  Home>Worksheets>Age 11-14 Algebra: Equations, formulae and identities  Click on the 'change' button and watch the numbers change. Click on the 'print' button to print a pupil worksheet and an answer sheet. The worksheets can be printed providing the password is entered. Buy a password Choose the topic: Primary A: Place value, ordering and rounding B: Properties of numbers & number sequences C: Fractions, decimals & percentages, ratio & proportion D: Mental calculation strategies (+ and -) E: Pencil & paper procedures (+ and -) F: Understanding multiplication & division G: Rapid recall of multiplication & division facts H: Mental calculation strategies (x and divide) I: Pencil & paper procedures (x and divide) J: Using a calculator K: Checking results of calculations L: Solving problems: making decisions M: Reasoning about numbers or shapes N: Problems involving 'real life', money or measures O: Handling data P: Measures Q: Shape and space Secondary A: Applying mathematics and solving problems B: Place value, ordering and rounding C: Integers, powers and roots D: Fractions, decimals, percentages, ratio and proportion E: Number operations and the relationships between them F: Mental methods and rapid recall of number facts G: Calculations: written methods H: Calculations: calculator methods I: Calculations: checking results J: Equations, formulae and identities K: Sequences, functions and graphs L: Geometrical reasoning: lines, angles and shapes M: Transformations N: Coordinates O: Construction & loci P: Measures and mensuration Q: Statistics R: Probability J: 2 3 4 5 6 7 8 9 10 11 12 13 14 15 17 18 19 20 21 24 25 26 27 28 29 31 32 33 34 35
 Simplify expressions Years 7-9 (age 11-14)
Simplify algebraic expressions.

J28: Simplify expressions
Use the 1, 2, 3 and 4 buttons to generate the worksheet:
 level 1: 2a + 3a level 2: 2ab - 4ab level 3: 2a - 3b + 5a -6b level 4: 2x³ - 4y + 2x³ - 7y

Years 9-11 (age 14-16) Use these buttons to generate the worksheet: 1: eg 2 x a x b 2: eg 2p x 3q 3: eg 3ab2 + 2ab 4: a mixture Use these buttons to generate the worksheet: 1: eg 2(3b + 4c) 2: eg 2(3b + 4c) + 3(2b - 3c) 3: eg 2b(3b + 4c)

J33: Factorise
Option 1: 6b + 8c Option 2: 6b2 + 8bc (Options 1 and 3, see above)

J34: Rearrange formulas : change the subject of a formula
Five levels of difficulty (buttons 1 to 5). Button 6 generates a variety.

 Construct and solve linear equations    Year 7 (age 11-12)
In an arithmagon, the number in a square is the sum of the numbers in the two circles on either side of it. What could the letters be? Find relationships between the letters. There are many possible solutions for the arithmagons. The answer sheet will give one set of solutions.   Year 7 (age 11-12)
Solve simple equations

J29: Balancing problems: what is the weight of a gold bar?
Use the 1 ,2 and 3 buttons to generate the equations. three levels of difficulty:
level 1: small whole number solutions

level 2: multiple of ten solutions

level 3:
gold bars on both sides

J3: Work out what number each shape represents (positive numbers)
J4: Work out what number each shape represents (positive and negative numbers)
J5: Work out the value of each letter (positive numbers)   Pyramid equations Years 8-9 (age 12-14)
In each pyramid each number is the sum of the two numbers immediately below. Find the value of n

J6: Pyramid 1 positive whole number solutions
J7: Pyramid 2 positive and negative whole number solutions
J8: Pyramid 3 positive whole number solutions.
J9: Pyramid 4 positive and negative whole number solutions
J10: Pyramid 5 positive whole number solutions
J11: Pyramid 6 positive and negative whole number solution

Square equations
Years 8-9 (age 12-14)
Work out the value of a and b so that each row and column adds up to the required total.

J12: Square equations 1: positive whole number solutions.

J13: Square equations 2: positive and negative whole number solutions. type 1 type 2 type 3(+), type 4( + and -) type 5(+), type 6( + and -) type 7 type 8

Linear equations Years 7-8 (age 11-13)

J14: Solve equations
Eight levels of difficulty
. Click on the 1 to 8 buttons to generate the equations.

J15: Solve inequations and equations
Seven levels of difficulty
. Click on the 1 to 7 buttons to generate the equations.

 Simultaneous equations Years 7-9 (age 11-14)
What numbers are hidden?

Two or three rows of polygon people are shown. Two numbers are hidden behind the shape people: one behind the triangle and one behind the circle. What are the hidden numbers?
J20a: Shape people and simultaneous equations (2 rows)
J20b: Shape people and simultaneous equations (3 rows)

Years 9-11 (age 14-16)

Click on the five option buttons to generate new simultaneous equations:
1. Positive answers and coefficients of x and y
2. Positive answers and positive and negative coefficients of y
3. Positive and negative answers and positive coefficients of x and y
4. Positive answers and positive and negative coefficients of x and y
5. Positive and negative answers and coefficients of x and y
 Use formulae    J18 and J19 examples

Substitute numbers into expressions.
Year 7 (age 12-13)

J17: Substitute positive numbers positive answers

Year 8 (age 12-13)

Time-distance-speed
Years 9-11 (age 14-16)

J25: Time-distance-speed formulae
Use the '1' and '2' buttons to generate a worksheet. The '2' button generates more difficult questions.
 Solve quadratic equations  Factorise   Use these buttons to generate the worksheet: 1: eg (x+3)(x+5) 2: eg (x-3)(x+5) 3: eg (2x+3)(3x+5) 4: eg (2x+3)(3x-5)

J27: Factorise
x² + 3x - 10 Five options:

 1: eg (x+3)(x+5) 2: eg (x-3)(x+5) prime coefficients of x² 4: eg (2x+3)(3x+5) 5: eg (2x+3)(3x-5)

eg: x² + 3x - 10 = 0.
Same options as above

J35: Solve equations using trial and improvement
Option 1 eg: x² + 3x = 35
Option 2: x³ - 4x = 35
Option 3: x³ - 4x² = 35 Active Maths Limited
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