MATHEMATICS National Qualifications - National 5 Paper 1 (non-calculator) Testing all units

Transcription

1 N5 Practice Examination MATHEMATICS National Qualifications - National 5 Paper 1 (non-calculator) Testing all units Time allowed - 1 hour Fill in these boxes and read carefully what is printed below Full name of centre Town Forename(s) Surname Date of birth Day Month Year Candidate number Seat number Total marks You may NOT use a calculator.. Use blue or black ink. Pencil may be used for graphs and diagrams only.. Write your working and answers in the spaces provided. Additional space for answers is provided at the end of the booklet. If you use space, write clearly the number of the question you are attempting. 4. Square ruled paper is provided. 5. Full credit will be given only where the solution contains appropriate working. 6. State the units for your answer where appropriate. 7. Before leaving the examination room you must give up booklet to the invigilator. If you do not, you may lose all the marks for paper. Pegasys 014

2 FORMULAE LIST The roots of ax + bx + c = 0 are x = b ( b 4ac) a Sine rule: a sina b sinb c sinc Cosine rule: a = b + c bc cos A or cos A = b c a bc Area of a triangle: Area = ½ ab sin C Volume of a sphere: Volume = 4 r 1 Volume of a cone: Volume = r h 1 Volume of a Pyramid: Volume = Ah Standard deviation: s = ( x x) x ( x) n 1 n 1 / n, where n is the sample size. Pegasys 014

3 All questions should be attempted Marks 1. Multiply out the brackets and simplify ( x)(5 x). (a) Express x 6x 4 in the form ( x a) b. (b) If the graph of y x 6x 4 is drawn, what would the coordinates and nature of the turning point be? Pegasys 014

4 Marks. Evaluate of A company made a profit of in 014. This was 0% more than the profit they made in 01. How much profit did they make in 01? 5. Vectors a and b have components as follows: a = 5 0 and b = 5 Find the components of the resultant vector b a. Pegasys 014

5 Marks 6. By calculating the discriminant, state the nature of the roots of y x 5x 4 7. Find the equation of the line which is parallel to y 4x 1 and passes through the point (, ). Give your answer in the form ax + by = c. Pegasys 014

6 8. The graph of y asin x bis shown in the diagram. Marks y 4 O A x (a) Write down the values of a and b. (b) What number should appear at point A on the graph? 1 9. Express 6 8 as a surd in its simplest form. Pegasys 014

7 Marks 10. Simplify 5 x 4y 4 6x y expressing your answer with positive indices. 11. Q In triangle PQ = 16cm and QR = 8cm. 16cm 8cm The value of sin P = 0 4. P R Find the exact value of sin R. Q 1. Given that P, change the subject of the formula to R. R Pegasys 014

8 Marks 1. A sector of a circle with radius 8cm is shown opposite. Angle MON x M x O If the exact length of the arc MN is centimetres, calculate the size of the angle marked x. 4 N 8cm 14. Simplify cos xtan x End of Question Paper Pegasys 014

9 N5 Practice Examination MATHEMATICS National Qualifications - National 5 Paper (Calculator) Testing all units Time allowed - 1 hour and 0 minutes Fill in these boxes and read carefully what is printed below Full name of centre Town Forename(s) Surname Date of birth Day Month Year Candidate number Seat number Total marks You may use a calculator.. Use blue or black ink. Pencil may be used for graphs and diagrams only.. Write your working and answers in the spaces provided. Additional space for answers If you use space, write clearly the number of the question you are attempting. is provided at the end of the booklet. 4. Square ruled paper is provided. 5. Full credit will be given only where the solution contains appropriate working. 6. State the units for your answer where appropriate. 7. Before leaving the examination room you must give up booklet to the invigilator. If you do not, you may lose all the marks for paper. Pegasys 014

10 FORMULAE LIST The roots of ax + bx + c = 0 are x = b ( b 4ac) a Sine rule: a sina b sinb c sinc Cosine rule: a = b + c bc cos A or cos A = b c a bc Area of a triangle: Area = ½ ab sin C Volume of a sphere: Volume = 4 r 1 Volume of a cone: Volume = r h 1 Volume of a Pyramid: Volume = Ah Standard deviation: s = ( x x) x ( x) n 1 n 1 / n, where n is the sample size. Pegasys 014

11 All questions should be attempted Marks 1. A painting was valued at in 01. The owner plans to sell it in 015 and hopes that it will be worth If the painting increases in value at the rate of 8% per annum, will it be worth in 015? You must show all your working and give a reason for your answer.. Write as a single fraction in its simplest form: 4b b 7x x Pegasys 014

12 Marks. In the diagram, QN = NR. PQ represents vector a and PR represents vector b. Q a P N b (a) Express QR in terms of a and b. R (b) Express QN in terms of a and b A conical container has a capacity of 5 litres and height 18 cm. Calculate its radius. Pegasys 014

13 Marks 5. Find the point of intersection of the lines which have equations x 4y 17 5x y The number of calls made to a call centre on weekdays gave a mean of 50 5 and a standard deviation of 5 4. At the weekend the number of calls gave a mean of 75 and a standard deviation of 4 6. Make two comparisons between the number of calls received at the call centre on weekday compared to weekends. the Pegasys 014

14 Marks 7. The diagram below shows the cross section of a cylindrical tank with radius 18cm. O x o 18 cm A B Diagram shows the cross-sectional view of the tank. There is liquid in the tank and its surface, AB, measures 7cm. It is thought that angle AOB is 90 o. Without using trigonometry, decide whether or not is the case. [Show working to justify your answer] 4 Pegasys 014

15 8. The graph in the diagram has equation y Marks y x x and cuts the x-axis at A and B. A B x Find the coordinates of the points A and B giving your answers correct to 1 decimal place. 5 Pegasys 014

16 9. The gable end of a building is shaped as shown in Diagram 1. Marks Diagram 1 It consists of a rectangle and five congruent isosceles triangles and has dimensions as shown in Diagram. 8 m Diagram 4 6 m Calculate the area of the gable end. 5 Pegasys 014

17 Marks 10. When a fish leaps from the water its path is in the shape of a parabola. The parabola can be represented by the equation This cartesian diagram shows the parabola. y 5 4x x. y A B x (a) If one unit on the graph represents a distance of 0cm, calculate how far the fish travels horizontally during one leap. (b) Does the fish reach a height of 1 75 metres on leap? You must show all your working to justify your answer. 4 Pegasys 014

18 Marks 11. Solve the equation 5cos x 4 for 0 < x < The national soft drink of Malta is called "Kinnie" and it is sold in various bottle sizes. Two are shown here: Kinnie 500 ml 6cm Kinnie 1650 ml 9cm The smaller bottle has a base diameter of 6cm and holds 500ml. The larger bottle has a base diameter of 9cm and it holds 1650ml. The bottles look alike but could they actually be mathematically similar? (Show calculations to justify your answer.) 4 Pegasys 014

19 1. Isosceles triangle ABC is shown below. Marks C Show that the length of AB can be given by the expression 6cm 4 6cm 0 RQ = 1 cos80 7 cm. 4 A 50 o B End of Question Paper Pegasys 014