Biggar High School Mathematics Department S1 Block 1 Revision Booklet GOLD
Contents MNU 3-01a MNU 3-03a MNU 3-03b Page Whole Number Calculations & Decimals 3 MTH 3-05b MTH 3-06a MTH 4-06a Multiples, Factors, Powers, Primes & Roots 6 MNU 3-20a MTH 3-20b MTH 3-21a MNU 4-20a MTH 4-20b Displaying Data & Statistics 8 MTH 3-17a Angles 12 MNU 3-04a MTH 3-18a MTH 4-18a Integers 14 MTH 3-14a MTH 3-15b Algebra 1 16 Answers 17 2
Whole Number Calculations & Decimals Success Criteria: MNU 3-01a, MNU 3-03a & MNU 3-03b I can round a number to any decimal places. I can round a number to any significant figures. I know the meaning of sum and product. I can use BIDMAS to correctly answer a calculation. I can multiply and divide whole numbers up to 3 digits and can use long multiplication and division. I can multiply and divide numbers by multiples of 10. I can mentally recall times tables up to 12. 1. Round the following to the nearest whole number: a) 2.6 b) 8.1 c) 4.5 d) 15.9 e) 20.3 f) 67.8 g) 9.5 h) 7.11 i) 2.92 j) 0.6 k) 14.22 l) 50.57 m) 399.9 n) 6.001 o) 1.345 2. Round the following to one decimal place: a) 1.36 b) 0.91 c) 0.55 d) 5.92 e) 2.31 f) 9.89 g) 19.55 h) 3.95 i) 0.99 j) 100.63 k) 1.282 l) 5.561 m) 3.919 n) 12.049 o) 11.453 3. Round the following to two decimal places: a) 0.189 b) 0.994 c) 2.177 d) 5.391 e) 0.531 f) 10.105 g) 13.201 h) 7.495 i) 30.199 j) 74.333 k) 101.389 l) 0.999 m) 42.131 n) 132.475 o) 9.999 4. Round the following to 1 significant figure: a) 17.051 b) 6.08 c) 0.00036 d) 0.909 e) 10.5 f) 40.50 g) 0.680 h) 0.03000 i) 23.045 j) 0.00202 3
5. Round the following to two significant figures: a) 49.483 b) 50790 c) 3456 d) 245790 e) 7008 f) 77.77 g) 365.4 h) 1.789 i) 808.65 j) 20.09 6. Answer the following questions mentally and as quickly as you can: a) 5 x 4 b) 2 x 4 c) 6 x 5 d) 3 x 7 e) 9 x 8 f) 2 x 7 g) 1 x 7 h) 0 x 4 i) 7 x 7 j) 10 x 5 k) 12 x 6 l) 11 x 11 m) 5 x 7 n) 8 x 4 o) 3 x 8 p) 9 x 4 q) 4 x 3 r) 8 x 6 s) 2 x 2 t) 6 x 3 u) 9 x 0 v) 11 x 5 w) 8 x 12 x) 10 x 2 7. Calculate the sum and product of each set of numbers below: a) 4 and 5 b) 2 and 9 c) 5 and 5 d) 12 and 4 e) 20 and 0.45 f) 30 and 34 g) 25 and 10 h) 45.3 and 60 i) 22.1 and 19 j) 101.3 and 45 8. Calculate: a) 2 + 7 x 3 b) 3 x 3 6 c) 4 1 x 3 d) 7 x 7 20 e) 2 x 5 + 2 x 3 f) 6 x 3 9 x 2 g) 12 x 3 8 x 3 h) 5 x 9 19 x 2 i) 3 + 18 3 j) 18 3 5 k) 7 21 7 l) 50 5 8 m) 32 8 + 10 x 3 n) 8 x 3 100 10 o) 200 10 100 50 p) 3.4 + 9 x 2 q) 1.3 x 2 2.05 r) 14.7 2.1 x 3 s) 3 x 7.1 20.5 t) 5.9 + 1.12 x 3 u) 6.7 x 2 11.9 v) 6.4 8 0.35 w) 5.7 9.1 7 x) 4.32 x 4 2 + 5 4
9. Calculate: a) 426 b) 391 c) 667 d) 923 x 4 x 7 x 9 x 8 e) 345 f) 193 g) 451 h) 784 x 24 x 18 x 44 x 22 10. Calculate: a) 5 355 b) 6 252 c) 8 584 d) 7 672 e) 12 816 f) 16 864 g) 14 1246 h) 11 1507 11. Calculate: a) 12 x 100 b) 22 x 100 c) 157 x 10 d) 75 x 10 e) 300 x 1000 f) 900 x 100 g) 510 10 h) 8100 100 i) 8000 10 j) 19000 1000 k) 12340 10 l) 90000 100 m) 53 x 200 n) 19 x 60 o) 105 x 300 p) 71 x 4000 q) 320 40 r) 6000 600 s) 12000 500 t) 720000 9000 u) 400 x 40 v) 9000 x 700 w) 20000 x 7000 x) 500000 x 20 5
Multiples, Factors, Powers, Primes & Roots Success Criteria: MTH 3-05a & b, MTH 3-06a & MTH 4-06a I can use prime decomposition to calculate HCF & LCM. I can define prime and composite numbers. I can express a composite number as a product of prime numbers. I can calculate square roots of appropriate numbers. 1. Write down all the square numbers between 1 and 200. 2. Write down all the prime numbers between 1 and 100. 3. Find the HCF of these numbers: a) 24 and 36 b) 18 and 27 c) 18 and 45 d) 22 and 44 e) 100 and 500 f) 54 and 56 g) 81 and 63 h) 15 and 75 i) 250 and 1250 j) 96 and 144 4. Find the LCM of : a) 5 and 6 b) 3 and 4 c) 6 and 9 d) 10 and 12 e) 15 and 20 f) 7 and 4 g) 2 and 8 h) 9 and 5 i) 3 and 9 j) 10 and 13 5. Which of these numbers are prime? Give a reason for your answer. a) 73 b) 87 c) 89 d) 21 e) 33 f) 47 g) 51 h) 1 i) 19 j) 91 6. Calculate without using a calculator: a) 2² b) 4² c) 7² d) 10² e) 12² f) 2³ g) 4³ h) 1 4 i) 9 1 j) 100 0 k) 9 2 l) 3 4 m) 1 100 n) 8 2 o) 4000 0 p) 6 2 q) 11 2 r) 2 4 s) 2 5 t)3 3 6
7. Work out using a calculator: a) 20² b) 55² c) 19² d) 17² e) 150² f) 22³ g) 47³ h) 90 4 i) 2 10 j) 3 7 k) 1 100 l) 3 8 m) 100 3 n) 10 6 o) 4 5 p) 61 2 q) 33 2 r) 224 4 s) 85 3 t)300 4 8. Express these numbers as a product of prime factors. Use a factor tree to help. a) 20 b) 25 c) 60 d) 18 e) 100 f) 40 g) 80 h) 160 i) 210 j) 512 k) 1024 l) 2048 9. Find the answer without using a calculator: a) b) c) d) e) f) g) h) i) j) k) l) m) n) o) p) q) r) 10. Calculate the following using a calculator, rounding your answer to 2 decimal places: a) b) c) d) e) f) g) h) i) j) k) l) m) n) o) p) q) r) 7
Displaying Data & Statistics Success Criteria: MNU 3-20a, MTH 3-20b & MNU 4-20a I can identify misleading information. I can interpret pictograms, frequency tables, bar charts, line graphs, pie charts and scatter graphs within context. I can interpret data, make my own conclusions and explain my reasoning. I can construct pictograms, frequency tables, bar charts, line graphs, pie charts and scatter graphs. I can interpret trends and correlations. I can construct frequency tables including cumulative and relative frequencies. I can explain why data from particular sources may or may not be reliable. I can explain how the sample size can affect the reliability of the data. I can calculate upper and lower quartiles of a data set. I can interpret a set of data, drawing conclusions from any trends or skew. 1. Kate keeps a record of her last 10 spelling test scores. a) What was Kate s score in week 3? b) In which 2 consecutive weeks did Kate s score stay the same? c) What was Kate s best score? d) How much did her score improve between weeks 4 and 5? 8
2. At a sci-fi convention, attendees were surveyed about their favourite Science Fiction films. The results are shown below: a) Collect this information in a frequency table. Include a cumulative frequency column. b) Display this information in a bar graph. c) Write a conclusion on the data you have collected and displayed. 3. As part of the school s healthy eating campaign, 400 pupils were asked to name their favourite fruit: Fruit Number of Pupils Apple 60 Banana 80 Orange 100 Grapes 100 Cherries 20 Pineapple 40 Display this information accurately in a pie chart. You may use a protractor. 4. State which form of correlation each of these scatter graphs shows: a) b) c) 9
5. For each of the following data displays, state what makes them either misleading, robust or vague: 6. The scatter graph shows the relationship between the height of sprinters in centimetres and their race time in seconds for the 100 metres race. a) Is there a correlation between height and race time? b) If so, write a statement about the height of sprinters and their race time. 10
7. Shane asked 8 of his closest friends what their favourite sport was. Here are his results: a) How did bias and sample size affect his data? b) What would your suggestions be for improving Shane s survey? 8. A group of business men and women who earn over 150,000 a year were asked their opinions on paying 50% tax on all earnings over 150,000. The pie chart shows the results of the survey: a) How could bias affect this survey? b) What would your suggestions be for carrying out a fairer survey? 9. Calculate the mean, median, mode, range and quartiles for each set of data: a) 78 82 74 45 68 75 93 54 61 70 48 66 62 51 77 b) 12 24 21 16 8 9 3 31 18 27 35 41 26 12 17 6 5 19 29 c) 153 147 160 146 162 158 159 149 152 150 163 11
Angles Success Criteria: MTH 3-17a I can calculate missing angles round a point. I can calculate supplementary and complementary angles. I can calculate vertically opposite angles. I can calculate corresponding and alternate angles. I can calculate the missing angles in a variety of triangles and quadrilaterals. I can calculate the missing angles in a variety of polygons. 1. Calculate missing angle x in each diagram below: 12
2. State what is meant by the terms supplementary and complementary. 3. Calculate missing angle x in each diagram below: 4. Copy the diagram shown and fill in all missing angles. 5. These are all regular polygons. Calculate the interior angle in each. a) b) c) d) e) 6. Calculate the missing interior angle in this polygon: 13
Integers Success Criteria: MTH 3-18a, MTH 4-18a, & MTH 3-04a I can perform simple integer calculations using all four operations. I can interpret and plot 3D co-ordinates. I can interpret and plot co-ordinates within all four quadrants. 1. Calculate: a) 3 4 b) 4 8 c) 1 5 d) 3 7 e) 10 20 f) 21 30 g) -1 + 2 h) -5 + 7 i) -8 + 5 j) -9 + 8 k) -10 5 l) -3-27 2. a) 7 + (-4) b) 10 + (-3) c) 9 (-12) d) 5 + (-5) e) 10 (-11) f) 35 + (-20) g) (-8) + (-2) h) (-3) + (-7) i) (-8) + (-7) j) (-20) + -(9) k) (-3) + (-5) l) (-50) + (-50) 3. a) 5 (-5) b) 0 (-6) c) 4 - (-1) d) 3 (-9) e) 10 (-11) f) 44 (-11) g) (-9) (-10) h) (-4) (-7) i) (-12) (-11) j) (-1) (-1) k) (-14) - (-12) l) (-100) (-99) 4. a) 3 x (-5) b) 3 x (-7) c) 2 x (-1) d) (-8) x (-7) e) (-1) x 5 f) (-12) x 3 g) (-5) x (-4) h) (-9) 3 i) (-12) 6 j) (-21) (-3) k) (-36) (-9) l) (-40) 8 14
5. The temperature at 12pm in Inverness was 5C. By 9pm, the temperature had fallen by 11C. What was the temperature at 9pm? 6. Write down the co-ordinates of points A to K shown on the co-ordinate grid below: I y 7. The diagram shows a cuboid drawn on a 3-D grid. Vertex A has coordinates (5, 2, 3). F E a) Write down the coordinates of vertex E. B and D are vertices of the cuboid. B O A G x b) Work out the coordinates of the C D midpoint of BD. z 8. Draw a set of co-ordinate axes with x and y values ranging from -5 to 5. a) Plot the points W(3,3), X(-2,3) and Y(-3,-3). b) Plot a fourth point Z to create a parallelogram. c) State the co-ordinates of Z. 15
Algebra 1 Success Criteria: MTH 3-15a & MTH 4-15a I can collect algebraic terms including square powers. I can add, subtract, multiply and divide algebraic terms. I can substitute a value into an algebraic formula and calculate it using BIDMAS. 1. Simplify the following expressions: a) a + a + a b) b + b b c) 3c c d) 3d + 4d e) 3e e + e f) 10f + 20f g) 18g 12g h) h + 9h i) 15i 12j + 9i j) 19j + 6j 20j k) 4k + 10k l) 100x 55x m) x + y + x n) 7x + 2y - 5x o) 21x 30 + 9x p) 18x + 10y 5y q) 4a + 9b + 32 + 6b a r) 100 + 6a 80 + 14a 3b s) 5 + x + x + 13 t) 5y + 8y + 4z u) 8x 2 + 2x 2 + 7x v) 9x 2 + 10 + 4x 2 + 7 w) 7x 2 y + 8 + ( 5x 2 y) + 4 x) 6x 3 + 9x + 10x 3 + 4x 2 y) 10x 4 + ( 8x 3 ) + 4x 3 + ( 5x 2 ) + 3x z) 6x 2 y 2x 2 y 10x 2 y + 8x 2 y 2. Simplify these expressions: a) 4a x 5a b) 2c² x c c) 16f³ 2f d) 4m³ x 4m e) 8p x 7m f) (3s x 2s) s² g) h³x 2ph h) 9t² 3t 3. If a = 3, b = 7 and c = 4, evaluate: a) a + b + c b) 3a c) 2b d) 10c e) a + 2b f) 4c + 2b g) b a h) 5c 5a i) ab j) bc k) a² l) a² + c 16
Answers Whole Number Calculations & Decimals MNU 3-01a, MNU 3-03a & MNU 3-03b 1. a) 3 b) 8 c) 5 d) 16 e) 20 f) 68 g) 10 h) 7 i) 3 j) 1 k) 14 l) 51 m) 400 n) 6 o) 1 2. a) 1.4 b) 0.9 c) 0.6 d) 5.9 e) 2.3 f) 9.9 g) 19.6 h) 4.0 i) 1.0 j) 100.1 k) 1.3 l) 5.6 m) 3.9 n) 12.0 o) 11.5 3. a) 0.19 b) 0.99 c) 2.18 d) 5.39 e) 0.53 f) 10.11 g) 13.20 h) 7.50 i) 30.20 j) 74.33 k) 101.39 l) 1.00 m) 42.13 n) 132.48 o) 10.00 4. a) 20 b) 6 c) 0.0004 d) 0.9 e) 10 f) 40 g) 0.7 h) 0.03 i) 20 j) 0.002 5. a) 49 b) 51000 c) 3500 d) 250,000 e) 7010 f) 78 g) 370 h) 1.8 i) 810 j) 20 6. a) 20 b) 8 c) 30 d) 21 e) 56 f) 14 g) 7 h) 0 i) 49 j) 50 k) 72 l) 121 m) 35 n) 32 o) 24 p) 36 q) 12 r) 48 s) 4 t) 18 u) 0 v) 55 w) 96 x) 20 7. a) 9, 20 b) 11,18 c) 10,25 d) 16, 48 e) 20.45, 9 f) 64, 1020 g) 35, 250 h) 105.3, 2718 i) 41.1, 419.9 j) 146.3, 4558.5 8. a) 23 b) 3 c) 9 d) 29 e) 16 f) 0 g) 12 h) 7 i) 9 j) 1 k) 4 l) 2 m) 34 n) 14 o) 18 p) 21.4 q) 0.55 r) 8.4 s) 0.8 t) 9.26 u) 1.5 v) 0.45 w) 4.4 x) 13.64 17
9. a) 1704 b) 2737 c) 6003 d) 7384 e) 8280 f) 3474 g) 19844 h) 17248 10. a) 71 b) 126 c) 73 d) 96 e) 68 f) 54 g) 89 h) 137 11. a) 1200 b) 2200 c) 1570 d) 750 e) 300,000 f) 90,000 g) 51 h) 81 i) 800 j) 19 k) 1234 l) 900 m) 10,600 n) 1140 o) 31,500 p) 284,000 q) 80 r) 10 s) 24 t) 80 u) 16,000 v) 6,300,000 w) 140,000,000 x) 100,000,000 Multiples, Factors, Powers, Primes & Roots Answers MTH 3-05a & b, MTH 3-06a & MTH4-06a 1. 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196 2. 2, 3, 5, 7, 11, 13, 17, 19, 23, 27, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 3. a) 12 b) 9 c) 9 d) 22 e) 100 f) 2 g) 9 h) 15 i) 250 j) 48 4. a) 30 b) 12 c) 18 d) 60 e) 60 f) 28 g) 8 h) 45 i) 9 j) 130 5. a) Prime b) Not Prime divides by 3 c) Prime d) Not Prime divides by 3 e) Not Prime divides by 3 f) Prime g) Not Prime divides by 3 h) Not Prime by definition i) Prime j) Not Prime divides by 7 6. a) 4 b) 16 c) 49 d) 100 e) 144 f) 18 g) 64 h) 1 i) 9 j) 1 k) 81 l) 81 m) 1 n) 64 o) 1 p) 36 q) 121 r) 24 s) 48 t) 27 18
7. a) 400 b) 3025 c) 361 d) 289 e) 22,500 f) 10,648 g) 103,823 h) 65,610,000 i) 1024 j) 2187 k) 1 l) 6561 m) 1,000,000 n) 1,000,000 o) 1024 p) 3721 q) 1089 r) 2,517,630,976 s) 614,125 t) 8,100,000,000 8. a) 20 4 5 2 2 b) 25 5 5 c) 60 10 6 2 5 2 3 d) 20 = 2 x 2 x 5 18 2 9 3 3 e) 25 = 5 x 5 100 10 10 2 5 2 5 f) 60 = 2 x 2 x 3 x 5 40 10 4 2 5 2 2 g) 18 = 2 x 3 x 3 80 8 10 4 2 2 5 2 2 h) 100 = 2 x 2 x 5 x 5 160 2 80 8 10 4 2 2 5 2 2 i) 40 = 2 x 2 x 2 x 5 210 10 21 2 5 3 7 80 = 2 x 2 x 2 x 2 x 5 160 = 2 x 2 x 2 x 2 x 2 x 5 210 = 2 x 3 x 5 x 7 19
j) k) 512 2 256 2 128 2 64 2 32 2 16 2 8 2 4 2 2 512 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 1024 2 512 2 256 2 128 2 64 2 32 2 16 2 8 2 4 2 2 1024 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 20
l) 2048 2 1024 2 512 2 256 2 128 2 64 2 32 2 16 2 8 2 4 2 2 2048 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 9. a) 5 b) 3 c) 2 d) 9 e) 7 f) 6 g) 8 h) 4 i) 1 j) 10 k) 13 l) 11 m) 1 n) 2 o) 3 p) 4 q) 5 r) 10 10. a) 44.55 b) 47.04 c) 27.68 d) 49.51 e) 104.64 f) 21.61 g) 2.65 h) 1.41 i) 2.24 j) 4.58 k) 14.14 l) 22.36 m) 1.44 n) 2.08 o) 2.80 p) 2.22 q) 4.64 r) 5.24 21
Number of Attendees Answers Displaying Data & Statistics MNU 3-20a, MTH 3-20b & MNU 4-20a 1. 2. a) 14 b) Weeks 3 & 4 c) 16 d) 2 marks a) Film Tally Frequency Cumulative Frequency Star Wars 9 9 Star Trek 6 15 Back to the Future 5 20 Ghostbusters 2 22 Transformers 4 26 b) 10 8 6 4 2 0 Star Wars Star Trek Back to the Future Ghostbusters Transformers Science Fiction Film c) The most popular film was Star Wars and the least popular film was Ghostbusters. The responses also show that 26 people were asked in total. 3. Pupils' Favourite Fruits Pineapple Cherries 10% 5% Apple 15% Grapes 25% Banana 20% Orange 25% 22
4. a) Positive correlation b) No correlation c) Negative correlation 5. a) Misleading - y-axis values are in intervals of 1% and does not start at 0% suggesting a larger change in score. b) Vague y-axis should have a range of 0 to 50, not 0 to 200. c) Robust Labels and percentages shown and accurate. d) Misleading Grid lines must be horizontal. e) Vague Not enough labels on y-axis. f) Vague Sectors should be labelled with percentages. g) Vague y-axis should be labelled. h) Vague No axes titles. i) Vague No information provided. 6. a) Yes. b) Taller sprinters generally have a shorter race time. This is possibly due to a longer leg length meaning that fewer strides are needed to finish the race. 7. a) Shane only asked 8 people a small sample. He also asked his closest friends who were most likely all boys who shared the same interests. b) Ask a larger sample of people made up of both boys and girls. 23
8. a) Only people who earned over 150,000 per year were asked. b) Ask a larger sample of people including those who earn less than 150,000 per year. 9. Mean Median (Q2) Mode Range Q1 Q2 a) 66.9 68 No Mode 48 57.5 76 b) 18.9 18 12 38 10.5 26.5 c) 154.5 153 No Mode 17 149.5 159.5 Answers Angles MTH 3-17a 1. a) 19 b) 40 c) 95 d) 65 e) 120 f) 150 g) 115 h) 100 i) 68 j) 75 k) 30 l) 128 2. 3. Supplementary angles are any two angles that have a sum of 180. Complementary angles are any two angles that have a sum of 90. a) 108 b) 99 c) 67 d) 20 e) 100 f) 77 4. 126 54 74 126 54 54 54 52 5. 6. a) 60 b) 120 c) 135 d) 108 e) 90 f) 77 50 24
Answers Integers MTH 3-18a, MTH 4-18a & MTH 3-04a 1. a) -1 b) -4 c) -4 d) -4 e) -10 f) -9 g) 1 h) 2 i) 3 j) -1 k) -15 l) -30 2. a) 3 b) 7 c) 21 d) 0 e) 21 f) 15 g) -10 h) -10 i) -15 j) -29 k) -8 l) -100 3. a) 10 b) 6 c) 5 d) 12 e) 21 f) 55 g) 1 h) 3 i) -1 j) 0 k) -2 l) -1 4. a) -15 b) -21 c) -2 d) 56 e) -5 f) -36 g) 20 h) -3 i) -2 j) 7 k) 4 l) -5 5. 6. -6 C A(4,3) B(1,2) C(-3,4) D(-1,2) E(-2,-1) F(-4,-3) G(-1,-2) H(4,-1) I(0,0) J(0,3) K(-3,0) 7. 8. a) E(5,2,0) b) M BD (2.5, 1, 3) a) Show your diagram to your teacher. b) Show your diagram to your teacher. c) Z(2,-3) 25
Answers Algebra 1 MTH 3-15a & MTH 4-15a 1. a) 3a b) 2b c) 2c d) 7d e) 3e f) 30f g) 6g h) 10h i) 12i j) 5j k) 14k l) 45x m) 2x + y n) 2x + 2y o) 30x 30 p) 18x +5y q) 3a + 15b + 32 r) 20a 3b + 20 s) 2x + 8 t) 13y + 4z u) 10x 2 + 7x v) 13x 2 + 17 w) 2x 2 y + 12 x) 16x 3 + 4x 2 + 9x y) 10x 4 4x 3 5x 2 + 3x z) 2x 2 y 2. a) 20a b) 2c 3 c) 8f 2 d) 16m 4 e) 56mp f) 6 g) 2h 4 p h) 3t 3. a) 14 b) 9 c) 14 d) 40 e) 17 f) 30 g) 4 h) 5 i) 21 j) 28 k) 9 l) 13 26