A 10 cm. The diagram represents a large cone of height 30 cm and base diameter 15 cm.

Transcription

1 0 cm 5 cm 5 cm 5 cm 0 cm B 0 cm B 0 cm 5 cm 5 cm The diagram represents a large cone of height 30 cm and base diameter 5 cm. The large cone is made by placing a small cone of height 0 cm and base diameter 5 cm on top of a frustum B. Calculate the volume of the frustum B. Give your answer correct to 3 significant figures. d cm h cm 3 d cm The diagram shows a frustum. The diameter of the base is 3d cm and the diameter of the top is d cm. The height of the frustum is h cm. The formula for the curved surface area, S cm, of the frustum is S = πd h d Rearrange the formula to make h the subject. Two mathematically similar frustums have heights of 0 cm and 30 cm. The surface area of the smaller frustum is 450 cm. (c) Calculate the surface area of the larger frustum. (Total 8 marks)

2 The diagram shows a sector of a circle with a radius of x cm and centre O. PQ is an arc of the circle. ngle POQ = 0. O 0 x cm P Q Write down an expression in terms of and x for (i) (ii) the area of this sector, the arc length of this sector. The sector is the net of the curved surface of this cone. rc PQ forms the circumference of the circle that makes the base of the cone. h cm x cm The curved surface area of the cone is cm. The volume of the cone is V cm 3. The height of the cone is h cm. Given that V = 3, find the value of h. (Total 5 marks)

3 y 6 P O x Rotate triangle P 90 clockwise about the point (0, ) Label the new triangle Q. Translate triangle P by the vector 5 6 Label the new triangle R. () (Total 3 marks) 4.5 cm 6 cm B 4.8 cm E 4 cm C D BE is parallel to CD. E = 6 cm, ED = 4 cm, B = 4.5 cm, BE = 4.8 cm. Calculate the length of CD. Calculate the perimeter of the trapezium EBCD.

4 The diagram represents a vertical flagpole, B. The flagpole is supported by two ropes, BC and BD, fixed to the horizontal ground at C and at D. B.8 m C 6.8 m 4 D B =.8 m. C = 6.8 m. ngle BD = 4. Calculate the size of angle BC. Give your answer correct to 3 significant figures. Calculate the length of the rope BD. Give your answer correct to 3 significant figures. y 5 4 (Total 6 marks) O x On the grid, rotate triangle 80 about O. Label your new triangle B. On the grid, enlarge triangle by scale factor, centre O. Label your new triangle C. (Total 5 marks)

5 y O x Triangle is reflected in the y axis to give triangle B. Triangle B is then reflected in the x axis to give triangle C. Describe the single transformation that takes triangle to triangle C. (Total 3 marks) 4 cm 0 cm The diagram shows a cylinder with a height of 0 cm and a radius of 4 cm. Calculate the volume of the cylinder. Give your answer correct to 3 significant figures. The length of a pencil is 3 cm. The pencil cannot be broken. Show that this pencil cannot fit inside the cylinder. (Total 5 marks)

6 6 cm B 8 cm C 3.5 cm E D 9 cm B is parallel to DE. CE and BCD are straight lines. B = 6 cm, C = 8 cm, CD = 3.5 cm, DE = 9 cm. (i) (ii) Work out the length of CE. Work out the length of BC. (Total 3 marks) B Jill rolls a ball from point C. t any point on its path, the ball is the same distance from point and point B. C On the diagram above, draw accurately the path that the ball will take. On the diagram, shade the region that contains all the points that are no more than 3 cm from point B.

7 B C O Work out the value of x. BCDEF is a regular hexagon and BQP is a square. ngle CBQ = x. straight line has equation y = x + The point P lies on the straight line. P has a y-coordinate of 5. Find the x-coordinate of P. Write down the equation of a different straight line that is parallel to y = x +. (c) Rearrange y = x + to make x the subject. () (Total 5 marks) Use the ruler and compasses to construct the perpendicular to the line segment B that passes through the point P. You must show all construction lines. B P (Total marks), B and C are points on the circumference of a circle, centre O. C is a diameter of the circle.

8 (i) Write down the size of angle BC. E F (ii) Give a reason for your answer. O 30º D, E and F are points on the circumference of a circle, centre O. ngle DOF = 30. (i) Work out the size of angle DEF. D (ii) Give a reason for your answer. lighthouse, L, is 3. km due West of a port, P. ship, S, is.9 km due North of the lighthouse, L. Calculate the size of the angle marked x. Give your answer correct to 3 significant figures. Find the bearing of the port, P, from the ship, S. Give your answer correct to 3 significant figures. () The two-way table gives some information about how 00 children travelled to school one day. Walk Car Other Total Boy Girl 8 6 Total Complete the two-way table. One of the children is picked at random. Write down the probability that this child walked to school that day. () One of the girls is picked at random. (c) Work out the probability that this girl did not walk to school that day. (Total 6 marks)

9 The diagram shows a 3-sided spinner and an ordinary dice. red green blue The spinner has green side, blue side and red side. lex spins the spinner once and rolls the dice once. Write down all the possible outcomes. (Total marks) my is going to play one game of snooker and one game of billiards. The probability that she will win the game of snooker is 3 3 The probability that she will win the game of billiards is 4 The probability tree diagram shows this information. my played one game of snooker and one game of billiards on a number of Fridays. She won at both snooker and billiards on Fridays. Work out an estimate for the number of Fridays on which my did not win either game. (Total 3 marks) Joan has two boxes of chocolates. The boxes are labelled and B. Box contains 5 chocolates. There are 6 plain, 4 milk and 5 white chocolates. Box B contains chocolates. There are 4 plain, 3 milk and 5 white chocolates. Joan takes one chocolate at random from each box. Work out the probability that the two chocolates Joan takes are not of the same type.

10 Mr Irvine has a farm. The table gives information about the number of animals on his farm. nimal Frequency Cow 5 Hen Pig 5 Sheep 8 Complete the accurate pie chart to show this information. Cow Mary recorded the heights, in centimetres, of the girls in her class. She put the heights in order Find (i) (ii) the lower quartile, the upper quartile. On the grid, draw a box plot for this data cm (Total 5 marks)

11 The scatter graph shows information about countries. For each country, it shows the percentage of the population in farming jobs and the percentage of the population living in towns Percentage living in towns Percentage in farming jobs Describe the relationship between the percentage of the population in farming jobs and the percentage of the population living in towns. Draw the line of best fit on the scatter graph. () () In Mathsland, the percentage of the population in farming jobs is 35%. (c) Use your line of best fit to estimate the percentage of Mathsland s population living in towns. () (Total 3 marks) The table shows information about the heights of 40 bushes. Height (h cm) Frequency 70 h < h < h < h < h < 95

12 Complete the cumulative frequency table. Height (h cm) 70 h < h < h < h < h < 95 Cumulative Frequency () On the grid, draw a cumulative frequency graph for your table. 40 Cumulative frequency Height ( h cm) (c) Use the graph to find an estimate for the median height of the bushes. cm ()