename(s) Surname Date of irth Day Month Year Candidate numer Seat numer. You may use a calculator.. Write your working in the spaces provided. 3. Full credit will e given only where the solution contains appropriate working.
FORMULAE LIST Circumference of a circle: C = d Area of a circle: A = r Theorem of Pythagoras: c a + = c a Trigonometric ratios in a right angled triangle: hypotenuse x o adjacent opposite tan x sin x o cos x o o opposite adjacent opposite hypotenuse adjacent hypotenuse
All questions should e attempted. Stewart pays 5 00 per month for his roadand internet connection. The internet company have just informed him that the charge is going to increase y 7%. How much per month will Stewart have to pay for his internet connection after the increase? 3. Mr. Agnew wishes to clean his upstairs windows. He has an 8 feet long ladder that he uses to reach the windows, 4 feet aove the ground. What angle does the ladder make against the house? Give your answer correct to decimal place. 4 feet x 8 feet 3 3. The engine sizes of cars in a car park were noted. 0 7 5 4 0 3 3 3 3 3 3 3 4 0 3 7 (a) Construct an ordered Stem and Leaf diagram to illustrate the aove information. 4 () Use the diagram to write down the median and range of the data.
4. Elaine is designing some jewellery for her final project at Art College. She is making a necklace which has some silver cues as part of the design. The cues she is using all have 8mm sides. 8mm (a) Calculate the volume of one of the small silver cues. Elaine starts with a silver cuoid 0mm y 5mm y 30mm and melts it down to form the cues. () How many complete cues could she make out of her silver cuoid? 3 (c) After she makes the necklace shown aove Elaine decides to make a pair of earrings to match. If she uses up all the cues in making them, how many cues would there e in each earring?
5. (a) Arthur is going on holiday and has to e at the airport, 80km from home, y 30am. How long will it take him to reach the airport travelling at 80km/h? [Answer in hours and minutes] 3 () Unfortunately Arthur does not leave the house until 5 mins after he should have. What speed should he now average so that he still makes it to the airport on time? 6. The Munro family have had a new kitchen installed. The kitchen company offered them two ways of paying for it. Option : 000 deposit and then 4 payments of 70 Option : 36 payments of 40 then pay the alance in one payment. If oth options cost the same, calculate how much would have to e paid after 36 months with Option. 4
7. (a) 6 cm The side of a ox of toiletries is in the shape of a rectangle and a semi-circle. cm Calculate the area of the side. 4 () The ox is in the shape of a prism. To find the volume of a prism we use the formula: Volume = area of side height Use this formula to find the volume of the ox which has a height 5cm. 8. In a group of 40 people, 4 of them owned a skateoard. What percentage is this?
9. Ciara recorded the numer of e-mails she sent over 80 days. (a) Complete the tale elow Numer of e-mails Frequency 5 6 7 4 8 3 9 0 3 9 6 3 6 4 4 Totals Numer of e-mails frequency () Calculate the mean numer of e-mails Ciara sent per day. 0. Gillian s lawn is shaped as in the diagram. All lengths are in metres. Gillian is going to put a decorative order round her lawn. The order does not go along the side of the house. The order is sold in metre lengths and costs 4 95 a length. (a) How many lengths of order are to e purchased? 0 LAWN HOUSE 6 8 () Calculate how much it would cost Gillian to put the order round her lawn. 4
Distance (miles). Ian and Sanjay are friends ut live in towns a numer of miles apart. They met up one Saturday for lunch. The graph elow shows their journeys. 50 40 Sanjay 30 0 0 Ian 0 noon.0 pm.40 pm.00 pm Time.0 pm.40 pm.00 pm (a) How far apart do the two men live? () Who arrived at the meeting place first and how long did he have to wait at the meeting place for the other person? (c) One of the men drove to the meeting place and the other cycled. Which man cycled? Give a reason for your answer. END OF QUESTION PAPER
Intermediate Paper ~ 005/06 Marking Scheme Qu Give one mark for each Illustrations for awarding mark a ans : 75 mark c d answer ans : 84 answer ans : 9 answer ans: 0 73 mark mark mark answer ans : -9 o C mark 75 (6 ) = 84 6 + 5 = 9 0 73 answer 3 - = -9 o C 3 ans : 50 3 marks finds missing % knows to find % of total answer 4 ans : 7 minutes 3 marks 5a c knows to divide y 8 knows to multiply y answer ans : points plotted two points plotted correctly third point plotted correctly ans: point plotted point plotted to make rectangle ans: (4, -4) marks mark mark coordinates stated 6 ans : 88 3 marks selects correct rate knows to multiply y 9 answer 7 ans : 0 8m 4 marks calculates area of rectangle finds height of triangle calculates area of triangle calculates total area 8 ans : 4 marks 4 states proaility simplifies 00 (5 + 0 + 5 + 30) = 0% 0% of 50 50 8 8 8 7 minutes (or y similar method) see diagram see diagram see diagram (4, -4) 3 per 000 3 9 88 4 = 8 8 metre may e sustituted in formula 0 5 4 = 4 0 8m /8.. = /4
Qu Give one mark for each Illustrations for awarding mark 9 ans : ar graph drawn 3 marks suitale scales on each axis axes laelled ars drawn correctly 0 ans : 675 dollars marks knows to multiply answer ans : 8 hours 45 minutes mark see diagram see diagram see diagram 5 300 675 dollars answer 8 hours 45 minutes Total 30 marks
Intermediate Paper ~ 005/06 Marking Scheme Qu Give one mark for each Illustrations for awarding mark ans : 6 05 3 marks knows how to find percentage calculates percentage adds to original cost ans : 38.9 3 marks 3a 4a c 5a Chooses correct Trig ratio evaluates ratio evaluates angle ans : stem and leaf drawn 4 correct stem correct leaves ordered leaves key shown 4 marks ans: ; 9 marks identifies median calculates range ans : 5 mm 3 knows how to find volume finds volume ans: 7 cues finds volume of cuoid knows to divide answer ans: 5 finds availale cues knows to divide y ans : hours 5 minutes sustitutes into correct formula finds numer of hours changes to hours and minutes ans: 90 km marks 3 marks marks 3 marks marks finds new time and sus into formula calculates speed 6 ans : 440 4 marks 4 knows to calculate total cost calculates total cost calculates cost of payments calculates alance to pay 7/00 5 05 6 05 Cos 4 / 8 or 0.7777 38.9 3 3 3 3 7 7 0 3 3 5 3 4 4 0 0 n = 7 = 9 8 8 8 5 mm 3 0 5 30 = 9 000 9 000 5 = 7 cues 7 7 = 0 0 = 5 T = D/S or T = 80/80 5 hours hours 5 minutes S = 80/ 90km/h (4 70) + 000 7 480 36 40 = 5 040 4 7 480 5 040 = 440
Qu Give one mark for each Illustrations for awarding mark 7a ans : 86 cm 4 marks 4 finds area of rectangle uses correct radius finds area of semicircle finds total area ans: 9 5cm 3 marks sustitutes in formula answer 8 ans : 60% marks 9a knows how to calculate percentage finds percentage ans : Tale completed marks completes last column finds total 6 = 7cm r = 3cm [may e sustituted in formula] 0 5 3 4 3 = 4 4 86 cm 86 5 9 5cm 3 4/40 00% 60% 5,, 8, 04, 98, 30, 99, 7, 78, 56 78 and 80 0a ans : 9.775 marks knows how to calculate mean knows how to calculate mean ans : 3 lengths 4 4 marks assemles info in right-angled triangle knows to use Pythagoras finds unknown length finds total length and numer of lengths 78 80 9 775 e-mails 6 6 + = 40 6 3 4 total = 0 + 8 + 6 3 = 4 3..; 3 lengths a ans : 64.35 mark calculates cost ans : 45miles mark reads distance from graph ans : Sanjay & 0mins + correctly interprets graph marks 3 4 95 = 64 35 45km Sanjay 0 mins c ans: Sanjay with reason interprets shape of graph any valid reason marks Sanjay Needed a rest, slower etc. Total 50 marks