INTEGERS, RECIPROCALS, FACTORS, MULTIPLES AND PRIME NUMBERS Homework 1H GRADES : E,D BIDMAS Follow the correct order of operations to calculate the following: 5 + 2 x 3 = 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) = 1 20 (4 + 10) = 1 (5 + 9) (2 x 1) = BRACKETS Put brackets into the questions to make them correct. 2 + 2 x 3 = 12 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 Homework 2H GRADES : D,C PRIME NUMBERS Answer TRUE or FALSE: 2 is a prime number 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 1 There are four prime numbers between 1 and 10 1 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: 21 12 3. 36 4. 50 5. 150 6. 54 7. 49 8. 84 RECIPROCALS Write down the reciprocal of each number 3 2 3. 5 4. 1 4 5. 1 2 6. 10 7. 1 8 8. 1 9 9. 5 10. 2 3 1 3 4 1 6 EXAM QUESTIONS 3.
INTEGERS, RECIPROCALS, FACTORS, MULTIPLES AND PRIME NUMBERS Homework 3H GRADES : D, C Multiples Write down the first six multiples of each number: 4 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. 36 and 10 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. 6 and 9 5 and 15 3. 12 and 8 4. 2 and 11 5. 12 and 8 6. 5 and 9 EXAM QUESTIONS 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 9 100 30.1 9.91 14 32 15 (8.8 + 111) x 4.9 40 50 7.21 7 103 8 4.05 x (6.9 + 9) 20 67 8.12 12 150 5.5 EXAM QUESTIONS 3.
ROUNDING AND APPROXIMATIONS Homework 5H GRADES : D,C SIGNIFICANT FIGURES Write each number correct to one significant figure. a) 27 b) 832 c) 8.12 d) 93 e) 77 f) 13.5 g) 95 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 9 19.89 5.2 05 9.03 3. 4.05 4.9 5. 09 EXAM QUESTIONS 3.
ROUNDING AND APPROXIMATIONS Homework 6H GRADES : C, B 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. 6.2 3.09 3.2 8.91 4.9 2 3.8 3. 9 17 8.14 0.515 4. 9.054 0.973 6.3 0.00462 5. 3 7.56 3.9 9.017 2 6. 5 3.2 1 9.2 1 HIGHEST AND LOWEST The length of a pencil is given as 9cm to the nearest cm. What is the minimum length that the pencil could be? 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 3.
ROUNDING AND APPROXIMATIONS Homework 7H GRADES : A UPPER AND LOWER BOUNDS EXAM QUESTIONS 3. 4. 5.
WHOLE NUMBER AND DECIMAL CALCULATIONS Homework 8H GRADES : D,C MULTIPLICATION AND DIVISION (WHOLE NUMBERS) MULTIPLYING DECIMALS DIVIDING WITH DECIMALS EXAM QUESTION
FRACTIONS Homework 9H GRADES : D,C ADDING AND SUBTRACTING FRACTIONS Fill in the boxes by adding the fractions. 1 + 3 1 2 2 3 2 5 3 8 2 7 Work out each question without a calculator. Show your working and write your answer in its simplest form. a) 1 3 3 1 1 1 3 1 b) c) d) 4 5 5 3 9 10 4 6 3. Work out each question with a calculator. a) 3 3 7 2 7 7 13 9 b) c) d) 4 15 10 3 9 10 15 20 EXAM QUESTIONS 3. 4. 5. 6. 7.
FRACTIONS Homework 10H GRADES : D,C MULTIPLYING FRACTIONS Fill in the boxes by multiplying the fractions. 1 x 3 1 2 2 3 2 5 3 8 2 7 MIXED NUMBERS 1 3 1 2 2 5 2 1 3 1 3. 5 2 2 1 2 3 3 4 DIVIDING WITH FRACTIONS 1 1 2 1 3 3 3 1 7 3 3. 4. 5. 2 4 5 10 4 8 10 5 9 4 EXAM QUESTIONS 3. 4., 5. 6. 7.,
FRACTIONS Homework 11H GRADES : B RECURRING DECIMALS EXAM QUESTIONS 3. 4. 5. 6. 7. 8. 9. 10.
SQUARES, CUBES, POWERS AND ROOTS Homework 12H GRADES : E, D,C POWERS AND ROOTS COLLECT A LETTER START 1000 8 32 49 64 P O U E T A 2 3 9 2 5 2 7 3 6 3 2 4 27 121 36 100 1 125 E D L N H I 4 3 2 5 5 3 10 3 6 2 0 2 216 16 343 0 25 81 I C R S T R 10 2 1 5 END 7 2 3 3 11 2 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 3. 4.
SQUARES, CUBES, POWERS AND ROOTS Homework 13H GRADES : C INDEX LAWS Write each of these as simply as possible using indices. a) 2x2x2x2x2 b) y x y x y x y c) 9x9x9 d) 8x8x8x8x8x8x8 Write down the value of the missing index. a) 2 2 3 x 2 2 b) 3 8 12 3 x 2 c) 5 2 9 5 x 5 d) x 3 2 2 2 7 e) (2 2 4 x ) 2 f) 6 x ( 2 ) 2 18 g) 3 3 9 2 x 3 h) 8 4 x 4 4 5 3. State whether each equation is TRUE or FALSE. a) 7 2 6 8 7 7 b) 8 3 2 c) 4 2 6 8 8 ( 5 ) 5 EXAM QUESTIONS 5. 6. 3. 7. 4. 8.
SQUARES, CUBES, POWERS AND ROOTS Homework 14H GRADES : A, A* FRACTIONAL POWERS and NEGATIVE POWERS EXAM QUESTIONS 3. 4. 5. 6. 7. 8. 9. 10. 1 1
SQUARES, CUBES, POWERS AND ROOTS Homework 15H GRADES : A, A* IRRATIONAL NUMBERS AND SURDS EXAM QUESTIONS 3. 4. 5. 6. 7.
POWERS OF 10 AND STANDARD INDEX FORM Homework 16H GRADES : A, A* STANDARD INDEX FORM EXAM QUESTIONS 3. 4. 5. 6.
PERCENTAGES Homework 17H GRADES : D,C PERCENTAGE INCREASE AND DECREASE Increase 90 by 10% 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 How much do they pay for the washing machine? 3.
PERCENTAGES Homework 18H GRADES : B, A COMPOUND PERCENTAGE EXAM QUESTIONS 3. 4. 5. 6. 7.
PERCENTAGES Homework 19H GRADES : B REVERSE PERCENTAGE EXAM QUESTIONS 3. 4. 5. 6.
RATIO AND PROPORTION Homework 20H GRADES : D,C EXAM QUESTIONS 3. 4. 5. 6.
RATIO AND PROPORTION Homework 21H GRADES : A DIRECT PROPORTION EXAM QUESTIONS 3. INVERSE PROPORTION EXAM QUESTIONS
ALGEBRAIC MANIPULATION Homework 22H GRADES : E,D,C EXAM QUESTIONS 1 13. 3. 14. 4. 15. 5. 6. 7. 8. 9. 10. 1
ALGEBRAIC MANIPULATION Homework 23H GRADES : B EXPANDING QUADRATIC EXPRESSIONS EXAM QUESTIONS 3. FACTORISING QUADRATIC EXPRESSIONS EXAM QUESTIONS 3. 4.
ALGEBRAIC MANIPULATION Homework 24H GRADES : A EXPANDING HARDER QUADRATIC EXPRESSIONS EXAM QUESTIONS 3. a) b) 4. 5. FACTORISING HARDER QUADRATIC EXPRESSIONS EXAM QUESTIONS 3. 4.
NON-LINEAR GRAPHS AND GRAPHICAL SOLUTION OF EQUATIONS Homework 25H GRADES : D,C EXAM QUESTION
NON-LINEAR GRAPHS AND GRAPHICAL SOLUTION OF EQUATIONS Homework 26H GRADES : A GRAPHICAL SOLUTION OF EQUATIONS 1 EXAM QUESTION below
NON-LINEAR GRAPHS AND GRAPHICAL SOLUTION OF EQUATIONS Homework 27H GRADES : A, A* GRAPHICAL SOLUTION OF EQUATIONS 2 EXAM QUESTIONS below 3.
COLLECTING DATA Homework 28H GRADES : D, C DATA COLLECTION SHEETS AND QUESTIONNAIRES Exam questions 3. 4.
COLLECTING DATA Homework 29H GRADES : A STRATIFIED SAMPLING Exam questions 3.
PRESENTING DATA AND INTERPRETING INFORMATION Homework 30H GRADES : D STEM AND LEAF DIAGRAMS Exam questions 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.
PRESENTING DATA AND INTERPRETING INFORMATION Homework 31H GRADES : D FREQUENCY DIAGRAMS Exam questions
PRESENTING DATA AND INTERPRETING INFORMATION Homework 32H GRADES : B CUMULATIVE FREQUENCY Exam questions
PRESENTING DATA AND INTERPRETING INFORMATION Homework 33H GRADES : B BOX PLOTS Exam questions
PRESENTING DATA AND INTERPRETING INFORMATION Homework 34H GRADES : A HISTOGRAMS Exam questions 3.
PRESENTING DATA AND INTERPRETING INFORMATION Homework 35H GRADES : B TIME SERIES Exam questions Copy the graph and plot all the other moving averages.
MEASURES OF AVERAGE AND SPREAD Homework 36H GRADES : C AVERAGES FROM TABLES Exam questions 3.
SCATTER DIAGRAMS AND CORRELATION Homework 37H GRADES : C SCATTER DIAGRAMS AND CORRELATION Exam questions 3.
PROBABILITY Homework 38H GRADES : B RELATIVE FREQUENCY - Exam questions
PROBABILITY Homework 39H GRADES : C, B TREE DIAGRAMS - Exam questions
PROBABILITY Homework 40H GRADES : B COMBINED PROBABILITIES (AND RULE / OR RULE) Exam questions 3. 4.
PROBABILITY Homework 41H GRADES : A DEPENDENT EVENTS Exam questions 3. 4.
Compound area + perimeter (mathswatch clip 73) Homework 42H GRADE : D 1) Find the area and perimeter of each shape.
Circumference of circles (mathswatch clip 72) Homework 43H GRADE : D
Area of circles (mathswatch clip 71) Homework 44H GRADE : D,C Volume of cuboids +
prisms(mathswatch clip 34 + 122) Homework 45H GRADE : D - C 1) Find the volume of the following cuboids 3cm 5cm 7cm 7cm 12cm 4cm 2) 3) 4) 5) A cuboid has a volume of 80cm 3 a width of 5cm and a depth of 2 cm find it s height?
Surface area (mathswatch clip 121) Homework 46H GRADE : C -B 1) Find the surface area of the following cuboids 3cm 7cm 5cm 7cm 12cm 4cm 2) 3) 4) A cuboid has a surface area of 36cm 2 a width of 5cm and a depth of 2 cm find it s height?
Volume of Spheres and Cones (mathswatch clip 177) Homework 47H GRADE : A-A* 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
Volume of Spheres and Cones (mathswatch clip 177) Homework 48H GRADE : A-A* 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
Length / Area of arcs, sectors Homework 49H GRADE : A-A* 1) The diagram shows a sector of a circle of radius 9 centimetres. Not drawn accurately 80º 9 cm Find the perimeter of the sector. 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 8 9 10 cm Calculate the length of wire used to make the clip. 3) A circle fits inside a semicircle of diameter 10 cm as shown. Calculate the shaded area. 10 cm
Polygons (mathswatch clip 70) Homework 50H GRADE : C 1) find angle x if the following shape is a rhombus x 32 o 2) 3)
Sequences Homework 51H GRADE : C 1) Write the first five terms of the following sequences whose n th terms are n+3 n 2 +3 3n 8n -2 2n 2 n 3 n 2-5 2) Find the n th 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 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. (a) 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. Write down the nth term of this sequence. 1, 9, 17, 25, 33,...
Straight lines ( mathswatch clip 114 + 143 ) Homework 52H GRADE : C 6 ) Find the midpoints of the following co-ordinates i ) (0,4) (3, 13) ii) (0,7) (2, -1) iii) (10,5) (22, 18)
Solving Equations (Mathswatch clip 105) 1) 4y + 3 = 2y + 10 2) 2x + 17 = 5x 4 3) 2x + 7 = 16 4x 4) 20x -15 = 18x -7 Homework 53H GRADE :D-B 5) 5(x + 3) = 2 (x + 6) 6) 4 (2y + 1) = 2 (12 - y) 7) 7-3x = 2 ( x + 1) x 3 2 2x 4 3 40 x 4 3 8) 5 9) 7 10) x 11) 2x 1 x 3 5 6 3 2 y 2 y 6 3 4 12) 16
Reflections and rotations (Mathswatch clip 74 + 75) Homework 54H GRADE :D-C
Circle theorems (Mathswatch clip 150) Homework 55H GRADE :B
Trial and improvement (Mathswatch clip 110) Homework 56H GRADE :C
Translation (Mathswatch clip 77) Homework 57H GRADE :C
Enlargement (Mathswatch clip 76) Homework 58H GRADE :C
Transformations (Mathswatch clip 74,75,76,77) Homework 59H GRADE :C-B y 6 5 A 4 3 2 1 5 4 3 2 1 O 1 2 3 4 5 1 x 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 The rectangle is rotated 90 clockwise about the point ( 1, 0) and then translated by 4 vector 5 y 6 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 4 B 3 C 2 1 A 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 3 4 5 x 1 2 3 4
Similar Shapes (Mathswatch clip 123) Homework 60H GRADE :C-B 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 20 cm 30 cm How much water does the larger bottle hold?
Dimensions of Formulae (Mathswatch clip 124) Homework 61H GRADE :C-B 2) a, b, and c represent lengths combine a, b, c, to find five formulae that could represent i) volume ii) area
Compound Measures (Mathswatch clip 126) Homework 62H GRADE :C-B
Bounds (Mathswatch clip 125) Homework 63H GRADE : B 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 64H GRADE : C
Real life graphs (Mathswatch clip 117) Homework 65H GRADE : C 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 Distance from home (km) 10 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 45 pm. (a) (b) Complete the travel graph. Calculate the average speed of the taxi............. Answer...km per hour (2) (2)
Substitution (Mathswatch clip 65) Homework 66H GRADE : C
Forming Equations (Mathswatch clip 106) Homework 67H GRADE : C
Changing the subject of a formulae (Mathswatch clip 107) Homework 68H GRADE : C