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!Constructions:Bisectors

Video72and78onwww.corbettmaths.com

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Question1: Drawa8cmlineandconstructitsperpendicularbisector

Question2: Drawa6cmlineandconstructitsperpendicularbisector

Question3: Drawthefollowinganglesandconstructtheiranglebisectors.

(a) 60° (b)40°(c)90° (d)110°

(e) 150° (f)54° (g)220°

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Question1: (i)Drawatriangle. (ii)Constructtheperpendicularbisectorforeachsideofthetriangle. (iii)Usingwheretheperpendicularbisectorsmeetasthecentre,drawthe circlethatpassesthrougheachvertexofthetriangle.

Question2: Createastoryboardtoshowhowtoconstructtheperpendicularbisectorofa line.Clearlyannotateeachstage.

Question3:Createastoryboardtoshowhowtoconstructtheanglebisectorofagivenangle. Clearlyannotateeachstage.

Question4: Canyouspotanymistakesinthequestionsbelow?

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Name:

Exam Style Questions

Ensure you have: Pencil, pen, ruler, protractor, pair of compasses and eraser You may use tracing paper if needed

Guidance

1. Read each question carefully before you begin answering it.2. Donʼt spend too long on one question.3. Attempt every question.4. Check your answers seem right.5. Always show your workings

Revision for this topic

© CORBETTMATHS 2014

1." Use ruler and compasses to construct the perpendicular bisector of AB." You must show clearly all your construction arcs.

(2)

2." Using ruler and compasses, construct the bisector of angle ABC.

(2)© CORBETTMATHS 2014

3."

" The line CD is drawn above." Use ruler and compasses to construct the perpendicular bisector of CD." You must show clearly all your construction arcs.

(2)


4." Using ruler and compasses, construct the bisector of angle ABC.

(2)


5." In the space below, use ruler and compasses to construct an equilateral triangle " with sides of length 5cm.

(2)


6." Use a ruler and compasses to construct a regular hexagon that is inscribed in the " circle below.

(2)


7." The diagram shows a triangle, ABC.

" (a) Using a ruler and compasses only, construct the perpendicular bisector of PR." You must show clearly all your construction arcs.

(2)

! (b) Repeat this construction on another side of the triangle.

(1)

" (c) The point of intersection of the two bisectors is the centre of the circle that " passes through P, Q and R.

" Draw this circle.

(2)


8." Use a ruler and compasses to construct the perpendicular to the line segment AB " that passes through the point P.

" You must show all construction lines.

(2)


9." Use a ruler and compasses to construct the perpendicular from the line segment AB " to the point C.

" You must show all construction lines.

(2)


� �

!Coordinates

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Question1: WritedownthecoordinatesofthepointsA,B,C,D,E,F,GandH.

Question2: Makeacopyofthegridshownandthenplotthepoints:

(a) A(3,1)(b) B(2,5)(c) C(5,4)(d) D(1,1)(e) E(4,0)(f) F(0,1)(g) G(3,3)(h) H(0,0)

Question3: WritedownthecoordinatesofthepointsA,B,C,D,E,F,GandH.

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https://corbettmaths.com/2013/04/15/coordinates/

https://corbettmaths.com/2013/04/15/coordinates/


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!Coordinates


Question4: Makeacopyofthegridshownandthenplotthepoints:

(a) A(1,4)(b) B(−1,1)(c) C(−3,−4)(d) D(2,−1)(e) E(−2,0)(f) F(−1,−2)(g) G(3,−2)(h) H(0,−4)(i) I(−2,2)(j) J(−4,−1)(k) K(0,1)

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Question1: Threepointsareshownonagrid. ABCDisarectangle.

(a)PlotD (b)WritedownthecoordinatesofthepointD

Question2: Twopointsareshownonagrid ABCisanisoscelestriangle.

(a)PlotC (b)WritedownthecoordinatesofthepointC

Question3: Makeacopyofthegridshown.

(a)PlotthepointA(−3,−2) (b)PlotthepointB(1,−2) (c)PlotthepointC(3,1) (d)PlotthepointD(−1,1) (e)WhattypeofquadrilateralisABCD?

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� �

!Coordinates


Foreachquestion4-5below,youwillneedcopiesofthisgrid.

Question4: (a)Plotthefollowingcoordinates

(3,0)(−3,−2)(1,−4)(1,2)(−3,0)(−1,−4)(3,−2)(−1,2)

(b)Jointheshapestomakeapolygon. (c)Namethepolygonthatyouhavedrawn.

Question5: (a)PlotthecoordinatesA(−4,1),B(1,−2)andC(2,1) (b)ABCDisakite. (c)PlotD (d)WritedownthecoordinatesofthepointD.

Question6: JameshasbeenaskedtoplotthecoordinatesA(−3,2),B(0,2),C(−1,−4)and D(4,−4)

Canyouspotanymistakes?

� Answers

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https://corbettmaths.com/2018/09/25/coordinates-answers/

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!ExpandingBrackets

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Question1: Expandthefollowingbrackets

(a) 5(y+3) (b)4(a+2) (c)8(w+10) (d)3(x−7)

(e)9(s−1) (f)2(8−t) (g)7(4+h) (h)10(a+2b+3c)

(i)4(3y+2) (j)5(2p−1) (k)3(7a+2) (l)9(2x−5)

(m)5(4+3t) (n)7(9−2c)(o)8(3w+1) (p)9(1−4p)

(q)11(2k−5) (r)20(6a+5c)(s)3(15w−7) (t)3(9−2a)


(a) −2(w+5) (b)−3(c+7)(c)−8(c+7) (d)−10(y−2)

(e)−7(g−3) (f)−4(2w+3)(g)−9(3w−5) (h)−9(5x−1)

(i)−5(6−c) (j)−6(4+3m)(k)−2(1+9c) (l)−5(8a−7w)


(a) a(c+2) (b)c(d−3) (c)a(b+c) (d)w(8−y)

(e)c(5+a) (f)w(a−9) (g)y(s+t) (h)2a(c−3)

(i)5x(y+8) (j)3a(2c+9)(k)6g(2c−1) (l)9k(2+d)

(m)5(2f+9w) (n)3y(5p+2)(o)2s(t+1) (p)−4a(8x−3)


(a) a(a+2) (b)y(y−5) (c)w(a+w) (d)c(9−c)

(e)p(2p+5) (f)2w(3w−1)(g)9y(2y+3) (h)4c(2a+5c)

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!ExpandingBrackets


(i)2u(3−u) (j)m(m²+3)(k)y(y²−7) (l)g²(g−8)

(m)2w(w²+6) (n)4a(2a²−3)(o)5c(3c²−a) (p)8w(3w²+3y)

(q) x²(x²+4) (r)3w²(7+2w²)

Question5: Expandandsimplify

(a) 5(y+3)+2(y+7) (b)6(2w+5)+9(w+2) (c)3(y−2)+4(2y+5)

(d)7(2g+3)−5(g+2) (e)6(x−2)−4(x−8) (f)2(3y−8)−5(2y−1)

(g)8(5+2m)+3(5−3m) (h)4(w+7)−2(2w+1) (i)9(1+2y)+3(3−y)

Question6: Expandandsimplify

(a) w(w+5)+w(w+7) (b)2g(4g+3)+g(g−7) (c)n(n−4)−n(5−n)

(d)2e(4e+3)−3e(e−5) (e)a(3+c)+c(a+2) (f)m(a+7)−a(4−3m)

(g)8c(8−3a)+3(4−c) (h)5y(3y+z)−2y(4y−3z)(i)4c(3c−c²)−2c²(4−5c)

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Question1:Canyouspotanymistakesinthequestionsbelow.

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!FormingExpressions


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Question1: Writeanalgebraicexpressionforeachofthefollowing

(a) 4morethanc (b)2lotsofa (c)3lessthanb (d)mdividedby5

(e) 7multipliedbys (f)wsubtract1 (g)esquared (h)yadd9

(i) msharedbetween3 (j)10timesx (k)klessthan8 (l)12lessthang


(a) caddp (b)fminusm (c)atimesb (d)pdividedbyz

(e) btakenawayfromu (f)kaddnaddr (g)wlessthanc (h)lmultipliedbym

(i) ymultipliedbymmultipliedbya


(a) mmultipliedby2andthenadd3 (b)hdividedby4andthenadd7

(c) psquaredandthenadd10 (d)tadd2andthenmultipliedby5

(e) 9timeseandthenadd1 (f)hdividedby3thenadd1

(g) msubtract6andthendividedby3 (h)ysquaredandthenmultipliedby4

(i) kmultipliedby4andthensquared (j)asquaredandthenmultipliedbyb

� Question1: Anorangecostsypence,anapplecostszpenceandabananacosts17pence. Writeanexpressionforthetotalcostof:

(a) 3oranges (b)5apples (c)2orangesand3apples

(d)2applesand1banana (e)mbananas (f)3orangesand3bananas

(g)20apples,10orangesand2bananas (h)4oranges,3applesandnbananas

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� �

!FormingExpressions


Question2: Ataxidrivercharges£mpermile. Writeanexpressionforthetotalcostof:

(a)A2milejourney (b)A15milejourney (c)Ajourneyofxmiles

Question3: Writeanexpressionfortheperimeterofeachshapebelow.

(a) (b) (c)

Question4: Alanisyyearsoldandhas8sisters. Writeanexpressionforhowoldeachsisteris.

(a) Bethis3yearsoldthanAlan.(b) Clarais2yearsyoungerthanAlan.(c) DonnaisthreetimesAlan’sage.(d) EmmaishalfAlan’sage.(e)FionaistwoyearsyoungerthanDonna.(f)GeorgiaistwiceBeth’sage.(g)Hannahis4yearsolderthanFiona.(h)IsabelleisthreetimesClara’sage.

Question5: Guy,EricandLukegoChristmasshopping. Writeanexpressionforhowmuchmoneyeachmanhasleftaftershopping.

(a) Guyhad£20andspends£yonpresents.(b) Erichad£mandspends£12onpresents.(c) Lukehad£aandspends£bonpresents.

Question6: ATVcosts£x.ADVDplayercosts£45lessthantheTV. WriteanexpressionforthetotalcostoftheTVandDVDplayer.

Question7: Aplumbercharges£15perhourplusa£yinitialcalloutcharge. Writeanexpressionforthetotalcostof:

(a)Ajoblasting3hours (b)Ajoblasting8hours (c)Ajoblastingnhours

�Answers

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https://corbettmaths.com/2016/07/29/textbook-answers-forming-expressions/

https://corbettmaths.com/2016/07/29/textbook-answers-forming-expressions/

Question Bank for grade 6

PERCENTAGE

Q1. Calculate the following.

a. 50% of 300 b. 75% of 400

c. 40% of 600 d. 25% of 360

e. 80% of 250 f. 37.5% of 240

g. 87.5 of 880 h. 12.5% of 320

i. 75% of 40 j. 40% of 75

Q2. In a survey of 100 cars, 47 were white, 23 were blue and 30 were red.

Express each of these numbers as a percentage of total.

Q3. 710 of the surface of the earth is water. Express this as a percentage.

Q4. There are 200 birds in a flock. 120 of them are female. What percentage of the flock is

a) Female b) Male

Q5. Write these percentages as fractions of 100.

a) 73% b) 28% c) 10% d) 25%

Q6. Write these fractions as percentages.

a) 27100 b)

310 c) 750 d)

14

Q7. Convert the following percentages to decimals.

a) 39% b) 47% c) 83%

d) 7% e) 2% f) 20%

Q8. Convert the following decimals to percentages.

a) 0.31 b) 0.67 c) 0.09

d) 0.05 e) 0.2 f) 0.75


Q9. In a survey of 100 cars, 45 were silver, 13 were blue and 30 were red.

Express each of these numbers as a fraction, a decimal and a percentage of the total.

Q10. 310 of the surface of the earth is land. Express this as a decimal and a percentage.

Q11. There are 500 students in a school. 220 of them are female. What percentage of the

school is: a) Female b) male

Q12. Write each of these percentages as a fraction in its simplest form.

a) 23% b) 68% c) 70% d) 75%

Q13. Write these fractions as percentages.

a) 49100 b)

910 c) 1750 d)

34

Q14. Convert the following percentages to decimals.

a) 69% b) 87% c) 83%

d) 3% e) 102% f) 220%

Q15. Convert each of these decimals to percentages.

a) 0.61 b) 0.17 c) 0.89

d) 0.08 e) 1.25 f) 2.75

Q16. Work out the following.

a. 10% of 60 b. 25% of 160 q. 87.5% of 80

c. 12.5% of 80 d. 37.5% of 80 r. 10% of 110

e. 46% of 50 f. 50% of 46 t. 45% of 90

g. 70% of 125 h. 7% of 125

i. 12% of 180 j. 36% of 180

k. 90% of 90 l. 7% of 375


m. 9% of 90 n. 60% of 180

o. 60% of 150 p. 9% of 9

Q17. 15% of students in a school of 720 students are left- handed. What number of students

are right handed?

Q18. At Cambridge college, 65% of the math students come from England. If there are 240

math students, how many are not from England?

Q19. A survey showed that 75% of vehicles passing a school were cars. If 4200 vehicles passed

the school in one day, how many were cars?

Q20. In a village of 3500 people, 12% are left-handed, and 15% of left handed people have

blonde hair. How many people in the village are blonde and left-handed?

Q21. Write the first quantity as a percentage of the second.

a. 36 out of 72 b. 18 out of 90

c. 6 out of 60 d. 36 out of 60

e. 7 out of 70 f. 21 out of 70

g. 45 out of 900 h. 135 out of 900

i. 11 out of 44 j. 11 out of 440

k. 5 out of 20 m. 54 out of 60

o. 49 out of 70 q. 180 of 900

s. 77 out of 440

Q22. A school football team plays 25 games in a season. They win 17, draw 2 and lose the rest.

Express the numbers won, drawn and lost as percentages of the total number of games played.

Q23. An airline has a fleet of 80 planes. Of these, 10 are being serviced at any one time. What

percentage of the fleet is available for flights?

Q24. A car manufacturer produces 175000 sports cars a year. They are only available in white,

black and red. 52500 are white, 78750 are black and the rest are red.

a) What percentage of the cars are black?

b) What percentage is white?

c) What percentage is red?


Q25. Copy and complete these sets of equivalent fractions and percentages.

1) 824 = 1

2) 59 = 18

3) 710 = % 4) 11100 = ___ %

5) 1350 = ____ % 6) 1751 = 1

9) 750 = 100 = ____%

7) 825 = 50 = ____ % 8) 10125 = 1000 = ____ % 10) 351000 = 200 = ____ %

Q26. Which of the following are equivalent (in proportion)? Give reasons for your answers.

1) 110 0.1 10% 2)

15 0.5 50% 7) 23 0.6 60%

3) 18 0.125 12.5% 4)

13 0.3 3% 8) 9100 0.9 9%

5) 45 0.8 8% 6)

38 0.375 37.5% 9) 120 0.05 5%

10) 2 2.0 200%

Q27. Copy and complete this table.

Fraction Ratio Percentage 12 1 to 2 50% 14 1 to ___ 25% 34 ____ to 4 18 1 to ____ 12.5% 38 ____ to 8 58 5 to ____ 78 87.5% 110 1 to ____ 10% 210 𝑜𝑟 15 ____ to 5 20% 310 3 to ____


410 𝑜𝑟 25 ____ to 5 610 𝑜𝑟 35 ____ to 5 710 70% 810 𝑜𝑟 45 910 9 to 10

Q28. Complete the following table.

Fraction Decimal Percentage 𝟏𝟐

0.25 𝟏𝟏𝟎

0.3

0.2

12.5%

Q29. Calculate the following, showing your method.

a. 75% of 64

b. 30% of 1550

c. 9% of 3400

d. 55.5% of 680

e. 3% of 73

Q30. Calculate the first number as a percentage of the second:

a. 35, 140

b. 72, 600

c. 23, 50

d. 40, 125

e. 17, 250

RATIO

Q1. Copy these set equivalent ratios and fill in the blanks.

a) 4 : 5 = 8: ___ = ___:50 = 12:____

b) 7 : 2 = 14:___= ___:10 = 49:____

c) 8 : 5 = ____: 50 = 32:____ = 4:____

Q2. A school has 20 teachers and 480 students.

What is the teacher : student ratio?

Q3. A college has 250 staff and 3500 students.

What is the staff : students ratio?

Q4. A town in America has 2400 families and 4200 cars.

What is the family : car ratio?

Q5. In a batch of 10 dozen eggs, 25 are cracked.

What is the ratio of cracked eggs to un-cracked eggs?

Q6. A ship has 300 crew to 750 passengers

What is the ratio of passengers to crew?

Q7. The teacher : student ratio in a school is 1:21

There are 24 teachers. How many students are there?

Q8. An alloy contains copper and tin in the ratio 3:1

40g of tin is used to make the alloy.

How much copper is used?

Q9. Which of the following pairs of ratios are in proportion? Give reasons for your answers.

a) 1 to 5 and 4 to 20 f) 2 to 6 and 3 to 9

b) 5 to 25 and 15 to 75 g) 18 to 12 and 40 to 60

c) 7 to 21 and 21 to 42 h) 9 to 18 and 18 to 9

d) 5 to 10 and 12 to 24 i) 6 to 30 and 5 to 20

e) 1 to 3 and 3 to 1 j) 5 to 25 and 20 to 100

Q10. Copy these pairs of equivalent fractions and fill in the missing numbers.

a) 32 𝑎𝑛𝑑 6

f) 89 𝑎𝑛𝑑 24

b) 78 𝑎𝑛𝑑 16 g) 45 𝑎𝑛𝑑 50

c) 34 𝑎𝑛𝑑 9 h)

1824 𝑎𝑛𝑑 3

d) 812 𝑎𝑛𝑑 12 i)

1636 𝑎𝑛𝑑 24

e) 410 𝑎𝑛𝑑 40 j) 19 𝑎𝑛𝑑 9

Q11. Simplify these ratios.

a) 27 : 36 f) 45 : 75

b) 28 : 70 g) 20 minutes : 1 hour

c) 3kg : 750g h) 8m : 75cm

d) 7 litres to 750ml i) $2 to 20 cents

e) 3 hours to 1 day j) 8 weeks to 1 year

Q12.

a) divide 250 in the ratio 3:2 i) divide 144 in the ratio 1:2

b) divide 10 kg in the ratio 3:2 j) divide 1 hour in the ratio 5:7

c) divide 8m , in the ratio 3:2 k) divide 45 km in the ratio 7:8

d) divide 4 hours in the ratio 3:2 l) divide 2 kg in the ratio 3:7

e) divide 3 litres in the ratio 3:2 m) divide 1 m in the ratio 2:3:5

f) divide 70 litres in the ratio 1:2:4 n) divide 1 hour in the ratio 5:6:9

g) divide 2 km in the ratio 3:8:9 o) divide 9 kg in the ratio 3:14:19

h) divide $75 in the ratio 3:5:7

Q13. Simplify the following ratios:

a. 3 : 48

b. 50 : 75 : 125

c. 45 : 360

d. 15 litres : 3 litres

e. 14000 ml : 2.8 litres

f. 2.5 cm : 5 m

g. 37 : 12

h. 2 34 : 1 25

Q14. A school has 25 teachers and 750 students. Write the teacher : student ratio in its simplest

form.

Q15. A builder mixes up a mortar by mixing 3 shovels full of cement with 12 shovels full of

sand. Write the cement: sand ratio in its simplest form.

ALGEBRA

Q1. Simplify the following expressions using the correct order of operations.

1) 2𝑎 + 3𝑎 − 4𝑎 2) 2𝑏 − 5𝑏 + 7𝑏 − 𝑏

3) 3𝑐 + 2𝑏 + 2𝑐 − 4𝑏 4) 5𝑑 − 4𝑓 + 3𝑒 − 2𝑑 + 𝑓 − 2𝑒

5) 4𝑔 + 2(3𝑔 − 4ℎ) + 2ℎ 6) 3(2𝑗 − 𝑘) − 4(𝑗 − 2𝑘)

7) 4𝑚 + 5(2𝑛 + 3𝑝) − 4(𝑛 − 𝑚 − 𝑝) 8) 8𝑞 + 6(4𝑞 − 3𝑟 + 5𝑡) + 2(𝑟 − 7𝑡)

9) 5𝑢 − 8𝑣 + 9(2𝑢 − 3𝑣) − 4(2𝑣 − 5𝑢) 10) 7(4𝑤 + 𝑥 + 2𝑦) − 5(𝑤 − 𝑥 + 3𝑦

Simplify the following expressions

a) 2𝑎 + 3𝑎 + 5𝑎

b) 4𝑏 − 2𝑏 + 7𝑏

c) 3𝑐 + 8 − 5𝑐 + 7 + 8𝑐

d) 4𝑑 − 5 + 8 − 2𝑑

e) 3𝑒 + 8𝑒 + 7 − 𝑒

f) 6𝑓 − 7𝑓 − 3 + 4𝑓 − 8

g) 4𝑔 + 6 − 8𝑔 − 9

h) 3ℎ − 7 − 9ℎ + 11

i) 6𝑖 − 3𝑖 − 14 + 9𝑖 − 4

j) 3𝑗 − 4 + 8𝑗 − 11 − 𝑗

Q7. Complete the following table by using algebraic shorthand to simplify, and the rules of

arithmetic (BODMAS) to calculate.

Simplify

a. 𝑥 + 𝑥 + 𝑥

b. 5𝑦 − 4𝑦

c. 𝑧 × 𝑧 × 𝑧

d. 𝑥 + 𝑥 + 𝑥 – 𝑦

e. 𝑥 + 𝑥 + 𝑦 + 𝑦

f. 𝑦 – 𝑦

g. 𝑥 × 𝑥 + 𝑦 × 𝑦

h. 5𝑥 + 3𝑥 – 2𝑦

Q8. Simplify

a. 5𝑥 + 7𝑥 – 𝑥

b. 3𝑥 + 10𝑥

c. 2𝑥 + 5𝑥 – 4𝑦

d. 6𝑥 – 3𝑥 + 2𝑦 – 𝑦

e. 2𝑎 + 5𝑎 – 3𝑎 + 6𝑏

f. 3𝑥 + 10 – 7 g. 4𝑧 + 2𝑤 + 2𝑧 + 𝑤 – 2𝑧 h. 7𝑐 – 𝑐 + 6𝑑 – 3 – 6𝑑 i. 6 + 3𝑎 – 3 – 𝑎 j. 4𝑥 + 𝑦 − 3𝑥 − 𝑦

k. 8𝑥² + 4𝑦² – 7𝑥² − 2𝑦²

l. 𝑥² + 𝑥𝑦 + 4𝑥² + 2𝑥𝑦

m. 3𝑥² + 2𝑥𝑦 – 𝑥𝑦 – 4𝑦²

n. 5𝑥²𝑦² – 3𝑥²𝑦 – 𝑥²𝑦² + 𝑥²𝑦

o. 3𝑥² – 5𝑥3 + 2𝑥²𝑦 − 𝑥²𝑦

p. 2𝑥² + 𝑦² − 𝑥𝑦 + 𝑥²

q. 6𝑥2 + 2𝑥 – 3𝑥2 + 𝑥

Q9. Translate each verbal phrase into an algebraic expression:

a. 6 multiplied by m

b. 13 plus f

c. Take away 4 from y

d. 10 times w

e. 7 more than g

f. k minus 16

g. One-Fifth of s

h. The total of r and 10

i. q reduced by the quotient of 2 and 3

j. b separated into 9 equal parts

k. sum of v and 3

l. d squared

m. 5 fewer than g

n. . x increased by 2

o. 8 divided by z

p. The sum of b and 6 divided by 2

q. 5 times the difference of q and 1

r. The quantity k plus 10 divided by 4

s. 5 divided by z cubed

t. 48 times the difference of a and 79

Q10. Simplify each expression.

a. 2 (𝑘 + 4) + 7(2𝑘 – 2) – 2

b. 12 + 4𝑛 + 5 – 2𝑛 – 10

c. 3𝑎 – 4 + 5𝑎 + 7 + 2(𝑎 + 1)

d. 3 + 2𝑠 – 4 + 3𝑠

e. 7𝑝 – 6 + 8𝑝 – 2 – 2𝑝

f. 15 – 3(𝑦 + 5 – 7)

g. 𝑐 + 6 + 4𝑐 – 3 + 4

h. 10𝑚 + 2 + 7𝑚 – 3 + 5𝑚

i. – 86 – 2(11𝑏) + 4 (5𝑏) + 26

j. 8(𝑟 + 9) + 7𝑟

k. – 20 + 5(7𝑡 – 2)

l. 4(3𝑧 + 5 + 7𝑧) – 12

m. 3𝑎²𝑏² 𝑥 12𝑎𝑏

4

n. 2𝑎𝑏 𝑥 (−3𝑎𝑏𝑐)

o. −49𝑚² ÷ 7𝑚

p. 15𝑒² ÷ 5𝑒

q. 6𝑥𝑦 𝑥 ( −4𝑥𝑦 )

Q11. Find the sum of:

a. (2𝑥 − 9𝑦 + 10) , (10𝑦 + 5𝑥 − 6) 𝑎𝑛𝑑 (−12𝑥 + 3𝑦)

b. (4𝑎² − 7𝑦³ + 18), (2𝑦³ − 6𝑎² − 9) 𝑎𝑛𝑑 (8𝑎² − 5𝑦³ + 15)

Q12. Subtract:

a. (2𝑎 − 3𝑏 + 6) 𝑓𝑟𝑜𝑚 (15𝑎 + 17𝑏 − 18)

b. (8𝑦2 + 8𝑥2)𝑓𝑟𝑜𝑚 ( 4𝑥2 − 6𝑦2)

c. (9𝑥 + 3𝑦 − 21) from the sum of (5𝑦 + 𝑥 2) 𝑎𝑛𝑑 (9 𝑥– 7𝑦 + 3)

d. (6𝑎² + 3𝑏² − 2) from the sum of (𝑎² + 7𝑏² − 12) 𝑎𝑛𝑑 (9 𝑏²– 7𝑎² + 13)

Q13. If a=5, b=-2 and c = 2; find the value of:

a. 𝑎² − 𝑏 + 𝑐³

b. 2𝑏³ − 6

c. 8𝑐² + 15

d. 2𝑎³ + 6𝑏² − 9𝑐

e. 18𝑎 − 2𝑏

AREA

Q1. Calculate the area of each of these triangles.

a) b) c)

Q2. Use the formula for the area of a triangle to work out the missing values in this value.

Base

length

Perpendicular

height

Area

a 7.2 cm 4.8 cm

b 20 cm 100 𝑐𝑚2

c 15 cm 15 𝑐𝑚2

d 11 cm 55 𝑐𝑚2

Q3. Calculate the area of each of these shapes.

a)

b)

c)

Q4. Calculate the area of the coloured region of each of these shapes.

a)

b)

Q5. Calculate the area of the following:

(a) (b)

4cm

(c) (d)

Q6. Calculate the volume of the following:

(a) A cube of side 7 m (b) A cube of side 10 cm

(c)

(d ) A cuboid measuring 2 cm by 5cm by 20cm

Q7. Calculate the area and perimeters of the following:

(a) (b)

PERIMETER

Q1. Calculate the perimeters of the following shapes.

(a) (b)

(c) (d)

(e) (f)

COORDINATES

Q1. Draw a grid with centre (0,0), the origin, and mark the x and y axes with scales from -8 to 8.

Marks these points on your grid.

A = (5,2) B = (7,3)

C = (-8,5) D = (-6,-8)

E = (7,-3) F = (6,-6)

G = (2,4) H = (2,4)

I = (3,-7) J = (3,-9)

Q2. Draw a separate grid with x and y axes from -6 to +6. Plot the points, join them up in order

and name the shape you have drawn.

a) A(3,2) B(-3,4) C(-2,-4) D(-2,2)

b) D(1,3) E(4,-5) F(-2,-5)

c) G(-6,4) H(0,-4) I(4,-2) J(-2,6)

Q3. Plot the P= (-6,4), Q= (6,4), and R= (6,-2). Plot point S such that PQRS is a rectangle.

a) Write down the coordinates of S.

b) Draw diagonals PR and QS. What are the coordinates of their point of intersection?

c) What is the area of PQRS?

Q4.(on the same graph of question 3)

On the same grid plot points M = (-8,4) and N = (4,4).

a) Joint points MNRS. What shape have you drawn?

b) What is the area of MNRS?

c) Explain your answer to parts b).

Q5. (on the same graph of question 3)

On the same grid plot point J where point J has y coordinate +10 and JRS forms an isosceles

triangle.

a) Write down the coordinates of J.

b) What is the x coordinate of all the points on the line of symmetry of triangles JRS?

Q6.(a) Draw a grid with both the axes running from -10 to + 10, as in the diagram above.

(b) Plot and label the following points.

(i) A (6,1)

(ii) B (-5,-3)

(iii) C (4,-6)

(iv) D (-8,5)

Q7. (a) Draw another grid as on question 1.

(b) Plot and label the following points.

(i) A (3,1)

(ii) B, (6,2)

(iii) C, (3,7)

(iv) D (-6,2)

(v) E (-3,2)

(vi) F (-3,7)

(c) Join A, B and C to form a triangle.

(d) Join D, E and F to form another triangle.

(e) In what way are the two triangles the same?

(f) In what way are they different?

Q8. Write down the coordinates of all points in the diagram below.

� �

!Substitution


�

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Question1: Ifa=7b=10c=3d=8ande=15 Findthevalueofeachexpression.

(a) a+5 (b)b−4 (c)c+d (d)e−d(e) 2a (f)4b (g)3e (h)5c

(i) (j) (k) (l)

(m)a² (n)b² (o)c² (p)d²

(q) 2a+1 (r)3b−7 (s)9c+11 (t)4e−45

(u) 2a+3c (v)4d−b (w)5a+2d (x)e−4c

(y) 30−4a (z)15−3c

Question2: Iff=5g=6h=4andi=2 Findthevalueofeachexpression.

(a) fg (b)hi (c)fgh (d)i³

(e) √h (f)3f+2g (g)5h+7i (h)9h−7i

Question3: Ifa=−2b=5 c=−6 d=10 ande=9 Findthevalueofeachexpression.

(a) a+4 (b)b−8 (c)c+e (d)a−d

(e) d−c (f)2c (g)7a (h)−7b

(i) 2d+3c (j)6e+3a (k)5a+7 (l)20+4a(m) ac (n)40−d (o)2e−a (p)bd+a

(q) (r) (s)√e (t)c²

Examples

Workout


Clickhere




https://corbettmaths.com/2012/08/20/substitution-into-expressions/

https://corbettmaths.com/2012/08/20/substitution-into-expressions/

� �

!Substitution


Question4: Ifa=1.5b=4 c=6 d=0.5 ande=−3 Findthevalueofeachexpression.

(a) 4(a+d) (b)5(c+b) (c)3(10−e) (d)abc

(e) e³ (f)d² (g)5b² (h)8e²+3

(i) (j) (k)

Question5: P=2L+2W,workoutPifL=8andW=3.

Question6: C=15h+30,workoutCifh=6.

�

Question1: Thecostofhiringacarforanumberofdaysiscalculatedusingtheformula

HireCost=30xNumberofDays+50

(a)Calculatethecostofhiringacarfor4days. (b)Calculatethecostofhiringacarfor9days. (c)Thehirecostis£110,howmanydayswasthecarhiredfor? (d)Thehirecostis£380,howmanydayswasthecarhiredfor?

Question2: Thecostofphotocopyingisgivenas:

Costinpence=3xnumberofblack&whitepages+15xnumberofcolourpages

(a)Ellaorders20black&whitepagesand6colourpages,workoutthecost. (b)Tomorders400black&whitepagesand70colourpages,workoutthecost.

Question3: Thetimeinminutes,takentocookachickenisgivenbytheformula

Time=40minutesperkilogramplus20minutes

(a)Workoutthetimetakentocooka5kgchicken. (b)Workoutthetimetakentocooka2.5kgchicken.

Apply




� �

!Substitution


Question4: Thisformulaisusedtocalculatetheweeklypayofalettingagent.

Weeklypay=basicpay+numberofhousesrentedxbonus

Thebasicpayis£400andabonusof£75ispaidforeachhouserented. MrsLewisrentsout5housesinoneweek. Calculateherpay.

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Question5: ThisformulacanbeusedtoconvertbetweenCelsiusandFahrenheit:

F=1.8C+32

(a)WorkoutthevalueofFwhenC=10 (b)WorkoutthevalueofFwhenC=20 (c)WorkoutthevalueofFwhenC=4 (d)WorkoutthevalueofCwhenF=35.6 (e)WorkoutthevalueofCwhenF=41 (f)WorkoutthevalueofCwhenF=112 (g)FindatemperaturewhenFandCarethesamevalue.

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�Answers


Clickhere


https://corbettmaths.com/2016/07/29/textbook-answers-substitution/


https://corbettmaths.com/2016/07/29/textbook-answers-substitution/


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iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii Examples ... · Question 5: Guy, Eric and Luke go Christmas shopping. Write an expression for how much money each man has left after shopping