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Maths Test 004

Maths Test 004

Note
Test 004 covers chapter 3 of the Edexcel Maths AS course.
There is no time limit.
The test will remain available until midnight on 21 July 2020.
The test total is 100 marks.

1. Solve the following simultaneous equations              (10)
   1. \( x + 2y = 3 \) and \( 3x - y = 2 \)
   2. \( 3x + 2y = 4 \) and \( 2x - y = 5 \)
   3. \( x = - 5y -11 \) and \( 3x - y - 15 = 0 \)
   4. \( x - 2y + 3 = 0 \) and \( 3x - 6y = -9 \)
   5. \( 3x + 8y = 11 \) and \( x - 4y = 2 \)


2. Solve the following simultaneous equations              (10)
   1. \( x + y = 10 \) and \( xy = 5 \)
   2. \( x^2 + y^2 = 29 \) and \( x - y = 3 \)
   3. \( 2y^2 - xy = 15 \) and \( 3x - y = 0 \)
   4. \( x + y = 9 \) and \( x^2 - 3xy + 2y^2 = 0 \)
   5. \( 5y - 2x = 1 + 2x \) and \( x^2 - y^2 +3x - 20 = 21 - 2x \)


3. Draw the graphs of each equation to use to estimate the solutions to the simultaneous equations         (10)
   1. \( y = 3x - 1 \) and \( y + 2x + 2 = 0 \)
   2. \( y = x^2 + 4x - 5 \) and \( 3y = 3x - 1 \)
   3. \( y + x^2 = 4 \) and \( y - x^2 = -1 \)
   4. \( x = y^2 + 3y - 2 \) and \( y = x^2 + 3x \)
   5. \( y = x^2 - 2x - 3 \) and \( 3xy = 9 \)


4. Find the set of values of \( x \) for which                      (10)
   1. \( 3x \lt 2x + 2 \)
   2. \( 5(3x-1) + 2 \gt 3x + 1 \)
   3. \( 2 + 3(x + 2) \le 3(2x - 3) + 4 \)
   4. \( 4x \lt -2(3x + 4) + 4(x - 1) \)
   5. \( 3x + 2 \ge 4(2x + 3) - (5x - 3)\)


5. Find the set of values of \( x \) for which                      (10)
   1. \( 3x \lt 2x - 5 \) and \( 2x - 2 \gt 5x - 8 \)
   2. \( 2(x - 1) \gt x + 2 \) and \( 3(2 - 3x) + 4 \gt x \)
   3. \( 3x - (2 - 3x) \gt 16 \) and \( 5(x + 1) \lt (3x - 1)\)
   4. \( 2x - ( 1 - x) \lt 0 \) and \( 2(x - 2) \gt - 10 \)
   5. \( 2(x - 1) + 4 + x \gt 3(x + 2) - 2x \) and \( 5(x - 1) + 1 \lt 11 + 2x \)


6. Find the set of values of \( x \) for which                      (10)
   1. \( x^2 - 3x + 1 \lt 0 \)
   2. \( 2x^2 + 2x \gt 3 \)
   3. \( - x^2 + 3x \lt 5 - x \)
   4. \( x(x - 1) + 2 \lt -10 \)
   5. \( 2x^2 + 3x - 8 \gt x^2 - x + 4 \)


7. On a coordinate grid, shade the region that satisifes the inequalities:               (20)
   1. \( y \gt x - 2 \), \(y \lt 4x \) and \( y \le 5 -x \)
   2. \( y \lt (3 - x) (2 + x) \) and \( y + x \ge 3 \)
   3. \( y \gt (x - 3)^2 \), \( y + x \ge 5 \), and \( y \lt x - 1 \)
   4. \( y \gt x^2 - 2 \) and \( y \le 9 - x^2 \)


8. The curves \( kx^2 - xy + (k + 1)x = 1 \) and \( -\frac{k}{2}x + y = 1 \) where k is a non-zero constant, intersect at a single point.
   1. Find the value of \( k \)                                              (5)
   2. Give the coordinates of the point of intersection of the curves.        (3)
   3. Write the equations.                                               (2)


9. Find the values of \( k \) for which \( kx^2 + 8x + 5 = 0 \) has real roots.          (3)


10. Find the values of \( k \) for which \( 2x^2 + 4kx - 5k = 0 \), where \( k \) is a constant, has no real roots.          (3)


11. Find the set of values of \( x \) for which the curve with equation \( y = 2x^2 + 3x - 15 \) is below the line with the equation \( y = 8 + 2x\).          (4)

End of Maths Test 004