Junior Cycle (Ireland) · Mathematics

Number and Algebra

53 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 53 questions

A prize of $\$ 54$ is shared by Amy and Ben in the ratio $4:5$. How much does Ben receive?
A prize of $\$ 48$ is shared by Amy and Ben in the ratio $3:5$. How much does Ben receive?
Solve $7 x + 6 = 62$ .
Solve $6 x + 6 = 72$ .
Solve ${3 x + 2 y = 7 3 x + 3 y = 9$ . What is the value of $x + y$ ?
Solve ${3 x + 3 y = 39 4 x + y = 34$ . What is the value of $x y$ ?
If $α$ and $β$ are the roots of $x^{2} + 2 x - 15 = 0$ , find $α \cdot β$ .
If $α$ and $β$ are the roots of $x^{2} - 9 x + 20 = 0$ , find $α + β$ .
If $α$ and $β$ are the roots of $x^{2} - 4 x - 5 = 0$ , find $α \cdot β$ .
What is the larger root of $x^{2} - 9 x + 20 = 0$ ?
What is the larger root of $x^{2} + 3 x - 28 = 0$ ?
What is the larger root of $x^{2} + 5 x + 6 = 0$ ?
Simplify $\frac{2 ^{5} \times 2 ^{4}}{2 ^{1}}$ , leaving the answer in index form.
Simplify $\frac{5 ^{8} \times 5 ^{6}}{5 ^{4}}$ , leaving the answer in index form.
The first term of an arithmetic sequence is $7$ and the common difference is $2$ . Find the sum of the first 23 terms.
The first term of an arithmetic sequence is $3$ and the common difference is $2$ . Find the sum of the first 10 terms.
The first term of an arithmetic sequence is $8$ and the common difference is $6$ . Find the $18 t h$ term.
The first term of an arithmetic sequence is $5$ and the common difference is $6$ . Find the sum of the first 11 terms.
The first term of an arithmetic sequence is $3$ and the common difference is $7$ . Find the sum of the first 19 terms.
A geometric sequence has first term $4$ and common ratio $3$ . Find its term number 5.
Find the greatest integer $x$ satisfying $3 x - 11 < 54$ .
Find the greatest integer $x$ satisfying $3 x - 10 < 20$ .
Find the greatest integer $x$ satisfying $2 x - 12 < 21$ .
$y$ varies inversely as $x$ . When $x = 2$ , $y = 6$ . Find $y$ when $x = 12$ .
$y$ varies inversely as $x$ . When $x = 4$ , $y = 12$ . Find $y$ when $x = 6$ .
$y$ varies directly as $x$ . When $x = 4$ , $y = 5$ . Find $y$ when $x = 6$ .
$y$ varies directly as $x$ . When $x = 3$ , $y = 5$ . Find $y$ when $x = 11$ .
$y$ varies directly as $x$ . When $x = 3$ , $y = 5$ . Find $y$ when $x = 10$ .
If $f (x) = 3 x^{2} - 2 x + 4$ , find $f (4)$ .
If $f (x) = x^{2} - 5 x - 1$ , find $f (- 1)$ .
If $f (x) = x^{2} - 4 x + 3$ , find $f (- 2)$ .
If $f (x) = 4 x^{2} + 3 x - 2$ , find $f (2)$ .
Find the minimum value of $x^{2} + 16 x + 62$ .
Find the minimum value of $x^{2} + 12 x + 33$ .
Find the minimum value of $x^{2} + 14 x + 46$ .
Find the minimum value of $x^{2} - 10 x + 32$ .
Find the minimum value of $x^{2} - 14 x + 42$ .
Find the minimum value of $x^{2} - 16 x + 65$ .
Find the minimum value of $x^{2} - 12 x + 29$ .
Find the minimum value of $x^{2} - 10 x + 31$ .
Find the remainder when $3 x^{3} - 4 x^{2} + 3 x + 1$ is divided by $x + 2$ .
Find the remainder when $x^{3} - x^{2} - 5 x + 2$ is divided by $x - 1$ .
Find the remainder when $2 x^{3} - 2 x^{2} - 5 x - 2$ is divided by $x - 1$ .
Find the remainder when $x^{3} - 3 x^{2} - x + 4$ is divided by $x + 2$ .
Find the remainder when $x^{3} + 4 x^{2} + 5 x + 6$ is divided by $x - 2$ .
Find the remainder when $2 x^{3} + 2 x^{2} - 2 x - 2$ is divided by $x + 3$ .
Find the remainder when $x^{3} + 4 x^{2} - 3 x + 4$ is divided by $x + 2$ .
Find the remainder when $x^{3} - 3 x^{2} + 4 x + 6$ is divided by $x + 3$ .
Factorise $x^{2} + x - 12$ .
Factorise $x^{2} + 3 x - 54$ .
Factorise $x^{2} + 4 x - 45$ .
Factorise $x^{2} - 3 x - 28$ .
Expand $(x + 9)^{2}$ .

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