National 5 Mathematics. Assessment 6

Transcription

1 National 5 Mathematics Assessment 6 Name: Form Class: Assessment Standards R. R. #R. # 9 7 Calculators may be used in this assessment All questions should be attempted Full credit will be given only where the solution contains appropriate working. State the units for your answer where appropriate.

2 FORMULAE LIST The roots of ax + bx + c = 0 are x = b ( b 4ac) a Sine rule: a sin A b sin B 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 Volume of a cone: Volume = r h Volume of a Pyramid: Volume = Ah Standard deviation: s = ( x x) x ( x) n n / n, where n is the sample size.

3 R. The diagram shows the parabola with equation What is the value of k? y kx # y x The equation of the quadratic function whose graph is shown below is of the form y = (x + a) + b, where a and b are integers. Write down the values of a and b. y x

4 Sketch the graph y = (x 4)(x ) on plain paper. Mark clearly where the graph crosses the axes and state the coordinates of the turning point. 4 A parabola has equation y = (x ) + 6. (a) Write down the equation of its axis of symmetry. (b) Write down the coordinates of the turning point on the parabola and state whether it is a maximum or minimum. Total (R.) #

5 R. / #R. 5 Solve the equation (x + )(4x 5) = 0. # 6 Solve the equation 6x +x = 0 using the quadratic formula. 4 7 Determine the nature of the roots of the equation x 8x + 8 = 0 using the discriminant. Total (R. / #R.) #

6 National 5 Mathematics Assessment 7 Practice Name: Form Class: Assessment Standards A. #A. R.5 A. # 8 9 Calculators may be used in this assessment All questions should be attempted Full credit will be given only where the solution contains appropriate working. State the units for your answer where appropriate.

7 FORMULAE LIST The roots of ax + bx + c = 0 are x = b ( b 4ac) a Sine rule: a sin A b sin B 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 Volume of a cone: Volume = r h Volume of a Pyramid: Volume = Ah Standard deviation: s = ( x x) x ( x) n n / n, where n is the sample size.

8 A. / #A. Sarah wishes to sow grass seed on a triangular plot of ground. The diagram gives the dimensions of the plot. # 4 m 60 m Calculate the area of this plot to the nearest square metre. The diagram shows how a golf ball was hit from the tee (T) to position B, a distance of 60m. The hole (H) is 0m from the tee. T m yards H 0 yards 60m B What is the shortest distance between the golf ball and the hole? 4

9 Ocean buoys in the Atlantic are positioned at Kestrel (K), Wagtail (W) and Pelican (P) as shown in the diagram below. N W 490 km K 40 0 km P Kestrel is 0 kilometres from Pelican. Wagtail is 490 kilometres from Pelican. Pelican is on a bearing of 40 from Kestrel. Calculate the bearing of Pelican from Wagtail. Give your answer to the nearest degree. Total (A. / #A.) #

10 R.5 4 Solve the equation 4 sin x = 0, 0 x 60. # Total (R.5) #

11 A. 5 The diagrams below show directed line segments u and v. # u v Draw the resultant of u + v.

12 6 The diagram below shows a square based model of a glass pyramid of height 6 cm. Square OABC has a side length of 7 cm. The coordinates of A are (7, 0, 0). C lies on the y-axis. z D y C B O A (7, 0, 0) x Write down the coordinates of D. 7 The forces acting on a body are represented by three vectors p, q and r as given below p =.6, q = and r = Find the resultant force. 8 Vector a = 7 and vector b = 5 Calculate. a + 4b

13 National 5 Mathematics Assessment 8 Bridging Assessment Name: Form Class: Practice R. R. 9 7 Calculators may be used in this assessment All questions should be attempted Full credit will be given only where the solution contains appropriate working. State the units for your answer where appropriate.

14 FORMULAE LIST The roots of ax + bx + c = 0 are x = b ( b 4ac) a Sine rule: a sin A 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 Volume of a cone: Volume = r h Volume of a Pyramid: Volume = Ah Standard deviation: s = ( x x) x ( x) n n / n, where n is the sample size.

15 Question Weight st Class postage nd Class postage Up to 40 mm (L) 65 mm (W) 0 5 mm (D) 0 00 g 6p 5p Up to 5 mm (L) 50 mm (W) 5 mm (D) 0 50 g g g 90 0 Over 5mm (L) 50 mm (W) 5 mm (D) g g g g g g 0 40 Your assessor will give you an envelope or a small packet. Measure the size and weight of your envelope or small packet and decide how much the postage will cost if it is posted st class. Use your measurements to justify your answer. Size: Weight: Cost of postage: Total (R.) #

16 Question A company wants to know what type of accommodation travellers typically use. The results of a survey on the passengers arriving at Glasgow Airport are shown in the table below: Type of accommodati on Business traveller Tourist Total Hotel Bed & breakfast Self-catering Friends Total (a) What is the probability that a traveller staying in Bed & Breakfast accommodation, selected at random, is a Business traveller? Give your answer as a fraction. Working Answer (b) Most business travellers stay in hotels, whereas most tourists stay in with friends. Comment on this statement. Use your working to justify your answer. Working Answer Total (R.) #