Algebraic Reasoning (OCR GCSE Maths: Foundation): Exam Questions

Write down an example to show that each of the following two statements is not correct.

The multiples of an odd number are always odd.

 All the digits in even numbers are even.

The $n$th even number is $2n$.

Write down an expression for the next even number.

$a$ and $b$ are two consecutive odd numbers.

Give an example to show that the value of $3\left(a+b\right)$ is a multiple of $12$

$p$ is a positive number.

$n$ is a negative number.

For each statement, tick the correct box.

Which of these is a correct identity?

Circle your answer.

The diagram shows a cube with edges of length $4$ cm and cone of radius $x$ cm and height $8$ cm.

The volume of the cube is equal to the volume of the cone.

Show that $x=\sqrt{\frac{k}{\pi }}$, where $k$ is an integer.

The $n$^th odd number is $2n+1$.

The next odd number after is $2n+3$.

Explain why.

Write down an expression, in terms of $n$, for the next odd number.

Here is a right-angled triangle.

Four of these triangles are joined to enclose the square $ABCD$ as shown below.

Show that the area of square $ABCD$ is $5x^2$.

$a$ and $b$ are two even numbers.

Give an example to show that the value of $3\left(a+b\right)$ is a multiple of $6$

Show that when $a$ and $b$ are both even numbers, the value of $3\left(a+b\right)$ will always be a multiple of 6

Here is a rectangular wooden block.

The measurements of the diagram are in centimetres.

Three of these wooden box are put together to construct a shelf.

The perimeter of the shelf is $P$ cm.

Show that $P=2x+6y$

Consider the statement,

'When $x$ and $y$ are whole numbers, $P$ is always a multiple of $2$."

Is this statement correct?
You must give a reason for your answer.

$(2x-3)(x+5)=2x^2+7x-15$

Darcy says that the statement in the box is an equation.

Ellis says that the statement in the box is an identity.

One of them is correct.

Explain which one of Darcy or Ellis is correct.

Solve by factorising.

$x^2-5x-6=0$