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Sample Practice Test Questions
Which of the following is not required to define the slope-intercept equation for a line?
x-intercept
A line on the coordinate grid can be defined by a slope-intercept equation: y = mx + b. For a given value of x, the value of y can be determined given the slope (m) and y-intercept (b) of the line. The slope of a line is change in y over change in x, \({\Delta y \over \Delta x}\), and the y-intercept is the y-coordinate where the line crosses the vertical y-axis.
A joint created by welding is __________ the original metal.
as strong or stronger than
The joint created by welding is as strong or stronger than the original metal.
What is \( \frac{1}{8} \) x \( \frac{1}{5} \)?
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{1}{8} \) x \( \frac{1}{5} \) = \( \frac{1 x 1}{8 x 5} \) = \( \frac{1}{40} \) = \(\frac{1}{40}\)
Find the value of c:
5c + z = -1
-2c - 3z = -3
You need to find the value of c so solve the first equation in terms of z:
5c + z = -1
z = -1 - 5c
then substitute the result (-1 - 5c) into the second equation:
-2c - 3(-1 - 5c) = -3
-2c + (-3 x -1) + (-3 x -5c) = -3
-2c + 3 + 15c = -3
-2c + 15c = -3 - 3
13c = -6
c = \( \frac{-6}{13} \)
c = -\(\frac{6}{13}\)
What is \( \frac{3}{3} \) - \( \frac{5}{5} \)?
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50]. The first few multiples they share are [15, 30, 45, 60, 75] making 15 the smallest multiple 3 and 5 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{3 x 5}{3 x 5} \) - \( \frac{5 x 3}{5 x 3} \)
\( \frac{15}{15} \) - \( \frac{15}{15} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{15 - 15}{15} \) = \( \frac{0}{15} \) =
A = 5 ft., the green box weighs 50 lbs., and the blue box weighs 80 lbs. What does distance B need to be for this lever to balance?
fAdA = fBdB
For this problem, the equation becomes:
50 lbs. x 5 ft. = 80 lbs. x dB
dB = \( \frac{50 \times 5 ft⋅lb}{80 lbs.} \) = \( \frac{250 ft⋅lb}{80 lbs.} \) = 3.13 ft.
"For every action, there is an equal and opposite reaction." This describes which of Newton's laws of motion?
third
Newton's third law of motion states that For every action, there is an equal and opposite reaction. When an object exerts a force on another object, the second object exerts a force of equal magnitude in the opposite direction on the first object.
This tool is a(n) __________.
punch
A punch is narrow and is used to drive objects like nails (pin punch) or for making guide marks for drilling (center punch) or patterns in wood or metal.
The standard unit of energy is the:
Joule
The Joule (J) is the standard unit of energy and has the unit \({kg \times m^2} \over s^2\).