HILLEL ACADEMY HIGH SCHOOL
MATHEMATICS
GRADE 9 (ACCELERATED)
EQUATIONS TEST #2
Section A
1) Given the expression:
2𝑥+1
𝑥−1
+
4𝑥 2 −9
2𝑥+3
a) Simplify to a single fraction
b) Hence solve
2𝑥+1
𝑥−1
+ 2𝑥+3
4𝑥 2 −9
=
2
3
2) By using the discriminant property of quadratics answer the following:
a) State whether the equation, 2𝑥 2 − 3𝑥 − 3 = 0 has two distinct solutions, one repeated solution or
no real solutions.
b) If the equation 𝑥 2 + (𝑘 − 2)𝑥 + (𝑘 + 1) = 0 has one repeated solution:
i)
show that 𝑘 2 − 8𝑘 = 0
ii) hence find 𝑘
3) Solve the following pairs of equations:
a) using substitution method
4𝑥 − 𝑦 = 52
𝑥 + 𝑦 = −2
b) using elimination method:
3(𝑥 − 1) − 2(7𝑦 + 3) = 14
5(4𝑥 + 3) + 3(4𝑦 + 1) = 66
4) Find the point(s) of intersection of the line 𝑥 + 2𝑦 = 10 and the curve 2𝑦 2 − 7𝑦 + 𝑥 = 0
PLEASE TURN OVER
Section B
5) The school tuck-shop has milk on 600mL and 1L cartons, and the number of 600mL cartons of milk
is represented as x:
a) If there are 54 cartons of milk in total, write an expression for the number of 1L cartons of milk
b) If there are 40L of milk in total, write an equation and hence find the number of each type of milk
they have.
6) The denominator of a fraction is greater than its numerator, 𝑛, by 5. If one is subtracted from both the
5
numerator and the denominator then the fraction is decreased by 42
.
a) Show that 𝒏𝟐 + 𝟗𝒏 − 𝟐𝟐 = 𝟎.
b) Hence find possible value(s) of the numerator of the original fraction.
7) The speed of a sparrow in still air is 𝒙 𝒌𝒎/𝒉𝒓 . When the wind is blowing at 𝟏 𝒌𝒎/𝒉𝒓, the sparrow
takes 5 hours to fly 𝟏𝟐 𝒌𝒎 to her nest and 𝟏𝟐 𝒌𝒎 back again. She goes out directly into the wind
and returns with the wind behind her.
a) Show that 𝟓𝒙𝟐 − 𝟐𝟒𝒙 − 𝟓 = 𝟎.
b) Hence find her speed 𝒙 in still air.
END OF TEST