Download National 5 Mathematics Practice Unit Assessment Relationships 1.3

National 5 Mathematics
Practice Unit Assessment
Relationships 1.3
1) Solve the following quadratic equations.
a) (x + 2)(x – 3) = 0
d) x2 + 3x – 4 = 0
b) (x – 8)(x – 7) = 0
e) x2 – 2x – 35 = 0
c) (x + 11)(x + 7) = 0
f) 2x2 – 15x + 18 = 0
2) Evaluate the discriminant for the following quadratic equations.
a) y = x2 + 5x + 2
e) y = 3x2 – 2x + 1
b) y = x2 + 3x – 4
f) y = 5 – 2x + 4x2
c) y = 2x2 + x – 8
g) y = 2 + 6x – 7x2
d) y = x2 – 9x + 3
h) y = 5x2 – 4
3) David thinks the value of the discriminant for the quadratic equation y = 3 – 2x – 4x2 is 50
and Duncan thinks it is 44. Their teacher says that they are both wrong but which answer is
closer to the correct answer? Justify your answer.
4) Solve the following quadratic equations giving the foots correct to one decimal place.
a) x2 + 8x + 2 = 0
d) 5x2 – 9x – 3 = 0
b) x2 + 4x – 6 = 0
e) 4x2 – 2x – 8 = 0
c) 3x2 + 11x + 1 = 0
f) 6 + 3x – 7x2 = 0
5) Explain why you cannot solve the quadratic equation 2x2 + 3x + 5 = 0.
6) For each of the following quadratic equations evaluate the discriminant and hence state the
nature of the roots.
a) y = x2 + 3x + 2
d) y = 2x2 – 8x + 1
b) y = x2 + 7x – 4
e) y = 4x2 – 28x + 49
c) y = x2 + 6x + 9
f) y = 10 + 4x – 7x2