year 10 mathematicsjuppmaths2016.weebly.com/uploads/2/6/1/3/26136393/2014_exam.p… · pakuranga...

NAME:

TEACHER:

Pakuranga College

Year 10 Mathematics

2014 Examination

Time: 2 hours

Answer ALL questions in the spaces provided in this booklet. Show ALL working.

Sections Page number Result

1 Number 2

2 Algebra 4

3 Graphs 6

4 Measurement 9

5 Trigonometry 12

6 Angles 15

7 Statistics 18

8 Probability 21

NAME:

TEACHER:

YEAR 10 MATHEMATICS, 2014

Section 1 Number


For Assessor’s use only

Curriculum Level

=========================================================================

QUESTION ONE

Tina’s teacher tells the class that they are not

allowed to use their phones as calculators! Tina

did not remember to bring her calculator to class.

Show how these questions could be solved

without a calculator (show working).

(a) Find 20% of 800

____________________________________

____________________________________

(b) 2

5+

3

4=

____________________________________

____________________________________

(c) 62 + □ = 77 – 1

____________________________________

____________________________________

(d) 23 − (4 + 2) + √16

____________________________________

____________________________________

____________________________________

(e) Find the lowest common multiple of 6 and 8.

____________________________________

____________________________________

(f) 5.2 × 103 × 4 × 105

____________________________________

____________________________________

QUESTION TWO

Some students weighed their phones. Here are

the weights (in g). Write them in order from

smallest to largest:

110.7, 112.0, 110.08, 111.3, 110.309

_______________________________________

QUESTION THREE

Complete the rounding table

Number Rounded to…

Nearest 100 2 d.p. 3 s.f.

4768.207

5211.3674

59.0099

QUESTION FOUR

A new smart phone has a recommended retail

price of $1049.

(a) Shady Sam says he can get it for 65% of the

recommended price. What is Shady Sam’s

price?

____________________________________

____________________________________

(b) Techfilla Company sells the phone at its

recommended price…but then holds a “30%

off everything sale”. What is the sale price

of the phone?

____________________________________

____________________________________

(c) CheapSellaz holds a 20% off sale and lists

the phone’s sales price as $782. What is

their non-sale price for the phone?

____________________________________

____________________________________

QUESTION FIVE

A phone cost a retailer $530 to get into the store.

72% profit is added to get the GST exclusive

selling price, then 15% GST is added.

(a) What will the GST inclusive selling price

be?

____________________________________

____________________________________

____________________________________

(b) If the price in (i) is then discounted 30%,

what will the new selling price be?

____________________________________

____________________________________

(c) What is the percentage decrease between the

original GST exclusive price and the

discount price in (ii)?

____________________________________

____________________________________

____________________________________

(d) Another phone has a GST inclusive price of

$870. What is the GST exclusive price?

(GST is 15%)

____________________________________

____________________________________

NAME:

TEACHER:


Section 2 Algebra



Curriculum Level

==========================================================================

QUESTION ONE If the first two scales are in perfect balance, what

needs to be added (in place of the question mark)

to balance the third set?

QUESTION TWO

Solve the following equations:

(a) 10 + = 32 – 4

(b) 53 – = 41

(c) 2n + 5 = 29

_______________________________________

(d) 6n – 4 = 3n + 8

_______________________________________

_______________________________________

(e) 5(n – 3) = 35

_______________________________________

_______________________________________

(f) (n – 4)(n + 3) = 0

_______________________________________

QUESTION THREE

Simplify the following expressions:

(a) p × p × p × p = ______________

(b) 4n – n = ______________

(c) 5n + 4p – 3n + p = ______________

(d) 7n × 8n = ______________

(e) (3n4)2 = ______________

(f) 2𝑦

5+

𝑦

3

________________________________

________________________________

(g) 14𝑛4𝑥

35𝑛𝑥 = ______________

QUESTION FOUR

Expand the following, simplify if necessary.

(a) 5(b + c) = ________________________

(b) 12(n + 4) = ________________________

(c) p(5p + 1) = ________________________

(d) n(6 – n) + 2(n + 3)

___________________________________

___________________________________

(e) 4(y + 3) – 3(y – 1)

___________________________________

___________________________________

(f) (x + 4)(x – 2)

___________________________________

___________________________________

(g) (p – 6)2 + 6p

___________________________________

___________________________________

QUESTION FIVE

To cater an afternoon tea, it was decided to

provide 3 biscuits per person and supply an extra

10 biscuits in case of greedy people!

The following formula was used:

b = 3n + 10

a) Explain what b and n stand for

___________________________________

___________________________________

b) How many biscuits will be needed for 20

people?

___________________________________

___________________________________

c) How many people were there at the last party

if they provided 175 biscuits?

___________________________________

___________________________________

QUESTION SIX

Fully factorise the following expressions

(a) 5p + 10 = _______________________

(b) 42n – 12 = ______________________

(c) x2 – 6x + 8 = ____________________

___________________________________

NAME:

TEACHER:


Section 3 Graphs



Curriculum Level

==========================================================================

SKILLS QUESTIONS

QUESTION ONE

Part of a dot-to-dot graph picture is shown

above, but two sections are missing. Complete

them by plotting the points listed and joining

them in the order they are given.

The first point and last point of each missing

section has already been plotted.

Section 1: (3, 1), (7, -2), (5, -3), (9, -7), (2, -7),

(3, -10)

Section 2:

(-5, -3), (-7, -2), (-3, 1), (-6, 2), (0, 7)

QUESTION TWO

Give the next two terms in each of these patterns

(a) 6, 10, 14, 18, _____ , ______

(b) 11, 8, 5, 2, ______ , ______

(c) 4, 6, 10, 16, 24, _______ , _______

(d) n + 4, 2n + 1, 3n – 2, 4n – 5, _____, ______

QUESTION THREE

Ellen is already excited about Christmas and

makes a Christmas tree pattern out of matches.

(a) Complete the table for pattern numbers and

numbers of matches.

Pattern (P) Matches (M)

1 4

2 7

3

4

5

(b) Write a rule linking the number of matches

to the pattern number.

M = _____________________________

(c) How many matches would be required to

make the tree that is Pattern number 23?

_______________________________________

_______________________________________

(d) What pattern number would require 244

matches to make?

_______________________________________

_______________________________________

_______________________________________

(e) If the rule in part (b) was plotted on a graph,

what would its y intercept be?

_______________________________________

QUESTION FOUR

Give the gradients of the lines shown above

(a) Gradient = __________

(b) Gradient = __________

(c) Gradient = __________

QUESTION FIVE

At 2pm one day, Petra left her house to walk and

visit Anna. Anna left her house to go on a walk.

Kelly stayed home. The graph shows the three

girls’ movements.

(a) Give the equations of each girl’s line.

Petra:

Anna:

Kelly:

(b) How fast does Petra walk?

___________________________________

(c) How far away from Anna does Kelly live?

How is this shown on the graph?

___________________________________

___________________________________

(d) How fast does Anna walk?

___________________________________

(e) Explain why Anna and Petra do not

necessarily meet each other.

___________________________________

___________________________________

NAME:

TEACHER:


Section 4 Measurement



Curriculum Level

========================================================================

QUESTION ONE

Circle the most sensible measurement

(a) Width of a bathroom sink might be:

47 m 47 cm 47 mm 47 L

(b) A bath soap might weigh:

90 cm 90 kg 90 g 90 mg

(c) Height of the bathroom door might be:

190 cm 190 kg 190 mm 190 m

(d) The area of a face cloth might be:

625 m2 625 mL 625 cm2 625 mm

QUESTION TWO Cherie doesn’t like her bath too hot. She took the

temperature of the bath water before and after

adding some cold to it (thermometer reads in

degrees Celsius). What were the temperature

readings?

First temperature: _________________

Second temperature: ______________

QUESTION THREE

(a) The dimensions of Cherie’s bath towel are

given above. What is the area of Cherie’s

towel?

________________________________________

(b) A towel weighs 500g per square metre. What

does Cherie’s towel weigh?

________________________________________

________________________________________

QUESTION FOUR

Give the conversions for these metric units:

(a) 49 cm = _____________ m

(b) 1.02 kg = ____________ g

(c) 154 mm = ____________ cm

(d) 24 mL = ______________ L

QUESTION FIVE

Cherie is considering several different toothbrush

holders. Calculate the volume of each one.

(a) Rectangular prism (cuboid)

____________________

____________________

____________________

(b) Cylinder

_________________

_________________

_________________

_________________

Reminder: Circle

area formula is

𝐴 = 𝜋𝑟2 Circumference

formula is

𝐶 = 2𝜋𝑟 𝑜𝑟 𝜋𝑑

QUESTION SIX

A toilet roll has the following dimensions: width

of 11 cm, diameter of roll = 10 cm, diameter of

cardboard tube = 4 cm.

(a) What is the volume of paper in the roll?

________________________________________

________________________________________

________________________________________

(b) The roll has 200 sheets of toilet paper, each

12 cm long. If it was unrolled, what would

the total area of the toilet paper be?

________________________________________

________________________________________

QUESTION SEVEN

Cherie’s friends know that she likes candles and

soaps for her bathroom.

(a) One friend gave her this soap, which is a

trapezium prism.

(i) What is the area of one of the soap’s

trapezium shaped faces?

_____________________________________

_____________________________________

(ii) What is the volume of the soap?

_____________________________________

(b) Cherie was also given this candle. It has a

square base and is pyramid-shaped.

(i) What is the volume of the candle?

_____________________________________

_____________________________________

_____________________________________

(ii) Sadly, the candle broke into pieces before

Cherie could light it. She melted down the

wax and created a new candle shaped like a

cube. What will the dimensions of the new

candle be?

_____________________________________

_____________________________________

Useful formulas for next questions:

Volume of sphere V = 4

3𝜋𝑟3

Volume of pyramid V = 1

3 base area × height

Area of trapezium = (𝑎+𝑏)

2× ℎ

NAME:

TEACHER:


Section 5 Trigonometry



Curriculum Level

==========================================================================

QUESTION ONE

Use your calculator to find the values of n or A.

Record your working.

(a) 42 + 72 = n2

___________________________________

(b) n2 + 82 = 122

___________________________________

(c) n = sin 35 × 8

___________________________________

(d) 9 × n = cos 52

___________________________________

(e) 4 ÷ 7 = tan A

___________________________________

QUESTION TWO

A boat is sailing due East of a radio beacon. A

plane is due North of the beacon. The plane and

boat are 18 km apart and the boat is 10 km from

the beacon.

(a) How far North of the beacon is the plane?

_______________________________________

_______________________________________

(b) What is the angle between the boat’s path

and a path that would take it towards the

plane? (The angle indicated on the diagram)

_______________________________________

_______________________________________

QUESTION THREE

A windsurfer sails a course marked by three

buoys that form a right-angled triangle.

The first leg of the course is 35 m. Calculate x

and y, the lengths of the other two legs.

_______________________________________

_______________________________________

_______________________________________

_______________________________________

QUESTION FOUR

A kayak’s sail is shaped like an isosceles

triangle. If it is 1.8 m wide at the top and the

equal sides are 3 m, calculate the height of the

sail.

_______________________________________

_______________________________________

QUESTION FIVE

A boat has two right-angled triangle-shaped

sails. The mainsail is 8m wide and the smaller

sail is 12 m high.

(a) Calculate x, the height of the mainsail.

_______________________________________

_______________________________________

_______________________________________

(b) Calculate A, the angle at the top of the

mainsail.

_______________________________________

_______________________________________

_______________________________________

(c) Calculate y, a length on the smaller sail.

_______________________________________

_______________________________________

_______________________________________

QUESTION SIX

The angle of elevation from a boat to a plane is

29o. The relative positions of the boat, plane and

a radio beacon on the horizontal are given in the

second diagram.

Calculate the height (altitude) at which the plane

is flying.

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

NAME:

TEACHER:


Section 6 Angles

Answer ALL questions in the spaces provided in this booklet.

Show ALL working


Curriculum Level

==========================================================================

QUESTION ONE

In the figure above…

(a) Draw a cross inside one acute angle.

(b) What size is angle ADC?

____________________________________

(c) The angle to the far right can be called ABC.

Give another three letter name for this angle.

____________________________________

(d) Put a tick inside an obtuse angle.

(e) What would the angles inside the shape

ABCD add to?

____________________________________

____________________________________

QUESTION TWO

(a) Size of angle? _____________________

(b) Size of angle AOC? ___________________

(c) Size of angle AOB? ___________________

(d) Size of angle BOC? ___________________

QUESTION THREE

Give the size of the marked angles. Give a

geometric reason for each one if you can.

(a)

A = _________________

because

_______________________________________

_______________________________________

(b)

A = _________________

because

_______________________________________

_______________________________________

B = _________________

because

_______________________________________

_______________________________________

QUESTION FOUR

This diagram shows an isosceles triangle situated

between parallel lines.

Calculate the size of angle E. You may need to

first work out some of the angles marked a-d.

Give a geometric reason and clearly identify

each angle you calculate.

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

QUESTION FIVE

Calculate the size of angle A.

You may need to calculate other angles in the

diagram to do so. Label any angle that you use

and give a geometric reason for its size.

Hint: You may need to extend the length of one

of the existing lines.

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

QUESTION SIX

Given that angle EBD is size x, give the sizes of

the other angles in the triangle in terms of x.

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________


Section 7 Statistics



Curriculum Level

==========================================================================

QUESTION ONE

(a) Describe the long-term trend in percentage of

cars exceeding the speed limit in urban areas.

_______________________________________

_______________________________________

_______________________________________

(b) Sam thinks the trends for the two speed

limits show similar movements. What kind

of graph could he use to look for a

correlation between the two sets of data?

_______________________________________

(c) Explain why the data for this graph is most

likely based on samples. Suggest how it

may have been collected.

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

(d) Explain why we can’t use this graph to find

how many cars exceeded the speed limit in

2011.

_______________________________________

_______________________________________

_______________________________________

(e) Estimate the percentage of cars that will

break the rural speed limit in 2014.

_______________________________________

NAME:

TEACHER:

QUESTION TWO

Sam managed to obtain some data about car

speeds in urban areas (where the speed limit is

50 km/h).

(a) Is speed discrete or continuous data?

_______________________________________

(b) How does the graph show that all speeds

were rounded? What were they rounded to?

_______________________________________

_______________________________________

_______________________________________

(c) Describe features of the distribution of

speeds.

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

(d) In this sample, did the majority of cars stay

within the speed limit? Give evidence for

your claim.

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

QUESTION THREE

Sam’s school is loaned a speed radar which

records car speeds to the nearest km/h. Sam uses

it for 10 minutes at the school gate and records

the following speeds:

52, 48, 55, 58, 53, 50, 49, 52, 53, 55, 59, 56, 51,

53, 53, 57, 54, 52, 56, 59, 51, 50, 49, 50, 53.

(a) Create a dot plot for the data given above,

using the scale below

(b) Complete the table of summary statistics for

the data.

Range

Median

Mean

Mode

Lower quartile

Upper quartile

(c) Sketch a box plot of the data above the scale

below

(d) Comment on whether Sam’s sample of cars

is random. For what reasons might you

question whether it is representative of all

cars that pass by the school entrance?

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

QUESTION FOUR

Sam decides to hold a survey to find out why a

lot of people speed past the school entrance. He

puts a survey in every letterbox he passes on his

way home from school. The survey includes

these questions:

1. What speed do you normally drive at

when passing Prince Albert High School?

2. How often do you break the speed limit?

3. Why do you break the speed limit?

Identify some problems with Sam’s sampling

and question design.

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

NAME:

TEACHER:


Section 8 Probability



Curriculum Level

==========================================================================

QUESTION ONE

Put a dot on the scale to represent the likelihood

of each event.

(a) Your teacher has a cat that can tap-dance and

speak Mandarin.

(b) The next baby to be born in Auckland will be

a boy.

(c) It will rain in your town sometime in the next

fortnight.

(d) All the kittens in a litter of 5 turn out to be

males.

QUESTION TWO

One study found that the probability of a female

being left handed is 0.09, but for a male it is

0.12.

(a) Complete the tree diagram for this situation

(b) Calculate the probability that a randomly

chosen person is female and left-handed.

____________________________________

(c) Calculate the probability that a randomly

chosen person is right-handed.

____________________________________

____________________________________

(d) If three people are selected at random from

the general population, what is the

probability that all of them are left-handed

males?

____________________________________

____________________________________

(e) In a co-ed school (both genders attend) with

700 students, how many left-handers would

we expect to have?

____________________________________

____________________________________

(f) Identify at least one assumption we would

have to make in order to calculate the answer

to the previous question.

____________________________________

____________________________________

____________________________________

____________________________________

QUESTION THREE

Jeremy has a theory that toast is more likely to

land with the butter side down. He tests this

theory by dropping a piece of toast 50 times.

(a) The toast lands butter side down 28 times.

Use this to give an estimate (as a fraction in

its simplest form) for the probability of toast

landing butter side down.

____________________________________

(b) A group of schools got together to carry out

10 000 trials of this experiment. They found

that the toast landed butter side down 6 248

times in their experiment.

(i) Give an estimate for the probability of

toast landing butter side down based on

this experiment.

____________________________________

____________________________________

(ii) Another group of schools decide to carry

out 10 000 trials of buttered toast drops.

Will they find that the toast lands butter

side down 6248 times? Explain.

____________________________________

____________________________________

____________________________________

____________________________________

____________________________________

____________________________________

(c) Which estimate (the one from Jeremy’s

experiment or the one from the group of

schools) is likely to be more accurate? Why?

____________________________________

____________________________________

____________________________________

____________________________________

____________________________________

QUESTION FOUR

An English teacher made a game involving two

spinners. Students have to spin both spinners

and put the parts together to make a “word”.

Some “words” are not proper English. Each

spinner has even-sized sections.

(a) If you play the game, what is the probability

of getting a word that ends in “ing”?

____________________________________

(b) How many “words” are possible?

____________________________________

(c) If you play the game and get a word ending

in “ing”, what is the probability that it is a

real word?

____________________________________

(d) Sarah gets hooked on the game and plays it a

lot. If she has 5 turns, what is the probability

that every “word” she makes begins with the

letter b?

____________________________________

____________________________________

(e) Sarah then plays 100 games and gets either

“coldest” or “colder” 25 times. Comment

on whether this result seems unusual.

____________________________________

____________________________________

year 10 mathematicsjuppmaths2016.weebly.com/uploads/2/6/1/3/26136393/2014_exam.p… · pakuranga...

Documents