Kuwait University Aptitude Tests (KUAT) · Mathematics and Quantitative Reasoning

Number and Algebra

52 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 52 questions

A prize of $\$ 42$ is shared by Amy and Ben in the ratio $2:5$. How much does Ben receive?
A prize of $\$ 120$ is shared by Amy and Ben in the ratio $3:7$. How much does Ben receive?
A prize of $\$ 30$ is shared by Amy and Ben in the ratio $2:3$. How much does Ben receive?
Solve $5 x + 8 = 53$ .
Solve ${3 x + y = 15 2 x + y = 13$ . What is the value of $x - y$ ?
Solve ${x + 3 y = 31 2 x + 2 y = 30$ . What is the value of $x y$ ?
If $α$ and $β$ are the roots of $x^{2} - 9 x + 14 = 0$ , find $α + β$ .
If $α$ and $β$ are the roots of $3 x^{2} - 9 x - 84 = 0$ , find $α + β$ .
If $α$ and $β$ are the roots of $x^{2} + 5 x + 6 = 0$ , find $α \cdot β$ .
If $α$ and $β$ are the roots of $3 x^{2} - 33 x + 90 = 0$ , find $α \cdot β$ .
What is the larger root of $x^{2} - 10 x + 21 = 0$ ?
What is the larger root of $x^{2} - 7 x + 10 = 0$ ?
Simplify $\frac{5 ^{7} \times 5 ^{5}}{5 ^{2}}$ , leaving the answer in index form.
Simplify $\frac{2 ^{8} \times 2 ^{3}}{2 ^{3}}$ , leaving the answer in index form.
The first term of an arithmetic sequence is $7$ and the common difference is $4$ . Find the $24 t h$ term.
The first term of an arithmetic sequence is $8$ and the common difference is $6$ . Find the $16 t h$ term.
The first term of an arithmetic sequence is $3$ and the common difference is $5$ . Find the $22 t h$ term.
The first term of an arithmetic sequence is $7$ and the common difference is $3$ . Find the $14 t h$ term.
A geometric sequence has first term $5$ 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 $4 x - 7 < 42$ .
Find the greatest integer $x$ satisfying $2 x - 12 < 26$ .
Find the greatest integer $x$ satisfying $2 x - 8 < 29$ .
$y$ varies directly as $x$ . When $x = 3$ , $y = 3$ . Find $y$ when $x = 10$ .
$y$ varies inversely as $x$ . When $x = 3$ , $y = 4$ . Find $y$ when $x = 12$ .
$y$ varies inversely as $x$ . When $x = 3$ , $y = 2$ . Find $y$ when $x = 6$ .
$y$ varies inversely as $x$ . When $x = 6$ , $y = 6$ . Find $y$ when $x = 2$ .
If $f (x) = 3 x^{2} + 3 x + 3$ , find $f (- 3)$ .
If $f (x) = x^{2} + 4 x + 3$ , find $f (- 1)$ .
If $f (x) = 3 x^{2} - 5 x + 5$ , find $f (- 1)$ .
If $f (x) = x^{2} - x - 3$ , find $f (2)$ .
Find the minimum value of $x^{2} - 6 x + 5$ .
Find the minimum value of $x^{2} + 10 x + 19$ .
Find the minimum value of $x^{2} - 14 x + 40$ .
Find the minimum value of $x^{2} + 12 x + 28$ .
Find the minimum value of $x^{2} - 6 x + 6$ .
Find the minimum value of $x^{2} + 2 x - 2$ .
Find the minimum value of $x^{2} + 4 x + 10$ .
Find the minimum value of $x^{2} + 12 x + 44$ .
Find the remainder when $x^{3} + 2 x^{2} + 2 x + 4$ is divided by $x - 2$ .
Find the remainder when $x^{3} + 2 x^{2} + 5 x + 4$ is divided by $x - 3$ .
Find the remainder when $2 x^{3} - 4 x^{2} - 3 x + 5$ is divided by $x + 3$ .
Find the remainder when $3 x^{3} + 4 x^{2} - x + 2$ is divided by $x + 2$ .
Find the remainder when $2 x^{3} + 3 x^{2} + 2 x - 6$ is divided by $x - 1$ .
Find the remainder when $x^{3} - 2 x^{2} + 3 x + 1$ is divided by $x - 2$ .
Find the remainder when $2 x^{3} + 3 x^{2} + 2 x + 4$ is divided by $x + 1$ .
Find the remainder when $x^{3} + 3 x^{2} + 5 x + 2$ is divided by $x + 1$ .
Expand $(x + 8)^{2}$ .
Factorise $x^{2} - 5 x - 14$ .
Expand $(x + 2)^{2}$ .
Expand $(x + 5)^{2}$ .
Factorise $x^{2} - 2 x - 24$ .

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