Gobezoch › Textbooks › Mathematics Grade 9

Mathematics Grade 9 Unit 3: SOLVING EQUATIONS

national exam questions have come from this unit. It runs 46 pages; one careful study pass takes about 3.5 hours, and its difficulty is harder among Mathematics units. Each section below lists the questions set from it, with the year, and opens the page that teaches it.

Read this unit
3.1 Revision on Linear Equation in One Variable · read p. 106
Not asked in a national paper yet.
3.2 Systems of Linear Equations in Two Variables · read p. 106
  • 2018 E.C., Q15 – Let $r_1$ and $r_2$ be the roots of the quadratic equation $2x^2+3x-4=0$. Which one of the following is equal to $\frac{1}{r_1^2}+\frac{1}{r_2^2}$?
  • 2018 E.C., Q45 – What is the solution set for the radical equation $\sqrt{x^2+3x}=2$?
  • 2017 E.C., Q18 – What is the solution set of the equation $|2x - 3| - 1 = 0$?
  • 2017 E.C., Q32 – Given the system of linear equations $\begin{cases}a_1x+b_1y=c_1\a_2x+b_2y=c_2\end{cases}$, where $a_1, a_2, b_1, b_2, c_1, c_2\in\mathbb{R}$ and $a_2, b_2, c_2\ne 0$, then which of the following is true?
  • 2016 E.C., Q10 – What is the solution set of the equation $\log_{4}(x+1)-2\log_{4}x=0.5$?
  • 2016 E.C., Q20 – Which one of the following is the solution set of the equation $(\sqrt{16})^{2x-1}=(\sqrt[3]{4096})^{3x-5}$?
  • 2016 E.C., Q43 – Which one of the following is the solution of the equation $(243)^{2x-3}= rac{(81)^{-3x+2}}{3}$ in the set of real numbers?
  • 2016 E.C., Q32 – Let $r_1$ and $r_2$ be the roots of a quadratic equation $ax^2+bx+c=0$, such that $r_1+r_2=-2.5$ and $r_1r_2=1.5$. Which one of the following can be the values of $a$, $b$ and $c$ respectively?
  • 2015 E.C., Q8 – Which one of the following interval(s) is the solution set of the quadratic inequality $10x^2 - 4x - 6 < 8x^2 + 4x - 12$?
  • 2015 E.C., Q41 – The solution set of the system $\begin{cases}2x-y+3z=1\x+y+3z=5\x-y+z=-1\end{cases}$ is
  • 2015 E.C., Q10 – Which one of the following expressions is equal to $\frac{x-3}{x+1}\div\frac{x+1}{x-1}$?
  • 2014 E.C., Q42 – Which one of the following intervals is the solution set of the inequality x 2 - 5x + 6 ≤ 0?
  • 2014 E.C., Q40 – The solution set of the equation given by $\log(x^2-3)=2\log(x-1)$ is:
  • 2014 E.C., Q43 – What is the solution of the system of linear equations $\begin{cases}2x+7y=-5\5x+11y=2\end{cases}$
  • 2014 E.C., Q7 – In rolling a fair die, what is the probability of obtaining 3 or 5?
3.3 Solving Non-linear Equations · read p. 123
Not asked in a national paper yet.
3.4 Applications of Equations · read p. 143
  • 2013 E.C., Q63 – A position of a particle is given by the equation $S(t) = 4t^3 - 4t + 1$ where $t$ is measured in seconds and $S$ in meters. Which of the following is NOT true about the motion of the particle?