General Secondary Certificate (Tawjihiya Kuwait) · Pure Mathematics

Number and Algebra

49 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 49 questions

A prize of $\$ 90$ is shared by Amy and Ben in the ratio $3:7$. How much does Ben receive?
A prize of $\$ 84$ is shared by Amy and Ben in the ratio $2:5$. How much does Ben receive?
A prize of $\$ 64$ is shared by Amy and Ben in the ratio $3:5$. How much does Ben receive?
Solve $5 x - 2 = 18$ .
Solve ${3 x + y = 28 2 x + 3 y = 28$ . What is the value of $x + y$ ?
Solve ${3 x + y = 27 3 x + 3 y = 33$ . What is the value of $x - y$ ?
If $α$ and $β$ are the roots of $3 x^{2} + 21 x + 36 = 0$ , find $α + β$ .
If $α$ and $β$ are the roots of $3 x^{2} + 15 x + 18 = 0$ , find $α \cdot β$ .
If $α$ and $β$ are the roots of $2 x^{2} + 4 x - 16 = 0$ , find $α + β$ .
If $α$ and $β$ are the roots of $x^{2} + 5 x + 4 = 0$ , find $α \cdot β$ .
What is the larger root of $x^{2} - 5 x + 6 = 0$ ?
What is the larger root of $x^{2} + 3 x - 18 = 0$ ?
What is the larger root of $x^{2} - 10 x + 21 = 0$ ?
Simplify $\frac{5 ^{7} \times 5 ^{4}}{5 ^{4}}$ , leaving the answer in index form.
The first term of an arithmetic sequence is $6$ and the common difference is $4$ . Find the $11 t h$ term.
The first term of an arithmetic sequence is $9$ and the common difference is $3$ . Find the $12 t h$ term.
A geometric sequence has first term $4$ and common ratio $2$ . Find its term number 4.
A geometric sequence has first term $3$ and common ratio $2$ . Find its term number 4.
Find the greatest integer $x$ satisfying $4 x - 7 < 47$ .
Find the greatest integer $x$ satisfying $3 x - 5 < 47$ .
Find the greatest integer $x$ satisfying $3 x - 10 < 53$ .
$y$ varies inversely as $x$ . When $x = 6$ , $y = 2$ . Find $y$ when $x = 12$ .
$y$ varies directly as $x$ . When $x = 6$ , $y = 4$ . Find $y$ when $x = 7$ .
$y$ varies directly as $x$ . When $x = 2$ , $y = 5$ . Find $y$ when $x = 7$ .
$y$ varies inversely as $x$ . When $x = 4$ , $y = 4$ . Find $y$ when $x = 2$ .
If $f (x) = x^{2} + x + 3$ , find $f (4)$ .
If $f (x) = x^{2} + 5 x + 4$ , find $f (2)$ .
If $f (x) = 2 x^{2} + 5 x - 1$ , find $f (4)$ .
Find the minimum value of $x^{2} - 10 x + 24$ .
Find the minimum value of $x^{2} + 2 x - 4$ .
Find the minimum value of $x^{2} - 12 x + 39$ .
Find the minimum value of $x^{2} + 6 x + 17$ .
Find the minimum value of $x^{2} + 8 x + 21$ .
Find the minimum value of $x^{2} - 14 x + 57$ .
Find the minimum value of $x^{2} - 12 x + 28$ .
Find the minimum value of $x^{2} + 2 x - 1$ .
Find the remainder when $x^{3} - 4 x^{2} - 5 x - 1$ is divided by $x - 2$ .
Find the remainder when $3 x^{3} - x^{2} - 5 x - 4$ is divided by $x - 3$ .
Find the remainder when $3 x^{3} + x^{2} + 5 x + 1$ is divided by $x + 1$ .
Find the remainder when $3 x^{3} + x^{2} + x - 6$ is divided by $x + 3$ .
Find the remainder when $3 x^{3} - x^{2} + 5 x - 5$ is divided by $x - 3$ .
Find the remainder when $2 x^{3} + 2 x^{2} - x + 3$ is divided by $x + 2$ .
Find the remainder when $3 x^{3} + 4 x^{2} - 2 x + 2$ is divided by $x - 1$ .
Find the remainder when $x^{3} - x^{2} - 3 x - 2$ is divided by $x - 1$ .
Factorise $x^{2} - 6 x - 27$ .
Factorise $x^{2} + 5 x - 36$ .
Factorise $x^{2} + 3 x - 40$ .
Factorise $x^{2} + x - 20$ .
Expand $(x + 8)^{2}$ .

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