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WorksheetsUnit 1 Remediation - Geometry
Total questions: 90
Worksheet time: 45mins
Two functions are given by the equations: f(x) = 2x + 3 and g(x) = 2x + 1. Which statement is true about the graphs of these two functions?
They have the same slope and the same y-intercept.
They have the same slope but different y-intercepts.
They have different slopes but the same y-intercept.
They have different slopes and different y-intercepts.
The table below shows values of two functions, f and g: x | f(x) | g(x) 1 | 4 | 5 2 | 6 | 7 3 | 8 | 9 Which of the following describes the relationship between f and g?
g(x) = f(x) + 1
g(x) = 2 × f(x)
g(x) = f(x) − 1
g(x) = f(x) ÷ 2
Which graph shows two linear functions with the same slope but different y-intercepts?
Two lines that cross at exactly one point
Two parallel lines
Two lines that overlap exactly
Two lines that never cross and have different slopes
Function f(x) = 3x − 2 and function g(x) = −x + 4 are given. Which statement is true?
f and g have the same slope.
f and g have the same y-intercept.
f and g have different slopes and different y-intercepts.
f and g are the same function.
A verbal description says: "Function f increases by 5 for every increase of 1 in x, and function g increases by 3 for every increase of 1 in x." Which equation pair matches this description?
f(x) = 5x + 1 and g(x) = 3x + 1
f(x) = 3x + 1 and g(x) = 5x + 1
f(x) = 1x + 5 and g(x) = 1x + 3
f(x) = 5 + x and g(x) = 3 + x
The mappings below show inputs and outputs for two functions: Function f: 1 → 4 2 → 6 3 → 8 Function g: 1 → 7 2 → 9 3 → 11 What is the rule for function g in terms of function f?
g(x) = f(x) + 3
g(x) = f(x) − 3
g(x) = 2 × f(x)
g(x) = f(x)/2
Which pair of equations represents two functions with the same y-intercept but different slopes?
f(x) = 2x + 3, g(x) = 2x + 3
f(x) = 2x + 3, g(x) = 3x + 3
f(x) = 2x + 3, g(x) = 2x + 4
f(x) = 2x + 3, g(x) = 3x + 4
Given the graph of two lines, one passes through points (0, 2) and (2, 6), the other passes through (0, 2) and (2, 4). What can you conclude?
The lines have the same slope and y-intercept.
The lines have different slopes and the same y-intercept.
The table shows values for functions f and g: | x | f(x) | g(x) | |---|------|------| | 0 | 1 | 3 | | 1 | 3 | 5 | | 2 | 5 | 7 | Which equation expresses g in terms of f?
g(x) = f(x) + 2
g(x) = 2 × f(x)
g(x) = f(x) - 2
g(x) = f(x)/2
The graph of f(x) = 4x + 1 and g(x) = 4x - 3 are shown. What is true about these two functions?
They are the same function.
They have the same slope, so they are parallel.
They have different slopes, so they intersect.
They have the same y-intercept.
Which verbal description matches the functions f(x) = 3x + 2 and g(x) = 3x - 1?
Both functions increase by 3 for every increase of 1 in x, but g starts 3 units below f.
f increases by 2 and g increases by -1 for every 1 increase in x.
f and g have different slopes and y-intercepts.
g increases faster than f by 3 units.
Two functions f and g are represented in a table:
| x | f(x) | g(x) |
|---|------|------|
| 1 | 5 | 10 |
| 2 | 7 | 14 |
| 3 | 9 | 18 |
Which expression defines g in terms of f?
(a)
Two linear functions have equations f(x) = mx + 1 and g(x) = mx + 3. What can be said about these functions?
They have the same slope but different y-intercepts.
They have different slopes and the same y-intercept.
They have the same slope and y-intercept.
They have different slopes and different y-intercepts.
The graph shows two lines: one passes the points (0, 0) and (1, 2), the other passes (0, 1) and (1, 3). What is true about these lines?
They are parallel because they have the same slope.
They intersect because they have different slopes.
They are the same line.
They have different y-intercepts and slopes.
The verbal description says: "Function f doubles the input and adds 1, function g doubles the input and subtracts 2." Which equations match this description?
f(x) = 2x + 1 and g(x) = 2x - 2
f(x) = 2x - 1 and g(x) = 2x + 2
f(x) = x + 1 and g(x) = x - 2
f(x) = 2 + x and g(x) = -2 + x
The mappings show: f: 1 → 3, 2 → 5, 3 → 7 g: 1 → 4, 2 → 6, 3 → 8 Which equation expresses g(x) in terms of f(x)?
g(x) = f(x) + 1
g(x) = f(x) - 1
g(x) = 2 × f(x)
g(x) = f(x)/2
The graph of two functions f and g shows two lines intersecting at point (1, 4). If f(x) = 2x + 2, what is g(1)?
2
4
6
8
Table of values for f and g: | x | f(x) | g(x) | |---|------|------| | 1 | 2 | 6 | | 2 | 4 | 10 | | 3 | 6 | 14 | Which is the equation for g?
g(x) = 2x + 2
g(x) = 4x + 2
g(x) = 4x + 1
g(x) = 4x + (–2)
Two linear functions f and g are defined by equations: f(x) = 5x + 3 and g(x) = 5x – 1. What is the difference between the y-values of f and g when x = 2?
0
2
4
6
The verbal description says: "Function f increases by 2 every time x increases by 1. Function g increases by 4 every time x increases by 1." Which statements are true?
f has a slope of 4, and g has a slope of 2.
Both functions have the same y-intercept.
g grows twice as fast as f.
f and g are the same function.
What type of solution does the equation 2x + 3 = 7 have?
No solution
One solution
Infinite solutions
Two solutions
The equation 5x - 4 = 5x + 1 has:
One solution
No solution
Infinite solutions
Two solutions
Which equation has infinite solutions?
3x + 5 = 3x + 5
4x + 1 = 4x - 2
2x - 3 = 7
x + 4 = 10
The equation 7x + 2 = 7x + 5 is:
True for one value of x
True for all values of x
Never true
True for two values of x
The equation 4x + 1 = 4x + 1 has:
No solution
One solution
Infinite solutions
Two solutions
How many solutions does the equation 3x + 2 = 3x + 7 have?
No solution
One solution
Infinite solutions
Two solutions
Which of the following equations has exactly one solution?
2x + 3 = 2x + 3
5x + 1 = 5x + 6
x + 4 = 9
3x + 2 = 3x + 2
The equation 6x - 4 = 6x - 4 is:
True for all x (infinite solutions)
False for all x (no solution)
True for exactly one x
True for two values of x
What is the solution type for 2x + 5 = 2x - 3?
One solution
No solution
Infinite solutions
Two solutions
The equation x + 7 = 12 has:
No solution
One solution
Infinite solutions
Two solutions
The equation 4(x - 2) = 4x - 8 has:
No solution
Exactly one solution
Infinite solutions
Two solutions
Which equation has no solution?
3x + 1 = 3x + 5
5x - 2 = 5x - 2
x - 3 = 7
2x + 4 = 2x + 4
How many solutions does 7x + 3 = 7x + 9 have?
One solution
No solution
Infinite solutions
Two solutions
The equation 8x + 2 = 8x + 2 is:
True for all values of x
True for no values of x
True for exactly one value of x
True for two values of x
The equation 2x + 5 = 10 has:
No solution
One solution
Infinite solutions
Two solutions
What type of solution does 4x + 1 = 4x + 3 have?
One solution
No solution
Infinite solutions
Two solutions
The equation 5(x + 2) = 5x + 10 has:
No solution
One solution
Which equation has exactly one solution?
3x + 6 = 3x + 6
x + 5 = 9
4x + 3 = 4x + 8
2x + 1 = 2x + 1
The equation 6x + 2 = 6x + 5 has:
No solution
One solution
Infinite solutions
Two solutions
How many solutions does x - 4 = 3 have?
None
One
Infinite
Two
What does the slope m of a line represent?
The y-intercept of the line
The steepness or rate of change of the line
The distance between two points
The x-value of a point
Why is the slope the same between any two distinct points on a linear graph?
Because the line is curved
Because the rate of change is constant
Because the points are always the same
Because the y-intercept changes
Which formula is used to calculate the slope between two points (x₁, y₁) and (x₂, y₂)?
m = (x₂ - x₁) / (y₂ - y₁)
m = (y₂ - y₁) / (x₂ - x₁)
m = y₂ + y₁
m = (x₂ + x₁) / 2
The slope between points (1, 3) and (4, 9) is:
2
3
6
1
If a graph is a straight line, the slope between any two points on the line is:
Always different
Always zero
Always the same
Always negative
Why does the slope remain constant on a linear graph?
Because the graph is a curve
Because the points are randomly placed
Because the change in y over the change in x is consistent
Because the y-intercept changes
Which of the following describes the slope of a horizontal line?
Undefined
Zero
Two points on a line are (2, 5) and (6, 13). What is the slope?
8
2
1
3
What does it mean if the slope between two points is the same as the slope between another two points on the same line?
The graph is nonlinear
The graph is a straight line
The points are identical
The y-intercept is zero
If the slope between (x₁, y₁) and (x₂, y₂) is 4, what will be the slope between (x₂, y₂) and (x₃, y₃) on the same line?
0
4
-4
Depends on the points
The slope of a line is calculated as m = (y₂ - y₁) / (x₂ - x₁). What happens if x₂ = x₁?
Slope is zero
Slope is undefined
Slope is positive
Slope is negative
12. A linear graph has a constant slope because:
the rate of change between variables remains the same
the graph curves upward or downward
the slope increases as x increases
the slope decreases as y increases
Which situation describes a line with a slope of 0?
A vertical line
A horizontal line
A diagonal line slanting upwards
A diagonal line slanting downwards
The slope between points (3, 7) and (5, 11) is:
2
4
1
3
What does it mean if the slopes between different pairs of points on a graph are different?
The graph is linear
The graph is nonlinear
The graph is horizontal
The graph is vertical
How can you tell from a graph that the slope is the same between any two points?
The graph is curved
The graph is a straight line
The points have the same y-value
The points have the same x-value
Which of the following is true about the slope of a line?
It changes depending on which points you pick
It is always positive
The slope between points (0, 0) and (2, 6) is:
3
2
6
4
Why is slope called the "rate of change"?
Because it shows how fast y changes as x changes
Because it shows the total distance between points
Because it shows the y-intercept
Because it shows the x-intercept
The slope of a line passing through points (1, 2) and (3, 10) is:
4
3
5
6
Given the table: | x | y | |---|---| | 0 | 3 | | 1 | 5 | | 2 | 7 | What is the slope of the line?
3
2
5
7
Using the same table above, what is the y-intercept?
3
0
-1
5
What is the value of y when x = 1?
0
3
5
7
What is the value of y when x = 2?
0
3
5
7
Given the graph of a line that crosses the y-axis at 4 and has a slope of -1, what is the equation of the line?
y = -x + 4
y = x + 4
y = -4x + 1
y = 4x - 1
The table below shows values of x and y: | x | y | |---|---| | 1 | 6 | | 2 | 10 | | 3 | 14 | What is the slope?
4
6
10
14
From the graph, a line passes through points (0, -2) and (3, 4). What is the slope?
2
-2
3
4
Given the table: | x | y | |---|---| | 0 | 1 | | 1 | 3 | | 2 | 5 | What is the slope?
1
2
3
4
Given the table: | x | y | |---|---| | 0 | 1 | | 1 | 3 | | 2 | 5 |
What is the y-intercept?
0
1
3
5
From the graph, a line passes through (0, 5) and (2, 9). What is the slope?
2
4
5
9
What is the slope?
1
2
3
6
What is the y-intercept of the line represented by the table in Question 17?
0
1
2
3
Write the linear equation for the table in Question 17.
y = 2x
y = x + 2
y = 3x + 1
y = 6x + 0
From the graph, a line passes through points (0, 0) and (4, 8). What is the equation of the line?
y = 2x
y = 4x
y = 8x
y = x + 4
What is √400?
18
19
20
21
What is √225?
12
13
14
15
Which of the following is a perfect square?
110
121
130
150
What is √81?
7
8
9
10
What is √196?
12
13
14
15
What is √256?
14
15
16
17
What is √169?
11
12
13
14
What is √100?
8
9
10
11
What is √36?
4
5
6
7
What is ³√27?
2
3
4
5
What is ³√125?
2
3
4
5
What is ∛64?
3
4
5
6
What is ∛343?
6
7
8
9
What is ∛512?
7
8
9
10
What is ∛1000?
8
9
10
11
Which number is a perfect cube?
150
216
250
300
