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Quadratic Equations Final Assessment

Section A: Core Concepts

Question 1mcq
Which equation is not quadratic?
A.5x+9=05x+9=0
B.x2+1=0x^2+1=0
C.2x2−3x=02x^2-3x=0
D.x(x−4)=0x(x-4)=0
Question 2mcq
Convert x2=5x+14x^2=5x+14 to standard form.
A.x2−5x−14=0x^2-5x-14=0
B.x2+5x+14=0x^2+5x+14=0
C.x2−5x+14=0x^2-5x+14=0
D.x2+14x−5=0x^2+14x-5=0
Question 3mcq
Solve x2−9=0x^2-9=0.
A.x=3,−3x=3,-3
B.x=9,−9x=9,-9
C.x=3x=3
D.x=−3x=-3
Question 4mcq
Solve x2+6x=0x^2+6x=0.
A.x=0,−6x=0,-6
B.x=6,−6x=6,-6
C.x=0,6x=0,6
D.x=−6x=-6 only
Question 5mcq
Which formula should be used to solve ax2+bx+c=0ax^2+bx+c=0?
A.x=−b±b2−4ac2ax=\frac{-b\pm\sqrt{b^2-4ac}}{2a}
B.x=b±b2+4ac2ax=\frac{b\pm\sqrt{b^2+4ac}}{2a}
C.x=−b±b2−4acax=\frac{-b\pm\sqrt{b^2-4ac}}{a}
D.x=−c±c2−4ab2ax=\frac{-c\pm\sqrt{c^2-4ab}}{2a}
Question 6mcq
Simplify 72\sqrt{72}.
A.626\sqrt{2}
B.12212\sqrt{2}
C.898\sqrt{9}
D.383\sqrt{8}

Section B: Solving Skills

Question 7mcq
For 2x2−3x+1=02x^2-3x+1=0, what is DD?
A.11
B.1717
C.−1-1
D.55
Question 8mcq
If D=0D=0, the roots are:
A.real and equal
B.real and distinct
C.not real
D.always negative
Question 9mcq
Find pp if x2+px+9=0x^2+px+9=0 has equal roots and p>0p>0.
A.66
B.33
C.99
D.1212
Question 10mcq
The square of a number exceeds the number by 2020. If the number is xx, which equation is formed?
A.x2−x−20=0x^2-x-20=0
B.x2+x−20=0x^2+x-20=0
C.x2−20x−1=0x^2-20x-1=0
D.2x−20=02x-20=0
Question 11mcq
Solve the number problem x2−x−20=0x^2-x-20=0.
A.x=5x=5 or −4-4
B.x=4x=4 or −5-5
C.x=10x=10 or −2-2
D.x=20x=20 or −1-1
Question 12mcq
If the number in the previous context is positive, which root is valid?
A.55
B.−4-4
C.Both roots
D.No root

Section C: Applications and Validation

Question 13mcq
Which correctly verifies x=3x=3 as a root of x2−6x+9=0x^2-6x+9=0?
A.9−18+9=09-18+9=0
B.3−18+9=03-18+9=0
C.9+18+9=09+18+9=0
D.6−9+3=06-9+3=0
Question 14mcq
For 2x2+x+1=02x^2+x+1=0, which method is safer if simple factorisation is not obvious?
A.Quadratic formula
B.Ignoring x2x^2
C.Dividing by xx
D.Taking square root of each term
Question 15mcq
A student solves (x−3)(x+5)=0(x-3)(x+5)=0 and writes x=3,5x=3,5. What is the mistake?
A.From x+5=0x+5=0, the root is −5-5, not 55.
B.From x−3=0x-3=0, the root is −3-3.
C.Both roots should be positive.
D.The equation has no roots.
Question 16mcq
A student expands (x+4)(x−1)=20(x+4)(x-1)=20 as x2+3x−4=20x^2+3x-4=20. What is the correct standard form?
A.x2+3x−24=0x^2+3x-24=0
B.x2+3x+16=0x^2+3x+16=0
C.x2−3x−24=0x^2-3x-24=0
D.x2+4x−20=0x^2+4x-20=0
Question 17mcq
Solve x2+2x−15=0x^2+2x-15=0.
A.x=3,−5x=3,-5
B.x=−3,5x=-3,5
C.x=1,15x=1,15
D.x=−1,−15x=-1,-15
Question 18mcq
Use the formula to solve x2+x−1=0x^2+x-1=0.
A.−1±52\frac{-1\pm\sqrt{5}}{2}
B.1±52\frac{1\pm\sqrt{5}}{2}
C.−1±5-1\pm\sqrt{5}
D.−1±32\frac{-1\pm\sqrt{3}}{2}

Section D: Mixed Challenge

Question 19mcq
What is DD for 4x2+4x+1=04x^2+4x+1=0?
A.00
B.3232
C.−12-12
D.11
Question 20mcq
The equation 4x2+4x+1=04x^2+4x+1=0 has:
A.real equal roots
B.real distinct roots
C.no real roots
D.one positive and one negative root
Question 21mcq
A train travels 300300 km. If its speed had been 1010 km/h more, the journey would take 11 hour less. If original speed is xx, which equation is correct?
A.300x−300x+10=1\frac{300}{x}-\frac{300}{x+10}=1
B.300x+10−300x=1\frac{300}{x+10}-\frac{300}{x}=1
C.300x−300(x+10)=1300x-300(x+10)=1
D.x(x+10)=300x(x+10)=300
Question 22mcq
A rectangle has area 154154 cm² and length 33 cm more than breadth. What is the breadth?
A.1111 cm
B.1414 cm
C.77 cm
D.2222 cm
Question 23mcq
In the rectangle problem x2+3x−154=0x^2+3x-154=0, why is x=−14x=-14 rejected?
A.Breadth cannot be negative.
B.It does not satisfy the equation.
C.It is not an integer.
D.It gives the same rectangle.
Question 24mcq
A student says x2+9=0x^2+9=0 has roots 33 and −3-3. What is the best correction?
A.x2−9=0x^2-9=0 has roots 33 and −3-3; x2+9=0x^2+9=0 has no real roots.
B.x2+9=0x^2+9=0 has only root 33.
C.x2+9=0x^2+9=0 has only root −3-3.
D.x2+9=0x^2+9=0 has roots 99 and −9-9.