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Maths Test 003

Maths Test 003

Note
Test 003 covers chapter 2 of the Edexcel Maths AS course.
There is no time limit.
The test will remain available until midnight on 17 July 2020.
The test total is 100 marks.

1. Explain each term               (10)
   1. range
   2. domain
   3. turning point
   4. roots
   5. discriminant


2. Solve the following equations         (10)
   1. \( x^2 - 4x + 3 = 0 \)
   2. \( x^2 + 11x - 12 = 0 \)
   3. \( x^2 - x - 6 = 0 \)
   4. \( x^2 - 5x + 6 = 0 \)
   5. \( x^2 - 9 = 0 \)


3. Solve the equations below         (10)
   1. \( x^2 - 4x = 0 \)
   2. \( 3x^2 + 11x + 6 = 0 \)
   3. \( -2x^2 + 11x - 12 = 0 \)
   4. \( 10x^2 - 31x + 15 = 0 \)
   5. \( - 4x^2 + 9 = 0 \)


4. Complete the square                      (10)
   1. \( x^2 + 6x \)
   2. \( x^2 - 8x -1 \)
   3. \( x^2 + x - 5 \)
   4. \( 2x^2 + 5x +3 \)
   5. \( 5x^2 - 4 \)


5. Solve by completing the square providing answers in exact form               (10)
   1. \( x^2 - 4x = 0 \)
   2. \( 2x^2 - 3x + 1 = 0 \)
   3. \( - x^2 - x + 6 = 0 \)
   4. \( 8 - 3x^2 = 0 \)
   5. \( 3x^4 + 3x^2 - 5 = 0 \)


6. Given \( p(x) = x^2 - 4x + 1\) and \( q(x) = 2x - 1 \), \( x \in \mathbb{R} \), find          (10)
   1. \( p(-1) \)
   2. \( -p(2) + 3q(1) \)
   3. \( \frac{q(5)}{2p(2)} \)
   4. \( p(x) = 2q(x) \)
   5. \( p(x) = (q(x))^2 \)


7. Sketch showing all intercepts and the turning point               (10)
   1. \( y = x^2 - 9 \)
   2. \( y = x^2 + 2x - 7 \)
   3. \( y = 3x^2 + 4x - 2 \)
   4. \( y + 2x = - x^2 + 5x + 2 \)
   5. \( x = y^2 + 4y - 2 \)


8. Find the roots of the following equations, in surd form ;          (10)
   1. \( f(x) = x - 4\sqrt{x} - 12 \)
   2. \( p(x) = x^6 - 6x^3 + 8 \)
   3. \( m(x) = x^{\frac{2}{3}} + 14x^{\frac{1}{3}} - 15 \)
   4. \( t(x) = x^4 - 12x^2 + 32 \)
   5. \( h(x) = 27x^{10} + 26x^5 - 1 \)


9. Given \( g(x) = x^2 + px + 14p - 3\), find          (10)
   1. find the discriminant in terms of \( p \)
   2. the value of \( p \) when \( g(x) \) has two equal roots
   3. the roots of \( g(x) \) when \( p = 2 \)
   4. the number of roots when \( p = -3 \)
   5. the minimum value of x, when \( p = 1 \)


10. When kicked by a girl, a football initially resting on the ground, follows a path described by the equation \( y = - 0.01x^2 + 0.975x + 16, x \gt 0 \).               (10)
    1. Rewrite \( y \) in the form \( y = A - B(x - C)^2 \).
    2. Find the distance away from the girl at which the ball is 32 cm above the ground.
    3. Find the greatest height of the ball.
    4. Find how far from the girl, the football will return to the ground.

End of Maths Test 003