Year 10 Set1a Christmas Exam Revision

Year 10 Set1A Christmas Exam Revision

Rational and Irrational Numbers and Surds

Express the following decimals as fractions; ...... 1. 0.6 2. 0.08 3. 0.7 2 4. 0.025 ...... 5. 0.19 6. 2.381 7. 0.05652 8. 0.014

Simplify; 9. (3  5)(4  5) 10. (7  2)2 11. ( 5  7)( 5  7) 12. (6  5 3)(6  5 3) 13. (9  4 5)(2  3 5) 14. ( 7  2) 2

Work out; 15. If a  6 , b  2 , c  12 find; 5c b (i) 3a 2 (ii) abc (iii) (iv) ab  7c (v) a 9c 16. If a  (3  6) , b  (3  6) find; (i) ab (ii) p  q (iii) p  q (iv) a 2 17. If a  8 , b  5 , c  40 , d  ( 3  2 5) , e  ( 3  2 5) find; b (i) abc (ii) b3 (iii) (iv) de (v) d  2e ca 2

Standard Form

Write the following numbers in standard form 1. 4300 2. 7210003. 0.000005 4. 0.00092 5. 301000 6. 0.0000805 7. 32 million 8. 0.00000028 Calculate the following without a calculator, giving your answer in standard form 9. (7 x 105) x (6 x 10-2) 10. (3 x 10-6) x (3 x 10-2) 11. (9 x 10-8) x (1.2 x 103) 12. (4.3 x 103) + (1.8 x 104) 13. (6.2 x 10-2) – (5.7 x 10-3) 14. (9.3 x 105) – (7.5 x 104) (8.6107 ) (1.2103 ) (6105 ) 15. 16. 17. (2104 ) (3102 ) (1.5101 )

Limits of Accuracy

1. Fiona drives to work. Each day she drives 49 miles, to the nearest mile. Calculate the least possible distance she drives in 5 working days. 2. Charlotte has 12 books which are each 30 mm thick, correct to the nearest millimetre. Calculate the upper and lower bounds of the total thickness of the 12 books. 3. The length of a table top is 2050mm, measured to the nearest 10mm. (a) Write down the least and greatest possible values of the length of the table top. (b) The width of the table top is 1040mm, measured to the nearest 10mm. Find the least possible perimeter of the table top. 4. Sally has a shelf which is 250 cm long, correct to the nearest centimetre. She cuts off a piece which is 75 cm long, correct to the nearest centimetre. What is the upper bound of the length of the remaining piece of shelf? 5. A rectangle has a length of 10.3 cm and a width of 3.6 cm. Both measurements are correct to the nearest 0.1 cm. Calculate the upper bound of the area of the rectangle. 6. Kerbstones are made in the shape of a cuboid.

The dimensions of the kerbstones are 50cm by 20cm by 10cm. All measurements are given correct to the nearest centimetre. Calculate the greatest possible length of 200 of these kerbstones laid along a straight road. Give your answer in metres. Explain any assumptions you have made in working out your answer. 7. Wall tiles for sale Length 30cm Width 15cm All measurements to the nearest centimetre.

(a) Is it always possible to tile an area of up to 8500cm2 using 20 of these tiles? You must give a reason and show your working. (b) Write down the maximum area that could be covered using 20 of these tiles. 8. Philip wants to fit a cupboard and a dishwasher side by side in his kitchen. The width of the cupboard is 50 cm, correct to the nearest centimetre. The width of the dishwasher is 60 cm, correct to the nearest centimetre. The space available measures 112 cm, correct to the nearest centimetre. Philip fits the cupboard and dishwasher side by side in this space. What is the lower bound of the space remaining?

Utility Bills

1. Mr Jones received an electricity bill shown below. Use the information on the bill to complete all of the missing entries and calculate the total amount that Mr Jones has to pay.

Wales Electricity Company Mr Jones 29 Sea View Grapville FR13 9RT

Meter reading Meter reading Tariff Units used Price of each Amount £ last time this time C-customer reading unit in pence E-estimated reading 58942 C 60583 C Units used ______8.16 ______Service Charge £21.37 ______Total charge before V.A.T. ______V.A.T. at 5% of the total charge ______Total charge including V.A.T. ______Previous credit carried forward 43.82 CR Amount to pay ______Percentages

1. A jacket costing £102 is reduced by 20% in a sale. Find the sale price. 2. Express 13.64 as a percentage of 88 3. The population of a city increased from 21,000 to 24,108. Find the percentage increase 4. Find the compound interest when £4500 is invested for 3 years at an interest rate of 2% p.a. 5. A car was bought and then sold a year later at 15% less than the buying price for £5,270. How much was the original cost of the car? 6. What percentage of 970 is 664.45? 7. A sofa costs £320 to make and is sold to make a profit of 45%. Find the selling price. 8. After a fire, the number of trees in a forest decreased from 1400 to 945. Find the percentage decrease. 9. A house was sold for £158,750 which was 27% more than the house was bought for. Find the original price of the house. 10. Find the compound interest when £1750 is invested for 2 years at an interest rate of 3.5% p.a.

Averages of Grouped Data in a Frequency Table

For each of the following tables of data, find an estimate for the mean, find the modal group, and state which class interval the median lies in.

1 Age Frequency 2 Score Frequency 3 Number Frequency 0 - 9 4 30 - 35 57 11 - 15 11 10 - 19 12 36 - 40 49 16 - 20 42 20 - 29 6 41 - 50 31 21 - 25 27 30 - 39 3 51 - 55 22 26 - 30 9 40 - 44 7 56 - 60 41 31 - 40 35 45 - 50 8 41 - 50 26

Cumulative Frequency

1. The table gives the grouped frequency distribution for the heights, measured to the nearest cm, of 120 plants.

Height 51 - 55 56 - 60 61 - 65 66 - 70 71 - 75 76 – 80 Number of plants 7 19 26 35 24 9

a) Complete the following cumulative frequency table.

Height (less than) 55.5 60.5 65.5 70.5 75.5 80.5 Cumulative frequency

b) On graph paper, draw a cumulative frequency diagram to show this information.

c) Use your cumulative frequency diagram to find: (i) the median (ii) the interquartile range

d) Use your cumulative frequency diagram to find: (i) how many plants had a height of 63cm or less (ii) what percentage of plants had a height of more than 72cm (iii) what fraction of plants had a height between 60cm and 78cm 2. Using the cumulative frequency diagram shown, complete the frequency table below;

Height Frequency

a) How many plants have a height more than 60cm? b) What percentage of plants have a height less than 40cm?

Foreign Currency

1. If £1 = 1.12 euros, then : a) Convert £630 to euros b) Convert 543.2 euros to pounds 2. If £1 = 1.68 canadian dollars, then: a) Convert £250 to Canadian dollars b) Convert 517.44 canadian dollars to pounds 3. If £1 = 150 japanese yen, then: a) Convert £1080 to Japanese yen b) Convert 113,475 japanese yen to pounds

Solving quadratic equations using the quadratic formula

Give your answers correct to two decimal places.

1. 2x2  5x  3  0 2. 3x2  6x 11  0 3. x2  7x 15  0 4. 5x2  33x  9  0 5. 4x2 19x  21  0 6. x2  23x 15  0 Solving quadratic equations by factorising

1. 16x2  8x  0 2. 8a2  24  0 3. 8x 2  2x  3  0 4. x2  5x  24  0 5. 4x 2  25 6. x2  9x  20  0 7. 3x 2 15  14x 8. 7x(3x 1)  0

Factorisation

2 1. 9 p  p 2. 6gh  9h 3. 8rt  6r 2 2 2 4. 18c 2 12cb 5. 6 pq  5p q 6. x2 11x  30 7. x2  2x  24 8. x2  2x 15 9. x2  8x 12 10. x2  6x  27 11. 4x2  36 12. 9x2  64 13. 16x2 1 14. x2  25 15. 81x2  49 16. 5x 2 13x  6 17. 6x 2  7x  2 18. 4x 2 17x 15 x2 11x  30 2x2  x 15 x2  36 19. 20. 21. x2  25 5x2 15x 3x2  22x  24

Indices

Simplify the following; 5 6 3 1. a 4b3  a 2b5 2. 5m 2n 8mn 5  3mn 3. (5r t ) u 4v 6 w2 48p 6 q 2 r 3 56m 2n 1 4. 5. 6. u 4vw5 8p 3r 7 7m 5n 4 4 2 9 1 1   2  7. 3 3 8. 4 4 9.  x  2m  3m n  7n   7 4 3 16e 3 14y 3 10r 2 10. 11. 12. 4 2  1 4e 3 2y 3 5r 2 1 3 2 7 15 1 13  4 5  2y 2  y 2 2n 5  9n 5  x y  13. 14. 15.   2 2 y 5 13 7 3n x 8 y 2

1 2 0.5 2 16. 64 2  43 17. 1000 3  52 18. 36 8

Evaluate the following; 1 19. 6-2 20. 10-5 21. 36 2 1 1  1 22. 27 3 23. 1600 2 24. 100 2  1 1 3 25. 8 3 26. 900  2 27. 16 2 4 2 2 28. 27 3 29. 64 3 30. 8000 3

Product of Prime Factors

1. Express the following as a product of prime factors in index notation and find the smallest number needed to multiply by to make each number a perfect square. a) 360 b) 288 c) 875 2. Find the Highest Common Factor of: a) 600 and 1250 b) 108 and 225 3. Find the Lowest Common Multiple of: a) 600 and 1250 b) 108 and 225 Straight line graphs

1. Draw the graph of on the grid below;

2. Write down the equation of a straight line which is parallel to 3. Find the equation of the following straight lines; a) b)

4. Find the mid-point of the line AB which has coordinates A (-2, 7) and B (-9, -3)

Simultaneous Equations

x  y  56 x  y  27 x  y  27 1. 2. 3. 3x  2y  137 5x  3y  105 6x  5y  41 2x  5y 16 4x  3y  22 2x  2y  8 4. 5. 6. 3x  2y  5 3x  4y  4 7x  5y 12 For each question, form a pair of simultaneous equations and solve them. 7. A man buys x adult tickets and y children’s tickets to see a concert. Altogether he buys 29 tickets. Adult tickets cost £15 each and children’s tickets cost £7 each. He spends £299 in total. 8. Two numbers have a sum of 33 and a difference of 7. 9. A man buys x adult tickets and y children’s tickets to see a concert. Altogether he buys 42 tickets. Adult tickets cost £27 each and children’s tickets cost £21 each. He spends £1056 in total. 10. A mans haircut costs £m and a boys haircut costs £n. One man and three boys pay a total of £23, while four men and three boys pay a total of £47. 11. Two numbers have a difference of 34 and a sum of 46.

Trial and Improvement

1. A solution to the equation x3  7x  30  0 lies between the values 3 and 4. Use a method of trial and improvement to find a solution correct to 1 decimal place. 2. Solve the following equation using the formula method, giving your answers correct to 2 decimal places; 5x 2  8x  2  0

Solving Equations

x  9 1. 5x 11  29 2. 8  7y  29 3.  3 5 4e 3m  8 6r 4.  5  1 5. 1 6. 12  7  3 2 7 21 7. 5   2 8. 4m  7  32  m 9. 3a 11 8a  7 x 2k  5 k  2 10. 6(3t  4)  4(5t  7) 11. 2(3  2h)  8(h  3) 12.   5 3 9 8 j 18 j  3 1 2e  9 3e  3 7  3q 4q  5 4 13.   14.   2 15.   8 2 2 3 4 5 2 5

Trigonometry

1. Find the missing letters: a) b) c)

33o z 21cm 9.3m 18o 16.7mm

x 11.3mm m

2. a) (i) Find the length AC b) (i) Find the length AC (ii) Find the angle DAC (ii) Find the angle AED A A

15m D 16.7cm

58 C 47 B 6.3cm B C 2.5cm D E 3. Jim and Jack start walking from their home. Jim walks 3.7Km north and Jack walks 5Km east. Find the bearing of:

(a) Jack from Jim

(b) Jim from Jack

B 4. 5. Q 5.8cm 9.3m 7.2m R 62o A 34o P 12.1m C (a) Find AC (a) Find QRP (b) Find the area of triangle ABC (b) Find the area of triangle PQR

6. Find TW 7. Find: (a) DAC V (b) CAB 9.2m 81o (c) BC U 8.8m A 17.3cm B 73o 35o W 31.6cm T 85o D C 25.8cm

8. A man prospecting for oil in the desert drives 46km on a bearing of 034o and then 38km on a bearing of 164o. (a) How far is the man from where he started? (b) On what bearing must he travel to return to his starting point?

Pythagoras’s Theorem

1. Find the length x 2. Find the length CD

A 9.7m 6.2m 19m x 13m D

3. Find the length of the sloping roof x: B 7m C x

9m Loci and Angle Constructions

1. Find and shade the region of points that satisfy both of the following conditions; (i) the points are closer to P than Q (ii) the points are within 7cm of Q

2. Max and Josh hide a box in their garden. Their box is further than 8m from AB, further than 3m from D and closer to AD than DC. Find and shade the region of the garden in which the box is hidden. Use a scale of 1cm to 1m.

B C 3. Find and shade the region of points that satisfy both of the following conditions; (i) the points are nearer to XY than to XZ (ii) the points are less than 7cm from X Y

4. ABCD is a rectangle. Find and shade the region of points inside the rectangle which satisfy all of the following conditions; (i) the points are nearer AB than BC (ii) the points are closer to A than D (iii) the points are further than 5cm from A

5. Using only a ruler and compass and showing all your construction arcs, construct an angle of: a) 90o b) 45o c) 60o d) 30o e) 120o Angles of polygons

1. Find the size of an interior angle in a regular pentagon 2. Find the size of an exterior angle in a regular octagon 3. A regular polygon has an exterior angle of 30o. How many sides does it have? 4. Find the angles represented by letters in the polygons below;

a) b) o o 66 o 102 137o f 27 144o 170o 132o 125o r o 123o 73 e Area

Find the area and perimeter of the following shapes: 1. 2. 3. 3cm 4. 7mm 6cm 5cm 12m 12m 5mm 4cm 11mm 7mm 9cm 3m 5. The tyres of a car have a diameter of 83cm. The car travels for 300m before stopping. How many complete turns will the tyres of the car have made? 6. Find the surface area of a cuboid which measures 6cm by 4cm by 5cm. 7. Find the surface area of a cylinder which has a height of 12cm and a radius of 4cm.

Find the area of the following shapes: 8. 9. 7cm 10.

8cm 11m 5cm 16cm 10cm 6m

12cm 10m 8cm