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Introduction to Polynomials: Final Assessment

Section A: Core Review

Question 1mcq
Factorise x2−16x^{2}-16.
A.x(x−4)x(x-4)
B.(x−4)2(x-4)^{2}
C.(x+4)2(x+4)^{2}
D.(x−4)(x+4)(x-4)(x+4)
Question 2mcq
Which option is an equation, not just an algebraic expression?
A.x2−5xx^{2}-5x
B.2x+32x+3
C.2x+3=112x+3=11
D.7a−4b7a-4b
Question 3mcq
Use the identity (a+b)2=a2+2ab+b2(a+b)^{2}=a^{2}+2ab+b^{2} to find (x+4)2(x+4)^{2}.
A.x2+4x+16x^{2}+4x+16
B.x2+8x+16x^{2}+8x+16
C.x2+8x+8x^{2}+8x+8
D.x2−8x+16x^{2}-8x+16
Question 4mcq
Which value of xx is not allowed in the rational expression 1x−5\frac{1}{x-5}?
A.55
B.00
C.−5-5
D.66
Question 5mcq
Which expression is not a polynomial?
A.77
B.x2+4xx^{2}+4x
C.3x3−x+13x^{3}-x+1
D.x−2+4x^{-2}+4
Question 6mcq
In −4x3+7x−2-4x^{3}+7x-2, what is the coefficient of x3x^{3}?
A.−2-2
B.77
C.−4-4
D.44
Question 7mcq
Which expression is a polynomial in one variable?
A.2x−1+32x^{-1}+3
B.3x2−2x+53x^{2}-2x+5
C.1x+2\frac{1}{x}+2
D.x+1\sqrt{x}+1
Question 8mcq
Which approach correctly demonstrates the idea: Classify polynomials by degree?
A.Use the correct definition or theorem and justify each step with mathematical reasoning.
B.Ignore the given conditions and choose any formula.
C.Use only a guess because diagrams are always exact.
D.Change the question so the answer becomes easier.

Section B: Application and Reasoning

Question 9mcq
Which approach correctly demonstrates the idea: Classify polynomials by number of terms?
A.Ignore the given conditions and choose any formula.
B.Use only a guess because diagrams are always exact.
C.Change the question so the answer becomes easier.
D.Use the correct definition or theorem and justify each step with mathematical reasoning.
Question 10mcq
Which expression is a linear polynomial?
A.3x33x^{3}
B.x2+1x^{2}+1
C.4x−94x-9
D.1x\frac{1}{x}
Question 11mcq
Factorise x2−16x^{2}-16.
A.(x−4)2(x-4)^{2}
B.(x−4)(x+4)(x-4)(x+4)
C.(x+4)2(x+4)^{2}
D.x(x−4)x(x-4)
Question 12mcq
Expand (x+2)(x+4)(x+2)(x+4).
A.x2+6x+8x^{2}+6x+8
B.x2+8x+6x^{2}+8x+6
C.x2+6x^{2}+6
D.2x+62x+6
Question 13mcq
Which approach correctly demonstrates the idea: Identify linear patterns from tables?
A.Ignore the given conditions and choose any formula.
B.Use only a guess because diagrams are always exact.
C.Change the question so the answer becomes easier.
D.Use the correct definition or theorem and justify each step with mathematical reasoning.
Question 14mcq
Which approach correctly demonstrates the idea: Write a rule for a linear pattern?
A.Use only a guess because diagrams are always exact.
B.Ignore the given conditions and choose any formula.
C.Use the correct definition or theorem and justify each step with mathematical reasoning.
D.Change the question so the answer becomes easier.
Question 15mcq
Which table shows a linear relationship?
A.(1,1),(2,4),(3,9)(1,1),(2,4),(3,9)
B.(1,3),(2,5),(3,7)(1,3),(2,5),(3,7)
C.(1,8),(2,8),(3,9)(1,8),(2,8),(3,9)
D.(1,2),(2,5),(3,10)(1,2),(2,5),(3,10)
Question 16mcq
For the line y=3x−2y=3x-2, what are the slope and yy-intercept?
A.Slope 33, y-intercept −2-2.
B.Slope −2-2, y-intercept 33.
C.Slope 3x3x, y-intercept 00.
D.Slope 11, y-intercept −2-2.

Section C: Challenge and Mixed Practice

Question 17mcq
Solve the equation 2x+3=92x+3=9.
A.99
B.22
C.44
D.33
Question 18mcq
The equations x+y=8x+y=8 and x−y=2x-y=2 are solved together. What is the value of xx?
A.66
B.33
C.55
D.44
Question 19mcq
Which value of xx is not allowed in the rational expression 1x−5\frac{1}{x-5}?
A.00
B.55
C.−5-5
D.66
Question 20mcq
A student must solve a computational thinking in algebra problem accurately. Which approach shows good step-by-step mathematical thinking?
A.Apply the relevant formula step by step, showing all working.
B.Memorise the answer from a previous similar question without re-deriving.
C.Skip straight to the answer without checking intermediate steps.
D.Round all values to the nearest ten before starting the calculation.
Question 21mcq
In 5x2−3x+75x^{2}-3x+7, which part is the constant term?
A.xx
B.5x25x^{2}
C.−3x-3x
D.77
Question 22mcq
Which option is an equation, not just an algebraic expression?
A.7a−4b7a-4b
B.x2−5xx^{2}-5x
C.2x+3=112x+3=11
D.2x+32x+3
Question 23mcq
Evaluate 2x+52x+5 when x=3x=3.
A.88
B.1111
C.1010
D.1313
Question 24mcq
Which expression is a polynomial in one variable?
A.3x2−2x+53x^{2}-2x+5
B.2x−1+32x^{-1}+3
C.1x+2\frac{1}{x}+2
D.x+1\sqrt{x}+1