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Algebra notation quiz
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Do you fully understand and have a handle on algebraic notation and terminology?
Take this quiz and find out.
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Question 1 of 10
1. Question
\(\large {{4.6}^{x}}={{6}^{x}}+{{6}^{x}}+{{6}^{x}}+{{6}^{x}}\)
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Do you understand the difference between a coefficient and an exponent and their respective functions?
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Question 2 of 10
2. Question
\(\large {{4.6}^{x}}={{6}^{x}}\times {{6}^{x}}\times {{6}^{x}}\times {{6}^{x}}\)
Correct
Incorrect
The coefficient indicates repeated addition and the exponent indicates repeated multiplication of the base.
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Question 3 of 10
3. Question
\(\large {{4}^{x}}=x+x+x+x\)
Correct
Incorrect
This is a base 4 with exponent of x. This indicates repeated multiplication, not addition. We need to multiply the 4 by itself x number of times.
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Question 4 of 10
4. Question
\(\large {{4}^{x}}=x\times x\times x\times x\)
Correct
Incorrect
Here repeated multiplication has been used, but for the incorrect value. The base is 4, not x. So the base needs to be multiplied by itself x times.
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Question 5 of 10
5. Question
\(\large -4{{x}^{-1}}=\frac{1}{4x}\)
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If you got this wrong, it means you do not fully understand the notation of negative exponents. The negative sign in exponents has a different function to the negative sign we use for subtraction or integers. Review negative exponents.
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Question 6 of 10
6. Question
\(\large -4{{x}^{-1}}=\frac{1}{-4x}\)
Correct
Incorrect
If you got this wrong, it means you do not fully understand the notation of negative exponents. The negative sign in exponents has a different function to the negative sign we use for subtraction or integers. The four is a negative number so you cannot make it positive in any way in this expression.
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Question 7 of 10
7. Question
\(\large -4{{x}^{-1}}=\frac{-4}{x}\)
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Incorrect
This is true because the -4 is an integer and stays -4. The negative exponent can be written as a positive exponent if it is moved to the denominator. This is one of the exponential laws but trying to memorize them is of little value unless you understand them.
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Question 8 of 10
8. Question
\(\large 4{{x}^{-1}}=\frac{4}{x}\)
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Incorrect
Revise negative exponents
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Question 9 of 10
9. Question
\(\large \frac{{{3}^{x}}}{3}={{1}^{x}} \)
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Incorrect
The misconception you probably have here is that you can “cancel” the 3’s. This indicates that you do not fully understand exponential notation.
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Question 10 of 10
10. Question
\(\large {{x}^{10}}\div {{x}^{2}}={{x}^{5}}\)
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You have probably applied one of the exponential laws incorrectly. Remember to understand them rather than just trying to memorize them. When dividing bases that are the same, you subtract the exponents.
Function notation Quiz
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A free assessment quiz on Function notation
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Question 1 of 10
1. Question
1 pointsIf \(\large f(x)= x^2 + 3x + 1\), then \(\large f(-1) = \)
Correct
Well done
Incorrect
Your function notation needs work
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Question 2 of 10
2. Question
1 pointsIf \(\large f(x)=3x – 1\) then \(\large f(x + h) = \)?
Correct
Great
Incorrect
Consider attending the workshop.
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Question 3 of 10
3. Question
1 pointsIf \(\large g(x)= \frac{x^2 – 6x + 3}{x-1}\), what is \(\large g(-1) = \)?
Correct
Yes that is right. Come for some enrichment anyway!
Incorrect
Revise function notation…we will be doing alot of that at the workshop.
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Question 4 of 10
4. Question
1 points\(\large f(y)= y^2 + 6y + 4\). Which of the following is equivalent to \(\large f(y)\)?
Correct
Well done
Incorrect
Revise completing the square.
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Question 5 of 10
5. Question
1 points\(\large g(x)= ax^3 + bx^2 + cx + d\). If \(\large a, b, c,\) and \(\large d\) are constants, and \(\large g(x)\) has roots -1, 5, and 3, which of the following is a factor of \(\large g(x)\)?
Correct
You are right!
Incorrect
Revise factor and remainder theorem. You will need it for cubic functions.
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Question 6 of 10
6. Question
1 points\(\large f(x) = 2^x + 1\). Which of the following is a graph of the function \(\large -f(x)\)?
Correct
Good!
Incorrect
This is a reflection across the x axis. Join us at the workshop for more revision on functions.
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Question 7 of 10
7. Question
1 points\(\large f(x)={{x}^{2}}-10x-24\)
Find the values of \(\large x\) for which \(\large f(x)>0\)Correct
You are right!
Incorrect
Your inequalities need work….come join us at the workshop
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Question 8 of 10
8. Question
1 points\(\large g(x)=\frac{3}{x}\)
The equation of this graph when it has a vertical shift of -3 units and a horizontal shift of 4 units is defined by \(\large h(x)\). What is the function for \(\large h(x)\)?Correct
Correct
Incorrect
Understanding the effects of the different variables in the hyperbola function will help you with questions such as these.
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Question 9 of 10
9. Question
1 points\(\large f(x)={{x}^{3}}-9x\)
The co-orindates of one of the turning points of this graph are:Correct
Looking good
Incorrect
This question requires an understanding of the function of the derivative in calculus.
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Question 10 of 10
10. Question
1 pointsIf the volume of a box is defined by the function: \(\large V=144x-48{{x}^{2}}+4{{x}^{3}}\)
Calculate the \(\large x\) – value such that the volume of the box is a maximum.Correct
Good work
Incorrect
This questions requires an understanding of maximizing and minimizing in calculus.
