Maths Practice Exercises 13+

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8 In quadrilateral ABCD, angle BAD = 90, AB = AD = 5 cm and BC = DC = 7 cm. (i) Make an accurate drawing of quadrilateral ABCD. B A (ii) Draw any lines of symmetry on your quadrilateral. (iii) Which type of quadrilateral have you drawn?

9 9 10. (i) The line AC is a diagonal of the rhombus ABCD. The length of the side AB is 6 cm. The length of AC is exactly 10 cm and the diagram below shows this line. Using a pencil, ruler and a pair of compasses, construct accurately the rhombus ABCD. A C (ii) Measure the length (in cm) of the diagonal BD. (iii) Calculate the area (in cm²) of the rhombus ABCD.

10 Alfie and Brenda are practising their hockey skills. The position of Alfie (A) is marked. N A Alfie passes the ball 50 metres to Brenda on a bearing of 140. (i) Plot the position of Brenda (B) using a scale of 1 cm : 5 m. Alfie now runs 30 m on a bearing of 210. (ii) Plot Alfie s new position (A ). Brenda (B) now passes the ball back to Alfie (A ). (iii) Find the distance in metres the ball travels from B to A. (iv) Find the bearing on which the ball travels from B to A.

11 A coastguard station (C) is positioned on the coast as shown below. A lifeboat station (L) is positioned on the coast to the east of C. N C L The coastguard receives a distress signal from a trawler which is 1 km from the coastguard station (C) on a bearing of 050. (i) Use a scale of 1 : to plot the position of the trawler (T). The lifeboat leaves the lifeboat station (L), and sails directly to the trawler. (ii) Use your scale drawing to find: (a) the distance in metres that the lifeboat travels to the trawler (b) the bearing on which the lifeboat travels to get to the trawler. (iii) If the lifeboat travels at 12 kilometres per hour, how long will it take to reach the trawler? Give your answer to the nearest minute.

12 Late at night, a yacht, Y, is in distress on a lake. A searchlight at rescue station A picks up the yacht on a bearing of 054, and a searchlight at rescue station B, on the opposite side of the lake, picks up the yacht on a bearing of 300. N N A B (i) Draw two lines on the diagram to locate the position of the yacht, Y. The scale of the map is 1 : (ii) What is the distance, in metres, of the yacht from rescue station A? (iii) What is the bearing of A from B?

13 From the base camp (C), the bearing of a polar bear (P) is 225. The weather station (W) is 90 m south of C. The bearing of the bear from W is 285. N C C (i) (ii) Using a scale of 1 : 1000, draw a diagram to show the positions of the weather station (W) and the polar bear (P). By using measurements on the diagram, find the distance of the polar bear from the weather station. Give your answer in metres to the nearest metre.

14 Bratby (B) is 9 km away from Addleton (A) on a bearing of 070. (ii) Using a scale of 1 : , mark the position of Bratby. N A (iii) What is the bearing of Addleton from Bratby? Creakybridge (C) is on a bearing of 115 from Addleton and 210 from Bratby. (iv) Mark the position of Creakybridge on the diagram. (v) What is the distance in kilometres from Bratby to Creakybridge?

15 girls were asked to name their favourite sport. The choices were swimming, hockey, tennis and netball. The results are to be shown in a pie chart, part of which has been drawn. 120 o Hockey (i) How many girls chose hockey? (2 A quarter of the girls chose netball. (ii) On your worksheet, draw a sector to show this, marking it clearly with both the angle and the sport. (2 Of the remainder, twice as many chose swimming as chose tennis. (iii) Show these sectors in the pie chart, marking them clearly with both the angle and the sport. (4

16 On a ramble, 72 people each chose a sandwich. They had the choice of ham, cheese, tuna, salad or chicken. Part of a pie chart showing their choice of sandwich is shown below. Cheese Ham 35 o (i) How many people chose a ham sandwich? Twice as many people chose tuna as chose cheese. Eleven chose a salad sandwich. The remainder chose a chicken sandwich. (ii) Complete the pie chart, writing the name of the sandwich filling and the size of the angle in each sector.

17 The temperature was measured at noon on each of the first ten days in March and the measurements are recorded in the table below. Date 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th Temperature ( C) (iii) Complete the line graph. (2 12 Temperature ( o C) x x x st 2 nd 3 rd 4 th 5 th 6 th 7 th 8 th 9 th 10 th Date in March

18 The conversion graph below can be used to change centimetres to inches Inches Centimetres Use the graph to answer the following questions, showing clearly where you take your readings. (i) (ii) How many inches are equivalent to 260 centimetres? There are 12 inches in 1 foot. Simon s height is 5 feet 10 inches. What is his height measured in centimetres?

19 The scatter graph below shows the marks for English examination papers 1 and 2 of a class of 20 children Paper 2 marks Paper 1 marks (i) What type of correlation does this scatter graph suggest? (ii) One pupil scored a higher mark on Paper 2 than Paper 1. On your graph, put a circle around the cross which represents this pupil. (iii) Draw by eye the line of best fit. (iv) Peter was absent for Paper 2 but he scored 73 marks on Paper 1. Use the scatter graph to estimate the mark Peter might have obtained on Paper 2 if he was typical of this group.