Expressions, Equations and Identities worksheet
10 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.
-
3 marks
Here is an expression.
\(8t^2 - 4t + 2\)
(a)State how many terms the expression has.
(b)State the coefficient of \(t^2\).
(c)State the constant term.
-
1 mark
Here are four statements.
A \(3x - 9\)
B \(3x - 9 = 27\)
C \(y = 3x - 9\)
D \(5(x + 5) \equiv 5x + 25\)
Write down the letter of the statement that is a formula. -
3 marks
Tomas charges for repairing a bike using the formula
\(C = 9n + 17\)
where \(C\) is the total charge in pounds and \(n\) is the number of parts. The call-out fee is included in the formula.
(a)Work out the total charge when \(n = 7\).
(b)Explain why \(C = 9n + 17\) is a formula and not an equation.
-
2 marks
\(8(x + c) \equiv 8x - 56\)
Find the value of \(c\).
-
2 marks
Show that
\(6(x - 1) + 7 \equiv 6x + 1\)
-
3 marks
Here is an expression.
\(9y^2 - 4y + 2\)
(a)Write down how many terms the expression has.
(b)Write down the coefficient of \(y^2\).
(c)Write down the constant term.
-
1 mark
Here are four statements.
A \(3x - 1\)
B \(3x - 1 = 13\)
C \(y = 3x - 1\)
D \(6(x - 6) \equiv 6x - 36\)
Write down the letter of the statement that is an identity. -
3 marks
Aisha charges for cleaning windows using the formula
\(C = 9n + 44\)
where \(C\) is the total charge in pounds and \(n\) is the number of windows. The travel charge is included in the formula.
(a)Calculate the total charge when \(n = 14\).
(b)Explain why \(C = 9n + 44\) is a formula and not an equation.
-
2 marks
\(6(x + c) \equiv 6x - 48\)
Find the value of \(c\).
-
2 marks
Show that
\(8(x + 4) - 1 \equiv 8x + 31\)
Answers
-
(a) \(3\)
(b) \(8\)
(c) \(2\) - C
-
(a) \(\text{£}80\)
(b) It is a rule for working the charge out from the number of parts, and it holds for any number of parts. An equation such as \(9n + 17 = 80\) is true only when \(n = 7\). - \(-7\)
- Expanding gives \(6x - 6 + 7 = 6x + 1\), which is the right-hand side.
-
(a) \(3\)
(b) \(9\)
(c) \(2\) - D
-
(a) \(\text{£}170\)
(b) It is a rule for working the charge out from the number of windows, and it holds for any number of windows. An equation such as \(9n + 44 = 170\) is true only when \(n = 14\). - \(-8\)
- Expanding gives \(8x + 32 - 1 = 8x + 31\), which is the right-hand side.