Wednesday, January 2, 2019

Algebra (CIE)

$\def\D{\displaystyle}$
1 (CIE 2012, s, paper 12, question 4)
Solve the simultaneous equations
$\D 5x + 3y = 2$ and $\D \frac{2}{x}-\frac{3}{y}=1.$
[5]

2 (CIE 2012, w, paper 22, question 1)
Solve the equation $\D |7x + 5| = |3x – 13|.$ [4]

3 (CIE 2012, w, paper 23, question 1)
Solve the equation $\D |5x + 7| = 13.$ [3]

4 (CIE 2015, s, paper 22, question 5)
Solve the simultaneous equations
$\D \begin{array}{rcl}
2x^2+3y^2&=&7y,\\x+y&=&4.
\end{array}$
[5]

5 (CIE 2016, w, paper 21, question 1)
Solve the equation $\D |4x - 3 |= x.$ [3]
     
6 (CIE 2017, march, paper 22, question 1)
Solve the equation $\D |5 - 3x |= 10.$ [3]

7 (CIE 2017, s, paper 22, question 1)
Solve $\D |5x + 3 |= |1 - 3x |.$ [3]

8 (CIE 2017, w, paper 21, question 4)
Solve the following simultaneous equations for $\D x$ and $\D y,$ giving each answer in its simplest surd form.
$\D \begin{array}{rcl}
\sqrt{3}x + y& =& 4\\
x - 2y &=& 5 \sqrt{3}
\end{array} $
[5]

9 (CIE 2017, w, paper 22, question 1)
If $\D z = 2 + \sqrt{3}$ find the integers $\D a$ and $\D b$ such that $\D az^2 + bz = 1 + \sqrt{3}.$  [5]

10 (CIE 2017, w, paper 22, question 3)
Solve the inequality $\D |3x - 1|>  3 + x.$ [3]

11 (CIE 2017, w, paper 23, question 2)
Solve the equation $\D |3x - 1| = |5 + x| .$  [3]

12 (CIE 2018, s, paper 11, question 1)
Solve the equations
$\D \begin{array}{rcl}
y - x &=& 4,\\
x^2 + y^2 - 8x - 4y - 16 &=& 0.
\end{array}$
[5]

Answers

1.  $\D x = \frac{1}{5},y=\frac{1}{3}$:
$\D x = 4; y = -6$
2. $\D x = 0.8;-4.5$
3. $\D 1.2,-4$
4. $\D x = \frac{4}{3},
\frac{8}{3}$
$\D x = 3; y = 1$
5. $\D x = 1; 0.6$
6. $\D -5/3; 5$
7. $\D x = -2; x = -0.25$
8. $\D x = 2 +\sqrt{3},y=1-2\sqrt{3}$
9. $\D a = 1; b = -3$
10. $\D x > 2; x < -.5$
11. $\D x = -1$
12.  $\D x = 4; y = 8$
$\D x = -2; y = 2$

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