Question 1
Choose the correct definition of the quadratic formula.
ANSWER: Multiple choice type 1
A: x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}
B: x=\dfrac{-b\pm\sqrt{b^2-4ac}}{4a}
C: x=\dfrac{b\pm\sqrt{b^2-4ac}}{2a}
D: x=\dfrac{b\pm\sqrt{b^2-4ac}}{4a}
Answer: A
Marks = 1
Question 2
For the following quadratic equations, determine the values for a, b and c in the quadratic formula.
2(a) x^2+x -10=0
ANSWER: Multiple Answers (Type 1)
Answer: a = 1, b = 1, c = -10
Marks = 1
2(b) 5x^2+3x-22=0
ANSWER: Multiple Answers (Type 1)
Answer: a = 5, b = 3, c = -22
Marks = 1
2(c) -x^2+3x+1=0
ANSWER: Multiple Answers (Type 1)
Answer: a = -1, b = 3, c = 1
Marks = 1
2(d) -x^2 -x-1=0
ANSWER: Multiple Answers (Type 1)
Answer: a = -1, b = -1, c =-1
Marks = 1
Question 3
For the following quadratic equations, determine the values for a, b and c in the quadratic formula.
3(a) 2x^2+x = -10
ANSWER: Multiple Answers (Type 1)
Answer: a = 2, b = 1, c = 10
Workings:
2x^2+x -10=0
a=2, b=1, c=10
Marks = 2
3(b) 5x^2=-3x+22
ANSWER: Multiple Answers (Type 1)
Answer: a=5, b=3, c=-22
Workings:
5x^2+3x -22=0
a=5, b=3, c=-22
Marks = 2
3(c)\dfrac{x^2}{3} = x+1
ANSWER: Multiple Answers (Type 1)
Answer: a=1, b=-3, c=-3
Workings:
x^2-3x -3=0
a=1, b=-3, c=-3
Marks = 2
3(d) x^2= \dfrac{7x-22}{3}
ANSWER: Multiple Answers (Type 1)
Answer: a=3, b=-7, c=22
Workings:
3x^2 -7x+22=0
a=3, b=-7, c=22
Marks = 2
Question 4
Use the quadratic formula to solve the following quadratic equations.
Give all answers to 2 decimal places.
You must show your working.
4(a) x^2+x -10=0
ANSWER: Multiple Answers (Type 2)
Answer: x= -3.70, x = 2.70
Workings:
a = 1, b = 1, c = -10
x = \dfrac{-1 \pm \sqrt{1^2 - (4 \times 1 \times -10)}}{2}
x= -3.70 and x = 2.70
Marks = 2
4(b) 5x^2+3x-22=0
ANSWER: Multiple Answers (Type 2)
Answer: x= -2.42, x = 1.82
Workings:
a = 5, b = 3, c = -22
x = \dfrac{-3 \pm \sqrt{3^2 - (4 \times 5 \times -22)}}{10}
x= -2.42 and x = 1.82
Marks = 2
4(c) -x^2+3x+1=0
ANSWER: Multiple Answers (Type 2)
Answer:x= -0.30, x = 3.30
Workings:
a = -1, b = 3, c = 1
x = \dfrac{-3 \pm \sqrt{3^2 - (4 \times -1 \times 1)}}{-2}
x= -0.30 and x = 3.30
Marks = 2
4(d) -x^2 -x + 5 = 0
ANSWER: Multiple Answers (Type 2)
Answer: x= -2.79 and x = 1.79
Workings:
a = -1, b = -1, c = 5
x = \dfrac{1 \pm \sqrt{(-1)^2 - (4 \times -1 \times 5)}}{-2}
x= -2.79 and x = 1.79
Marks = 2
Question 5
Solve for x, using the quadratic formula;
x^2+10x+20=0
ANSWER: Multiple Choice (Type 1)
A:x = 5 \pm \sqrt{5}
B: x = 5 \pm \sqrt{10}
C: x = -5 \pm \sqrt{5}
D: x = -5 \pm \sqrt{10}
Answer: C
Workings:
a = 1, b = 10, c = 20
\dfrac{-10 \pm \sqrt{10^2 - (4 \times 1 \times 20)}}{2 \times 1}
\dfrac{-10 \pm \sqrt{20}}{2}
x = -5 \pm \sqrt{5}
Marks = 3
Question 6
Solve for x, using the quadratic formula;
x^2-2(x+5) = 4x+8
Give your answer to 2 decimal places.
ANSWER: Multiple Answers (Type 1)
Answer: x = 8.20, x = -2.20
Workings:
x^2-6x-18=0
a = 1, b = -6, c = -18
x = \dfrac{-(-6) \pm \sqrt{(-6)^2 - (4 \times 1 \times (-18))}}{2 \times 1}
= \dfrac{6 \pm \sqrt{36 - (-72)}}{2}
= \dfrac{6 \pm \sqrt{108}}{2}
= 3 \pm 3\sqrt{3}
x = 8.20, x = -2.20
Marks = 3
Question 7
Solve for x, using the quadratic formula;
3x^2-42x+147=0
ANSWER: Simple text answer
Answer:
Workings:
x^2 - 14x + 49 = 0
a = 1, b= -14, c = 49
x = \dfrac{-(-14) \pm \sqrt{(-14)^2 - (4 \times 1 \times 49)}}{2 \times 1}
= \dfrac{14 \pm \sqrt{196 - 196}}{2}
x = 7
Marks = 2
Question 8
Solve for x, using the quadratic formula.
x^2-6 = \dfrac{2x+12}{-6}
ANSWER: Multiple Choice (Type 1)
A: x = \dfrac{-1 \pm \sqrt{145}}{6}
B: x = \dfrac{-1 \pm \sqrt{48}}{6}
C: x = \dfrac{1 \pm \sqrt{145}}{6}
D: x = \dfrac{1 \pm \sqrt{148}}{6}
Answer: A
Workings:
6x^2 + 2x - 24 = 0
Simplifies to
3x^2 + x - 12=0
a = 3, b = 1, c = -12
\dfrac{-1 \pm \sqrt{1^2 - (4 \times 3 \times (-12))}}{2 \times 3}
\dfrac{-1 \pm \sqrt{145}}{6}
Marks = 3