end of semester exams december- 2018 practice questions

Year 9 End of Semester Exams

December- 2018 Practice Questions

Questions Q2.

(a) Show that

(2)

(b) Show that

(3) (Total for question = 5 marks)

Q3.

(a) Show that

(2)

(b) Show that

(3) (Total for Question is 5 marks)

Q4. Show that

(Total for question = 2 marks) Q5.

The table shows some information about the five Great Lakes in North America.

(a) Work out the total surface area of the five Great Lakes. Give your answer in standard form.

........................................................... m2

(2)

Loch Ness is the largest lake in Scotland. The lake has a volume of water of 7.45 × 109 m3

The volume of water in Lake Superior is k times the volume of water in Loch Ness.

(b) Work out the value of k. Give your answer correct to 3 significant figures.

k = ...........................................................

(2)

(Total for question = 4 marks) Q6. Use ruler and compasses to construct the bisector of angle ABC.

You must show all of your construction lines.

(Total for Question is 2 marks) Q8.

(a) Write 0.000451 in standard form. ...........................................................

(1)

(b) Work out

Give your answer in standard form.

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

(2) (Total for question = 3 marks)

Q9. Use ruler and compasses to construct the bisector of angle PQR. You must show all your construction lines.

(Total for question = 2 marks)

Q10. Use ruler and compasses only to construct the perpendicular bisector of line AB. You must show all your construction lines.

(Total for question = 2 marks)

Q11. Show that

(Total for Question is 2 marks)

Q12. Here is the straight line L drawn on a grid.

Find an equation for L.

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

(Total for question = 2 marks) Q13. Work out the size of each exterior angle of a regular polygon with 15 sides.

........................................................... ° (Total for Question is 2 marks)

Q14.

The diagram shows two points S and T. The bearing of T from S is 043°

Work out the bearing of S from T. ...........................................................°

(Total for question = 2 marks) Q15. (a) Find the gradient of the line with equation 3y − 2x = 6

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

(b) Find an equation of the line with gradient −3 that passes through the point (2, 5).

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

(Total for question = 4 marks) Q16.

The diagram shows a quadrilateral ABCD. The quadrilateral ABCD is made from two identical isosceles triangles, ABD and CBD. DA = DB = DC. Angle BAD = Angle BCD = 35° Angle ADC = x°

Work out the value of x.

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

(Total for Question is 4 marks)

Q17.

PQR is an isosceles triangle. QRS is a straight line. PQ = PR.

Angle PRS = 118°

Work out the value of x.

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

(Total for question = 3 marks) Q18.

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)

Q19.

ADC is a straight line. BDE is a straight line.

Angle DBC = 80° Angle BDC = 40°

(a) Write down the value of x.

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

(1)

(b) Work out the value of y.

y = ...........................................................

(1)

(c) Work out the value of z.

z = ...........................................................

(2)

(Total for question = 4 marks)

Q20.

AB is parallel to CD EF is a straight line.

(a) (i) Find the value of x

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

(ii) Give a reason for your answer.

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

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

(2)

Here is a pentagon.

(b) Work out the value of y.

y = ...........................................................

(3)

(Total for question = 5 marks)

Q21.

ABC is a straight line. ABDE is a quadrilateral.

(a) (i) Work out the value of x.

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

(ii) Give a reason for your answer.

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

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

(2)

(b) Work out the value of y.

y = ...........................................................

(3)

Each exterior angle of a regular polygon is 18°

(c) Work out the number of sides of this regular polygon.

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

(2)

(Total for question = 7 marks)

Q22.

The diagram shows point A and point B on a map. The point C is due south of A The bearing of C from B is 235°

(a) Mark the point C on the map.

(2)

The bearing of a point D from B is 168°

(b) Find the bearing of B from D

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

(2)

Gordon measures a length on the map as 6.3 cm correct to 1 decimal place.

(c) Write down the lower bound for this length.

........................................................... cm

(1)

(Total for question = 5 marks)

Mark Scheme Q1.

Q2.

Q3.

Q4.

Q5.

The correct answer, unless clearly obtained by an incorrect method, should be taken to imply a correct method.

Q6.

Q7.

Q8.

Q9.

Q10.

Q11.

Q12.

Q13.

Q14.

The correct answer, unless clearly obtained by an incorrect method, should be taken to imply a correct method.

Q15.

Q16.

Q17.

Q18.

Q19.

Q20.

Q21.

Q22.