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TONGA SCHOOL CERTIFICATE

2018

MATHEMATICS

Time Allowed: 3 Hours

YOU MUST HAND IN THIS BOOKLET TO THE SUPERVISOR AT THE END OF THE

EXAMINATION.

MARKER CODE

STUDENT ENROLMENT NUMBER (SEN)

QUESTION AND ANSWER BOOKLET

INSTRUCTIONS:

1. Write your Student Enrolment Number (SEN) on the top right-hand corner of this page.

2. This paper consists of SEVEN Questions and is out of 70 Skill Level.

QUESTIONS TOPICS TOTAL SKILL

LEVEL

ONE NUMBERS 10

TWO ALGEBRA 14

THREE GRAPHS OF FUNCTIONS 10

FOUR MEASUREMENT 10

FIVE TRIGONOMETRY 10

SIX PROBABILITY 10

SEVEN DIFFERENTIATION AND INTEGRATION 6

TOTAL 70

3. Answer ALL questions in the spaces provided in this booklet.

4. In addition to this booklet, you should also receive Formulae Sheet No. 80/1

5. Use a BLUE or BLACK ball point pen only for writing.

6. If you need more spaces for answers, ask the supervisor for extra paper. Write your Student

Enrolment Number (SEN) on each addition sheet, number the questions clearly and insert them

in the appropriate part of your booklet.

7. Check that your paper consists of 19 pages and that pages 17-19 has been deliberately left blank.

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QUESTION ONE NUMBERS

1. i. Define by identifying the elements of Rational numbers.

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ii. Show on a number line the set of whole numbers less than 5.

2. i. Express 81

3% as a fraction in its simplest form.

ii. Calculate 81

3% of $80.

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3. Simplify 2.7:1.8

On a sunny day, a tree 3m high casts a shadow of length 1.5m at the same time a

building casts a shadow of length 24m.

4. Calculate the height of the building.

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QUESTION TWO ALGEBRA

1. Simplify the following expressions.

i. 3𝑥2𝑦 − 4𝑦𝑥2

ii. 𝑤𝑧3 ÷ 𝑧𝑤

iii. 2𝑥2+𝑥−1

𝑥+1

2. i. Name the type of equation that (𝑥 − 2)(𝑥 + 1)(𝑥 − 1) = 0 belongs to.

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ii. Solve (𝑥 − 2)(𝑥 + 1)(𝑥 − 1) = 0.

3. Use the Elimination method to solve the pair of simultaneous equations;

𝑎 + 13 = 5𝑏

𝑎 + 4 = 2𝑏

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4. The width (w) of the rectangle given below is 4cm less than its length (x). Its area is 12cm2.

x

w

i. Express w in terms of x.

ii. Calculate the width of the rectangle.

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12cm2

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QUESTION THREE GRAPHS OF FUNCTIONS

Use the parabola in Figure 1 to answer questions 1, 2 and 3.

Figure 1

1. Write the equation (in factored form) of the parabola.

2. Find the turning point.

3. State the range.

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4. The equation of a line is 2y = 1 – 3x.

Calculate the gradient of the line.

5. Sketch the graph of the exponential function, 𝑦 = 2𝑥 .

6. Draw the graph of the in-equation, 2𝑦 + 𝑥 < 3.

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QUESTION FOUR MEASUREMENT

1. Convert 21𝑐𝑚3 to 𝑚𝑚3.

2. The height of a door is 2.1 m. Find the limit of accuracy of the door’s height.

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Figure 2, is a playing field made up of a rectangle and a sector.

Figure 2

3. Calculate the minimum length of fencing material needed to enclose the field.

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Figure 3 shows a solid sphere with 3cm radius placed inside an open cylinder with 6cm

diameter and 6cm height.

Figure 3

4. Calculate how much more surface area that the cylinder has than the sphere.

(Ignore points of contact of sphere and cylinder).

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QUESTION FIVE TRIGONOMETRY

ABC is a right angle triangle with the hypotenuse of 13cm and shortest side of 5cm Use ABC to

answer question 1 and 2.

13cm

5cm

1. Calculate the length of side BC.

2. State the value of sin.

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B C

A

13

3. Calculate the area of the isosceles triangle given below.

4. A soccer goal is 8m wide. A player shoots for goal when he is 25m from one goal post

and 20m from the other. Calculate the angle where the shot is made in order to score a

goal.

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6cm

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QUESTION SIX PROBABILITY

1. Define the following terms.

i. Trial .

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ii. Equally likely outcomes.

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2. The height of high school students is normally distributed with a mean of 195cm and a

standard deviation of 5cm.

i. Find the interval that contained 68% of high school students’ height.

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ii. Out of 1000 high school students, calculate the expected number of students with a

height between 190cm and 120cm.

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A bag contains 5 red balls and 3 green balls. Two balls are drawn in succession from the bag.

The first ball is not replaced before the second ball is drawn.

3. Calculate the probability of drawing two different colour balls.

(Hint : Use a probability tree)

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QUESTION SEVEN DIFFERENTIATION AND INTEGRATION

Sam drives at a distance of 264km in 51

2 hours from town A to town B.

1. Find the average speed of Sam’s journey from town A to B.

2. Find the derivative of 𝑓(𝑥) = 2𝑥2 − 1.

3. Find the anti-derivative of 𝑓(𝑥) = 2𝑥2 − 1.

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