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INTEGERS, RECIPROCALS, FACTORS, MULTIPLES AND PRIME NUMBERS GRADES : E,D Homework 1H BIDMAS Follow the correct order of operations to calculate the following: 1. 5 + 2 x 3 = ___ 2. 10 ÷ 2 + 7 = ___ 3. 7 + 9 ÷ 3 = ___ 4. 2 x 3 + 7 x 2 = ___ 5. 8 ÷ 4 – 2 x 1 = ___ 6. 5 x 10 + 9 ÷ 1 = ___ 7. 2 + 4 x 4 + 1 = ___ 8. (2 + 4) x 8 = ___ 9. (3 – 1) x (9 – 4) = ___ 10. 30 – (7 + 6) = ___ 11. 20 – (4 + 10) = ___ 12. (5 + 9) ÷ (2 x 1) = ___ BRACKETS Put brackets into the questions to make them correct. 1. 2 + 2 x 3 = 12 2. 4 – 1 x 7 = 21 3. 2 + 1 x 1 + 2 = 9 4. 9 ÷ 3 x 2 + 1 = 9 5. 50 ÷ 7 + 3 = 10 6. 6 + 2 x 4 + 3 = 51 1234 Use the digits 1, 2, 3, and 4 to make correct calculations. Use brackets where appropriate. 1 = ________________________________ 2 = _________________________________ 3 = ________________________________ 4 = _________________________________ 5 = ________________________________ 6 = _________________________________ 7 = ________________________________ 8 = _________________________________ 9 = ________________________________ 10 = _________________________________ EXAM QUESTION INTEGERS, RECIPROCALS, FACTORS, MULTIPLES AND PRIME NUMBERS GRADES : D,C Homework 2H PRIME NUMBERS Answer TRUE or FALSE: 1. 2 is a prime number 2. 9 is a prime number 3. 15 is a prime number 4. 7 is a prime number 5. 19 is a prime number 6. 23 is a prime number 7. 21 is a prime number 8. 8 is a prime number 9. 27 is a prime number 10. 3 is the smallest prime number 11. There are four prime numbers between 1 and 10 12. 99 is a prime number 13. There are three primes between 20 and 30 PRIME FACTORS Write each number as a product of its’ prime factors: 1. 21 2. 12 3. 36 4. 50 5. 150 6. 54 7. 49 8. 84 RECIPROCALS Write down the reciprocal of each number 1. 3 2. 2 3. 5 4. 1 4 5. 1 2 6. 10 7. 1 8 8. 1 9 9. 5 10. 2 3 11. 3 4 12. 6 EXAM QUESTIONS 1. 2. 3. INTEGERS, RECIPROCALS, FACTORS, MULTIPLES AND PRIME NUMBERS GRADES : D, C Homework 3H Multiples Write down the first six multiples of each number: 1. 4 2. 3 3. 7 4. 9 5. 15 6. 12 7. 8 8. 11 Highest Common Factor Find the Lowest Common Factor (HCF) for each pair of numbers. 1. 36 and 10 2. 50 and 30 3. 45 and 27 4. 100 and 36 5. 88 and 56 6. 36 and 32 Lowest Common Multiple Find the Highest Common Multiple (LCM) for each pair of numbers. 1. 6 and 9 2. 5 and 15 3. 12 and 8 4. 2 and 11 5. 12 and 8 6. 5 and 9 EXAM QUESTIONS 1. 2. 3. 4. ROUNDING AND APPROXIMATIONS Homework 4H GRADES : E, D ESTIMATING Copy the lists below and match up the questions to the estimated answers. The first one has been done for you. QUESTIONS ESTIMATED ANSWERS 3.92 x 5.05 3 6.9 x 2.9 100 30.1 ÷ 9.91 11.4 √32 15 (8.8 + 11.11) x 4.9 40 50 ÷ 7.21 7 √103 8 4.05 x (6.9 + 2.9) 20 67 ÷ 8.12 12.2 √150 5.5 EXAM QUESTIONS 1. 2. 3. ROUNDING AND APPROXIMATIONS GRADES : D,C Homework 5H SIGNIFICANT FIGURES 1. Write each number correct to one significant figure. a) 27 b) 832 c) 8.12 d) 93 e) 77 f) 13.5 g) 95 2. Use a calculator to work out the answers and write them down correct to 1 significant figure. a) 50 x 23 b) 5.25 x 7 c) 910 x 12 d) 9.5 x 7.3 e) 93 x 77 3. Write each number correct to two significant figures. a) 275 b) 0.03451 c) 8.12 d) 0.956 e) 7.04 f) 7.05 g) 959 4. Write each number correct to three significant figures. a) 27589 b) 0.03451 c) 8.1254 d) 0.95621 e) 0.0704124 f) 7.05555 g) 959595 ESTIMATING CALCULATIONS By approximating each number, estimate the answers to these calculations. You must show how you reached your estimate. 4.9 15.21 1.9 1. EXAM QUESTIONS 1. 2. 3. 2. 19.89 5.2 1.05 9.03 3. 4.05 4.9 5.09 ROUNDING AND APPROXIMATIONS GRADES : C, B Homework 6H ROUNDING IN CALCULATIONS Give your final answer to each question correct to two decimal places. Remember not to round during the intermediate steps of the calculation. 1. 6.2 3.09 3.2 8.91 2. 4.9 1.2 3.8 3. 9 8.14 2.17 0.515 4. 9.054 0.973 6.3 0.00462 5. 7.563 3.9 9.017 6. 5 3.2 2 2.1 9.2 1.1 HIGHEST AND LOWEST 1. The length of a pencil is given as 9cm to the nearest cm. What is the minimum length that the pencil could be? 2. The height of a door is 210cm to the nearest 10cm. What is the maximum height that the door could be? 3. The width of a piece of paper is given as 18.4cm correct to one decimal place. a) What is the minimum width that the paper could be? b) What is the maximum width that the paper could be? EXAM QUESTIONS 1. 2. 3. ROUNDING AND APPROXIMATIONS UPPER AND LOWER BOUNDS EXAM QUESTIONS 1. 2. 3. 4. 5. Homework 7H GRADES : A WHOLE NUMBER AND DECIMAL CALCULATIONS Homework 8H MULTIPLICATION AND DIVISION (WHOLE NUMBERS) MULTIPLYING DECIMALS DIVIDING WITH DECIMALS EXAM QUESTION 1. 2. GRADES : D,C FRACTIONS GRADES : D,C Homework 9H ADDING AND SUBTRACTING FRACTIONS 1. Fill in the boxes by adding the fractions. 1 3 1 2 2 3 + 2 5 3 8 2 7 2. Work out each question without a calculator. Show your working and write your answer in its’ simplest form. a) 1 3 4 5 b) 3 1 5 3 c) 1 1 9 10 d) 3 1 4 6 c) 7 7 9 10 d) 13 9 15 20 3. Work out each question with a calculator. a) 3 3 4 15 EXAM QUESTIONS 1. 2. 3. 4. 5. 6. 7. b) 7 2 10 3 FRACTIONS GRADES : D,C Homework 10H MULTIPLYING FRACTIONS Fill in the boxes by multiplying the fractions. 1 2 3 5 1 2 2 3 x 3 8 2 7 MIXED NUMBERS 1. 1 3 1 2 2 5 2. 2 1 3 1 5 2 3. 3 3 4 8 3. 2 1 2 3 3 4 5. 7 3 9 4 DIVIDING WITH FRACTIONS 1. 1 1 2 4 2. 2 1 5 10 EXAM QUESTIONS 1. 2. 3. , 4. 5. 6. 7. , 4. 3 1 10 5 FRACTIONS RECURRING DECIMALS EXAM QUESTIONS 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Homework 11H GRADES : B SQUARES, CUBES, POWERS AND ROOTS GRADES : E, D,C Homework 12H POWERS AND ROOTS ‘COLLECT A LETTER’ START 1000 P 8 O 32 U E 49 64 T A 23 92 52 73 63 24 27 121 36 100 1 125 E D L N H I 4 2 5 10 6 3 5 3 3 2 02 216 16 343 0 25 81 I C R S T R 1 END 7 3 10 2 5 2 3 112 1) √25 3² √36 2³ √100 2) √100 4² 2² √81 √121 3) 5² 4² + 2² √144 √25+√36 1³ + 3³ 4) √36 - √4 4² - 2² 1³ + 2³ √100 - 3² 1³ + 1² EXAM QUESTIONS 1. 2. 3. 4. SQUARES, CUBES, POWERS AND ROOTS GRADES : C Homework 13H INDEX LAWS 1. Write each of these as simply as possible using indices. a) 2x2x2x2x2 b) y x y x y x y c) 9x9x9 d) 8x8x8x8x8x8x8 2. Write down the value of the missing index. a) 2 2 23 2 x b) 38 3x 212 c) 52 5 x 59 d) 2 x 23 2 7 e) (2 2 ) 4 2 x f) (26 ) x 218 g) 39 3x 2 3 h) 48 45 x 4 c) (54 ) 2 56 3. State whether each equation is TRUE or FALSE. a) 7 2 7 6 78 b) 83 82 8 EXAM QUESTIONS 1. 5. 2. 6. 3. 7. 4. 8. SQUARES, CUBES, POWERS AND ROOTS Homework 14H FRACTIONAL POWERS and NEGATIVE POWERS EXAM QUESTIONS 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. GRADES : A, A* SQUARES, CUBES, POWERS AND ROOTS IRRATIONAL NUMBERS AND SURDS EXAM QUESTIONS 1. 2. 3. 4. 5. 6. 7. Homework 15H GRADES : A, A* POWERS OF 10 AND STANDARD INDEX FORM STANDARD INDEX FORM EXAM QUESTIONS 1. 2. 3. 4. 5. 6. Homework 16H GRADES : A, A* PERCENTAGES Homework 17H PERCENTAGE INCREASE AND DECREASE 1. Increase £90 by 10% 2. Increase £110 by 50% 3. Increase £120 by 5% 4. Decrease £40 by 20% 5. Decrease £700 by 30% 6. Decrease £320 by 5% 7. Increase £620 by 25% 8. Decrease £180 by 60% EXAM QUESTIONS 1. 2. How much do they pay for the washing machine? 3. GRADES : D,C PERCENTAGES COMPOUND PERCENTAGE EXAM QUESTIONS 1. 2. 3. 4. 5. 6. 7. Homework 18H GRADES : B, A PERCENTAGES REVERSE PERCENTAGE EXAM QUESTIONS 1. 2. 3. 4. 5. 6. Homework 19H GRADES : B RATIO AND PROPORTION EXAM QUESTIONS 1. 2. 3. 4. 5. 6. Homework 20H GRADES : D,C RATIO AND PROPORTION DIRECT PROPORTION EXAM QUESTIONS 1. 2. 3. INVERSE PROPORTION EXAM QUESTIONS 1. 2. Homework 21H GRADES : A ALGEBRAIC MANIPULATION Homework 22H EXAM QUESTIONS 1. 12. 2. 13. 3. 14. 4. 15. 5. 6. 7. 8. 9. 10. 11. GRADES : E,D,C ALGEBRAIC MANIPULATION EXPANDING QUADRATIC EXPRESSIONS EXAM QUESTIONS 1. 2. 3. FACTORISING QUADRATIC EXPRESSIONS EXAM QUESTIONS 1. 2. 3. 4. Homework 23H GRADES : B ALGEBRAIC MANIPULATION Homework 24H EXPANDING HARDER QUADRATIC EXPRESSIONS EXAM QUESTIONS 1. 2. 3. a) b) 4. 5. FACTORISING HARDER QUADRATIC EXPRESSIONS EXAM QUESTIONS 1. 2. 3. 4. GRADES : A NON-LINEAR GRAPHS AND GRAPHICAL SOLUTION OF EQUATIONS EXAM QUESTION Homework 25H GRADES : D,C NON-LINEAR GRAPHS AND GRAPHICAL SOLUTION OF EQUATIONS GRAPHICAL SOLUTION OF EQUATIONS 1 EXAM QUESTION 1. below Homework 26H GRADES : A NON-LINEAR GRAPHS AND GRAPHICAL SOLUTION OF EQUATIONS GRAPHICAL SOLUTION OF EQUATIONS 2 EXAM QUESTIONS 1. 2. 3. below Homework 27H GRADES : A, A* COLLECTING DATA Homework 1H DATA COLLECTION SHEETS AND QUESTIONNAIRES Exam questions 1. 2. 3. 4. GRADES : D, C COLLECTING DATA STRATIFIED SAMPLING Exam questions 1. 2. 3. Homework 2H GRADES : A PRESENTING DATA AND INTERPRETING INFORMATION Homework 3H STEM AND LEAF DIAGRAMS Exam questions 1. 2. 3. (a) How many people were asked? (b) What was the median number of driving lessons? (c) Work out the range of the number of driving lessons. GRADES : D PRESENTING DATA AND INTERPRETING INFORMATION FREQUENCY DIAGRAMS Exam questions 1. 2. Homework 4H GRADES : D PRESENTING DATA AND INTERPRETING INFORMATION CUMULATIVE FREQUENCY Exam questions 1. 2. Homework 5H GRADES : B PRESENTING DATA AND INTERPRETING INFORMATION BOX PLOTS Exam questions 1. 2. Homework 6H GRADES : B PRESENTING DATA AND INTERPRETING INFORMATION HISTOGRAMS Exam questions 1. 2. 3. Homework 7H GRADES : A PRESENTING DATA AND INTERPRETING INFORMATION Homework 8H TIME SERIES Exam questions 1. Copy the graph and plot all the other moving averages. 2. GRADES : B MEASURES OF AVERAGE AND SPREAD AVERAGES FROM TABLES Exam questions 1. 2. 3. Homework 9H GRADES : C SCATTER DIAGRAMS AND CORRELATION SCATTER DIAGRAMS AND CORRELATION Exam questions 1. 2. 3. Homework 10H GRADES : C PROBABILITY RELATIVE FREQUENCY - Exam questions 1. 2. Homework 11H GRADES : B PROBABILITY TREE DIAGRAMS - Exam questions 1. 2. Homework 12H GRADES : C, B PROBABILITY Homework 13H COMBINED PROBABILITIES (AND RULE / OR RULE) Exam questions 1. 2. 3. 4. GRADES : B PROBABILITY DEPENDENT EVENTS Exam questions 1. 2. 3. 4. Homework 14H GRADES : A Compound area + perimeter (mathswatch clip 73) 1) Find the area and perimeter of each shape. Homework 1H GRADE : D Circumference of circles (mathswatch clip 72) Homework 2H GRADE : D Area of circles (mathswatch clip 71) Volume of cuboids + Homework 3H GRADE : D,C prisms(mathswatch clip 34 + 122) Homework 4H GRADE : D - C 1) Find the volume of the following cuboids 7cm 3cm 5cm 7cm 12cm 4cm 2) 3) 4) 5) A cuboid has a volume of 80cm3 a width of 5cm and a depth of 2 cm find it’s height? Surface area Homework 5H GRADE : C -B (mathswatch clip 121) 1) Find the surface area of the following cuboids 7cm 3cm 7cm 12cm 4cm 5cm 2) 3) 4) A cuboid has a surface area of 36cm2 a width of 5cm and a depth of 2 cm find it’s height? Volume of Spheres and Cones Homework 6H GRADE : A-A* (mathswatch clip 177) 1) 4) A marble paperweight consists of a cuboid and a hemisphere as shown in the diagram. The hemisphere has a radius of 4 cm. 4 cm 5 cm 10 cm 10 cm Not to scale Calculate the volume of the paperweight. Volume of Spheres and Cones Homework 6H GRADE : A-A* (mathswatch clip 177) 1) 4) A marble paperweight consists of a cuboid and a hemisphere as shown in the diagram. The hemisphere has a radius of 4 cm. 4 cm 5 cm 10 cm 10 cm Not to scale Calculate the volume of the paperweight. Length / Area of arcs, sectors Homework 7H GRADE : A-A* 1) The diagram shows a sector of a circle of radius 9 centimetres. Not drawn accurately 9 cm 80º Find the perimeter of the sector. Give your answer in terms of . 2) A giant paper clip is placed alongside a centimetre ruler. The curved ends are semicircles. Not drawn accurately 0 1 2 3 4 5 6 7 cm Calculate the length of wire used to make the clip. 3) A circle fits inside a semicircle of diameter 10 cm as shown. 10 cm Calculate the shaded area. 8 9 10 Polygons Homework 8H (mathswatch clip 70) 1) find angle x if the following shape is a rhombus x 32o 2) x 3) GRADE : C Sequences Homework 9H GRADE : C 1) Write the first five terms of the following sequences whose nth terms are n2+3 n+3 2n2 3n n3 8n -2 n2-5 2) Find the nth term of the following; 3, 8, 13, 18, 23, …. 20, 13, 6, -1, …. 2, 8, 18, 32, 50, ….. ½ , 1, 4 ½ , 8, 12 ½ , …… A sequence of numbers is shown. 5 (a) 9 13 17 21 (a) Find an expression for the nth term of the sequence. (b) Explain why 83 will not be a term in this sequence. Part of a number grid is shown below. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 The shaded cross is called C11 because it has the number 11 at the centre. This is Cn n–7 n Fill in the empty boxes. (b) Kevin notices the following number sequence in the grid. 1, 9, 17, 25, 33,... Write down the nth term of this sequence. Straight lines Homework 10H ( mathswatch clip 114 + 143 ) 6) Find the midpoints of the following co-ordinates i) (0,4) (3, 13) ii) (0,7) (2, -1) iii) (10,5) (22, 18) GRADE : C Solving Equations (Mathswatch clip 105) 8) 9) 10) 11) 12) 1) 4y + 3 = 2y + 10 2) 2x + 17 = 5x – 4 3) 2x + 7 = 16 – 4x 4) 20x -15 = 18x -7 5) 5(x + 3) = 2 (x + 6) 6) 4 (2y + 1) = 2 (12 - y) 7) 7 - 3x = 2 ( x + 1) x3 5 2 2x 4 7 3 40 x 4 x 3 2x 1 x 3 5 6 3 2 y2 y6 16 3 4 Homework 11H GRADE :D-B Homework 12H Reflections and rotations (Mathswatch clip 74 + 75) GRADE :D-C Circle theorems (Mathswatch clip 150) Homework 13H GRADE :B Trial and improvement (Mathswatch clip 110) Homework 14H GRADE :C Translation (Mathswatch clip 77) Homework 15H GRADE :C Enlargement (Mathswatch clip 76) Homework 16H GRADE :C Transformations Homework 17H GRADE :C-B (Mathswatch clip 74,75,76,77) y 6 5 4 A 3 2 1 –5 –4 –3 –2 –1 O 1 2 3 4 5 x –1 –2 –3 –4 (i) Describe fully the single transformation that takes the shaded triangle to triangle A. (ii) On the grid above translate the shaded triangle by 2 squares to the right and 4 squares down. y 6 The rectangle is rotated 90’ clockwise about the point ( 1, 0) and then translated by 4 vector 5 4 2 –6 –4 –2 0 2 4 6 x –2 –4 –6 Draw the Final position of the rectangle after these transformations. The diagram shows four shapes, A, B, C and D. 6 5 B 4 3 2 A C 1 –4 –3 –2 –1 O 1 2 3 4 5 6 7 8 –1 –2 –3 D –4 (a) Describe fully the single transformation that takes shape A onto shape B. (b) Describe fully the single transformation that takes shape B onto shape C. (c) Describe fully the single transformation that takes shape C onto shape D. (b) Triangle P is an enlargement of the shaded triangle. Find the scale factor and centre of enlargement. y 6 5 4 3 2 1 P –5 –4 –3 –2 –1 O 1 2 –1 –2 –3 –4 (i) What is the scale factor of the enlargement? 3 4 5 x Similar Shapes Homework 18H GRADE :C-B (Mathswatch clip 123) Two similar bottles are shown below. The smaller bottle is 20 cm tall and holds 480 ml of water. The larger bottle is 30 cm tall. Not to scale 30 cm 20 cm How much water does the larger bottle hold? Dimensions of Formulae Homework 19H (Mathswatch clip 124) 2) a, b, and c represent lengths combine a, b, c, to find five formulae that could represent i) volume ii) area GRADE :C-B Compound Measures (Mathswatch clip 126) Homework 20H GRADE :C-B Bounds Homework 21H GRADE : B (Mathswatch clip 125) 6) Sameera runs 100m (to the nearest 10m) in 12 seconds (correct to the nearest second). Last time she ran the race her maximum possible speed was 8.2 metres per second – can she be sure that she has run faster his time? Give a reason for this answer Real life graphs (Mathswatch clip 117) Homework 22H GRADE : C Real life graphs Homework 23H GRADE : C (Mathswatch clip 117) Mr Smith leaves the home at 10 am to go to the shopping mall. He walks to the station where he catches a train. He gets off the train at the mall. The travel graph shows his journey. 15 10 Distance from home (km) 5 0 10 am 11 am 12 am 1pm 2 pm Time After shopping Mr Smith goes home by taxi. The taxi leaves the mall at 1 pm and arrives at his home at 1.45 pm. (a) Complete the travel graph. (2) (b) Calculate the average speed of the taxi. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... Answer .......................................................km per hour (2) Substitution (Mathswatch clip 65) Homework 24H GRADE : C Forming Equations Homework 25H GRADE : C (Mathswatch clip 106) GRADE : C Changing the subject of a formulae (Mathswatch clip 107) Homework 26H