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Cambridge Lower Secondary Mathematics Workbook 8 2nd Edition Lynn Byrd, Greg Byrd, Chris Pearce - Solutions

11 What goes in the box,=0.004 44×b 4.4+0.40 x=4.4=44 Ca d 4+f=0.444 44+=4400=40 44.4 x e
10 Which symbol, x or +, goes in each box?0.1=550 ab 46 0.01 =0.46 0.1=37 c3.7 d208 0.01 =2.08 f505 e0.19 0.1=1.9 0.01 =5.05
9 Work out the answers to these questions.Use inverse operations to check your answers.27×0.1 b27.9×0.01 C 0.2-0.1 d2.7+0.01 a
8 Work out5+0.1 b5.6+0.1 55.6+0.1 d0.55+0.1 ac 5+0.01 f5.6+0.01 55.6+0.01 h0.55+0.01 eg
7 Work out 33×0.1 b999×0.1 30×0.1 8.7×0.1 aC P77×0.01 700×0.01 7×0.01 ef 70×0.01 hg
6. Work out these.1.6 16 160 1600 All the answers are in the rectangle.16+0.1 b0.16+0.1 a0.16-0.01 d16=0.01 C 7 Work out a 330.1 b 9990.1 C 300.1 d 8.70.1 e 770.01 f 70 0.01 g 700 0.01 h 70.01 8 Work out a 50.1 b 5.6-0.1 C 55.6+0.1 d 0.550.1 e 50.01 f 5.6+0.01 g 55.6+0.01 h 0.55 0.01 9 Work out
5 Copy and complete Copy the workings.2+0.01=2×100=b 5+0.01=5x a11 d12+0.01=12×30+0.01=30×=c Il
4 Copy and complete the workings.4+0.1=4×10=b 7+0.1=7x a=20-0.1=20×25=0.1=25x dc 11=e.g. 6+0.01=6× 100= 600+0.01 is the same as x100 5 Copy and complete the workings. a 2 0.01 2100=| C 300.01=30 =]] b 5 +0.01=5x]=[] d 120.01 12x=
3 Work out these.0.12 1.2 12 120 All the answers are in the rectangle.120×0.1 b12×0.1 a12000×0.01 d12×0.01 Ue.g. 6=0.1=6×10=60+0.1 is the same as ×10
2 Copy and complete the workings.300×0.01=300+100 500×0.01=500+b a11 800×0.01=800=d 650×0.01=650+c=11
1 Copy and complete the workings.20×0.1=20+10=70×0.1=70+b a=80×0.1=80+d 75×0.1=75+c 11 e.g. 600×0.01 =600+ 100=6×0.01 is the same as +100
16 Arun and Marcus are discussing inequalities.Read what they say.Write each pair of inequalities as one inequality using i Arun's method ii Marcus's method.b a y 12 y≤4andy≥0 d x>7 and x≤25 x > 10 and x The inequalities y 14 and y> 2 can be written together as 2 < y < 14. The
15 Write the inequality shown by each number line. Use the letter y.0 ba T24 25 26 22 23 2 3 4 0
14 Copy each number line. Show each inequality on its number line.0.75
13 Match each inequality with: the correct smallest integer blargest the correct integer athe correct list of integers. Smallest Largest Inequality List of integers integer integer A 1.9 x 5.5 i 0 P 5 W 1, 2, 3, 4, 5, 6 B 0.2 < x < 6.1 ii 2 Q 7 X 0, 1, 2, 3, 4 C -0.5 x 4.9 iii 3 R 6 Y 2, 3, 4, 5 D
12 This is part of Raj's homework.Question a Show the inequality 5 - < n ≤ 8-on a number line.5 4b Write i the smallest integer n could beü the greatest integer n could be i a list of the integer values n could be.Answer 0.b smallest integer is 5 57 00 i largest integer is 9 il n could be 5, 6,
11 Write true (T) or false (F) for each statement.The first one is done for you.8 > y > 2 means the same as 2 < y < 8 ab 10 > > > 0 means the same as 0 < > < 10 1≥y>-4 means the same as | ≤y≤-4 c3 > > > -3 means the same as -3 < y < 3 d
10 For each inequality, write ithe smallest integer y could be ii the largest integer y could be ili a list of the integer values y could be.32
9 This is part of Lori's homework.Question Use the inequality -3 < x < 3 to write i the smallest integer x could be u the largest integer x could be i a list of the integer values x could be.Answer i smallest integer is -3 ü largest integer is 3 ii x could be -3, -2, -1, 0, 1, 2, 3 Explain the
8 Copy and complete these equivalent inequalities. a x> 4 is equivalent to 2x> C y 1 is equivalent to y+9>[ x
7 Write the inequality shown by each number line. Use the letter x. a b 24 25 26 27 28 29 29 30 31 d -15-14-13-12-11-10 -3 -2 32 22 33 34 35 36 2
6 Copy each number line. Show each inequality on its number line. a 5
5 Match each inequality with the correct number line.Remember that:· an open circle (O) is for the ·a closed circle (@) is for the ≤ inequality.The first one is done for you: A and iii A 2x7 B C 2
4 Write in words what each inequality means. Part a is done for you.7
3 Write each statement as an inequality. Part a is done for you.x is greater than or equal to 8 and less than 12 8 € x < 12 ab y is greater than I and less than 7 m is greater than or equal to 0 and less than or equal to 5 cd n is greater than 0 and less than or equal to 5
2 Match each inequality with the correct meaning. The first one is done for you: A and iii A 0x5 B 0x5 C 0
1 Write True (T) or False (F) for each statement. Part a is done for you.4 < x < 9 means 'x is greater than 4 and less than 9'T ab 4 ≤ x < 9 means 'x is greater than 4 and less than or equal to 9'4 < x ≤ 9 means 'x is greater than 4 and less than or equal to 9'c d4 ≤ x ≤ 9 means 'x is
15 Here is a secret code box. 8 11 8 3 7 Solve each equation below. 4 5 2 9 Use your answers to fill in the letters in the code box to find the name of a Winter Olympic sport. L 4(x-5)=8 G 2(2x+3)+5x=24 H 2(x+3)=3x-3 E 12+3(x+4)=36 0 I 6 x-5=1 S 30=6(2x-1) 5x+3-2x-1=17 B 2(x-5)=3(2x-14)
14 Solve these equations.4 52-3=7*y=32 ba 54(3m-3)=20 2(5m-4)=12 dc
13 a Complete the workings to solve this equation.X+4 6 =3 x+4=36 x+4=18 x=0b these Solve equations.3x-1=7 +2 -4 X+2 i ii 2
12 A square has a side length of 7cm. A rectangle has a length of 1-3cm and a width of 4cm. 8 The square has the same perimeter as the rectangle. Work out the value of y. Show all your working.
11 a The total area of this rectangle is 52 cm2. Write an equation to represent the problem.b Solve the equation to work out the value of y.c Show how you can check your answer is correct. 4cm 2ycm 7cm
10 For each part of this question iWrite an equation to represent the problem.ii Solve the equation.Arti thinks of a number. He divides it by 2 then subtracts 9.a The answer is 5.What number did Arti think of?b Han thinks of a number. She multiplies it by 4 then subtracts 1.The answer is the same
13 a simplify 4(2x+3)+5(x-4)+3(5-2.x) Expand and b Factorise your answer to part a.14 Read what Zara says.Show that Zara is wrong. Explain the mistake she has made.15 Awen expands an expression, collects like terms and factorises the result.Work out the missing terms.201 +4)-4(@++6a(a-8)=8(a2--2)16
12 a Copy and complete this spider diagram.around the edge are all equivalent to the The four expressions in the middle. expressionb Which expression around the edge is the correct fully factorised expression? +8x) 24x + 32x (12x+) +4x)
11 Copy and complete each factorisation. a C e f 2a+4h+8=2(a+2h+ 12tu+16u-20=4(3tu+-5) 7k-k-ak=k(0-0) 6n2-9n+3mn=3n-1+) b 5b-25+5j=5(b-+1) 3e+4e+ef=e(3e++)
10 Copy and complete these factorisations.14cd-7c=7c(2d-b 12a+8ab=4a(+2b)a 21g+15gh=3g(30w-15tw=15w(c+d 1
9 Factorise each expression.7m2+m b5a7-15a+2+91 Ca 12y-16y2 8h-4h2 3y+ 12y2 fd e162+8e 15e +6i hg
8 Each expression on a grey card has been factorised to give an expression on a white card. Match each grey card with the correct white card. 3x+15x 5x(3x+1) 4x+12x ii 2x(2x+5) 4x+10x 3x(x+5) 15r2+5x iv 4x(x+3) ABCD
7 Factorise each expression.Make sure you use the highest common factor.9w-3 5z+15 b2y-14 20x+4 da C14a-21 12-6b 6v+8 fh 14+21d eg
6 Copy and complete these factorisations. All the numbers you will need are in the cloud. a C 4x+6=2(2x+) 35y+10=5(y+) b 6x-15=3(2x-) d 28y-63-7-
5 Use your answers to Question 4 to factorise these expressions. a 6x+3= C 10y-2= b 12x+4= d 24y-6=
4 Expand these brackets. a 3(2x+1)=6x+ C 2(5y-1)=- b 4(3x+1)= + d 6(4y-1)=a 3(2x+1)=6x+ b 4(3x+1)= + C 2(5y-1)= d 6(4y-1)=
3 Copy and complete these factorisations. All the numbers you will need are in the cloud. a 2x+8=2(x+ C 5y-25=5(y- b 3x+9=3(x+) d7y-14=7-D) 23 4 5
2 Factorise these expressions. Use your answers to Question 1. The first one is done for you.a C 2x+12=2(x+6) 5y-15= b 3x+15= d 4y-28=
1 Expand these brackets. Use the boxes to help if you want to.The first one is done for you. a 2(x+6) b 3(x+5) a 2(x+6) C X x 6 2 2x 12 b 3(x+5) x 5 3 3(x+5)= + d 4(y-7) -3 X y -7 4 2(x+6)=2x+12 5(y-3) 5 y 5(y-3)=- 4(y-7)=-
15 Fill in the missing numbers and letters in these expressions. Use all the numbers and letters from the cloud. a 4(3x+)=x+28 C 6(-3)=30.x- e b 3x(2x)=6-3x dx(9-)=45x-5x 2(x+4)+3(4x)=16x-16 fx(4x+1)(x-5)=2x+x 1 7 28 5 11 12 18 x 2x 5.x
14 Write down and then simplify an expression for the area of this compound shape. 5.xcm (2x-1)cm (3x+4) cm 3.x cm
13 This is part of This Sofia's homework.She has made a mistake in every question. Question Expand and simplify each expression. 1. 3(a+5)-3(3a+5) 2. p(4q+r)+q(2r-4p) 3. 5b (b+3a) + a(4a + 6b) Answer 1. 3(a+5)-3(3a+5)=3a+15-9a-15 6a+30 2. p(4q+r)+q(2r-4p) = 4pq+ pr+2qr-4pq = 3pr+pq=4p2qr 3. 5b
12 Expand and simplify each expression. a C a(a+3)+a(a+4) c(3c+4)+c(5c+6) e e(3+4e)-e(5e-6) b b(b+3)+b(4b+5) d d(3d+4)-d(d+5) f f(3f+4g)-5(6f-7g)
11 Write down and then simplify an expression for the area of each rectangle. (2x + 1)cm b (3y-2)cm 4cm 2ycm
10 Here are some expression cards. Sort the cards into groups of equivalent expressions. A 8y(5+6y) B 4y(5y+6y) C 2y(24y+20) D 2y2(10+12y) LU E 4(10y+12y) F 4y(6y+5) G y(20+24y) H y(40+48y)
9 a b b(b-5) e Expand each expression. Three of them have been started for you. a(a+1)=axa+ax1=a+ i(3i+7x)=ix3i+ix7x=31+ f j(3a-7j) C c(3c+6) d e(4e+9) g k(3k-6x) h 3m(m+3x) i j 2a(3+2a+b) 3r(3r-x-3)=3rx3r-3rxx-3rx3=92-0-0 k 3x(-z-y-x)
8 Expand and simplify each expression.a (a+7)+8(a+9)b 8(b+7)+6(5b+6)c 7(c+8)+9(8+7c)d 7(8d+9)-8(d+7)e 6(5+6e)-7(8e+9)f 9(8f+7g)-6(5g-6f)
7 Read what Marcus says.Is Marcus correct?Explain your answer. If I expand 4(a-7) and 4(7-a) I will get the same answer, as both expressions have exactly the same terms in them.
6 Expand the brackets. a 7(8i+9) b 6(8+7j) d 7(8-91) e 6(9a+8m) g 7(7c-8x) h 6(9px+8y) C 5(6k-7) f 5(7b+6n)
5 Expand the brackets.5(b+7)6(a+6)b 7(c-8)a C5(8 +e)d 6(d-9)f 7(7+)e 6(6-g)h 5(7-h)g
4 Copy and complete the boxes to simplify these expressions. Some have been started for you. a 3(2x+1) X 2.x 1 3 6.x C 3(2x+1)=6x+ 2(3y-7) X 3y -7 2 -14 2(3y-7)=-14 b 5(4x+9) 5 4.x 9 5(4x+9)=| + d 5(8y-5) X 8y -5 5 5(8y-5)=
3 Copy and complete the boxes to simplify these expressions. Some have been started for you. a 3(x+5) X .x 5 3 3.x 3(x+5)=3x+ C 5(y-1) Xy -1 5 -5 5(y-1)=-5 b 2(x+9) 2 2(x+9)= d 4(y-8) .r 9 + X y -8 4 4(-8)=-
2 Copy and complete the boxes to show two different ways to multiply 6 by 58. a 6x58 6(50+8) b 6x58 6(60-2) X 50 8 6 658=+= X 60 -2 6 658=+=
1 Copy and complete the boxes to work out the answers. a 418 X 10 8 4 418=+= b 321 20 20 1 3 321=+=
16 The formula below is used to calculate the distance travelled by an object. sut+at at where: s=distance u = starting speed a=acceleration t=time Work out the distance travelled by an object when a u=0, a 6 and 1=5 bu=30, a=-4 and 1=10
15 a Use the formula D= wp+4 to work out the value of D whenw=2.5 and p=6.b Rearrange the formula D= wp +4 to make p the subject.c Use your formula to work out the value of p when D= 100 and w= 12.
14 Write any values of x that make each pair of expressions equal.3.x+ 1 and 3.x2+1 b4-x and x-4 aSAN +5 and 2+5 d3(x+2) and 2(x+3)c
13 When x=-4, all of these expressions except one have the same value. Which is the odd one out? x-7 (x+1)2 36 x-5 2x+17 5-x x
12 Make x the subject of each formula. Write if A, B or C is the correct answer. a y=x-8 A x=y-8 B x=y+8 C x=8y b y=kx A x=ky B x=y C k y=x+w A x=y-w B x=y+w C x=w-y d y= A x=y B x=1 C x=ry y e y=2x+1 A X=y+1 B x=2y+1 C x=y-1
11 Pedro uses this formula to work out the volume of a triangular-based pyramid: bhl V=5 where: V is the volume 6 b is the base h is the height I is the length. Pedro compares two pyramids.Pyramid A has a base width of 4cm, base length of 3 cm and height of 16cm. Pyramid B has a base width of 6cm,
10 Use the formula A= xh to work out A when a=5, b=7 and h=4.
9 Harsha uses the formula V = Ah to work out V when A=6 and h=12. This is what she writes. a b 6+12 V = 3 = 18 3 = 6 Explain the mistake she has made. Work out the correct answer.
8 Use the formula d=161+38 to work out d when 1=2.
7 a i words b Write a formula for the number of seconds in any number of minutes, using Use your formula from part a to work out the number of seconds in 30 minutes. ii letters.
6 Work out the value of the expression aa- 6 when a=4 b 30-b when b=6 a+b when a=3 and b=4 d - when c=5 and d=6 e 3p when p=4 f 5q2+1 when q=10 g 1 when 1=2 h 10 when y=4 i z-2 when z=2 j when s=10 10
5 Use the formula H= ky to work out the value of H whenk=9 and v=3 bk=8 and v =- 2.a
4 Work out the value of the expression a+3 when a=7 bb+6 when b =- 4 awhen d =- 35 3c when c =- 3 dc 5a+b when a=3 and b =- 5 fc-d when c= 14 and d=7 e5e+2f when e=3 and f=5 h2(g +h) when g =9 and / =- 20 gi 3.x-7 when x =- 5 j10(9-x) when x=6*- 10 when x=20 k1£+/. when:x=30 and y =- 30.4 2 10
3 when x=6 a 2x+1 2xx+1=2x6+1 (Work out the multiplication before the addition) =12+1 = b 3.x-1 3xx-1=3x6-1 (Work out the multiplication before the subtraction)d 10- e 10--10- =10- 2(x+4) 2x(x+4)=2x(6+4) (Work out the division before the subtraction) (Work out the bracket before the multiplication)
2 Work out the value of each expression when x=4 and y=3. a x+y b x-y C 12 Complete the working to find the value of each expression
1 Match each expression with its correct value when x=6. The first one is done for you: A and iii A x+3 i 13 B x-5 4 C 7+x D 10-x E 2x F x 2 S. < 9 iv 12 3 vi 1
13 Sion thinks of a number, y. a Choose the correct expression from the cloud for when Sion adds 3 to one-quarter of y, then multiplies by 8 adds 8 to one-third of y, then multiplies by 4 b C d adds 4 to three-quarters of y, then multiplies by 8 adds 3 to three-eighths of y, then multiplies by 4.
12 The price of one kilogram of lemons is $1. The price of one kilogram of potatoes is Sp. The price of one kilogram of rice is Sr. Write an expression for the total cost of a 1 kilogram of potatoes, 3 kilograms of lemons and 2 kilograms of rice 3 kilograms of potatoes and one-quarter of a kilogram
11 The longest side of a triangle is acm. The second side is bcm shorter than the first side. The third side is half as long as the second side. Write an expression, in its simplest form, for the perimeter of the triangle.
10 Write an expression for the perimeter and an expression for the area of each rectangle. Simplify each expression. a v+3cm 8wcm b 9.xcm 58 yem
9 a i ii iii iv b Write an expression for one-quarter of x add 5 three-fifths of x subtract two one add one-half of x eleven subtract five-sixths of x. Describe in words each of these expressions. i-9 2 2x +10 3 !!! 2x 25-3 iv 12+ 9 225 7x 10
8 This is part of Kim's homework.Question Write an expression for a one-fifth of x add 7 b six subtract two-thirds of y Answers x+7 a 5 66-24Are Kim's answers correct? If not, write the correct answers.
7 a Sort these cards into groups of equivalent expressions.b Which card is on its own? 7xx x-7 A B C 8 8 FL 7.x 78 Xx G H 8 88 7+x D 8 80 I LU E x7 80 x+7 J 8 80
6 Shen thinks of a number, n. Write an expression for the number Shen gets when he multiplies the number by 7 then adds 4 n+4 a b divides the number by 6 then subtracts 8-8 C adds 4 to the number then divides by 5(4+1) 5 subtracts 4 from the number then divides by 5(4-5):5
5 Match each description on the left with the correct expression on the right. The first one is done for you: A and v A Multiply n by 3 and subtract 8 3(n+8) B Add 8 and n then multiply by 3 8(n+3) C Multiply n by 3 and add 8 3(n-8) DE D Add 3 and n then multiply by 8 ix 8(n-3) Subtract 3 from n
4 Zalika has a box that contains c one-dollar coins. Choose the correct expression from the cloud to show the total number of one-dollar coins in the box when a she takes 2 out C-2 b she puts 2 more in C+2 C she takes out half of the coins d she doubles the number of coins in the box. c-2 c+2 2c
3 This tin contains some sweets.I halve the number of sweets in the tin. Copy and complete the working to show how many sweets are in the tin now, when the tin started with a 4 sweets: 4+2=2 b 10 sweets: 10+2=5 C 12 sweets: 12+2=6 d x sweets: x2 y 429 S y sweets: y2 f s sweets: s2 2 2 Sweets When
2 This box contains some books. I double the number of books in the box. Copy and complete the working to show how many books are in the box now, when the box started with a 3 books: 3x2=6 8 books: 8x2=16 e y books: yx2=2yb 5 books: 52=10 dx books: xx2=2x fb books: bx2 = 26
1 This bag contains y counters. Match each statement on the left with the correct expression on the right. A The first one is done for you: A and ii I add 1 counter to the bag, so there are now y-8 B I take 1 counter out of the bag, which leaves C D E LL F I add 5 counters to the bag, so there are
13 Read what Marcus says: 24-42 and so 34=43 Is Marcus correct? Give a reason to support your answer.
12 124=20736
11 Write as a power of 5 a 125
10 Work out and write the answer in index form. a 4523 b 9435 C 32226 d 272 36 b 1252 C 1254
9 Find the missing power of 6.a 65+6=62 b68+6=64 C6= 62=66 d6+6=6
8 Work out and write the answer in index form.a 8ª =8 b56+52 c210+22 d36 + 33 124+124 e
7 Find the missing power.4ª×4= 76 a=45 b 74×7 15 C153×15=156 d× 154=154
6 54=625Write as a power of 5 625ªa 6252 b625%c
5 Write 4 as a power of 2.a bWrite 4' as a power of 2.Write 93 as a power of 3.c
4 Write as a single power(53)2(153)2 d (3+)a b

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