elementary surds, graphs of linear equations, linear equation problems - One Line Questions
1.
What is the slope of the line represented by the equation $2x + 3y = 6$? —
-2/3
2.
Which of the following points is on the line $y = 3x - 1$? —
(2, 5)
3.
Which of the following points lies on the line $x - y = 2$? —
(3, 1)
4.
Rationalize the denominator of $\frac{1}{\sqrt{7} - \sqrt{3}}$ —
$\frac{\sqrt{7} + \sqrt{3}}{4}$
5.
Rationalize the denominator of $\frac{3}{\sqrt{5}}$ —
$\frac{3\sqrt{5}}{5}$
6.
Rationalize the denominator of $\frac{1}{2 + \sqrt{3}}$ —
$2 - \sqrt{3}$
7.
If $x = \sqrt{5} + \sqrt{2}$ and $y = \sqrt{5} - \sqrt{2}$, what is the value of $x^2 - y^2$? —
$8\sqrt{10}$
8.
If $x = \sqrt{10} - \sqrt{7}$, find the value of $x + \frac{1}{x}$ —
$2\sqrt{10}$
9.
If $x = 3 - \sqrt{2}$, find the value of $x - \frac{1}{x}$ —
$2\sqrt{2}$
10.
If $x = \sqrt{3}$, what is the value of $x^3$? —
$3\sqrt{3}$
11.
Simplify the expression: $\sqrt{18} + \sqrt{50} - \sqrt{32}$ —
$4\sqrt{2}$
12.
What is the value of $(\sqrt{a} + \sqrt{b})(\sqrt{a} - \sqrt{b})$? —
$a - b$
13.
Find the equation of a line with slope 2 and y-intercept 5. —
$y = 2x + 5$
14.
Which of the following equations represents a line passing through the origin (0,0)? —
$y = 2x$
15.
If $x-y=1$ and $x+y=5$, find the value of x. —
3
16.
If a line passes through points (1, 2) and (3, 6), what is its slope? —
2
17.
The graph of $y = -x + 3$ has a slope of: —
-1
18.
What is the value of $(\sqrt{3} + \sqrt{2})^2 + (\sqrt{3} - \sqrt{2})^2$? —
19.
The sum of two consecutive integers is 35. Find the smaller integer. —
16
20.
Solve the equation: $2x + 3 = 7$ —
2
21.
What is the y-intercept of the line $y = 2x + 4$? —
4
22.
Solve: $4(x-1) = 12$ —
3
23.
If $x$ is an integer such that $2x + 1 < 7$, what is the largest possible value of $x$? —
2
24.
What is the value of $(\sqrt{12})^2 \div (\sqrt{3})^2$? —
4
25.
Solve for x: $5x - (x+3) = 9$ —
3
26.
Simplify: $\sqrt{72} \div \sqrt{8}$ —
3
27.
Solve for y: $5y - 2 = 18$ —
4
28.
Simplify: $\frac{\sqrt{27}}{\sqrt{3}}$ —
3
29.
If $x+y=10$ and $x-y=2$, find the value of y. —
4
30.
If the point (a, 3) lies on the line $x + y = 7$, find the value of a. —
4
31.
If $x = \sqrt{7}$, find the value of $x^2 - 3$. —
4
32.
If $a = 2 + \sqrt{3}$, find the value of $a + \frac{1}{a}$ —
4
33.
Find the value of $x$ if $3x - 5 = 10$ —
5
34.
If $x+4 = 9$, find the value of $x$. —
5
35.
If $x = \sqrt{2}$, find the value of $(x^2 + 1)^2$ —
9
36.
If $\frac{x}{2} + \frac{x}{3} = 5$, what is the value of $x$? —
5
37.
If the point (4, k) lies on the line $3x - y = 5$, find the value of k. —
7
38.
What is the value of $\sqrt{16} + \sqrt{9}$? —
7
39.
Find x: $\frac{2x}{5} = 4$ —
10
40.
The difference between two numbers is 5. If the larger number is 12, find the smaller number. —
7
41.
Simplify: $\sqrt{50} \times \sqrt{2}$ —
10
42.
A number when added to 5 gives 12. Find the number. —
7
43.
If $\frac{1}{\sqrt{x}} = \frac{1}{3}$, find the value of x. —
9
44.
What is the sum of a number and its double if the result is 21? —
7
45.
Two numbers differ by 3. Their sum is 15. Find the larger number. —
8
46.
Find the x-intercept of the line $2x + 3y = 12$. —
6
47.
Evaluate: $(\sqrt{5})^2 \times (\sqrt{2})^2$ —
10
48.
A number is 7 more than another number. Their sum is 23. Find the smaller number. —
7
49.
If the sum of three consecutive integers is 30, find the middle integer. —
10
50.
The graph of the equation $x+y=0$ passes through which quadrant(s)? —
II and IV