grade: ix level: extended holidays(summer break)homework...

PATHWAYS WORLD SCHOOL: Mathematics Department

Grade: IX Level: Extended Holidays(summer break)Homework

Topics: All topics covered in Grade 8 Session-2014-2015

CALCULATOR IS PERMITTED/NOT PERMITTED

All the answers must be given to 3 sf , angle to 1 dp or the degree of accuracy specified in the

question.

Show a neat sketch of the graph wherever needed with ALL NECESSARY DETAILS ON IT.

Q1. n( ) = 21, n(A B) = 19, n(A B’ ) = 8 and n(A) = 12.

Complete the Venn diagram to show this information.

[3]

2. The table gives the average surface temperature (°C) on the following planets.

Planet Earth Mercury Neptune Pluto Saturn Uranus

Average temperature 15 350 –220 –240 –180 –200

(a) Calculate the range of these temperatures. [1]

(b) Which planet has a temperature 20°C lower than that of Uranus? [1]

3. A house was built in 1985 and cost $62 000. It was sold in 2003 for $310 000.

(a) Work out the 1985 price as a percentage of the 2003 price. [2]

(b) Calculate the percentage increase in the price from 1985 to 2003. [2]

4. (i) Hassan sells oranges for $0.35 per kilogram. He reduces this price by 40%.

Calculate the new price per kilogram. [2]

(ii) The price of $0.35 per kilogram of oranges is an increase of 25% on the previous

day’s price. Calculate the previous day’s price. [2]

Answer

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

A B


5. In 2004 Colin had a salary of $7200.

(a) This was an increase of 20% on his salary in 2002. Calculate his salary in 2002. [2]

(b) In 2006 his salary increased to $8100. Calculate the percentage increase from 2004 to

2006. [2]

6. Each year a school organises a concert.

(i) In 2004 the cost of organising the concert was $385. In 2005 the cost was 10% less

than in 2004. Calculate the cost in 2005. [2]

(ii) The cost of $385 in 2004 was 10% more than the cost in 2003. Calculate the cost in

2003. [2]

7. The points A(6, 2) and B(8, 5) lie on a straight line.

(a) Work out the gradient of this line. [1]

(b) Work out the equation of the line, giving your answer in the form y = mx + c. [2]

8.

NOT TO SCALE

(a) Calculate the gradient of the line l. [2]

(b) Write down the equation of the line l. [2]

0

5

10

y

x

l


9.

One of the lines in the diagram is labelled y = mx + c. Find the values of m and c. [2]

10.

NOT TO SCALE

x

y

2 3 4 5 6 7 80

1

4

3

2

1

8

7

6

5

ym

xc

= +

y

C (4,3)

B (1, 2)

A

4x y = 62x + 3y = 17

x


In the diagram, the line AC has equation 2x + 3y = 17 and the line AB has equation 4x – y =6.

The lines BC and AB intersect at B (1, –2). The lines AC and BC intersect at C (4, 3).

(a) Use algebra to find the coordinates of the point A. [3]

(b) Find the equation of the line BC. [3]

11. The equation of a straight line can be written in the form 3x + 2y – 8 = 0.

(a) Rearrange this equation to make y the subject. [2]

(b) Write down the gradient of the line. [1]

(c) Write down the co-ordinates of the point where the line crosses the y axis. [1]

12. A straight line passes through two points with co-ordinates (6, 8) and (0, 5).

Work out the equation of the line. [3]

13. Find the co-ordinates of the mid-point of the line joining the points A(2, –5) and B(6, 9). [2]

14. Magazines cost $m each and newspapers cost $n each. One magazine costs $2.55 more than

one newspaper. The cost of two magazines is the same as the cost of five newspapers.

(i) Write down two equations in m and n to show this information. [2]

(ii) Find the values of m and n. [3]

15. Angharad had an operation costing $500. She was in hospital for x days.

The cost of nursing care was $170 for each day she was in hospital.

(a) Write down, in terms of x, an expression for the total cost of her operation and nursing

care. [1]

(b) The total cost of her operation and nursing care was $2370.

Work out how many days Angharad was in hospital. [2]

16. Two quantities c and d are connected by the formula c = 2d + 30.

Find c when d = –100. [1]


17.

NOT TO SCALE

The right-angled triangle in the diagram has sides of length 7x cm, 24x cm and 150 cm.

(a) Show that x2 = 36 [2]

(b) Calculate the perimeter of the triangle. [1]

18.

NOT TO SCALE

(a) (i) Write down an expression for the area of rectangle R. [1]

(ii) Show that the total area of rectangles R and Q is 5x2 + 30x + 24 square

centimetres. [1]

150 cm

24x cm

7xcm

( + 4) cmx

( + 12) cmx

( + 2) cmx

R

Q

4x cm


19. (i) On Monday a shop receives $60.30 by selling bottles of water at 45 cents each.

How many bottles are sold? [1]

(ii) On Tuesday the shop receives x cents by selling bottles of water at 45 cents each.

In terms of x, how many bottles are sold? [1]

(iii) On Wednesday the shop receives (x – 75) cents by selling bottles of water at 48 cents

each. In terms of x, how many bottles are sold? [1]

20. Solve the simultaneous equations

[3]

21. Solve the inequality 4 –5x < 2(x + 4). [3]

22. Solve the simultaneous equations

0.4x + 2y = 10,

0.3x + 5y = 18. [3]

23. Solve the equation

[3]

24. Solve these simultaneous equations.

x + 2y – 18 = 0

3x – 4y – 4 = 0 [3]

,1622

1 yx

.192

12 yx

,3

52

4

2

xx


25.

NOT TO SCALE

A shop has a wheelchair ramp to its entrance from the pavement.

The ramp is 3.17 metres long and is inclined at 5° to the horizontal.

Calculate the height, h metres, of the entrance above the pavement.

Show all your working. [2]

26. NOT TO SCALE

The diagram shows a pencil of length 18 cm. It is made from a cylinder and a cone.

The cylinder has diameter 0.7 cm and length 16.5 cm. The cone has diameter 0.7 cm and

length 1.5 cm.

(a) Calculate the volume of the pencil.

[The volume, V, of a cone of radius r and height h is given by V = [3]

(b)

NOT TO SCALE

pavement

entrance

5°

3.17 mh m

0.7 cm

16.5 cm 1.5 cm

h

l

.3

1 2hr

18 cm

wcm

x cm


Twelve of these pencils just fit into a rectangular box of length 18 cm, width w cm and

height x cm.

The pencils are in 2 rows of 6 as shown in the diagram.

(i) Write down the values of w and x. [2]

(ii) Calculate the volume of the box. [2]

(iii) Calculate the percentage of the volume of the box occupied by the pencils. [2]

27.

NOT TO SCALE

A, B, C and D lie on a circle, centre O, radius 8 cm.

AB and CD are tangents to a circle, centre O, radius 4 cm.

ABCD is a rectangle.

(a) Calculate the distance AE. [2]

(b) Calculate the shaded area. [3]

28. The numbers 0, 1, 1, 1, 2, k, m, 6, 9, 9 are in order (k ≠ m).

Their median is 2.5 and their mean is 3.6.

(i) Write down the mode. [1]

(ii) Find the value of k. [1]

(iii) Find the value of m. [2]

A B

D C

O

E


29. The quiz scores of a class of n students are shown in the table.

Quiz score 6 7 8 9

Frequency (number of students) 9 3 a 5

The mean score is 7.2. Find

(i) a, [3]

(ii) n, [1]

(iii) the median score. [1]

30. A block of cheese, of mass 8 kilograms, is cut by a machine into 500 equal slices.

(a) Calculate the mass of one slice of cheese in kilograms. [1]

(b) Write your answer to part (a) in standard form. [1]

31. The mass of the Earth is of the mass of the planet Saturn.

The mass of the Earth is 5.97 × 1024

kilograms.

Calculate the mass of the planet Saturn, giving your answer in standard form, correct to 2

significant figures. [3]

32. Use the formula to calculate the value of P when V = 6 × 106 and R = 7.2 × 10

8. [2]

33. A spacecraft made 58 376 orbits of the Earth and travelled a distance of 2.656 × 109

kilometres.

(a) Calculate the distance travelled in 1 orbit correct to the nearest kilometre. [2]

(b) The orbit of the spacecraft is a circle. Calculate the radius of the orbit. [2]

95

1

R

VP

2


34. All 24 students in a class are asked whether they like football and whether they like

basketball.

Some of the results are shown in the Venn diagram below.

= {students in the class}.

F = {students who like football}.

B = {students who like basketball}.

(i) How many students like both sports? [1]

(ii) How many students do not like either sport? [1]

(iii) Write down the value of n(F B). [1]

(iv) Write down the value of n(F′ B). [1]

35. = {1,2,3,4,5,6,7,9,11,16} P = {2,3,5,7,11} S = {1,4,9,16} M = {3,6,9}

(a) Draw a Venn diagram to show this information. [2]

(b) Write down the value of n(M ′ P). [1]

36. Yasmeen is setting up a business. She borrows $5000 from a loan company .The loan

company charges 6% per year simple interest. How much interest will Yasmeen pay after 3

years? [2]

37. When x = –3 find the value of x3 + 2x

2. [2]

38. Alphonse spends $28 on food. This amount is of his allowance. Calculate

his allowance. [2]

F B

127 2

9

4


39.

NOT TO SCALE

An old Greek coin is a cylinder with a diameter of 30 millimeters and a thickness of

2 millimeters. Calculate, in cubic millimeters, the volume of the coin.

[The volume of a cylinder, radius r, height h, is πr2h.] [2]

40. (a) Expand the bracket and simplify the expression

7x + 5 – 3(x – 4). [2]

(b) Factorise 5x2 – 7x. [1]

41. Camilla has $5 to spend in the market.

She buys kilograms of bananas priced at 80 cents per kilogram and 3 yams priced at

45 cents each.

How much money does she have left? [3]

42.

Country Area (km2)

Brazil 8.51 × 106

Panama 7.71 × 104

Guyana 2.15 × 105

Colombia 1.14 × 106

The table above gives the areas of four South American countries, correct to 3 significant

figures.

(a) List the countries in order of area, smallest to largest.

Answer (a) ………… < Guyana < ………… < ………… [1]

30 mm

2 mm

2

11

grade: ix level: extended holidays(summer break)homework...

Documents