MEP Practice Book ES Find the gradient of each line in the diagram below. 3 C
|
|
- Lawrence Strickland
- 6 years ago
- Views:
Transcription
1 Graphs MEP Practice Book ES.5 Gradient. Find the gradient of each line in the diagram below A C B Which of the following lines have positive negative (c) zero gradient in the grid below? 4 A B C D 4 4 H E G 4 F
2 .5 MEP Practice Book ES. Find the gradient of the four lines shown on the grid below. 4 A C B 4 4 E D 4 4. Find the gradient of the line that joins the points with coordinates (, ) to (4, 8) (, ) to (7, ) (c) (, 4) to (, ) (d) (, ) to (, 8) (e) (4, ) to (, ) (f) (5, ) to (, 5) 5. For the line =, complete the coordinates A (,? ), B (,? ), C (,? ) D (,? ) What is the gradient of the line AB, BC, CD? What do ou notice? 6. A quadrilateral is formed b joining the points A to B, B to C, C to D, D to A, where A, B, C, D have coordinates A (, ), B (, ), C (, ), D (, ) Which of the four lines found has the largest gradient? Which of the four lines has the smallest gradient?
3 MEP Practice Book ES.6 Application of Graphs. The diagram shows a conversion graph between Pounds ( ) and Euros according to the echange rate on 7 November 6. 5 Pounds ( ) Euros How man Euros can be echanged for 5? How man Pounds can be echanged for 4 Euros?. 6 4 Cost ( ) Units of electricit The graph shows the cost, in pounds, of electricit used b one person. The cost is made up of a fied standing charge, plus the cost of the number of units of electricit used.
4 .6 MEP Practice Book ES Use the graph to find the standing charge in pounds, the cost, in pence, of one unit of electricit. (LON). This graph can be used to convert between pounds ( ) and French Francs French Francs 4 5 Pounds ( ) Use the graph to convert (i) 6 to French Francs, (ii) 55 French Francs to pounds. 6 7 Jim is going to the USA. The bank will echange.58 dollars for. It also charges a commission of % for the echange. Jim wants to echange 5 for dollars at the bank. Work out how man dollars he would receive. (LON) 4
5 MEP Practice Book ES 4. The table below shows volumes epressed in imperial and metric measure. Imperial measure in fluid ounces Metric measure in litres Plot these entries on a suitable grid. One of the entries in the metric column is incorrect. (i) Draw the conversion graph showing the connection between imperial and metric measure and write down the incorrect metric entr. (ii) Use our graph to estimate the correct metric entr. (NEAB) 5. Hannah goes to the shop to bu a loaf of bread. The shop is 8 m from the house. She leaves home at 5 and walks to the shop at a stead speed. She takes 6 minutes to reach the shop and then 5 minutes to bu a loaf of bread. She then walks home at a stead speed arriving at 548. On a cop of the diagram draw a distance-time graph to represent her journe. Distance from home (km) 5 5 Time 6 (SEG) 5
6 .6 MEP Practice Book ES 6. The graph below shows the distance travelled b a car on a journe to work. 4 F Distance (m) 8 D E 6 4 B C A Time (s) 48 The car stopped at two sets of traffic lights. How long did the car spend waiting at each set of lights? On which part of the journe did the car travel fastest? (c) (i) How far did the car travel? (ii) How long did it take for the whole journe? (iii) What was the car's average speed for the whole journe? 7. The graph below shows the speed of a train as it sets off from a station. 4 6 Speed (m/s) Time (s) 6
7 MEP Practice Book ES Find the distance travelled b the train after 4 seconds 8 seconds (c) 6 seconds What is the formula that connects the time of travel and distance travelled for t 6? 8. The graphs of the average weight for different heights for women and men are shown. 9 8 Men 7 Women Weight (kg) Height (cm) Jim and his wife Linda are both 6 cm in height. Use the graphs to estimate the difference in their weights. 8 Arthur and his wife Pam both weigh 75 kg. Use the graphs to estimate the difference in their heights. Show all our working. (c) The actual difference in the heights of Arthur and Pam is cm. Give a possible reason wh the graphs give a different answer. (SEG) 7
8 .6 MEP Practice Book ES 9. The table shows the repaments required on loans of different amounts, for ear. Amount of loan ( ) Monthl Repament ( ) Plot these pairs of values on a cop of the grid below. Join them with a straight line. 4 Monthl repament ( ) Amount of loan ( ) I can afford to repa 8 a month. Use the graph to find out the largest amount I could borrow. (c) Use our graph to find the monthl repament on a loan of. (d) Phil borrows 5. Altogether his monthl repaments amount to more than 5. How much more? (MEG). The following distance-time graph shows the journes made b a van and a car starting from Oford, travelling to Luton, and returning to Oford. How far had the car travelled when it met the van for the second time? Calculate, in miles per hour, the average speed of the car between 95 and. (c) During which period of time was the van travelling at its greatest average speed? 8
9 MEP Practice Book ES Distance (miles) car van Time (SEG). 5 Distance in miles from Manchester 5 am am noon pm pm pm 4pm 5pm 6pm 7pm 8pm Time The graph represents part of Mrs Hinton's journe from Manchester to London. Mrs Hinton stopped for a rest at a service station. (i) Write down the time at which she stopped. (ii) For how long did she stop? For part of her journe Mrs Hinton had to slow down because of a traffic queue. For how man miles did she travel at this lower speed? Mrs Hinton spent an hour at a meeting in London. She then returned home to Manchester, travelling at a stead speed of 5 miles an hour. (c) Use this information to complete the graph of her journe. (LON) 9
10 .6 MEP Practice Book ES. The diagram shows the travel graph of a train. 8 6 Distance from station 4 (km) Time (minutes) Find the greatest speed at which the train travelled. Give our answer in km/h. Calculate the average speed for the whole journe in km/h. (NEAB). This is a conversion graph for gallons and litres. 4 Litres Gallons Use the graph to convert (i) 4 gallons to litres (ii) litres to gallons. 5 gallons is approimatel 5 litres. Eplain how ou can use the graph to show this. (AQA)
11 MEP Practice Book ES 4. The graph is used to convert negative temperatures between F and C. C O F Use the graph to convert F into C. Use the graph to convert 5 C into F..7 Scatter Plots and Lines of Best Fit (AQA). The etension of a spring for a variet of attached weights is given in the table below. Mass (grams) 4 6 Etension (cms) Plot the data on a scatter diagram. What tpe of correlation does this table show? Draw a line of best fit. What do ou think would be the etension for a mass of 5 grams?
12 .7 MEP Practice Book ES. Annie asked a four teenagers to sa how much time the spent doing homework one evening, and how much time the spent watching TV. Here is a scatter diagram to show the results. A D Number of hours spent doing homework B C Number of hours spent watching TV Which of the four points, A, B, C or D, represents each of the statements shown below? Write down one letter for each of the names. LUCY sas I spent most of m evening doing homework. I onl watched one programme on TV. TOM sas I watched a lot of TV last night and I also did a lot of homework CHRIS sas I went out last night. I didn't do much homework or watch TV. (c) Make up a statement which matches the fourth point. What does the graph tell ou about the relationship between time spent watching TV and time spent doing homework?
13 MEP Practice Book ES (d) Annie also drew scatter diagrams which showed that: Older students tend to spend more time doing homework than ounger students. There is no relationship between the time students spend watching TV and the time students spend sleeping. On a cop of the aes below, show what Annie's scatter diagram ma have looked like. 4 Hours spent doing homework 8 Age of students (ears) Hours spent sleeping 5 4 Hours spent watching TV. Each week during the summer season, a seaside resort recorded the rainfall and the number of deckchair tickets sold. Some of the results are plotted on the scatter diagram on the net page. (c) What does the scatter diagram tell ou about the connection between the rainfall and the number of deckchair tickets sold? On a cop of the diagram draw in a line of best fit. In the first week of June onl 5 deckchair tickets were sold. How much rain do ou think the resort had that week?
14 .7 MEP Practice Book ES number of 4 deckchair tickets sold mm of rain (NEAB) 4. Ten bos of different ages were set the same General Knowledge test. The results are shown in the table below. Bo A B C D E F G H I J Age (months) Score The mean of the ages of the bos is 58 months. Calculate the mean of their scores. 4
15 MEP Practice Book ES The results in the table have been plotted on the following scatter graph. 4 Marks scored Age in months 8 (i) (ii) (iii) Does the scatter graph show the sort of result ou would epect? Eplain our answer. On a cop of the scatter graph draw a line of best fit. Taking age into account, to which bo would ou award a prize for the best performance? 5. The table below shows the number of Compact Discs (CDs) and the number of Long Plaing Records (LPs) that were sold from 984 to Number of CDs (millions) Number of LPs (millions) 7 million CDs were sold in 99. Write the number 7 million in figures. In which ear did the sale of CDs overtake the sale of LPs? (i) (ii) Draw a scatter graph to show the sale of CDs against the sale of LPs. What does our scatter diagram tell ou about the connection between the sale of CDs and the sale of LPs? 5
16 .7 MEP Practice Book ES 6. Tom breeds hamsters. The number of hamsters is epected to treble each ear. Tom had hamsters on..96. Date Estimated number of hamsters (c) On a suitable grid, draw a smooth curve to represent this information. Use our grid to estimate the number of hamsters Tom would have on Write down an epression to find the estimated number of hamsters n ears after..96. (LON) 7. Below are the ears and times of some world records for running the mile. Glen Cunningham sec Roger Bannister sec Michael Jaz sec John Walker 975 sec Steve Cram sec Noureddine Morcelli 99 5 sec These data are used to plot a scatter diagram. 5 4 Time (s) Year 6
17 MEP Practice Book ES (i) On a cop of the scatter diagram, draw the line of best fit. (ii) Sebastian Coe ran a new world record in 979. (iii) Use the line to estimate his time. Eplain wh the line ou have drawn can onl be used to estimate times for a limited number of ears. (c) Roger Bannister's actual time of 9. seconds is known to be correct to the nearest tenth of a second. What is the shortest time that it could actuall be? In 99 Noureddine Morcelli's time for running the mile was 5 seconds. B taking 5 miles to be equal to 8 kilometres, calculate what his time for the 5 metres would have been, assuming that his average speed was the same. Give our answer to the nearest second..8 The Equation of a Straight Line. Find the equation of the straight line with gradient = and - intercept = gradient = and - intercept = (c) gradient = and - intercept = (d) gradient = and - intercept =. Write down the gradient and -intercept of each of the following lines. = = + 4 (c) = (d) = + (e) = ( + ) (f) = +. The diagram shows the straight lines passing through the points (, ) and (4, ). Find the gradient of the line, the -intercept of the line, (c) the equation of the line
18 .8 MEP Practice Book ES 4. Write down the gradient and -intercept of each of the following lines. = 4 = + (c) = 4 (d) = 5 (e) = 4 (f) = 5. Find the equation of each line shown in the diagram below. 5 C D E 4 B A Find the equation of the line that passes through the points with coordinates: (, ) and (, 5) (, 5) and (, ) (c) (, ) and (4, ) (d) (, ) and (, ) 8
19 MEP Practice Book ES 7. The scatter diagram represents the profits made b a compan over the ears 965 to Profit (millions) Year Use the diagram to calculate an estimate of the profit the compan would epect to get in the ear if this trend continues. (NEAB) 8. The line = + c passes through the point (, 8). Find the value of c. 9. The line = m + passes through the point (, 7). Find the value of m.. The charges made b a removal firm consist of a fied charge of 5, and a variable charge of 5 per mile travelled. Write down the formula for the total cost,, in terms of the distance travelled, miles. Draw a graph of this relationship for and use it to estimate the distance travelled when the total cost is.. Complete a cop of the table of values for =. = 9
20 .8 MEP Practice Book ES On a cop of the following grid plot our values for and. Join our points with a straight line (c) Write down the coordinates of the points where our graph crosses the -ais. (LON). This table shows the diameter, d, and the circumference, c, of four circular objects. The have been measured to the nearest centimetre. Object d c p coin cm 6 cm tin of beans 6 cm 8 cm saucer 7 cm cm plate cm cm On a cop of the following grid, plot c against d for each object. Draw a straight line to show the relationship between c and d. Write down the equation of this straight line.
21 MEP Practice Book ES c d. The diagram shows the points A (, ), B (, ) and C (8, 7). C A B Not drawn accuratel O Find the equation of the straight line which passes through A, B and C. (AQA)
22 MEP Practice Book ES.9 Horizontal and Vertical Lines. Write down the equation of each line marked in the following diagram. C B A D E F. Draw the lines =, = 7, =, =. Write down the coordinates of the points where the cross and find the area of the rectangle enclosed b these lines.. Draw the line =, =, = 4, =. What are the coordinates of the centre of the rectangle formed? 4. Draw the square which has corners at the points with coordinates (, ), (, 4), (, ) and (, 4) What are the equations of the lines that form the sides of the square? 5. Draw the lines =, = 8, =. What is the area of the triangle enclosed?
23 MEP Practice Book ES. Solutions of Simultaneous Equations b Graphs. 4 C Use the graph above to solve = + = = 7 7 (c) = + 6 = + 6 = +. Solve graphicall the following sets of simultaneous equations. + = 4 + = 5 + = = (c) 5 = (d) 4 + = + = =
24 . MEP Practice Book ES The diagram shows the graphs of the equations + and = 5 Use the diagram to solve the simultaneous equations + = = 5 (LON) 4. Jane bus litres of oil and 4 litres of petrol for. Richard bus litres of oil and litres of petrol for. The cost of litre of oil is. The cost of litre of petrol is. Therefore + 4 = and + = Draw the graphs of these equations. What is the cost of one litre of petrol? (SEG) 5. Fift-one students went to a pop concert. Let represent the number of men. Let represent the number of women. The number of women is related to the number of men b the two equations On the following graph, the line + = 5 = + + = 5 has been drawn Draw the line = + on a cop of the graph. Use the graph to write down the number of men and women who went to the pop concert. 4
25 MEP Practice Book ES (c) At another pop concert there were fewer than 5 students but there were at least men. B drawing another line on our graph, find the region that represents the possible values of and. Label the region with the letter R. 5 4 Number of women 4 5 Number of men (SEG) 6. Beth was asked to draw the graph of = + 4. She plotted the si points shown in the following diagram. (i) From the shape of the graph, how can ou tell that one of the points is in the wrong place? (ii) On a cop of the diagram, draw the graph of = + 4. B drawing another straight line on the diagram, solve the simultaneous equations = + 4 = 5
26 . MEP Practice Book ES (MEG) 7. Errol's house has a meter which measures the amount of water he uses. Errol can pa on Tariff A for the number of water units that he uses. The graph on the net page can be used to find out how much he must pa for his water on Tariff A. Use the graph to find how much he must pa when he used (i) 6 units, (ii) 4 units. Errol uses water units. This costs c. Use the information from the graph to find a formula for c in terms of. Instead of Tariff A, Errol could pa for his water on Tariff B. The table shows how much Errol would have to pa for his water on Tariff B. Number of water units used () Cost ( c) (c) Plot a graph on a cop of the grid to show this information. 6
27 MEP Practice Book ES Errol wants to be charged the smaller amount for the water he uses. (d) Use the graph to find how man units Errol can use before Tariff A becomes dearer than Tariff B Cost in Number of units. Graphs of Common Functions. State whether each equation below would produce the graph of a function. linear, quadratic, cubic or reciprocal = = (c) = 5 (d) = (e) = (f) = + 4 7
28 . MEP Practice Book ES. Each of the following graphs is the sketch of a linear, quadratic, cubic or reciprocal function. State which it is for each graph. (c) (d) (e) (f). Each equation below has been sketched. Select the most suitable graph for each equation. A: = B: = C: D: = E: = = F: = + (c) (d) (e) (f) 4. Which of the following functions is illustrated b each of the graphs below? = +, = +, =, = +, = 8
29 MEP Practice Book ES A B (SEG) 5. The radius, r, and value, v, of gold coins were measured and recorded. r (cm) v ( ) Which of these graphs represents the information shown in the table? v v v A r v B r C r D r Which of these equations describes the information shown in the table? v = k r, v = kr, v = kr, v = 6. A cuboid has the dimensions shown. k r where kis a constant. (SEG) cm 5 cm 4 cm Not to scale The volume, V, of the bo is given b ( )( ) V = 4 5 9
30 . MEP Practice Book ES Draw a graph of V against for 4. Use our graph to find the maimum volume of the cuboid. Find the maimum total surface area of the cuboid when the volume is cm. (SEG) ( ) can be written in the form + p q, where p and q are integers. Find the value of (i) p (ii) q Hence, or otherwise, (i) sketch the graph of = (ii) write down the minimum value of (LON) 8. Four graphs are sketched. O Graph A O Graph B O Graph C O Graph D Complete the following statements. (i) = + 4 matches graph..... (ii) = + 4 matches graph..... (iii) + = 4 matches graph..... Sketch the graph of = on a cop of the aes opposite. O (AQA)
31 MEP Practice Book ES. Graphical Solutions of Equations. Draw a graph of = for. Use our graph to solve the equations = 6 =. The following sketch shows the graph of = Use the graph to write down the value of the positive solution to + 8 = (LON). = 4 Complete a cop of the table of values. On a cop of the following grid draw the graph of = 4. (c) (d) B drawing a suitable straight line on the grid, solve the equation 4 = Using the method of trial and improvement, or otherwise, solve the equation 4 = correct to one decimal place.
32 . MEP Practice Book ES (LON) h s The diagram shows part of the graph of = 4 +.
33 MEP Practice Book ES Use a cop of the graph to find approimate solutions in the range < < of 4 + =. B drawing suitable straight lines on our grid, find approimate solutions in the range < < of the equations (i) 4 = (ii) 5 + = (LON) 5. Ale is using "trial and improvement" to solve the equation =. First he tries = and finds the value of is. B tring other values of find a solution of the equation correct to one decimal place. You must show all our working. =, (i) Draw the graph of =, for values of from to 4. (ii) B drawing suitable line on our graph show that the equation = has two solutions. (SEG) 6. The diagram shows the graph of = for values of from to 4. 4 Use a cop of the graph to find three values of which satisf the equation =.
34 . MEP Practice Book ES The equation = k is satisfied b onl one value of between and 4. What can be said about the number k? (c) (i) On a cop of the diagram, draw the reflection of the graph in the -ais. (ii) Write down the equation of this reflection. (MEG) 7. Complete the table of values for the graphs of = and = = 5 6 = (i) On graph paper draw the graphs of = and = + 6 (ii) Use our graphs to solve the equation + 4 =. (LON) 8. Draw the graph of = 5 and = for Use our graph to estimate, correct to one decimal place, the solution of + 5 = (SEG) 9. A child's to consists of a set of different sized blocks which are in the shape of cubes. The cost, C pence, of making each block is made up of two parts: a fied cost of 4 pence, and a cost that is proportional to the cube of the length, centimetres, of the block. When = ; C = 56. Find the equation connecting and C. The cost, D pence, of decorating each block is given b the equation D = 4 + Another child's to is in the shape of a stick. 4
35 MEP Practice Book ES The cost, D pence, of decorating a stick of length, centimetres, is given b the equation D = Use a graphical method to find the value of when the cost of decorating the block and the stick is the same. (SEG). The graph of n = 8 5. is given. t On a cop of the grid below draw a graph so that the equation can be solved. n 8 5 t. = t t 4 5 (i) Use our graph to find the value of t at the point of intersection of the two curves. (ii) 8 Write the equation 5. = t in the form 4 =..... t Simplif the right hand side as far as possible. (c) For the equation n = 8 5. estimate the rate of decrease of n when t =. t (d) Estimate, b drawing, the gradient of the tangent at the point when t = 4, on the graph ou have drawn. (SEG) 5
36 . MEP Practice Book ES. John places a cake in his freezer. The temperature, T C, of the cake after t minutes is given b the formula T t = ( ) 8 Cop and complete the table below. t(minutes) 4 T C Draw the graph of T against t. (c) (d) John knows that the cake's temperature is 4 C when he places it in the freezer. He does not know the formula for its temperature after t minutes. He estimates that its temperature will fall b C ever minute. On our grid, draw the graph showing how John thinks the temperature will var during the first three minutes. Use our graph to find the time when the estimated temperature is the same as the true temperature of the cake. 6
37 MEP Practice Book ES. The grid below shows the graph of = +. = O B drawing appropriate straight lines on a cop of the graph, solve the equations: a) + = b) + = (AQA) 7
38 . MEP Practice Book ES. Cop and complete this table and draw the graph of = 7 + for values of from to on a cop of the grid below B drawing suitable straight lines on the graph, solve these equations. (i) 7 + = (ii) 8 + = (OCR) 8
MEP Practice Book ES Find the gradient of each line in the diagram below. 3 C
Graphs MEP Practice Book ES.5 Gradient. Find the gradient of each line in the diagram below. 6 5 4 A C B 4 5 6. Which of the following lines have positive negative (c) zero gradient in the grid below?
More informationF8-18 Finding the y-intercept from Ordered Pairs
F8-8 Finding the -intercept from Ordered Pairs Pages 5 Standards: 8.F.A., 8.F.B. Goals: Students will find the -intercept of a line from a set of ordered pairs. Prior Knowledge Required: Can add, subtract,
More informationSTRAND G: Relations, Functions and Graphs
UNIT G Using Graphs to Solve Equations: Tet STRAND G: Relations, Functions and Graphs G Using Graphs to Solve Equations Tet Contents * * Section G. Solution of Simultaneous Equations b Graphs G. Graphs
More information3.1 Functions. The relation {(2, 7), (3, 8), (3, 9), (4, 10)} is not a function because, when x is 3, y can equal 8 or 9.
3. Functions Cubic packages with edge lengths of cm, 7 cm, and 8 cm have volumes of 3 or cm 3, 7 3 or 33 cm 3, and 8 3 or 5 cm 3. These values can be written as a relation, which is a set of ordered pairs,
More information13 Graphs Positive Coordinates. Worked Example 1. Solution
Graphs MEP Pupil Tet. Positive Coordinates Coordinates are pairs of numbers that uniquel describe a position on a rectangular grid. The first number refers to the horizontal (-ais) and the second the vertical
More informationHigher tier unit 6a check in test. Calculator
Higher tier unit 6a check in test Calculator Q1. The point A has coordinates (2, 3). The point B has coordinates (6, 8). M is the midpoint of the line AB. Find the coordinates of M. Q2. The points A, B
More informationChapter 5: Polynomial Functions
Chapter : Polnomial Functions Section.1 Chapter : Polnomial Functions Section.1: Eploring the Graphs of Polnomial Functions Terminolog: Polnomial Function: A function that contains onl the operations of
More informationLEVEL 6. Level 6. Page (iv)
LEVEL 6 Number Page N9... Fractions, Decimals and Percentages... 69 N20... Improper Fractions and Mixed Numbers... 70 N2... Prime Numbers, HCF and LCM... 7 Calculating C22... Percentage of an Amount...
More informationReady To Go On? Skills Intervention 4-1 Graphing Relationships
Read To Go On? Skills Intervention -1 Graphing Relationships Find these vocabular words in Lesson -1 and the Multilingual Glossar. Vocabular continuous graph discrete graph Relating Graphs to Situations
More informationFair Game Review. Chapter 2. and y = 5. Evaluate the expression when x = xy 2. 4x. Evaluate the expression when a = 9 and b = 4.
Name Date Chapter Fair Game Review Evaluate the epression when = and =.... 0 +. 8( ) Evaluate the epression when a = 9 and b =.. ab. a ( b + ) 7. b b 7 8. 7b + ( ab ) 9. You go to the movies with five
More informationSAMPLE. Interpreting linear relationships. Syllabus topic AM2 Interpreting linear relationships. Distance travelled. Time (h)
C H A P T E R 5 Interpreting linear relationships Sllabus topic AM Interpreting linear relationships Graphing linear functions from everda situations Calculating the gradient and vertical intercept Using
More informationGraphically Solving Linear Systems. Matt s health-food store sells roasted almonds for $15/kg and dried cranberries for $10/kg.
1.3 Graphicall Solving Linear Sstems GOAL Use graphs to solve a pair of linear equations simultaneousl. INVESTIGATE the Math Matt s health-food store sells roasted almonds for $15/kg and dried cranberries
More information1.2 Visualizing and Graphing Data
6360_ch01pp001-075.qd 10/16/08 4:8 PM Page 1 1 CHAPTER 1 Introduction to Functions and Graphs 9. Volume of a Cone The volume V of a cone is given b V = 1 3 pr h, where r is its radius and h is its height.
More informationPaper 2 and Paper 3 Preparation Paper
Paper 2 and Paper 3 Preparation Paper You will need a calculator Ensure you have: Pencil, pen, ruler, protractor, pair of compasses and eraser Guidance 1. Read each question carefully before you begin
More informationLarkrise Maths Curriculum Pitch & Expectations Shape, Space & Measure
Larkrise Maths Curriculum Pitch & Expectations Shape, Space & Measure Measurement Compare, describe and solve practical problems for lengths and heights, mass/weight, capacity and volume time Measure and
More informationFractions, Decimals, Ratio and Percentages (FDRP) Measures (MEA)
Termly assessment Number and Place Value (NPV) Addition and Subtraction (AS) Multiplication and Division (MD) Fractions, Decimals, Ratio and Percentages (FDRP) Measures (MEA) Geometry (GEO) Statistics
More informationUNIT 29 Using Graphs to Solve Equations: CSEC Revision Test
UNIT 9 Using Graphs to Solve : UNIT 9 Using Graphs to Solve 1. Shell bus 3 litres of oil and 40 litres of gasoline for $30. The cost of one litre of oil is $ and the cost of one litre of gasoline is $.
More informationMathematics in Y3 Year Group Expectations
Mathematics in Y3 Year Group Expectations What the National Curriculum requires in mathematics in Y3 NUMBER PLACE VALUE: count from 0 in multiples of 4, 8, 50 and 100; find 10 or 100 more or less than
More informationGraphs and Functions
CHAPTER Graphs and Functions. Graphing Equations. Introduction to Functions. Graphing Linear Functions. The Slope of a Line. Equations of Lines Integrated Review Linear Equations in Two Variables.6 Graphing
More informationName: Teacher: Form: LEARNER JOURNAL. Set: Mathematics. Module 2 END OF YEAR TARGET: GCSE TARGET:
Name: Teacher: Form: Set: LEARNER JOURNAL Mathematics Module 2 END OF YEAR TARGET: GCSE TARGET: MODULE 2 use a number line to represent negative numbers use inequalities with negative numbers compare and
More informationProcessing, representing and interpreting data
Processing, representing and interpreting data 21 CHAPTER 2.1 A head CHAPTER 17 21.1 polygons A diagram can be drawn from grouped discrete data. A diagram looks the same as a bar chart except that the
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. A) 2, 0 B) 2, 25 C) 2, 0, 25 D) 2, 0, 0 4
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Select from the list of numbers all that belong to the specified set. ) Integers, 7, -7, 0, 0, 9 A),
More informationPaper 2 and Paper 3 Preparation Paper
Paper 2 and Paper 3 Preparation Paper Ensure you have: Pencil, pen, ruler, protractor, pair of compasses and eraser You will need a calculator Guidance 1. Read each question carefully before you begin
More informationPosition. By the end of the year, it is expected that children will be able to sequence events in chronological order. My Numeracy Targets Year 1
My Numeracy Targets Year 1 Number and place value Multiplication and Division Addition and subtraction I can count up and down from 0 to 100 and more. I can count, read and write numbers up to 100. I can
More informationLESSON Constructing and Analyzing Scatter Plots
LESSON Constructing and Analzing Scatter Plots UNDERSTAND When ou stud the relationship between two variables such as the heights and shoe sizes of a group of students ou are working with bivariate data.
More informationOaktree School Curriculum Ladder. Maths: Geometry & Measure Step 2 (7-12)
Maths: Geometry & Measure Step 2 (7-12) I can look for hidden objects- sight, hearing or touch I can match objects by size I can fill a container I can take objects out of a container I can help build
More informationSupporting our children to aim high!
Reach for the Sky Supporting our children to aim high! St Mary s CE School Maths Support Resources Parents often ask us, how can I help my child in maths? Firstly, we provide parents with the expectations
More informationMaths Target Wall Year 1
Maths Target Wall Year 1 I can count up and down from 0 to 100 and more. I can count, read and write numbers up to 100. I can count in 2 or 5 or 10 When you show me a number, I can tell you what is one
More informationMEP Practice Book SA (a) Write down the coordinates of the point A. Copy the diagram and mark with a cross the position of B on the grid.
UNITS 13 16 MEP Practice Book S13-16 Miscellaneous Exercises Note Starred* questions are for cademic Route only. 1. y 5 4 3 1 1 3 4 5 Write down the coordinates of the point. B is the point with coordinates
More informationAnswers. Investigation 4. ACE Assignment Choices. Applications
Answers Investigation ACE Assignment Choices Problem. Core Other Connections, ; Etensions ; unassigned choices from previous problems Problem. Core, 7 Other Applications, ; Connections ; Etensions ; unassigned
More informationMath 3 Coordinate Geometry part 1 Unit November 3, 2016
Reviewing the basics The number line A number line is a visual representation of all real numbers. Each of the images below are examples of number lines. The top left one includes only positive whole numbers,
More informationA9.1 Linear programming
pplications 9. Linear programming 9. Linear programming efore ou start You should be able to: show b shading a region defined b one or more linear inequalities. Wh do this? Linear programming is an eample
More informationGRAPHS AND GRAPHICAL SOLUTION OF EQUATIONS
GRAPHS AND GRAPHICAL SOLUTION OF EQUATIONS 1.1 DIFFERENT TYPES AND SHAPES OF GRAPHS: A graph can be drawn to represent are equation connecting two variables. There are different tpes of equations which
More informationProblem 1: The relationship of height, in cm. and basketball players, names is a relation:
Chapter - Functions and Graphs Chapter.1 - Functions, Relations and Ordered Pairs Relations A relation is a set of ordered pairs. Domain of a relation is the set consisting of all the first elements of
More informationMATHEMATICS (SYLLABUS D) 4024/02
CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level MATHEMATICS (SYLLABUS D) 4024/02 Paper 2 Additional Materials: Answer Booklet/Paper Electronic calculator Geometrical
More informationACTIVITY: Forming the Entire Coordinate Plane
.5 The Coordinate Plane How can ou graph and locate points that contain negative numbers in a coordinate plane? You have alread graphed points and polgons in one part of the coordinate plane. In Activit,
More informationG r a d e 1 0 I n t r o d u c t i o n t o A p p l i e d a n d P r e - C a l c u l u s M a t h e m a t i c s ( 2 0 S )
G r a d e 0 I n t r o d u c t i o n t o A p p l i e d a n d P r e - C a l c u l u s M a t h e m a t i c s ( 0 S ) Midterm Practice Exam Answer Key G r a d e 0 I n t r o d u c t i o n t o A p p l i e d
More informationPARRENTHORN HIGH SCHOOL Mathematics Department. YEAR 11 GCSE PREPARATION Revision Booklet
PARRENTHORN HIGH SCHOOL Mathematics Department YEAR GCSE PREPARATION Revision Booklet Name: _ Class: Teacher: GEOMETRY & MEASURES Area, Perimeter, Volume & Circles AREA FORMULAS Area is the space a 2D
More informationCore Connections, Course 3 Checkpoint Materials
Core Connections, Course 3 Checkpoint Materials Notes to Students (and their Teachers) Students master different skills at different speeds. No two students learn eactl the same wa at the same time. At
More informationYear 1 Yearly Overview
Year 1 Yearly Overview Counting Identifying, representing and estimating Reading and writing Comparing Count to and across 100, forwards & backwards, beginning with 0 or 1, or from any given number Count,
More informationGeneral Certificate of Secondary Education Higher Tier
Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Pages 3 Mark General Certificate of Secondary Education Higher Tier 4 5 6 7 Mathematics (Linear) B Paper 1 Non-calculator
More informationNational Curriculum 2014: Progression in Mathematics
Number and Place Value Year 1 Year 2 Year 3 count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number count, read and write numbers to 100 in numerals, count in different
More informationLarkrise Maths Curriculum Document Shape, Measure, Data. Maths Curriculum June 2014 Shape, Measure, Data
Maths Curriculum June 2014 Shape, Measure, Data 1 Year 1 Measurement Geometry properties of shapes Geometry position and direction Compare, describe and solve practical problems for: lengths and heights
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
MATH 7 - COLLEGE ALGEBRA FINAL REVIEW MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Select from the list of numbers all that belong to the specified
More informationMedium Term Plans for Mathematics (revised 2018) - Year Five (Summer Term)
Oral mental starters (ongoing, throughout the term): Identify multiples and count from (and back to) 0 in multiples of, 4, 6, 7, 8, 9, 11,1,, 0, 100 and 1000 Recall and use multiplication and division
More informationWhat You ll Learn. Why It s Important
How do ou think music sales have changed over the past 1 ears? ears? In what format do ou bu the music ou listen to? In what format did our parents bu the music the listened to as students? Wh might record
More informationThursday 9 June 2016 Morning
Oxford Cambridge and RSA F Thursday 9 June 2016 Morning GCSE MATHEMATICS A A503/01 Unit C (Foundation Tier) * 5 9 9 9 2 0 0 4 0 1 * Candidates answer on the Question Paper. OCR supplied materials: None
More informationStage 5 PROMPT sheet. 5/3 Negative numbers 4 7 = -3. l l l l l l l l l /1 Place value in numbers to 1million = 4
Stage PROMPT sheet / Place value in numbers to million The position of the digit gives its size / Negative numbers A number line is very useful for negative numbers. The number line below shows: 7 - l
More informationBETWEEN PAPERS PRACTICE (F&H)
BETWEEN PAPERS PRACTICE (F&H) Summer 2018 QUESTIONS Not A best Guess paper. Neither is it a prediction... only the examiners know what is going to come up! Fact! You also need to REMEMBER that just because
More informationUsing a Table of Values to Sketch the Graph of a Polynomial Function
A point where the graph changes from decreasing to increasing is called a local minimum point. The -value of this point is less than those of neighbouring points. An inspection of the graphs of polnomial
More informationIB SL REVIEW and PRACTICE
IB SL REVIEW and PRACTICE Topic: CALCULUS Here are sample problems that deal with calculus. You ma use the formula sheet for all problems. Chapters 16 in our Tet can help ou review. NO CALCULATOR Problems
More informationST GREGORY S RC JMI MATHEMATICS NATIONAL CURRICULUM SEPTEMBER 2014 STATUTORY PROGRAMME OF STUDY Y1 Y6
ST GREGORY S RC JMI MATHEMATICS NATIONAL CURRICULUM SEPTEMBER 2014 STATUTORY PROGRAMME OF STUDY Y1 Y6 GROUP / CHILD Y1 NUMBER NUMBER & PLACE VALUE ADDITION & SUBTRACTION MULTIPLICATION & DIVISION count
More informationInt 1 Checklist (Unit 1) Int 1 Checklist (Unit 1) Whole Numbers
Whole Numbers Know the meaning of count and be able to count Know that a whole number is a normal counting number such as 0, 1, 2,, 4, Know the meaning of even number and odd number Know that approximating
More informationYear 5 PROMPT sheet. Negative numbers 4 7 = -3. l l l l l l l l l Place value in numbers to 1million = 4
Year PROMPT sheet Place value in numbers to million The position of the digit gives its size Millions Hundred thousands Ten thousands thousands hundreds tens units 7 Negative numbers A number line is very
More informationNUMBER AND PLACE VALUE ADDITION AND SUBTRACTION MULTIPLICATION AND DIVISION FRACTIONS Count to and across 100, forwards
2014 STATUTORY REQUIREMENTS OVERVIEW - YEAR 1 NUMBER AND PLACE VALUE ADDITION AND SUBTRACTION MULTIPLICATION AND DIVISION FRACTIONS Count to and across 100, forwards Read, write and interpret Solve one-step
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
MATH 7 - COLLEGE ALGEBRA FINAL REVIEW MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Select from the list of numbers all that belong to the specified
More informationInmans Primary School Mathematics Long Term Plan
Year 1 Inmans Primary School Mathematics Long Term Plan Number Number and place value Count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number Count, read and write
More informationWhole Numbers. Integers and Temperature
Whole Numbers Know the meaning of count and be able to count Know that a whole number is a normal counting number such as 0, 1, 2, 3, 4, Know the meanings of even number and odd number Know that approximating
More informationYear 6 Step 1 Step 2 Step 3 End of Year Expectations Using and Applying I can solve number problems and practical problems involving a range of ideas
Year 6 Step 1 Step 2 Step 3 End of Year Expectations Using and Applying I can solve number problems and practical problems involving a range of ideas Number Number system and counting Fractions and decimals
More informationYear 6 Step 1 Step 2 Step 3 End of Year Expectations Using and Applying I can solve number problems and practical problems involving a range of ideas
Year 6 Step 1 Step 2 Step 3 End of Year Expectations Using and Applying I can solve number problems and practical problems involving a range of ideas Number Number system and counting Fractions and decimals
More informationMATHEMATICS ASSESSMENT RECORD - YEAR 1
MATHEMATICS ASSESSMENT RECORD - YEAR 1 Count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number Count, read and write numbers to 100 in numerals; count in multiples
More informationDonnington Primary School Mathematics Statements
Year 1 / Band 1 Count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number Count, read and write numbers to 100 in numerals; count in multiples of twos, fives and
More informationMaths - Knowledge Key Performance Indicator Milestones Milestones Year 5 Year 6
Addition and Subtraction Number and Place Value Maths - Knowledge Key Performance Indicator Milestones Milestones Year 5 Year 6 I can read numbers to at least 1 000 000 I can write numbers to at least
More informationNumber. Measure. Geometry. Key:
Year R Maths - Key Performance Indicator Can count reliably with numbers from one to 0. Can find one more or one less than a given number. Using quantities or objects, can add or subtract two single digit
More informationEssential Question: How do you graph an exponential function of the form f (x) = ab x? Explore Exploring Graphs of Exponential Functions. 1.
Locker LESSON 4.4 Graphing Eponential Functions Common Core Math Standards The student is epected to: F-IF.7e Graph eponential and logarithmic functions, showing intercepts and end behavior, and trigonometric
More informationAnswers Investigation 4
Answers Investigation Applications. a. At seconds, the flare will have traveled to a maimum height of 00 ft. b. The flare will hit the water when the height is 0 ft, which will occur at 0 seconds. c. In
More informationMedium Term Plans for Mathematics (revised version) - Year Five (Summer Term)
Oral mental starters (ongoing, throughout the term): Identify multiples and count from (and back to) 0 in multiples of, 4, 6, 7, 8, 9, 11,1,, 0, 100 and 1000 Recall and use multiplication and division
More informationWhat You ll Learn. Why It s Important
How do ou think music sales have changed over the past 1 ears? ears? In what format do ou bu the music ou listen to? In what format did our parents bu the music the listened to as students? Wh might record
More informationStratford upon Avon School Mathematics Homework Booklet
Stratford upon Avon School Mathematics Homework Booklet Year: 7 Scheme: 1 Term: 1 Name: Show your working out here Homework Sheet 1 1: Write 7:43 pm using the 24 hour clock 11: Find the area of this shape.
More informationLinear Equations in Two Variables
Section. Linear Equations in Two Variables Section. Linear Equations in Two Variables You should know the following important facts about lines. The graph of b is a straight line. It is called a linear
More information2. A square has a side length of 9 mm. What is the area of the square? A 18 mm² B 36 mm² C 49 mm² D 81 mm²
Chapter 3 Test. BLM 3 18. For #1 to #5, select the best answer. 1. Which number is not a perfect square? A 9 B 16 C 55 D 121 2. A square has a side length of 9 mm. What is the area of the square? A 18
More informationMathematics: Planning and Assessment from National Curriculum Year 1
Mathematics: Planning and Assessment from National Curriculum Year Number & Place Value Addition & Subtraction Multiplication & Division Fractions Measurement Geometry: Properties of Shapes Count to and
More informationLesson 2.1 Exercises, pages 90 96
Lesson.1 Eercises, pages 9 96 A. a) Complete the table of values. 1 1 1 1 1. 1 b) For each function in part a, sketch its graph then state its domain and range. For : the domain is ; and the range is.
More information2014 National Curriculum - Maths Band 1
2014 National Curriculum - Maths Band 1 count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number read, write and interpret mathematical statements involving addition
More informationWhat is the relationship between the real roots of a polynomial equation and the x-intercepts of the corresponding polynomial function?
3.3 Characteristics of Polnomial Functions in Factored Form INVESTIGATE the Math The graphs of the functions f () 5 1 and g() 5 1 are shown.? GOAL Determine the equation of a polnomial function that describes
More informationMath 2 Coordinate Geometry Part 1 Slope & Transformations
Math 2 Coordinate Geometry Part 1 Slope & Transformations 1 MATH 1 REVIEW: THE NUMBER LINE A number line is a visual representation of all real numbers. Each of the images below are examples of number
More informationMaths Curriculum Overview Year 1
Year 1 Count to and across 100, forwards and backwards beginning with 0 or one from any given number Count, read and write numbers to 100 in numerals, count in multiples of twos fives and tens Given a
More informationStage 5 PROMPT sheet. 5/3 Negative numbers 4 7 = -3. l l l l l l l l l /1 Place value in numbers to 1million = 4
Millions Hundred thousands Ten thousands Thousands Hundreds Tens Ones Stage PROMPT sheet / Place value in numbers to million The position of the digit gives its size / Negative numbers A number line is
More informationread, write and interpret mathematical statements involving addition (+), subtraction (-) and equals (=) signs
Year 1 NUMBER Number and place value count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number count, read and write numbers to 100 in numerals; count in multiples
More informationRelationships In Data. Lesson 10
Relationships In Data Lesson 0 Lesson Ten Concepts Overall Epectations Appl data-management techniques to investigate relationships between two variables; Determine the characteristics of linear relations;
More informationFractions (including decimals - from Yr 4 - and percentages - from Yr 5) recognise, find and name a half as one of two equal parts of an.
Year 1 count to across 100, forwards backwards, beginning with 0 or 1, or from any given count, read write to 100 in numerals; count in multiples of twos, fives tens given a, identify one more one less
More informationConnecticut Common Core Algebra 1 Curriculum. Professional Development Materials. Unit 4 Linear Functions
Connecticut Common Core Algebra Curriculum Professional Development Materials Unit 4 Linear Functions Contents Activit 4.. What Makes a Function Linear? Activit 4.3. What is Slope? Activit 4.3. Horizontal
More informationY1 - Maths Long Term Plan
Y1 - Maths Long Term Plan - 2015-2016 Number and Place Value Fractions Measurement Geometry Count to and across 100, forwards and backwards or from any given Count, read and write s to 100 in numerals
More informationAdjacent sides are next to each other and are joined by a common vertex.
Acute angle An angle less than 90. A Adjacent Algebra Angle Approximate Arc Area Asymmetrical Average Axis Adjacent sides are next to each other and are joined by a common vertex. Algebra is the branch
More informationYear 1 End of Year Maths Targets. Pupil Name AUT 2 SPR 2 SPR 1 AUT 1 SUM 1 SUM 2 TARGETS
Year End of Year Maths Targets Pupil Name Number and place value I can count to and across 00, forward and backwards,beginning with 0 or from any number. I can count in multiples of, 5 and 0. I can count,
More informationCrockerne Church of England Primary Non-Negotiables. Mathematics
Key Skills To be able to solve problems using a range of strategies. To reason mathematically, following a line of enquiry. Mathematical language and targets Mathematics Number (Number and Place value)
More information2) The following data represents the amount of money Tom is saving each month since he graduated from college.
Mac 1 Review for Eam 3 Name(s) Solve the problem. 1) To convert a temperature from degrees Celsius to degrees Fahrenheit, ou multipl the temperature in degrees Celsius b 1.8 and then add 3 to the result.
More informationCurriculum Maps for Progress in Understanding Mathematics Assessment Termly content for Year 6
Term-by-term mathematics assessment across primary school Curriculum Maps for Progress in Understanding Mathematics Assessment Termly content for Year 6 The PUMA tests provide thorough coverage of the
More informationPaper 2 and Paper 3 Predictions
Paper 2 and Paper 3 Predictions Ensure you have: Pencil, pen, ruler, protractor, pair of compasses and eraser You will need a calculator Guidance 1. Read each question carefully before you begin answering
More informationNumber and place value Addition and subtraction Multiplication and division Fractions (inc decimals and percentages Pupils should be taught to:
Year 1 Year 2 Number and place value Addition and subtraction Multiplication and division Fractions (inc decimals and percentages count to and across 100, forwards read, write and interpret solve one-step
More informationNC2014 MATHEMATICS LIST OBJECTIVES and CHILD SPEAK TARGETS
NC2014 MATHEMATICS LIST OBJECTIVES and CHILD SPEAK TARGETS MATHEMATICS Key Stage 1 Year 1 Key Stage Strand Objective Child Speak Target Notes Count to and across 100, forwards and backwards, beginning
More informationContent Standards Two-Variable Inequalities
-8 Content Standards Two-Variable Inequalities A.CED. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate aes with labels and scales.
More informationFunctions Review Packet from November Questions. 1. The diagrams below show the graphs of two functions, y = f(x), and y = g(x). y y
Functions Review Packet from November Questions. The diagrams below show the graphs of two functions, = f(), and = g()..5 = f( ) = g( ).5 6º 8º.5 8º 6º.5 State the domain and range of the function f; the
More informationProperties of Quadrilaterals
MIAP Chapter 6: Linear functions Master 6.1a Activate Prior Learning: Properties of Quadrilaterals A quadrilateral is a polgon with 4 sides. A trapezoid is a quadrilateral that has eactl one pair of parallel
More informationChapter 2: Introduction to Functions
Chapter 2: Introduction to Functions Lesson 1: Introduction to Functions Lesson 2: Function Notation Lesson 3: Composition of Functions Lesson 4: Domain and Range Lesson 5: Restricted Domain Lesson 6:
More informationShape 2 Assessment Calculator allowed for all questions
Shape Assessment Calculator allowed for all questions Foundation Higher All questions Time for the test: 50 minutes Use the π button or take π to be.4 Name: _ Grade Title of clip Marks Score Percentage
More informationNumber and Place Value KS1 Y1 Count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number.
South Hylton Primary School Maths Curriculum 2014 Number and Place Value KS1 Y1 Count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number. Count, read and write numbers
More information6-1: Solving Systems by Graphing
6-1: Solving Sstems b Graphing Objective: To solve sstems of linear equations b graphing Warm Up: Graph each equation using - and -intercepts. 1. 1. 4 8. 6 9 18 4. 5 10 5 sstem of linear equations: two
More informationYEAR 1. Geometry Properties of shapes Position and direction
Number place value Addition subtraction Multiplication division Fractions Measurement Properties of shapes Position direction YEAR count to across 00, forwards backwards, beginning with 0 or, or from any
More informationChapter12. Coordinate geometry
Chapter1 Coordinate geometr Contents: A The Cartesian plane B Plotting points from a table of values C Linear relationships D Plotting graphs of linear equations E Horizontal and vertical lines F Points
More information