Level 4 End of year Test Revision

Transcription

1 1 Level 4 End of year Test Revision Scientific Notation 1) Write the following numbers in scientific notation: a) b) c) d) 607 e) 87 f) 1 million g) h) i) j) k) ¼ billion l) ¾ million 2) Change the following back into their original numbers: a) x 10 5 b) 5.72 x 10 6 c) 8.7 x 10-3 d) 3.15 x 10 2 e) 1.5 x 10-7 f) 3 x 10-4 g) 8.43 x 10 3 h) 2.9 x 10-2 i) 5.9 x 10-7 j) 1.27 x 10 5 k) 9.23 x 10 5 l) 8 x 10 0 Prime products 3) State the prime factors of: a) 25 b) 34 c) 54 d) 400 e) 55 f) 24 g) 400 h) 90 i) 480 Fractions 4) Express the fractions below as top heavy' or improper fractions: a) 4 3 / 5 b) 12 1 / 2 c) 3 6 / 7 d) 14 2 / 3 e) 2 11 / 12 5) Rewrite the top heavy fractions as whole numbers and fractions:- a) 23 / 5 b) 24 / 7 c) 37 / 6 d) 57 / 3 e) 42 / 15

2 2 6) Find the following answers in their simplest form: a) 5 / / 5 b) 5 4 / / 7 c) 10 / 11-3 / 2 d) 9 7 / / 2 7) Find the following answers in their simplest form: a) 1 / 7 x 3 / 4 b) 4 / 9 x 3 / 5 c) 5 1 / 11 x 1 3 / 2 d) 13 / 20 x 3 1 / 2 8) Find the following answers in their simplest form: a) 5 / 2 3 / 7 b) 4 / 9 3 / 5 c) 2 10 / / 4 d) 3 / 2 7 / 20 Proportion 9) Nine iced buns cost How much does one iced bun cost? 10) Five sweets cost 30pence. How much would eight sweets cost? 11) Three cartons of orange juice costs How much would five cartons cost? 12) A wall 8metres by 3 metres costs 72 to paint. How much would it cost to paint a wall 6 metres by 5 metres? 13) Three men take 4 hours to tidy Mrs Brown s garden. How long would it take one man to do the same job? 14) Two men take 5 hours to paint a fence. How long would it take one man? 15) Three woman take 10 minutes to wash a car. How long would it take one woman? 16) It took 6 people 40 minutes to mop the dance floor of their local church hall. How long would it take two people? 17) Two dozen chickens have enough food to last them 6 days. How long will the same amount of food feed 4 chickens? 18) Mary can sew 360 stitches in twelve minutes. How long will it take her to sew 240 stitches?

3 3 Algebra 19) Simplify the following: a) 4x + 7x + x b) 6a - 2a + 3a - 4a c) 8x x - 2 d) 10t t + 8 e) 3a 2 + 5b + 2a 2 - b f) 3x 2 - y 2 + 2x 2 + 5y 2 g) 16z + 9t + 12z - 7t h) 24q + 13r - 5q + 8y - 4r i) 77t + 55t - 18t + 9u + 10v j) 3a 2 + 6a 2 + 7b 4b 20) Expand the following:- a) 4(x + 8) b) 5(x 7) c) 3(3x - 5) d) 7 (2x + 3) e) 8 (5x 6) f) 7(3 2x) g) 5(2 7x) h) 9(12 5x) i) 2(4y + 5z 9) j) 8(3a + 8j 5k) 21) Remove the brackets and simplify a) x(x + 4) b) x(x + 6) c) x ( 2x 7) d) 7(x + 6) + 3x + 6 e) 3(x + 5) + 7x + 2 f) 5(2x 4) + 3x + 15 g) 4(4x 7) + 7(2x + 3) h) 5(2x + 3) + 4(5x + 3) i) 5(2x + 4) + 7(x 2) j) x (x + 3) + x (x + 2) k) x (x + 5) + x (x + 7) l) 2(a + 3) m) -4 (b + 5) n) -3(u v) o) -2m(m+3) p) x(x y) q) y 2(y 5) r) m 3(m - 5) 22) Factorise fully:- a) 5x + 35 b) 6y 26 c) x 2 + 7x d) 15y xy e) 4x 16 f) 12y 9 g) 15w 25 h) x 2 + 5x i) 77xy + 11y j) y k) 21x 2 + 7x l) 16x 2 y + 32x y 2

4 4 23) Solve the following:- a) a + 7 = 28 b) b - 8 = 17 c) c - 19 = 71 d) d = 13.5 e) 2e = 26 f) 4f = 28 g) 6g = 42 h) 9h = 99 j) 3j + 2 = 17 k) 5k - 1 = 24 l) 4m - 7 = 13 m) 12n - 13 = 108 n) 5p - 6 = 2p + 12 o) 10q + 35 = 2q + 75 p) 13r + 2 = 2r 97 q) 5(t + 5) = 3t + 30 r) 10(2v - 1) = 5(v + 6) s) ½ x + 4 = 9 t) ¼x - 7 = -4 u) ¾x - 1 = 5 v) ¾x + 2 = ½x + 3 w) / 4 x = 1 / 8 x + 22 x) / 8 x = 1 / 3 x + 8 Statistics 24) Find the mean, median, mode and range of the data below: ) The mean age of a group of eight girls was 15. One more girl joined the group and the mean changed to 14. How old was the girl? 26) The mean weight of a group of seven girls was 54kg. One more girl joined the group and the mean changed to 53kg. What was the weight of the eight girl? 27) The mean height of a group of six boys was 128cm. One more boy joined the group and the mean changed to 131. How tall was the extra boy? 28) Construct a frequency table using appropriate intervals for the data below:

5 5 29) Here are a set of class test results a) Calculate the mean, mode and median for this set of data. b) Calculate the range 30) 60 people were asked what their favourite animal was. Type of pet Frequency Angle Dog Cat Fish Other Total Copy and complete the table below and draw a pie chart to reflect the information Probability 31) Find the probability of picking the colours listed below from a bag containing the following cards: blue blue red green yellow green blue pink black white red red yellow green a) P(red) b) P(blue) c) P( green or yellow) d) P( colour that s not white) e) P( colour with four letters in it)

6 6 32) From the list of numbers below, calculate the following probabilities: a) P( number bigger than 7) b) P( number less than 8) c) P(even number) d) P(odd number) e) P(prime number) f) P(number divisible by 3) Profit and Loss Calculations 33) Scarf Rack in Dalkeith bought a box of 6 identical scarves for The scarves were then all sold for each. How much profit was made when all the ties were sold? 34) I bought an old bicycle for 15. It cost me for new tyres and 6.75 for a new chain. a) How much did the bicycle cost me altogether? b) If I then sold the bicycle for 55, how much profit did I make? 35) I bought a second hand car for and sold it a year later, when I made a loss of 950. How much did I sell the car for? 36) Claire bought a rowing machine for 195 and en exercise bike for 120. A year later she sold the rowing machine for 265 and the bike for 95. Did she make a profit and how much did she make altogether?

7 7 Linear Patterns 37) A steam cleaner company asks for a 5 hire charge plus 2 per hour of hire. a) Copy and complete the table of hire charges and write down a formula connecting the letters C and T:- Time in Hours (T) Cost in s (C) ??? b) Use your formula to find the cost of hiring a steam cleaner for 10 hours? 38) For each of the tables, determine a formula in the form y =...x ±... a) x y b) x y c) x y d) x y

8 8 Areas 39) Find the area of each shape a) b) 8cm 5cm 12cm 8cm c) d) 5cm 6cm 20cm 12cm e) f) 8cm 6cm 28cm 21cm 15cm

9 9 g) 18cm 18cm 27cm 35cm 40) Find the area of the shaded sections: 25cm 20cm 12cm 25cm 31cm 40cm

10 10 41) Find the missing edge lengths: a) b)?cm 8cm Area = 28cm 2 Area = 32cm 2 7cm?cm c) d) 17cm 8cm Area = 180cm 2 Area = 125cm 2?cm?cm 15cm Circles 41) Find the area of a circle with the following radius: a) 2 cm b) 3 cm c) 7cm 42) Find the area of a circle with the following diameter: a) 9 cm b) 12 cm c) 24 cm

11 11 43) Find the perimeter of: 10cm 10cm a) b) 20cm 12cm 8cm 44) Find the area of the shaded sections: 30cm (a) 7cm (b) Speed, distance, time 45) a) A plane flew 2860 miles from Glasgow to New York in 6 hours and 30 minutes. Calculate the speed of the plane. b) David cycled 60km at an average speed of 24km per hour. How long did it take him? c) A jet travelled at 800km per hour and managed to fly a distance of 2720km on a full tank of fuel. How long did the flight take?

12 12 d) David walks at an average speed of 8 km/hour. His last walk took 2 hours and 20 minutes. How far did he walk? 46) This graph show s Lauren s motor cycle trip from her home to her aunt s home and back. a) On her way to her aunt s, she stopped for a break. For how long? b) How far does her aunt stay from Lucy s house? c) Calculate the speed for the return journey. Pythagoras 47) Calculate the length of the missing side x cm 12.5cm 7.8cm

13 13 48) Mrs Harpur is convinced her new board set square is not right angled! Using the converse of Pythagoras, is she correct? 45cm 27cm 54cm Trigonometry 49) Find the size of the unknown angle. x o 9m 14m 50) Find the length of the unknown side. 33 o 12cm x cm