Name: _______________________________________________

Year 9 Mathematics Test 2

Linear Graphs, Inequalities Graphs, Angles

Date:

Time: 1 hour 30 minutes Total marks available: 70 Total marks achieved: ______

Questions Q1. (a) On the grid, draw the graph of y = –2x + 4 for values of x from –1 to 5

(4)

(b) Show by shading on the grid, the region defined by all three of the inequalities y 2x + 4 y 4 x 1

Label your region R. (3)

(Total for question = 7 marks)

Q2. (a) On the grid, draw the graph of y = 3x + 2 for values of x from 2 to 3

(3) (b) Mark with a cross (×) a point on the grid that satisfies both the inequalities

x > 2 and y > 3x + 2

Label this point P. (2)

(Total for question = 5 marks)

Q3.

(a) Complete the table of values for 2x + y = 4

(2)

(b) On the grid, draw the graph of 2x + y = 4 for values of x from 1 to 4

(2)

(c) Show, by shading on the grid, the region which satisfies all three of the inequalities

x 1, y 2 and 2x + y 4

Label the region R.

(2)

(Total for Question is 6 marks)

Q4. Here is the straight line L drawn on a grid.

Find an equation for L.

...........................................................

(Total for question = 2 marks)

Q5.

(a) The straight line L passes through the points (0, 12) and (10, 4). Find an equation for L.

........................................................... (3)

(b) Find an equation of the straight line which is parallel to L and passes through the point (5, 11).

........................................................... (2)

(Total for Question is 5 marks)

Q6. The points (1, –1) and (4, 7) lie on the straight line L.

Find an equation for L.

Give your equation in the form ax + by= c where a, b and c are integers.

...........................................................

(Total for question = 4 marks)

Q7.

(a) Find the gradient of the line with equation 3x + 4y = 10

........................................................... (3)

(b) Find the coordinates of the point of intersection of the line with equation 3x + 4y = 10 and the line with equation 5x 6y = 23 Show your working clearly.

(.............................. , ..............................) (5)

(Total for question is 8 marks)

Q8.

ABCD is a parallelogram. Angle DCB = 110° X is the point on DC such that AX bisects the angle DAB.

Calculate the size of angle AXC.

........................................................... °

(Total for question = 4 marks)

Q9. Here is a regular 10-sided polygon.

Work out the value of x. Show your working clearly.

x = ...........................................................

(Total for question = 4 marks)

Q10.

ABC and EDC are straight lines. AE is parallel to BD. Angle EAC = 40° Angle ACE = 30° Work out the size of angle x. Give reasons for your answer.

x = ........................................................... °

(Total for question = 3 marks)

Q11.

ABCDEF is a hexagon. G is a point on AF. H is a point on BC. GH is parallel to AB. (a) Give a reason why x = 107

..............................................................................................................................................

(1) (b) Work out the value of y.

y = ........................................................... (4)

(Total for question = 5 marks)

Q12. Each interior angle of a regular polygon is 156°

Work out the number of sides of the polygon.

...........................................................

(Total for question = 3 marks)

Q13. Each exterior angle of a regular polygon is 18°

Work out the number of sides of this regular polygon.

...........................................................

(Total for question = 2 marks)

Q14.

The diagram shows two congruent regular pentagons and part of a regular n-sided polygon A. Two sides of each of the regular pentagons and two sides of A meet at the point P. Calculate the value of n. Show your working clearly.

n = ...........................................................

(Total for question = 5 marks)

Q15.

EFG is a triangle. AB is parallel to CD.

(a) Write down the value of p

p = ........................................................... (1)

(b) Write down the value of q

q = ........................................................... (1)

Here is a hexagon.

(c) Work out the value of x

x = ........................................................... (3)

(Total for question = 5 marks)

Q16.

Work out the size of each exterior angle of a regular polygon with 15 sides.

........................................................... °

(Total for Question is 2 marks)