2014 form 5 tsc exam for mathematics - … tsc/tsc mathematics 2014.pdf · mathematics . question...
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MARKER CODE
Student Personal Identification Number (SPIN)
TONGA GOVERNMENT MINISTRY OF EDUCATION AND TRAINING
TONGA SCHOOL CERTIFICATE 2014
MATHEMATICS QUESTION AND ANSWER BOOKLET
Time allowed: 3 Hours
YOU MUST HAND THIS BOOKLET TO THE SUPERVISOR BEFORE YOU LEAVE
THE EXAMINATION ROOM.
INSTRUCTIONS 1. This examination has TWO COMPULSORY SECTIONS:
SECTION A: Short Answers 20 Marks
SECTION B: Eight Questions worth a total of 80 Marks 2. All your answers for SECTION A and SECTION B must be written in the
spaces provided for each question in this booklet. SHOW ALL YOUR WORKING.
3. If you need more spaces for answers, ask the Supervisor for extra paper. Write your SPIN on all additional sheets used and clearly number the questions. Attach the additional sheets at the appropriate places in this booklet.
4. Useful Mathematical Formulae are printed on page 24 of this booklet. 5. Show all necessary working.
Note: Unless otherwise stated, i) All variables stand for real numbers ii) Diagrams are NOT drawn to scale
6. Before you begin to answer the questions, WRITE YOUR Student Personal Identification Number in the right – hand box at the top of the page, and on the inside of the back cover of this booklet.
100TOTAL MARKS
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SECTION A: SHORT ANSWERS (20 MARKS)
Answer ALL TWENTY (20) questions. You should not spend more than 40 minutes in this section. Write the answers ONLY in the space provided for each question. Each question is worth ONE (1) mark.
1. Simplify .
____________________________________________________________________________
2. Evaluate 2 .
____________________________________________________________________________
3. Convert 0.375m to mm.
____________________________________________________________________________
4. Use the grid below to draw a line with a gradient of
5. Manu’s step-ladder is shown in the diagram.
Angle IHF = 119°. HF = GF. Calculate the size of angle HFG.
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3 6. Write the coordinates of Point B' after a translation of 5 units right and 5
units up of B.
Coordinates of Point B: ( ____, ____ )
7. The national flag pole at Pangai Lahi represented by RT is 35 metres high. A cable TC, 45 metres long, helps secure the flag pole.
Calculate the distance of point C from the base of the flag pole, R.
8. Solve 30 0
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4 9. Calculate the mean of 4, 5, 12, 13, 16 and 22.
10. For the line 2 3 4 0, find the y – intercept.
11. Considering these numbers: 11, 17, 27, 33, 43, 51, and 57.
List all the numbers that is prime.
12. The diagram below is a diagram of a clothes rack. The clothes rack is made up of rhombuses.
Angle ABE 50°. Calculate angle FDG
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5 13. For the shape below, write down the number of axes of symmetry.
Number of axes of symmetry: _______________________
14. When three is subtracted from four times a number, the result equals the
number squared.
Write an equation to show this. Do NOT solve the equation.
15. Calculate the side marked x in the diagram below. Express your answer as a
whole number. 16. A circle of diameter 13cm has been removed from the edge of a circle of
diameter 30cm. Calculate the perimeter of the remaining shape.
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6 17. Sifa puts $1200 in his bank account. The bank pays 5.5% interest per year.
Calculate how much interest Sifa will earn in the first year.
18. A local travel agency in Tongatapu arranged 540 flights to the outer islands in
a month. The flights went to Vava’u, Ha’apai, ‘Eua, Niuatoputapu and Niuafo’ou in the ratio of 5 : 4 : 3 : 2 : 1.
Calculate the number of flights that went to ‘Eua.
19. Make g the subject of 9 4 15 .
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20. Given that and . Find in fraction form.
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SECTION B: LONG ANSWERS (80 MARKS)
ANSWER ALL EIGHT (8) QUESTIONS IN THIS SECTION. Write the answer to each question in the spaces provided. It is for your best interest to SHOW ALL YOUR WORKING, as some marks are allocated for correct methods and partially correct answers. Each question is worth a total of 10 marks.
QUESTION ONE (10 MARKS) a) Tevita’s plane tickets and accommodation for a holiday in Vava’u cost $1200.
If the plane tickets cost Tevita $670, what percentage of the cost was his accommodation? (2 Marks)
b) When Tevita saw this polo – shirt with “60% off sale at the airport. The polo –
shirt has a marked price of $75.
Calculate the sale price of the polo – shirt? (2 Marks)
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9 c) When Tevita arrived in Vava’u, he discovered that his plane ticket and
accommodation was discounted by 22.5%. Tevita paid this discounted amount of $1200 for his ticket and accommodation.
What was the usual cost of a ticket and accommodation to Vava’u? Round your answer to 2 decimal places (3 Marks)
d) Tevita has $200 to buy a souvenir to take home from a
local handcraft shop. The shop has a whale bone craft for sale at $240 CT inclusive (Consumption Tax). The shop has a ‘We will pay the CT’ sale and CT is 15%.
Does Tevita have enough money to buy the whale bone carving? Calculate the CT amount of $240. You must justify your answer with calculations. (3 Marks)
a) and simplify: 3 7 (2 Marks)
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Q.1
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10 QUESTION TWO (10 MARKS)
a) The area of this triangle is 112 . Calculate the height h. (2 Marks) b) The surface area of a sphere is 4 .
Write an expression for the surface area of a hemisphere (include the flat surface) (2 Marks)
c) ate the volume of this brick where 3 cylinders have been removed. (3 Marks)
Calcul
:
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11 d) Locate and label the centre of enlargement D for which (2 Marks) e) Calculate the scale factor for the enlargement in d) above. (1 Mark)
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12 QUESTION THREE (10 Marks)
a) Expand and simplify 2 3 1 . (2 Marks)
b) The diagram shows a square courtyard with a square pool in one corner.
The area of the cou , and the courtyard extends 8m beyond the pool.
rtyard is 225
Solve the equation 225 8 , to find x, the length of the side of the pool. (3 Marks)
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13 c) The sum of two numbers (x and y) is 33, and their difference is 5.
Find these two numbers.(Hint: Write two equations and solve simultaneously) (5 Marks)
5
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14 QUESTION FOUR (10 MARKS)
a) Sketch the graph of for 0° 360°. Label all points correctly. (2 Marks)
b) An isosceles triangle has two sides of length 11cm, and its area is 40 . Calculate the sizes of the interior angles. (3 Marks)
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15 c) Draw the image of triangle ABC as reflection on mirror line m. Label the image
as ′ ′ ′. (2 Marks)
a)
i. Write the translation that maps diagram ABCD to A'B'C'D'. (1 Mark)
________________________________________________
ii. Rotate diagram A'B'C'D' by 90° using the origin (0) as the centre of rotation. Label the image as A''B''C''D''. (2 Marks)
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16 QUESTION FIVE (10 Marks)
a) Use the grids alongside to draw the graphs of:
i). 2 2
(2 Marks)
ii). 4
(3 Marks)
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iii). 1 1 2 (3 Marks)
iv). 6
(2 Marks)
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18 QUESTION SIX (10 Marks)
a) The following Time – Series graph shows the total sales in the Neiafu Ice – Cream Shop from
Summer 2010 to Spring 2013.
i. Draw a line on the above graph to show the general trend. (1 Marks) ii. What does this graph show about seasonal factors? (2 Marks)
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19 b) The table shows the number of males and females in a Form 5 that play sport
for a school. There are 34 students in Form 5.
GENDER
MALE FEMALE
SPORTS
Play sport for school 11 9
Do not play sport for the
school 6 8
A student is selected in random from this Form 5.
i. What is the probability that the student is male and does not play sport for the school? ____________________________________ (2 Mark)
ii. What is the probability that the student is female?
____________________________________ (2 Mark)
iii. What is the probability that the student plays sport for the school?
____________________________________ (1 Mark)
iv. Given that a student who plays sport for the school is chosen, what is the probability that the student is female?
____________________________________ (2 Mark)
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20 QUESTION SEVEN (10 Marks)
a) The diagram shows a rectangular stained – glass window, ABCD.
One of the pieces of glass in the window, EFGHI, is a regular pentagon.
Calculate the size of angle DEI, giving reasons for your answers.(4 Marks)
b) Construct an angle of 60° at A. (2 Marks)
A ________________________________________
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21 c)
O is the centre of the circle. ABC and DB are tangents to the circle. Angle AED is °. Show that BCD is an isosceles triangle. You must give a geometric reason for each step leading to your answer. (4 Marks)
4
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22 QUESTION EIGHT (10 Marks)
a) Orange juice is sold in 250mL plastic bottles. The amount of liquid in a sample of bottles is measured to the nearest millimetre. This graph shows the result.
i) How many bottles with 248 millilitres? (1 Mark)
ii) Complete the frequency table for these results and calculate the mean amount of juice per bottle in this sample. (3 Marks)
Volume of
orange juice (to nearest mL)
246 247 248 249 250 251
Frequency 1 4
Mean
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iii) Calculate the percentage of bottles contained less than 250mL (2 Marks)
b) Use the Sine Rule, to calculate the length marked x in the triangle below. (2 Marks)
c) A ship should have headed north but instead headed 39o off course. After travelling a distance of 15 km, how far is the ship from its correct course? (2 Marks)
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Useful Formulae 1. Qu r 11. Special Triangles ad atic Equation
If 0 √ i)
2. Trian lg e
Area
3. Trapezium
Area
4. Circle ii)
Circumference 2
Area
5. Sphere
Volume
Surface Area 4
6. Cone
Volume
7. Cylinder
Volume
Curved Surface Area 2
8. Sine Rule
9. Cosine Rule
2
10. eIdentiti s i). tan
ii). 1
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Student Personal Identification Number (SPIN)
(80/1) MATHEMATICS
For Markers Use Only
SECTION Mark Check Marker
SECTION A Short Answer 20
SECTION B (Long Answer) Question One 10
Question Two 10
Question Three 10
Question Four 10
Question Five 10
Question Six 10
Question Seven 10
Question Eight 10
TOTAL 100