Specimen Assessment 1
Applications 1.1
1. Find the equation of the line that is parallel to the line 4x + 2y -5 =0, passing through the
point (2, 1).
(2)
C(1,6
2.
𝑦 = 2𝑥 − 2
B
ABCD is a kite.
Diagonal BD has the equation
𝑦 = 2𝑥 − 2 and point C has
coordinates (1 , 6 ).
Note the diagram is not
drawn to scale.
Find the equation of the
diagonal AC
A
D
3. Calculate the size of the obtuse angle between the line y =4x -3 and the
x-axis.
(2)
(2, #2.1)
4. The design of a conveyour belt in a bottling plant is shown in the diagram. If the gradient
of the belt is greater than 0.4, the bottles will fall over.
Is the design compliant with this limitation?
(1, #2.1)
You must justify your answer.
Applications 1.2
5.
The two circles are congruent. The centre of the upper circle A is (6, 6). Find the equation of
the other circle.
(2)
6. Show that the line x + 3y - 11 = 0 is a tangent to the circle ( x+1)2 + (y +6)2 = 90.
(6, #2.1)
Expressions and Functions 1.4
7.
8. Three wind turbines are to be built at points A (5, 1, 2), B(7, 5, -4) and C (10, 11, -13),
placed on a straight line. a)Show that the turbines are marked correctly in a straight
line?
b) Show that the distance between B and C is one and a half times the distance
between A and B.
You must justify your answer.
(4, #2.2)
9. The points P, Q and R lie on a straight line. If Q divides the line in the ratio 5:2 find
the coordinates of Q.
(3)
10.