# Algebra topics for intermediate level

Below are the intermediate topics available for the category "Algebra" at Free Maths Games.

These free maths topics offer a complete set of basic Algebra topics for intermediate pupils aged 11 to 14. The Algebra category is divided into sub-categories such as "Algebraic notation", "Formulas", "Graphs", etc. Each sub-category has multiple sub-sub-categories, and within them are the topics with between 6 and 10 question and answer pairs for the lessons, plus additional question answer pairs for the games and tests.

For each question/answer pair in a topic you get the question as picture, equation or text, the spoken question read by a robot, and an answer as both number or text and as audio. For most topics there are also 3 wrong answers prepared for each question.

## age 12 (20 topics)

### Algebra ➔ Algebraic notation

#### Algebra ➔ Algebraic notation ➔ Algebraic notation

y + y
Interpret algebraic notation
For each expression, convert between algebraic notation and expanded form e.g. 3c = c + c + c
2x + 5x
Like and unlike terms
Decide whether each expression consists of like terms or unlike terms
3x + 2y + 4
3 terms
How many terms
Count the number of terms in each of the given expressions
4y + 7
Match expressions to descriptions
Match simple algebraic expressions to the the correct word description of the expression

### Algebra ➔ Formulas

#### Algebra ➔ Formulas ➔ Perimeter of shapes

P = 2 L + 2 W
Perimeter: rectangles
Form an expression for the perimeter of each of the rectangles in terms of x and y

#### Algebra ➔ Formulas ➔ Substitute in values

J = k + 2m
k = 2, m = 3
Two positive integer variables
Calculate the value of J by substituting in the given positive integer values for the 2 variables k and m

#### Algebra ➔ Formulas ➔ Perimeter of shapes

P = 4 x L
Perimeter: squares
Form an expression for the perimeter of each of the given squares in terms of x

### Algebra ➔ Graphs

#### Algebra ➔ Graphs ➔ Coordinates

Coordinates of a point
In each instance identify the correct coordinates for the point on the graph
Plotting coordinates
Take the plotted points and the additional point coordinates to identify the polygon that is formed

### Algebra ➔ Sequences

#### Algebra ➔ Sequences ➔ Generating terms

Find term from rule
Find the specified term given the first term and the rule
41,39,37..
Find the rule
For each arithmetic or geometric sequence find the rule to extend the sequence
9, 18, 27 ..
Next term
For each given arithmetic sequence, find the next term

### Algebra ➔ Simplify expressions

#### Algebra ➔ Simplify expressions ➔ Add and subtract

x² + 2x
Simplify expressions by adding and subtracting unlike terms e.g. a + a - b or 2x - 3y + 5x
5x-x+2x
Simplify expressions by adding and subtracting like terms such as 5x - 3x + 6x

#### Algebra ➔ Simplify expressions ➔ Multiply terms

P-2p x 3p
Multiply like terms
Simplify expressions by multiplying like terms with no exponents to give answers raised to a power
P-2p x 3q
Multiply unlike terms
Simplify expressions by multiplying quantities of unlike terms with no exponents e.g. 2b x 3c

#### Algebra ➔ Simplify expressions ➔ Add and subtract

3y³ - y³
Subtract like terms
Simplify expressions by subtracting quantities of like terms such as 5x - 3x or 13x² - 5x²
4y² + 3y²
Simplify expressions by adding algebraic like terms such as a + a or b² + 3b² or 5c³ + 3c³

### Algebra ➔ Solving equations

#### Algebra ➔ Solving equations ➔ Linear equations

x + 3 = 7
Terms on one side, one-step equations
In each instance use simple algebraic methods to solve for the given variable in these one-step equations
4x + 4 = 12
Terms on one side, two-step equations
For each two-step equation use algebraic methods to solve for the given variable

## age 13 (30 topics)

### Algebra ➔ Factorise

#### Algebra ➔ Factorise ➔ Linear expressions

x(3 + y)
Common terms
Factorise out common terms only
4(2x + 3y)
Common number factors
Factorise out common numbers

### Algebra ➔ Formulas

#### Algebra ➔ Formulas ➔ Perimeter of shapes

P = 4 x L
Form expression: perimeter of squares
Form an expression for the perimeter of each of the given squares in terms of x
P = 2L + 2W
Form expression: perimeter of rectangles
Form an expression for the perimeter of each of the given rectangles in terms of x and y
Form expression: perimeter of triangles
Form an expression for the perimeter of each of the given triangles in terms of x

#### Algebra ➔ Formulas ➔ Area of shapes

A = L x L
Express the area of squares
Express the area of each of the given squares in terms of x
A = L x W
Express the area of rectangles
Express the area of each of the given rectangles in terms of x

#### Algebra ➔ Formulas ➔ Angles

Form expression: angles in triangle
Form simplified expressions for the sum of the interior angles of each triangle in terms of x

#### Algebra ➔ Formulas ➔ Formula from words

Expressions from words
Form an expression for each of the given scenarios in terms of x and y

#### Algebra ➔ Formulas ➔ Substitute in values

J = k + 2m
k = 2, m = 3
Two positive integer variables
Calculate the value of J by substituting in the given positive integer values for the 2 variables k and m
K = 2n - 3p
n = -2, p = -3
Two negative integer variables
Calculate the value of K by substituting in two negative integer variables n and p

### Algebra ➔ Graphs

#### Algebra ➔ Graphs ➔ Linear graphs

Graphs of form y = c, x = c
Identify the correct equation for graphs with lines parallel to the x-axis or the y-axis
y = x + 3
Get value of y
For each equation plotting a linear graph get the value of y given the value of x

### Algebra ➔ Sequences

#### Algebra ➔ Sequences ➔ Generating terms

-4, 8, -16, ..
Term-to-term
For each arithmetic or geometric sequence, find the next term
2, 4, 6, 8, ..
Position to term
Find the value of term n for the given linear sequences

#### Algebra ➔ Sequences ➔ nth term expressions

3n+12
Find the nth term value
Given an nth term rule, find the value of the specified term in the sequence

### Algebra ➔ Simplify expressions

#### Algebra ➔ Simplify expressions ➔ Add and subtract

5x - y² + 2x
Simplify like & unlike terms
Simplify the given expressions by adding and subtracting like and unlike terms
⅕x + ⅐x
Add unit fractions of like terms
Add unit fraction amounts of like terms e.g. ⅕x + ⅐x
¾x - ½x
Subtract fractions of like terms
Subtract fractional amounts of like terms e.g. ¾x - ½x

#### Algebra ➔ Simplify expressions ➔ Multiply terms

P-4p⁴ x 2p⁴
Multiply like terms
Simplify expressions by multiplying like terms with exponents e.g. 2y² x 2y²

#### Algebra ➔ Simplify expressions ➔ Divide terms

4xy ÷ 2x
Divide unlike terms
Divide unlike terms with coefficients but no exponents e.g. 4xyz / xz

#### Algebra ➔ Simplify expressions ➔ Brackets

3x(1+x)
Bracket with x outside
Expand expressions with single brackets that have coefficients of x outside the bracket e.g. 5x(3y - 6x)
3(x+1)
Expand a single bracket
Use multiplication to expand a single simple bracket expression e.g. 5(4 + 3x)

#### Algebra ➔ Simplify expressions ➔ Divide terms

4x⁵ ÷ x²
Divide unlike terms with exponents
Simplify expressions by dividing unlike terms with coefficients and exponents e.g. 6x⁵y / 3x²

#### Algebra ➔ Simplify expressions ➔ Multiply terms

P-3p x q x p
Multiply like & unlike terms
Simplify expressions by multiplying like & unlike terms with exponents and / or coefficients e.g. b x 3c² x b² x d

### Algebra ➔ Solving equations

#### Algebra ➔ Solving equations ➔ Linear equations

Terms on both sides
Use algebraic methods to rearrange and solve for x, terms on both sides, no fractions
x + 3 = 7
Terms on one side, one-step equations
In each instance use simple algebraic methods to solve for the given variable in these one-step equations
4x + 4 = 12
Terms on one side, two-step equations
For each two-step equation use algebraic methods to solve for the given variable
4(x + 4) = 12
Equations with brackets
For each equation, expand the bracket and solve for the given variable
Terms on one side, fractions
Use algebraic methods to rearrange and solve for x, terms on one side, with fractions

## age 14 (33 topics)

### Algebra ➔ Factorise

#### Algebra ➔ Factorise ➔ Linear expressions

x(3 + y)
Common terms
Factorise out common terms only
4(2x + 3y)
Common number factors
Factorise out common numbers
4x(2 + 3y)
Both terms and numbers
Factorise out both terms and numbers in each of the given expressions

### Algebra ➔ Formulas

#### Algebra ➔ Formulas ➔ Substitute in values

p = -2
q = -3
r = -4
Negative integers: 3 variables
Calculate S by substituting in negative integer values for the 3 variables p, q and r
J = k + m + n
k=2, m=3, n=4
Positive integers: 3 variables
Calculate the value of J by substituting in positive integer values for the 3 variables k, m and n

#### Algebra ➔ Formulas ➔ Perimeter of shapes

P = 4 x L
Form expression: perimeter of squares
Form an expression for the perimeter of each of the given squares in terms of x
P = 2L + 2W
Form expression: perimeter of rectangles
Form an expression for the perimeter of each of the given rectangles in terms of x and y
Form expression: perimeter of triangles
Form an expression for the perimeter of each of the given triangles in terms of x

#### Algebra ➔ Formulas ➔ Area of shapes

A = L x L
Express the area of squares
Express the area of each of the given squares in terms of x
A = L x W
Express the area of rectangles
Express the area of each of the given rectangles in terms of x

#### Algebra ➔ Formulas ➔ Angles

Form expression: angles in triangle
Form simplified expressions for the sum of the interior angles of each triangle in terms of x

#### Algebra ➔ Formulas ➔ Formula from words

Expressions from words
Form an expression for each of the given scenarios in terms of x and y

#### Algebra ➔ Formulas ➔ Substitute in values

K = 2n - 3p
n = -2, p = -3
Two negative integer variables
Calculate the value of K by substituting in two negative integer variables n and p
3s + t
Fraction values
Calculate by substituting in 2 fraction variables s and t

#### Algebra ➔ Formulas ➔ Make x the subject

y = 3x
Basic linear formulas
Use algebraic methods to make the specified variable the subject of each of the linear formulae

### Algebra ➔ Graphs

#### Algebra ➔ Graphs ➔ Linear graphs

For each linear graph or pair of points on a line, find the gradient of the line
Parallel lines
Interpret equations of form (or reducible to) y = mx + c to identify which would produce parallel lines
y = mx + c - gradient, y-intercept
For each equation of form y = mx + c identify the gradient or the y-intercept of the line

#### Algebra ➔ Graphs ➔ Identify and interpret

Identify graphs
Identify the correct equation for each of the given graphs

#### Algebra ➔ Graphs ➔ Quadratic graphs

For each quadratic equation, given a value for x, calculate a value for y

### Algebra ➔ Sequences

#### Algebra ➔ Sequences ➔ Generating terms

-4, 8, -16, ..
Term-to-term
For each arithmetic or geometric sequence, find the next term
2, 4, 6, 8, ..
Position to term
Find the value of term n for the given linear sequences

#### Algebra ➔ Sequences ➔ nth term expressions

7 - 4n
Sequence from nth term rule
Identify the sequence that follows the given linear nth term expression
2n+1
nth term rule from sequence
Choose the correct nth term expression for each of the linear sequences
3n+12
Find the nth term value
Given an nth term rule, find the value of the specified term in the sequence

### Algebra ➔ Simplify expressions

#### Algebra ➔ Simplify expressions ➔ Add and subtract

⅕x + ⅐x
Add unit fractions of like terms
Add unit fraction amounts of like terms e.g. ⅕x + ⅐x
¾x - ½x
Subtract fractions of like terms
Subtract fractional amounts of like terms e.g. ¾x - ½x

#### Algebra ➔ Simplify expressions ➔ Multiply terms

P-4p⁴ x 2p⁴
Multiply like terms
Simplify expressions by multiplying like terms with exponents e.g. 2y² x 2y²

#### Algebra ➔ Simplify expressions ➔ Brackets

(x+1)(x-1)
Expand two binomials
In each instance use FOIL or a similar technique to expand the double brackets e.g. (x + 3)² = x² + 6X + 9

#### Algebra ➔ Simplify expressions ➔ Multiply terms

P-3p x q x p
Multiply like & unlike terms
Simplify expressions by multiplying like & unlike terms with exponents and / or coefficients e.g. b x 3c² x b² x d

### Algebra ➔ Solving equations

#### Algebra ➔ Solving equations ➔ Linear equations

Terms on both sides
Use algebraic methods to rearrange and solve for x, terms on both sides, no fractions
Terms on both sides, fractions
Use algebraic methods to rearrange and solve for x, terms on both sides, with fractions
Terms on one side, fractions
Use algebraic methods to rearrange and solve for x, terms on one side, with fractions

In addition to the Algebra topics shown above, the intermediate section of Free Maths Games has 4 other top level categories of topics to choose from. Each top level category offers a full breadth of topics to cover the intermediate curriculum. Use these topics to reinforce key maths concepts in a fun and engaging way that will keep your pupils enthused and energised with the maths they are learning. The top level categories available are: