Mr. J Gallagher
Algebra - Worksheet
Junior Cert - Ordinary Level
Add and subtract the like terms
Simplify the following expressions
a)16a – 4c + 10b + 6a – 7b + 3c
b)-14x + 11y + 4x – 13y
Evaluating Expressions
Evaluate the following expressions when x = 2, y = -3
a)x2 – 4xy
b)6xy + 3x2y
c)x2 – y2
Multiplying Brackets
Simplify the following expressions
a)4(3x - 4) + 3(-2x + 5)
b)-3(2x – 6y) – 4(x – y)
c)(3x - 4) (-2x + 5)
Simplifying Fractions
Simplify the following expression
a), hence solve
b), hence solve
c), hence solve
Inequalities
Linear – Solve the following inequality and graph your solution on a number line
a)2x – 3 5, x R
b)3x – 1 > 8, x N
c)4x + 3 < 3x + 10, x R
Factorising
Factorise the following expressions
a)x2 + 2x
b)2y2 + 4y
c)4xy – 12x2
d)3x2y – 15xy
e)x2 – 49
f)4x2 – 25
g)36y2 – 16x2
h)ax + ay + bx + by
i)3ax – 2ay + 3bx – 2by
j)4x – 4y + abx – aby
a)Factorise x2 – x – 20
hence solve x2 – x – 20 = 0
b)Factorise x2 + 3x – 10
hence solve x2 + 3x – 10 = 0
c)Factorise x2 + 4x + 3
hence solve x2 + 4x + 3 = 0
Linear Equations
Solve the following equations
a)x + 2 = 0
b)4x + 3 = 15
verify your answer for b)
c)3x – 1 = 2x + 11
d)3(x + 2) = 0
e)4(x – 2) = 3(2x + 4)
f)2(2x + 1) – 3 (x – 1) = 9
Simultaneous Equations
Linear Simultaneous Equations – Solve the following for x & y
a)x – y = 1
2x + y = 11
b)3x + 2y = 5
2x – y = 1
c)2x + 3y = 7
5x + y = 11
d)x + 4y = 3
4x + 3y = -1
Evaluating Functions
If the function f(x) = 5x – 2, find
a)f(-1)
b)f(3)
c)f(x) = 3
If the function f(x) = x2 – 6, find
a)f(-1)
b)f(3)
c)f(x) = 3
Graphing Functions
Graph the following linear functions
a)f: x 2x + 1 in the domain, -3 x 3.
- Find the value when f(x) = 0
- Find the value when x = 2.5
b)f: x 3x – 2 in the domain, -2 x 4.
Find the value when f(x) = 0
Find the value when x = 2.5
Graph the following quadratic functions
a)f: x x2 – 4x – 5 in the domain, -3 x 3.
Find the values when f(x) = 0
Find the value when x = 2.5
b)f: x 2x2+ 4 in the domain, -3 x 3.
Find the values when f(x) = 0
Find the value when x = 2.5
Real Life Examples
- Brendan thinks of a number, adds three and the answer is fifteen. Represent this statement as an equation. Solve the equation and check your answer.
- Ryan thinks of a number then subtracts five and the answer is ten. Represent this statement as an equation. Solve the equation and then check your answer.
- A farmer has a number of cows and he plans to double that number next year, when he will have twenty-four. Represent this statement as an equation. Solve the equation and check your answer.
- A new student enters class and the class now has twenty-five students. Represent this statement as an equation. Solve the equation and check your answer.
- The temperature increases by eighteen degrees and the temperature is now fifteen degrees. Represent this statement as an equation. Solve the equation and check your answer.
- A farmer doubles the amount of cows he has and then buys a further three cows. He now has twenty-nine. Represent this statement as an equation. How many did he originally have?
- Emma and her twin brother will have a total age of forty-two in five years time. Represent this statement as an equation. How old are they at the moment?
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