Algebra – Worksheets



Algebra – WorksheetsAlgebra – Taflenni GwaithAlgebraic ExpressionsUp to level 6Mynegiadau Algebraidd(Mae angen i bob lythyren algebra fod mewn italics)Hyd at lefel 6Non CalculatorAT2 L6Heb GyfrifiannellAT2 L61 Use algebra to write expressions for the perimeters of the following shapes.2 In the diagrams below the brick on top is made by adding the two bricksbelow. Find the value, in terms of algebra, of the blank bricks.3 Pencils cost x pence and pens cost 5 pence more than pencils.(i) Write in algebra the cost of 3 pencils?(ii) What is the cost of a pen?(iii) What is the total cost of 3 pencils and a pen?4 A certain box of chocolates contains n chocolates. A shop keeper removes 4chocolates from each box.(i) How many chocolates are there in each box?(ii) A boy buys 3 boxes of chocolates. How many chocolates does he buyaltogether. Simplify your answer.5 Bicycles normally cost x pounds. However in a sale they are reduced by ?20.(i) What is the sale price of a bike.(ii) How much would 5 bikes cost at the reduced price. Simplify youranswer.1 Defnyddiwch algebra i ysgrifennu mynegiadau am berimedrau’r siapiau canlynol neu Ysgrifennwch fynegiadau, yn nhermau x,ar gyfer berimedrau’r siapiau canlynol.2 Yn y diagramau isod, mae’r fricsen uchaf yn cael ei chreu drwy adio’r ddwy fricsen oddi tani. Ysgrifennwch fynegiad algebraidd ar gyfer gwerth y briciau gwag.3 Mae pensiliau’n costio x ceiniog, tra bod beiros yn costio 5 ceiniog yn fwy na phensiliau.(i) Ysgrifennwch fynegiad, yn nhermau x,ar gyfer, gost 3 pensil.(ii) Beth yw cost beiro?(iii) Beth yw cyfanswm cost 3 phensil ac un beiro?4 Mae bocs arbennig o siocledi yn cynnwys n siocled. Mae siopwr yn tynnu 4 siocled o bob bocs.(i) Sawl siocled sydd ym mhob bocs?(ii) Mae bachgen yn prynu 3 bocs o siocledi. Sawl siocled mae e’n eu prynu i gyd. Symleiddiwch eich ateb.5 Mae beiciau’n costio x punt fel arfer. Ond, mewn sêl, mae ?20 o ostyngiad yn y pris.(i) Beth yw pris beic ar y sêl.(ii) Faint fyddai cost 5 beic ar y pris gostyngol. Symleiddiwch eich ateb.Forming equations with anglesUp to level 6Ffurfio hafaliadau gydag onglauHyd at lefel 6Forming Equations WorksheetAT2 L6Taflen waith Ffurfio HafaliadauAT2 L61 Form equations based on the angles of the following shapes and solve the equations.Remember: Angles in a triangle = 180?Angles in a Quadrilateral = 360?1 Ffurfiwch hafaliadau yn seiliedig ar onglau’r siapau canlynol a datryswch yr hafaliadau.Cofiwch: Nifer yr onglau mewn triongl = 180?Nifer yr onglau mewn pedrochr = 360?Forming equations with perimetersUp to level 6Ffurfio hafaliadau gyda pherimedrauHyd at lefel 6Forming EquationsNon CalculatorAT2 L6Ffurfio HafaliadauHeb GyfrifiannellAT2 L61 Form equations based on the perimeters of the following shapes and solve the equations.Remember to look out for missing sides.Perimeter = 50 cm1 Ffurfiwch hafaliadau yn seiliedig ar berimedrau’r siapau canlynol a datryswch yr hafaliadau.Cofiwch edrych yn ofalus am ochrau coll.Perimedr = 50 cmFunction machinesUp to level 5Peiriannau RhifHyd at lefel 5Non CalculatorAT2 L5Heb GyfrifiannellAT2 L51 Use the function machine to complete the table below2 Use the following function machine backwards to find the values of x in the table.3 The following function machine is used to convert temperatures between ?C (Celsius)and ?F (Fahrenheit).i) Use the function machine to convert the following temperature in ?C (Celsius)to ?F (Fahrenheit).Celsius (?C)Fahrenheit (?F)ii) Use the function machine backwards to convert temperatures from ?F to ?C1 Defnyddiwch y peiriant rhif i gwblhau’r tabl isod.2 Defnyddiwch y peiriant rhif canlynol tuag yn ?l i ddarganfod gwerthoedd x yn y tabl.3 Defnyddir y peiriant rhif canlynol i drawsnewid tymereddau rhwng ?C (Celsius)a ?F (Fahrenheit).i) Defnyddiwch y peiriant rhif i drawsnewid y tymheredd canlynol mewn ?C (Celsius)i ?F (Fahrenheit).Celsius (?C)Fahrenheit (?F)ii) Defnyddiwch y peiriant rhif tuag yn ?l i drawsnewidy tymereddau o ?F i ?CInequalitiesAnhafaleddauNon CalculatorAT2 L7Heb GyfrifiannellAT2 L7Remember, you must never end up with negative x terms!1 Solve the following single inequalities:2 Solve the following double inequalities. State the integer values that satisfy theinequalities.3 (i) Solve the following inequality: 3x - 2 > 17 - 2x(ii) What is the least integer that satisfies this inequality?Cofiwch, ddylech chi fyth orffen gyda thermau x negyddol!1 Datryswch yr anhafaleddau canlynol:2 Datryswch yr anhafaleddau dwbl canlynol. Nodwch y gwerthoedd cyfanrifol sy’n bodloni’r anhafaleddau.3 (i) Datryswch yr anhafaledd canlynol: 3x - 2 > 17 - 2x(ii) Beth yw’r cyfanrif lleiaf sy’n bodloni’r anhafaledd hwn?Linear equationsUp to level 5Hafaliadau llinol Hyd at lefel 5Solving EquationsNon CalculatorAT2 L5Datrys hafaliadauHeb GyfrifiannellAT2 L5Steps for solving equations:1 Collect x terms on one side of equation.2 Collect numbers on the other side.3 Divide by the number in front of x.Remember to change signs when you move something over the = sign.Exercise 1 - Simple EquationsExercise 2 - Multiples of xDivide both sides by the number in front of x.Exercise 3Remember to collect the numbers on the other side.Camau datrys hafaliadau:1 Casglwch y termau x ar un ochr yr hafaliad.2 Casglwch y rhifau ar yr ochr arall.3 Rhannwch gyda’r rhif o flaen x.Cofiwch newid yr arwyddion pan fyddwch yn symud rhywbeth dros yr arwydd = .Ymarfer 1 – Hafaliadau SymlYmarfer 2 – Lluosrifau xRhannwch y ddwy ochr gyda’r rhif o flaen x.Ymarfer 3Cofiwch gasglu’r rhifau ar yr ochr arall.Linear equationsUp to level 6Hafaliadau llinolHyd at lefel 6Solving EquationsNon CalculatorAT2 L6Datrys HafaliadauHeb GyfrifiannellAT2 L6Steps for solving equations:1 Collect x terms on one side of equation.2 Collect numbers on the other side.3 Divide by the number in front of x.Remember to change signs when you move something over the = sign.Exercise 1 - Simple EquationsExercise 2 - Multiples of xDivide both sides by the number in front of x.Exercise 3Remember to collect the numbers on the other side.Exercise 4More care is needed in this exercise as there are x terms and numbers on bothsides.Camau datrys hafaliadau:1 Casglwch y termau x ar un ochr yr hafaliad.2 Casglwch y rhifau ar yr ochr arall.3 Rhannwch gyda’r rhif o flaen x.Cofiwch newid yr arwyddion pan fyddwch yn symud rhywbeth dros yr arwydd = .Ymarfer 1 - Hafaliadau SymlYmarfer 2 - Lluosrifau xRhannwch y ddwy ochr gyda’r rhif o flaen x.Ymarfer 3Cofiwch gasglu’r rhifau ar yr ochr arall.Ymarfer 4Mae angen mwy o ofal yn yr ymarfer hwn, gan fod termau x a rhifau ar y ddwy ochr.Linear equations with bracketsUp to level 7Hafaliadau llinol gyda chromfachauHyd at lefel 7Solving EquationsNon CalculatorAT2 L6&7Datrys HafaliadauHeb GyfrifiannellAT2 L6&7Steps for solving equations:1 Expand brackets.2 Collect x terms on one side of equation.3 Collect numbers on the other side.4 Divide by the number in front of x.Remember to change signs when you move something over the = sign.Camau datrys hafaliadau:1 Ehangwch y cromfachau.2 Casglwch y termau x ar un ochr yr hafaliad.3 Casglwch y rhifau ar yr ochr arall.4 Rhannwch gyda’r rhif o flaen x.Cofiwch newid yr arwyddion pan fyddwch yn symud rhywbeth dros yr arwydd = .Exercise 1Solve the following equations, you just have to divide both sides by the number in front of x.Exercise 2Exercise 3More care is needed in this exercise as there are x terms and numbers on bothsides.Exercise 4Remember you must expand brackets first.Ymarfer 1Datryswch yr hafaliadau canlynol; y cyfan sydd angen i chi ei wneud yw rhannu’r ddwy ochr gyda’r rhif o flaen x.Ymarfer 2Ymarfer 3Mae angen mwy o ofal yn yr ymarfer hwn, gan fod termau x a rhifau ar y ddwy ochr.Ymarfer 4Cofiwch fod rhaid i chi ehangu’r cromfachau yn gyntaf.Simultaneous equationsUp to level 7Hafaliadau cydamserol Hyd at lefel 7Simultaneous EquationsNon CalculatorAT2 L7Hafaliadau CydamserolHeb GyfrifiannellAT2 L7AlgebraicallySteps1 Get the same number of y terms in both equations by multiplying.2 Eliminate the y terms by adding or subtracting.3 Solve to find x.4 Substitute the value for x into one of the original equations.5 Solve to find y.Graphically1 Solve the following equations graphically. Use the table method to plot your lines.2 Solve the following equations graphically. Use the x = 0 and y = 0 method to plot your lines.Drwy AlgebraCamau1 Cewch yr un nifer o dermau y yn y ddau hafaliad drwy luosi.2 Dileewch y termau y drwy adio neu dynnu.3 Datryswch i ddarganfod x.4 Amnewidiwch werth x yn un o’r hafaliadau gwreiddiol.5 Datryswch i ganfod y.Yn Graffigol1 Datryswch yr hafaliadau canlynol gan ddefnyddio graff. Defnyddiwch y dull tabl i blotio eich llinellau.2 Datryswch yr hafaliadau canlynol gan ddefnyddio graff. Defnyddiwch y dull x = 0 a y = 0 i blotio eich llinellau.Straight line graphsUp to level 6Graffiau llinell sythHyd at lefel 6Straight Line GraphsNon CalculatorAT2 L6Graffiau Llinell SythHeb GyfrifiannellAT2 L61 Name the lines A, B, C and D2 Use the table method to plot the following lines:3 Sketch the following graphs, and state the values of m (gradient) and c (y-intercept).4 Use the x = 0 and y = 0 method to plot the following lines:5 Plot the following coordinates, find the value of the gradient and the y - intercept and hence find the equation of each line.1 Labelwch y llinellau yn A, B, C a D2 Defnyddiwch y dull tabl i luniadu’r llinellau canlynol:3 Brasluniwch y graffiau canlynol, a nodwch werthoedd m (graddiant) a c (rhyngdoriad-y).4 Defnyddiwch ddull x = 0 a y = 0 i blotio’r llinellau canlynol:5 Plotiwch y cyfesurynnau canlynol, darganfyddwchddwch werth y graddiant a’r rhyngdoriad-y ac o ganlyniad darganfyddwch hafaliad pob llinell. ................
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