GCE O/L Mathematics (Sri Lanka) · Mathematics

Algebra and Equations

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

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All 72 questions

Solve $x^{2} - x - 12 = 0$ and give the larger root.
Solve the simultaneous equations $2 x + 3 y = 38$ and $x - 4 y = - 25$ . Find the value of $x + y$ .
If $y = 4 x^{2} - 6$ , find $x$ when $y = 58$ and $x > 0$ .
Find the sum of the first $16$ terms of the arithmetic progression $6, 8, 10, 12, \dots$
The length of a rectangle is $2 cm$ more than its width. Its area is $15 cm^{2}$ . Find the width.
In an arithmetic progression the term number $3$ is $6$ and the term number $6$ is $18$ . Find the term number $25$ .
Expand and simplify $(4 x - 5)^{2}$ .
Solve $2 x - 5 = 13$ .
Solve the simultaneous equations $2 x + 2 y = 8$ and $4 x - 3 y = - 5$ . Find the value of $x - y$ .
Find the least integer value of $x$ that satisfies $3 x + 9 \geq 17$ .
Given $v = u + a t$ , find $a$ when $v = 19$ , $u = 3$ and $t = 4$ .
Find the sum of the first $20$ terms of the arithmetic progression $8, 11, 14, 17, \dots$
Simplify $\frac{x ^{2} - 16}{x ^{2} + 7 x + 12}$ .
In an arithmetic progression the term number $4$ is $14$ and the term number $9$ is $34$ . Find the term number $24$ .
Solve $x^{2} + 4 x - 21 = 0$ and give the larger root.
Solve $\frac{x + 6}{2} = 1$ .
How many positive integers $x$ satisfy $3 x - 5 < 10$ ?
Given $v = u + a t$ , find $a$ when $v = 31$ , $u = 3$ and $t = 7$ .
Find the term number $16$ of the arithmetic progression $2, 6, 10, 14, \dots$
The length of a rectangle is $4 cm$ more than its width. Its area is $117 cm^{2}$ . Find the width.
Simplify $\frac{x ^{2} - 36}{x ^{2} + 10 x + 24}$ .
In an arithmetic progression the term number $6$ is $21$ and the term number $10$ is $37$ . Find the term number $25$ .
Using $a^{2} - b^{2} = (a - b) (a + b)$ , evaluate $4 0^{2} - 2^{2}$ .
Solve $3 x - 5 = - 2$ .
Solve the simultaneous equations $2 x + y = 4$ and $x - y = 5$ . Find the value of $x + y$ .
Find the least integer value of $x$ that satisfies $2 x + 9 \geq 25$ .
If $y = 6 x^{2} - 3$ , find $x$ when $y = 93$ and $x > 0$ .
Find the sum of the first $20$ terms of the arithmetic progression $3, 9, 15, 21, \dots$
The length of a rectangle is $6 cm$ more than its width. Its area is $187 cm^{2}$ . Find the width.
In an arithmetic progression the term number $6$ is $29$ and the term number $10$ is $49$ . Find the term number $25$ .
Expand and simplify $(x - 5) (x + 1)$ .
Solve $x^{2} - 6 x - 16 = 0$ and give the larger root.
Solve $\frac{x + 3}{4} = 4$ .
Solve the simultaneous equations $3 x + 2 y = - 9$ and $3 x - 4 y = 9$ . Find the value of $x + y$ .
How many positive integers $x$ satisfy $3 x - 7 < 14$ ?
Given $v = u + a t$ , find $a$ when $v = 41$ , $u = 6$ and $t = 7$ .
Find the term number $10$ of the arithmetic progression $2, 5, 8, 11, \dots$
Simplify $\frac{x ^{2} - 4}{x ^{2} + 5 x + 6}$ .
In an arithmetic progression the term number $4$ is $16$ and the term number $8$ is $36$ . Find the term number $19$ .
Solve $\frac{x + 9}{3} = 6$ .
Solve the simultaneous equations $x + y = 3$ and $3 x - 4 y = 2$ . Find the value of $x - y$ .
How many positive integers $x$ satisfy $5 x - 6 < 29$ ?
Given $v = u + a t$ , find $a$ when $v = 13$ , $u = 7$ and $t = 2$ .
Find the sum of the first $8$ terms of the arithmetic progression $4, 10, 16, 22, \dots$
The length of a rectangle is $7 cm$ more than its width. Its area is $198 cm^{2}$ . Find the width.
Simplify $\frac{x ^{2} - 1}{x ^{2} + 6 x + 5}$ .
In an arithmetic progression the term number $4$ is $11$ and the term number $8$ is $23$ . Find the term number $17$ .
Expand and simplify $(x - 6) (x + 7)$ .
Solve $\frac{x + 5}{5} = 5$ .
Solve the simultaneous equations $4 x + y = 18$ and $x - 2 y = 9$ . Find the value of $x + y$ .
How many positive integers $x$ satisfy $2 x - 4 < 8$ ?
If $y = 6 x^{2} - 7$ , find $x$ when $y = 89$ and $x > 0$ .
Find the sum of the first $11$ terms of the arithmetic progression $5, 11, 17, 23, \dots$
Simplify $\frac{x ^{2} - 16}{x ^{2} + 6 x + 8}$ .
In an arithmetic progression the term number $6$ is $26$ and the term number $11$ is $51$ . Find the term number $15$ .
Expand and simplify $(4 x + 5)^{2}$ .
Solve $3 x + 8 = 5$ .
Given $v = u + a t$ , find $a$ when $v = 36$ , $u = 6$ and $t = 6$ .
Find the sum of the first $13$ terms of the arithmetic progression $4, 7, 10, 13, \dots$
The length of a rectangle is $2 cm$ more than its width. Its area is $99 cm^{2}$ . Find the width.
Simplify $\frac{x ^{2} - 36}{x ^{2} + 7 x + 6}$ .
Expand and simplify $(x + 6) (x - 2)$ .
Solve $3 x + 7 = 10$ .
Find the least integer value of $x$ that satisfies $2 x + 6 \geq 30$ .
Given $v = u + a t$ , find $a$ when $v = 35$ , $u = 7$ and $t = 7$ .
Find the term number $11$ of the arithmetic progression $6, 8, 10, 12, \dots$
The length of a rectangle is $7 cm$ more than its width. Its area is $144 cm^{2}$ . Find the width.
Simplify $\frac{x ^{2} - 9}{x ^{2} + 5 x + 6}$ .
In an arithmetic progression the term number $3$ is $14$ and the term number $6$ is $26$ . Find the term number $21$ .
Expand and simplify $(2 x - 2)^{2}$ .
Factorise $20 x^{2} - 4 x$ completely.
Solve $\frac{x + 7}{4} = 7$ .

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