Algebraic Reasoning Practice Questions

Here are four statements.

A $\;5x + 3 = 18$

B $\;2(x + 4) = 2x + 8$

C $\;x^2 = 25$

D $\;6x - x = 5x$

Write down the letters of the two statements that are identities.

Show that $4(n + 3) - 2(n - 1)$ is equivalent to $2(n + 7)$.

Write down an expression, in terms of $c$ and $w$, for Hasan's total score.

Hasan's total score is $0$.

Hasan says, "This means I cannot have answered any questions at all."

Explain why Hasan could be wrong.

Show that the sum of three consecutive integers is always a multiple of $3$.

Bella says,

"The sum of four consecutive integers is always a multiple of $4$."

Give an example to show that Bella is wrong.

Show that $A = 10x + 8$.

Priya says that the area of the trapezium could be $6$ cm$^2$.

Explain why Priya cannot be correct.

Show that $(x + 3)^2 - (x + 1)^2 \equiv 4(x + 2)$.

Marcus chooses two whole numbers that differ by $2$.

Use part (a) to explain why the difference between the squares of his two numbers must be a multiple of $4$.

Show that the sum of the squares of two consecutive integers is always an odd number.

Leah says,

"The sum of the squares of two consecutive integers is always a prime number."

Give an example to show that Leah is wrong.