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Maths Test 006

Maths Test 006

Note
Test 006 covers chapter 5 of the Edexcel Maths AS course.
There is no time limit - the average person should complete the test in an hour and a half.
The test will remain available until midnight on 27 July 2020.
The test total is 140 marks.

1. Find the equation of the line between each pairs of points and express in the form \( y = mx + c \).           (20)
   1. \( ( - 3, 2)( 1, 2) \)
   2. \( ( 2, -5)( 3, -2) \)
   3. \( ( -2, -7)( -5, 1) \)
   4. \( ( 3b, 2b)( - 4b, b) \)
   5. \( ( p, p^2)( q, q^2) \)


2. Write each of the equations in the prior question in the form \( ax +by + c = 0\).           (10)


3. Find the value of letter for the given gradients and points.           (20)
   1. the line joining \( ( c, 4) \) and \( ( 7, 6) \) has the gradient \( \frac{3}{4} \)
   2. the line joining \( ( 7, 2) \) and \( ( f, 3f) \) has the gradient \( 4 \)
   3. the line joining \( ( 3, -4) \) and \( ( -g, g) \) has the gradient \( -3\)
   4. the line joining \( ( -1, 2d) \) and \( ( 1, 3) \) has the gradient \( -\frac{1}{3} \)
   5. the line joining \( ( 3, -5) \) and \( ( 6, a) \) has the gradient \( 4 \)


4. Find the gradient, y-intercept and x-intercept for each equation           (20)
   1. \( -2x +3y - 2 = -3 \)
   2. \( 1 + \frac{1}{2}y + \frac{2}{3}x = 4 \)
   3. \( x - \frac{y}{2} + 4 = 5x \)
   4. \( 4y - 2\frac{1}{5}x -3 = \frac{2}{3} + y \)


5. Find the value of \( a \) and \( b \).           (20)
   1. The equation \( ax - 2y + b = 0 \) has a gradient \( 3 \) and passes through \( ( 1, 5) \)
   2. The line \( l \) passes through \( ( 1, 4) \) with gradient \( 2 \) intersects with \( 5x - 8y -15 = 0 \) at point \( P(a,b)\).
   3. The line \( l \)₁ with equation \( y + 7 = 3x \) intersects with \( l \)₂ with equation \( ax + 4y - 17 = 0 \) at \( P(-3, b) \).
   4. The line \( l \)₁ with equation \( ay -1 = 2x \) intersects with \( l \)₂ with equation \( x + by - 5 = 0 \) at \( P(1, 2) \).


6. The vertices of triangle \( ABC \) are \( A( 2, 5) \), \( B( 3, -2) \), and \( C( -4, -1 ) \).           (20)
   1. Find the equations of each side.
   2. Find the length of each side.


7. The vertices of quadrilateral \( ABCD \) have coordinates \( A( -1, 5) \), \( B( 7, 1) \), \( C( 5, -3), \) and \( D( -3, 1) \).           (30)
   1. Show that quadrilateral \( ABCD \) is a rectangle.
   2. Find the length of each side.

End of Maths Test 006