Algebra – Worksheets
Algebraic Expressions
Up to level 6
Non Calculator
AT2 L6
1 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 bricks
below. 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 4
chocolates 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 buy
altogether. 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 your
answer.
Forming equations with angles
Up to level 6
Forming Equations
Worksheet
AT2 L6
Algebra – Taflenni Gwaith
Mynegiadau Algebraidd
(Mae angen i bob lythyren algebra fod
mewn italics)
Hyd at lefel 6
Heb Gyfrifiannell
AT2 L6
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.
Ffurfio hafaliadau gydag onglau
Hyd at lefel 6
Taflen waith
Ffurfio Hafaliadau
AT2 L6
1 Form equations based on the angles of
the following shapes and solve the
equations.
1 Ffurfiwch hafaliadau yn seiliedig ar
onglau’r siapau canlynol a datryswch yr
hafaliadau.
Remember: Angles in a triangle = 180º
Angles in a Quadrilateral = 360º
Cofiwch: Nifer yr onglau mewn triongl =
180º
Nifer yr onglau mewn pedrochr = 360º
Forming equations with perimeters
Up to level 6
Ffurfio hafaliadau gyda pherimedrau
Hyd at lefel 6
Forming Equations
Non Calculator
AT2 L6
1 Form equations based on the
perimeters of the following shapes and
solve the equations.
Ffurfio Hafaliadau
Heb Gyfrifiannell
AT2 L6
1 Ffurfiwch hafaliadau yn seiliedig ar
berimedrau’r siapau canlynol a
datryswch yr hafaliadau.
Remember to look out for missing sides.
Cofiwch edrych yn ofalus am ochrau coll.
Perimeter = 50 cm
Perimedr = 50 cm
Function machines
Up to level 5
Non Calculator
AT2 L5
1 Use the function machine to complete
the table below
Peiriannau Rhif
Hyd at lefel 5
Heb Gyfrifiannell
AT2 L5
1 Defnyddiwch y peiriant rhif i gwblhau’r
tabl isod.
2 Use the following function machine
backwards to find the values of x in the
table.
2 Defnyddiwch y peiriant rhif canlynol
tuag yn ôl i ddarganfod gwerthoedd x yn
y tabl.
3 The following function machine is used
to convert temperatures between ºC
(Celsius)
and ºF (Fahrenheit).
3 Defnyddir y peiriant rhif canlynol i
drawsnewid tymereddau rhwng ºC
(Celsius)
a ºF (Fahrenheit).
i) Use the function machine to convert
the following temperature in ºC (Celsius)
to ºF (Fahrenheit).
Celsius (ºC)
Fahrenheit (ºF)
i) Defnyddiwch y peiriant rhif i
drawsnewid y tymheredd canlynol mewn
ºC (Celsius)
i ºF (Fahrenheit).
Celsius (ºC)
Fahrenheit (ºF)
ii) Use the function machine backwards
to convert temperatures from ºF to ºC
ii) Defnyddiwch y peiriant rhif tuag yn ôl i
drawsnewidy tymereddau o ºF i ºC
Inequalities
Non Calculator
AT2 L7
Remember, you must never end up with
negative x terms!
Anhafaleddau
Heb Gyfrifiannell
AT2 L7
Cofiwch, ddylech chi fyth orffen gyda
thermau x negyddol!
1 Solve the following single inequalities:
1 Datryswch yr anhafaleddau canlynol:
2 Solve the following double inequalities.
State the integer values that satisfy the
inequalities.
3 (i) Solve the following inequality: 3x - 2
> 17 - 2x
(ii) What is the least integer that satisfies
this inequality?
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 equations
Up to level 5
Hafaliadau llinol
Hyd at lefel 5
Solving Equations
Non Calculator
AT2 L5
Steps 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.
Datrys hafaliadau
Heb Gyfrifiannell
AT2 L5
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 = .
Exercise 1 - Simple Equations
Ymarfer 1 – Hafaliadau Syml
Exercise 2 - Multiples of x
Divide both sides by the number in front
of x.
Ymarfer 2 – Lluosrifau x
Rhannwch y ddwy ochr gyda’r rhif o flaen
x.
Exercise 3
Remember to collect the numbers on the
other side.
Ymarfer 3
Cofiwch gasglu’r rhifau ar yr ochr arall.
Linear equations
Up to level 6
Solving Equations
Non Calculator
AT2 L6
Steps for solving equations:
1 Collect x terms on one side of
equation.
Hafaliadau llinol
Hyd at lefel 6
Datrys Hafaliadau
Heb Gyfrifiannell
AT2 L6
Camau datrys hafaliadau:
1 Casglwch y termau x ar un ochr yr
hafaliad.
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.
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 = .
Exercise 1 - Simple Equations
Exercise 2 - Multiples of x
Divide both sides by the number in front
of x.
Ymarfer 1 - Hafaliadau Syml
Ymarfer 2 - Lluosrifau x
Rhannwch y ddwy ochr gyda’r rhif o flaen
x.
Exercise 3
Remember to collect the numbers on the
other side.
Ymarfer 3
Cofiwch gasglu’r rhifau ar yr ochr arall.
Exercise 4
More care is needed in this exercise as
there are x terms and numbers on both
sides.
Ymarfer 4
Mae angen mwy o ofal yn yr ymarfer
hwn, gan fod termau x a rhifau ar y ddwy
ochr.
Linear equations with brackets
Up to level 7
Hafaliadau llinol gyda chromfachau
Hyd at lefel 7
Solving Equations
Non Calculator
AT2 L6&7
Steps 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.
Exercise 1
Solve the following equations, you just
have to divide both sides by the number
in front of x.
Datrys Hafaliadau
Heb Gyfrifiannell
AT2 L6&7
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 = .
Ymarfer 1
Datryswch yr hafaliadau canlynol; y cyfan
sydd angen i chi ei wneud yw rhannu’r
ddwy ochr gyda’r rhif o flaen x.
Exercise 2
Ymarfer 2
Exercise 3
More care is needed in this exercise as
there are x terms and numbers on both
sides.
Ymarfer 3
Mae angen mwy o ofal yn yr ymarfer
hwn, gan fod termau x a rhifau ar y ddwy
ochr.
Exercise 4
Remember you must expand brackets
first.
Ymarfer 4
Cofiwch fod rhaid i chi ehangu’r
cromfachau yn gyntaf.
Simultaneous equations
Hafaliadau cydamserol
Up to level 7
Simultaneous Equations
Non Calculator
AT2 L7
Algebraically
Steps
1 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.
Hyd at lefel 7
Hafaliadau Cydamserol
Heb Gyfrifiannell
AT2 L7
Drwy Algebra
Camau
1 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.
Graphically
1 Solve the following equations
graphically. Use the table method to plot
your lines.
Yn Graffigol
1 Datryswch yr hafaliadau canlynol gan
ddefnyddio graff. Defnyddiwch y dull tabl
i blotio eich llinellau.
2 Solve the following equations
graphically. Use the x = 0 and y = 0
method to plot your lines.
2 Datryswch yr hafaliadau canlynol gan
ddefnyddio graff. Defnyddiwch y dull x =
0 a y = 0 i blotio eich llinellau.
Straight line graphs
Up to level 6
Straight Line Graphs
Non Calculator
AT2 L6
1 Name the lines A, B, C and D
Graffiau llinell syth
Hyd at lefel 6
Graffiau Llinell Syth
Heb Gyfrifiannell
AT2 L6
1 Labelwch y llinellau yn A, B, C a D
2 Use the table method to plot the
following lines:
2 Defnyddiwch y dull tabl i luniadu’r
llinellau canlynol:
3 Sketch the following graphs, and state
the values of m (gradient) and c (yintercept).
3 Brasluniwch y graffiau canlynol, a
nodwch werthoedd m (graddiant) a c
(rhyngdoriad-y).
4 Use the x = 0 and y = 0 method to plot
the following lines:
4 Defnyddiwch ddull x = 0 a y = 0 i
blotio’r llinellau canlynol:
5 Plot the following coordinates, find the
value of the gradient and the y - intercept
and hence find the equation of each line.
5 Plotiwch y cyfesurynnau canlynol,
darganfyddwchddwch werth y graddiant
a’r rhyngdoriad-y ac o ganlyniad
darganfyddwch hafaliad pob llinell.