1 Each symbol stands for a number. Find the value of each symbol. a + b 7 c 48 d. Find a quick way to work out 90 ( ).

Transcription

1 Cambridge Essentials Mathematis Etension 7 A1.1 Homework 1 A1.1 Homework 1 1 Eah symbol stands for a number. Find the value of eah symbol. a 8 = 17 b = 64 4 = 24 d + 5 = 6 2 = and = 8. Find the value of eah epression. a + b 7 48 d = 7 Find a quik way to work out 90 ( ). Eplain how you got your answer. 4 = 15 Write down the number that is a 6 more than b 8 less than 4 times d less than 40 5 = 4 and = 12. Write a pair of values for and. 6 Paula has sweets. Write how many sweets eah of Paula s friends has. a Jak has 6 more than Paula. b Asif has half as many as Paula. Clare has times as many as Paula. d Kelly has 4 1 less than Paula. 7 Eah letter stands for a number. Find the value of eah letter. a p + 4 = 7 b t 5 = 5 f = 21 d k 2 = 9 e m + m = 24 8 g = 20 and h = 4. Find the value of eah epression. a g + 6 b h g h d g 2 e g h f 60 h 9 a b = 72. Write four different values for a and b.

2 Cambridge Essentials Mathematis Etension 7 A1.1 Homework an be written in words as five more than. Write these in words. a 7 b + 2 d 4 e 8 + f 6 g 2 h n stands for a number. 4 more than n is written with symbols as n + 4. Write these with symbols. a 2 less than n b 5 times n 10 more than n d half of n e double n f 7 less than n g 12 times n h 6 more than n i n less than Look at this table. Age (in years) Ahmed Brad Carla a b a Write eah statement using the letters a, b, and. The first one has been done for you. i Ahmed is 16 years older than Brad. Answer: a = b + 16 ii Carla is 1 years old. iii Carla is three years younger than Brad. iv Ahmed s age is three years more than Brad s age and Carla s age added together. b Write in words the meaning of eah of these. The first one has been done for you. i b = 16 Answer: Brad is 16 years old. ii b + = 29 iii a = 2 b iv a = + 19 Original material Cambridge University Press

3 Cambridge Essentials Mathematis Etension 7 A1.1 Homework 2 A1.1 Homework 2 1 Copy and omplete eah sequene. Write the rule that tells you how to get from one term to the net. a 1, 19, 25,,, 4 b 65, 5,, 29,, 5, 2, 2, 41,, 59 d,, 10.5, 14,, 21, The first term of a sequene is 99 and the terms derease by 1. Write the first five terms of the sequene. In a sequene, eah term is half the term before. The seond term is 56. Write the first five terms of the sequene. 4 Here is a sequene of patterns made from irles. Pattern 1 Pattern 2 Pattern a Pattern 1 has irles. How many irles are there in Pattern 2? How many in Pattern? b Draw the net two patterns in the sequene. How many irles are there in eah one? Write the numbers of irles in the first five patterns as a sequene. d What is the term-to-term rule for this sequene? 5 The sequene 6, 12, 18, 24,... an be written like this. 1st term 2nd term rd term 4th term Copy and omplete. The 5th term is 6 = The 100th term is = The 10th term is 6 = The nth term is

4 Cambridge Essentials Mathematis Etension 7 A1.1 Homework 2 6 Write down the first five terms of the sequenes with these nth terms. a n + 8 b n n + 7 d 100 (6 n) 7 The nth term of a sequene is 2 n + 5. What is the 8th term of this sequene? 8 This is a sequene of patterns. Eah pattern is made from heagons. Think of eah pattern as one heagon at the top with sets of three heagons below it. In this way, the number of heagons in the patterns make a sequene. Pattern 1 Pattern 2 Pattern = = = 10 Copy and omplete. a The number of heagons in Pattern 4 is 1 + = b The number of heagons in Pattern 10 is + = The number of heagons in Pattern n is What is the nth term of eah sequene? a 7, 14, 21, 28, 5,..., b 5, 9, 1, 17, 21,..., 10, 18, 26, 4, 42,..., d 70, 65, 60, 55, 50, Sharif is making houses with arrows. 1 house 2 houses houses 6 arrows a Find the number of arrows in the pattern with n houses. b How many arrows will be needed for 20 houses? Original material Cambridge University Press

5 Cambridge Essentials Mathematis Etension 7 A1.2 Homework A1.2 Homework 1 Copy and omplete these funtion mahines. a n b n n 7 18 n d n 2 Draw a funtion mahine for Use the input values 0, 4, 1 and 25. Copy and omplete these funtion mahines. a n b 1 2n 2 6 5n Arrange the operations + 6, and 4 in different ways in the funtion mahine. a Make the output 18. b Make the output 26. Make the largest possible output. 2 Copy and omplete the funtion mahine a 1 b so that these are the outputs

6 Cambridge Essentials Mathematis Etension 7 A1.2 Homework 6 Copy and omplete the funtion mahine in two different ways Copy and omplete. 4 8 Copy and omplete this funtion mahine in two different ways Copy and omplete this funtion mahine so that the output is always the same as the input Chek your answer using the input values 2, and a Copy and omplete the table of and y values for this funtion mahine. + 2 y y b Copy and omplete this mapping diagram using values from your table. 11 A funtion uses the rule n? Here are some inputs and outputs for this funtion. What is the funtion? Original material Cambridge University Press

7 Cambridge Essentials Mathematis Etension 7 A2.1 Homework 1 A2.1 Homework 1 1 Work these out. a b (4 + 6) d e f (10 ) 2 g h 11 (8 + 5) i j 2 ( ) k l (10 2) 2 2 Find the value of eah of these epressions when = 4. a + 5 b 5 8 d 1 4 e ( + 5) f ( 1) 2 g 17 ( + 2) h ( + 2) 2 i 40 j 2 k l Find the value of eah of these epressions when p = 6 and q =. a p + q b p q pq d p 6q e p + 2q f 18 (p + q) g q(p + 1) h p 2 q 2 i 45 p + q j 6 p q + 1 k q p l 24 p q m pq 2 n p 2 q o 5 pq p p 2 + q 2 4 Simplify these epressions. a b d e f 4 7 g 10 4 h + y + y + y i + 2y + y j yz + 4yz k k + m + 2k m l 5 + 8m m m n 5k 2 6 k 2 4 o p 2 + 7p + 2p 2 + p 4 5 Write these epressions in words. a n n b 2(n + 6) d 2 n + 6

8 Cambridge Essentials Mathematis Etension 7 A2.1 Homework 2 A2.1 Homework 2 1 Write a formula for the perimeter P of eah shape. Write your formula in its simplest form. a b 8 p p + 5 p p d m 2m + 1 e y y y f t + 1 2t + 1 t + 1 m + 6 y 2t + 1 g + h i y 2y + 1 2y + 1 2y + 1 2y y y y 2 Guy thinks of three different retangles, A, B and C. Eah one has a perimeter of Use the information below to draw the three retangles. Label the sides. a One of the side lengths of retangle A is 2. b One of the side lengths of retangle B is. One of the side lengths of retangle C is 2 +. g = y a Find g when y = 20 and = 4. b Find g when y = 25 and = 10. Find g when y = 10 and = 50. d Find y when g = 6 and = 1..

9 Cambridge Essentials Mathematis Etension 7 A2.1 Homework 2 4 In these diagrams, lines are drawn from eah square to eah irle. squares 4 squares squares 2 irles 2 irles irles 6 lines 8 lines 9 lines a i In another diagram, there are 5 squares and 2 irles. How many lines do you predit an be drawn? ii Draw a line diagram for 5 squares and 2 irles. How many lines have you drawn? Was your predition in part i orret? b Write a formula to work out the number of lines. Use s for the number of squares for the number of irles l for the number of lines. i Use your formula to find l when s = 5 and = 4. ii Use your formula to find l when s = 10 and = 6. iii Use your formula to find s when l = 28 and = 7. 5 This formula onverts a temperature in degrees Celsius ( C) to degrees Fahrenheit ( F). F = 9 C C is the temperature in degrees Celsius, and F is the temperature in degrees Fahrenheit. a Use the formula to onvert 100 C to degrees Fahrenheit. b Use the formula to onvert 10 C to degrees Fahrenheit. Use the formula to onvert 0 C to degrees Fahrenheit. Original material Cambridge University Press

10 Cambridge Essentials Mathematis Etension 7 A2.2 Homework A2.2 Homework 1 Write an epression for the output of eah funtion mahine. a + 6 b 7 10 d 1 e 4 f g h i Draw a funtion mahine to represent eah epression. a + 2 b ( + 2) 2 + d m 9 2 e y y f g 5(d + 4) h 4m + 5 i 2k 7 Here are reverse funtion mahines. Write the value of for eah. a 7 b Write the inverse of eah operation. a Add 6 b Multiply by 7 Divide by d Subtrat 2 e 1 f 4 g 6 h 11 i 100 j 5.6 k l This funtion mahine represents the equation 5 1 = a Copy and omplete the reverse funtion mahine. 7 b Use the reverse funtion mahine to solve the equation 5 1 = 7.

11 Cambridge Essentials Mathematis Etension 7 A2.2 Homework 6 For eah equation below i draw a funtion mahine ii draw the reverse funtion mahine iii use the reverse funtion mahine to solve the equation a 8 = 4 b 7t + 8 = 15 (d + 2) = 9 d 6(m + 5) = 72 e 2p 4 = 11 f 2( 4) = g t 5 1 = 6 h k 15 9 = 11 i 2 y +1 = 5 7 Look at these equations = = 7 Sita says that has the same value in eah equation. a Is she orret? b Draw funtion mahines to eplain your answer. 8 Use algebra to solve these equations. The first one is done for you. a 5p 1 = 9 5p = p = 10 p = 10 5 p = 2 b 2d + 7 = 9 6z 17 = 25 d q 1 = 4 5 e 2g 4 = 1 f 4m + 11 = 19 g t + 4 = 9 h 4( 1) = 24 i 7(p + ) = 49 j y 1 2 = 4 Original material Cambridge University Press

12 Cambridge Essentials Mathematis Etension 7 A.1 Homework 1 A.1 Homework 1 1 a Write an epression for these instrutions. Start with n, subtrat 5 and multiply the answer by. b Write this epression in words Find the value of ( 4) 10 when = 8. 2 a Eplain the differene between n and n +. b Copy and omplete. i n n ii n + n Copy and omplete these funtion mahines. The first one has been done for you. a b + 4 2( ) d Solve these equations. a + 2 = 71 b 9 = 72 = d = 2 e + 6 = 11 f ( + 5) = 6 4

13 Cambridge Essentials Mathematis Etension 7 A.1 Homework 1 5 The perimeter of this triangle is 41 m. 1 m + 6 m 2 a Write an equation for the perimeter of the triangle. Simplify your equation. b Solve the equation. Find the lengths of the sides of the triangle. 6 Catrin, Laila and Za are playing a game. Catrin has n points. Laila has 5 more points than Catrin. Za has half as many points as Laila. They have 40 points altogether. a Write this information as an equation and simplify it. b Solve the equation. How many points does Za have? 7 The smallest of four onseutive odd numbers is n. a The sum of the four onseutive odd numbers is 88. Write this information as an equation and simplify it. b Solve the equation to find n, the smallest of the onseutive numbers. 8 This is a pentagon. The angles of a pentagon add up to a Write an equation for the total of the angles of this pentagon. Simplify it. b Solve the equation to find. Find the size of the largest angle in the pentagon. Original material Cambridge University Press

14 Cambridge Essentials Mathematis Etension 7 A.1 Homework 2 A.1 Homework 2 1 Eplain why a + b = b + a, but a b is not equal to b a. 2 If = m + n, whih of the following are always true? m = n n = n = m m n = m Simplify these epressions. a 7y 4y b 4m + 2my m + kt + 5tk 4 Epand the brakets in these epressions. Simplify where possible. a 7( + 2y + ) b 4(2m ) + 5m 5(a + 2b) 2a + b d 2( + 4) + (5 + ) 5 This regular heagon has sides of length 2a + b. 2a + b a Write an epression for the perimeter. Use brakets. 2a + b 2a + b b Multiply out the brakets. 6 Solve these equations by epanding the brakets first. 2a + b 2a + b 2a + b a 7( ) = 28 b 5 + ( + 1) = 5 (2y 1) + 2(y + 4) = 17 d 6 + ( + 4) = 24 7 Look at these epressions a What value of makes the two epressions equal? Show your method. b What value of makes the first epression three times as big as the seond epression? Show your method. 8 In the diagram, the value in eah square is found by adding the values in the irles on either side. a Write and solve an equation to find n. b Copy the diagram. Find the two missing numbers.

15 Cambridge Essentials Mathematis Etension 7 A.2 Homework A.2 Homework 1 y = 2. Copy and omplete this mapping diagram for the input numbers 2, and 4. 2 Draw mapping diagrams like the one in question 1 for eah of these funtions. Use values of and y from 0 to 10. a y = 2 1 b y = 2( 1) y = + 2 d y = 1 a Whih of these labels ould math the partly ompleted mapping diagram? b The orret funtion also maps 6 to 9. Whih is the orret label? 4 This simple mapping diagram uses values of from to 4. y What funtion does the mapping represent? 5 Draw simple mapping diagrams, like those in question 4, for these funtions. Use values from to a y = ( 2) b y = 5 1 y = 2 + 4

16 Cambridge Essentials Mathematis Etension 7 A4.1 Homework 1 A4.1 Homework 1 1 In the diagram, A and C are opposite verties of a retangle ABCD. AB is horizontal. Write the equation of the line through these pairs of verties. a A and B b A and D B and C d C and D 2 Write the oordinates of the point where eah pair of lines interset. a = 2 and y = 5 b = 1 and y = 10 = 4 and y = d y = and y = 10 e = 6 and y = + 1 f y = 17 and y = 2 Write the equation of eah line. a The line parallel to AB and passing through ( 10, 7). b The line parallel to BC and passing through (14, 9). The line parallel to AC and passing through: i (0, 2) ii (0, 1) iii (4, 7) iv ( 5, 9)

17 Cambridge Essentials Mathematis Etension 7 A4.1 Homework 2 A4.1 Homework 2 1 a Copy and omplete the table for the equation y = y b Sketh the graphs of y = 2 + 1, = 4 and y = 5 on the same diagram. Find the oordinates of the points of intersetion of eah pair of lines. i y = and = 4 ii = 4 and y = 5 iii y = and y = 5 2 a Copy and omplete the table for the equation y = y b Draw the line y = 2. i Write the oordinates of the point where the line rosses the -ais. ii Write the oordinates of the point where the line rosses the y-ais. a Copy and omplete the table for the equation y = y b Plot the values from your table as oordinates on a opy of the aes. Draw and label the lines y = 2 and y = 6. d Write down the oordinates of the point where the lines ross.

18 Cambridge Essentials Mathematis Etension 7 A4.2 Homework A4.2 Homework 1 You an use this graph to work out the ost of a length of arpet. a Find the ost of eah length of arpet to the nearest pound. i 6.5 m ii 5 m iii 2.5 m iv 7.1 m b What length of arpet, to the nearest 0.1 m, an be bought for eah prie. i 50 ii 20 iii 100 iv 72 2 a Copy and omplete the table for y = y Plot the values from your table as oordinates. Draw the line y = 5. b Use your graph to solve these equations. i 5 = 1 ii 5 = 7 iii 5 = 4 iv 5 = 2.5 v 5 = 2 vi 5 =.5 Copy and omplete these steps to solve the equation 4.5 =. 4.5 = 5 = =

19 Cambridge Essentials Mathematis Etension 7 A5.1 Homework 1 A5.1 Homework 1 1 This retangle is 2a wide and b long. Write a simplified epression for b 2a a the area b the perimeter 2 a Look at these three ards. You an see two of the epressions. The third is hidden The mean of the three epressions is 5. What is the hidden epression? b Write a set of three epressions that has a mean value of What is the mean value of these three epressions? Show your working. Write your epression as simply as possible. A teaher has a large pile of ards. An epression for the total number of ards is 4n a The teaher puts the ards into two piles. The number of ards in the first pile is n + 7. Write an epression to show the number of ards in the seond pile. b The teaher uses all the ards to make two equal piles. Write an epression to show the number of ards in eah pile.

20 Cambridge Essentials Mathematis Etension 7 A5.1 Homework 1 4 This trapezium is made from two triangles and a retangle. a a Write an epression for length using a and b. b Write epressions for these. h i the area of the retangle b b ii the area of one triangle iii the total area of the trapezium 5 a Write an epression in terms of b. 5b b Write an epression y in terms of a. Write your epressions as simply as possible. 7a + 5 y 4a + 2b The lowest of four onseutive even numbers is n. a Write down, in terms of n, an epression for the seond lowest even number. b Write an epression for the sum of the four onseutive even numbers and simplify it. Find an epression for the number midway between the highest and the lowest onseutive even numbers. 7 In this diagram, P has oordinates (n + 2, n) a P is mapped to Q by a translation right. Find the oordinates of Q. b P is mapped to R by a translation 5 right and 2 down. Find the oordinates of R. P is mapped to T by a refletion in the y-ais. Find the oordinates of T. 8 A is the point (2m + 1, 5n ) and B is the point (6m 5, 9n + 11). Find the oordinates of the point midway between A and B. Original material Cambridge University Press

21 Cambridge Essentials Mathematis Etension 7 A5.1 Homework 2 A5.1 Homework 2 1 Three equilateral triangles are drawn in the orners of a bigger equilateral triangle forming the shaded regular heagon. The large triangle has side length a and eah small triangle has side length b. Write a formula for P, the perimeter of the heagon, in terms of a and b. 2 The ost of a raffle tiket at the shool fair is 5p. A ustomer buys n raffle tikets and gives the raffle-tiket seller pounds. Write a formula for C, the hange given in pene. Saha is arranging square tables in rows for a hildren s birthday party. a b 1 table 2 tables tables a Copy and omplete this table. Number of tables Number of hildren 4 6 b How many hildren an be seated in a row of 10 tables? Find a formula for, the number of hildren that an be seated in a row of t tables. 4 Here are some patterns made out of heagons. Pattern 1 Pattern 2 Pattern a Pattern 1 has 10 outside edges. How many outside edges are there in Pattern 2? b How many outside edges are there in Pattern? How many will there be in Pattern 8? d Find a formula for the number of outside edges in the nth pattern.

22 Cambridge Essentials Mathematis Etension 7 A5.1 Homework 2 5 Blak and white tiles are arranged to make patterns. Pattern 1 Pattern 2 Pattern a Draw Pattern 4. b Copy and omplete the table for the number of white tiles. Pattern numbers Number of white tiles 8 How many white tiles are in Pattern 10? d Whih pattern will ontain 40 white tiles? e Find a formula for the number of white tiles in the nth pattern. 6 a Write the net two terms in this sequene., 10, 17, 24,... b What is the 10th term of the sequene? Find a formula for the nth term of the sequene. 7 Write a formula for y in terms of for eah of these funtion mahines. a + 5 y b 2 4 y 5 y d 1 5 y 8 a Copy and omplete this funtion mahine to show the formula y = y 2. b i Copy and omplete this funtion mahine to show the formula y = 7 ( + 2) y ii Simplify the formula y = 7 ( + 2) as muh as possible. Draw another funtion mahine to show your simplified formula. It should ontain just two operations. Original material Cambridge University Press

23 Cambridge Essentials Mathematis Etension 7 A5.2 Homework 1 A5.2 Homework 1 1 Solve these equations. Give your answers as frations or mied numbers in their lowest terms. a p + 5 = 0 b 4y + 2 = 5 2m 5 = 4 d 6 10q = 27 e = 8t + 7 f 52 = a 2 Solve these equations. Give your answers as deimals. a = 2 b 10m + 8 = = 4n + 5 d 29 5q = 22 e 1 = 17 5a f 8 18 = 20 Find. a b Write and solve an equation to find the value of a. a 6a b 8a The sum of four onseutive multiples of 5 is 10. The lowest of these numbers is. Write an equation and solve it to find. 6 Peter, Melanie, April and Jak reeived a total of 8 hoolate eggs. Jak had one less than Peter. Peter had five less than Melanie. April had half as many as Melanie. How many eggs did eah person have?

24 Cambridge Essentials Mathematis Etension 7 A5.2 Homework 2 A5.2 Homework 2 1 The highlighted square ontains the numbers 9, 10, 16 and 17. The sum of these numbers is 52. Whih numbers should the square ontain, so that the sum is 124? Begin by starting with a square like this n 2 Solve these equations a 2( + 8) = 26 b 9( ) = 99 12(14 ) = 72 Solve these equations by epanding the brakets first. a 8( + 7.5) = 84 b 7(p + 5) 1 = = ( + 7) 4 Solve these equations a m t = 1 b 6 = 5 49 a +.5 = The nth term of a sequene is a Whih term has value 16? n b How many terms have a value of less than 100? Show that there isn t a term with value 20.

25 Cambridge Essentials Mathematis Etension 7 A5. Homework A5. Homework 1 This is a graph of Gail s journey to the shops. Gail starts by walking from home to the bus stop. a How far is it to the bus stop from Gail s house? b How long does she wait for a bus? How long does the bus journey take? Gail then walks the rest of the way to the shops. d How long does the total journey from home to the shops take? e f What is the total distane that she walks? How far away from Gail s home are the shops? Gail gets lift home with a friend. g How long does her return journey take from the shops to home? h How long was she out of the house altogether?

26 Cambridge Essentials Mathematis Etension 7 A5. Homework 2 William throws a ball up into the air and athes it on the way down. One of these graphs shows the speed of the ball while it is in the air. Whih one? Give a reason for your answer. Water is poured at a onstant rate into eah of the following beakers. a Whih beaker does eah graph below represent? Eplain your hoie. i ii iii b Draw graphs for eah of the other beakers. Label eah graph with the letter of the beaker it represents. Original material Cambridge University Press