# Click on the question you wish to answer, in any order:

## Purple questions are about STATISTICS

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*If you need help on a particular question, click on the HINT button

### Question 1. How many sides has a pentagon?

An octagon has 8 sides and a pentagon has fewer!

A pentagon has 5 sides.

### Question 2. Calculate 3 x 104 + 4 x 103 and leave the answer in standard form

Work out each of the two terms separately then add them. If you use your calculator the EXP button may be useful.

30000 + 4000 = 34000
= 3.4 x 104

### Question 3. Evaluate (4x + 3)2 if x = −2

Remember that the square of a negative number gives a positive number.

25

### Question 4. What is the sum of the interior angles of a quadrilateral?

Any quadrilateral can be split into 2 triangles. How many degrees in a triangle?

360°

### Question 5. What is the size of the interior angle of a regular octagon?

The exterior angles of any octagon add up to 360°?

135°

Remember BEDMAS

32

### Question 7. List the prime numbers between 20 and 30.

Prime numbers have only two factors.Themselves and 1. i.e. 37

23 and 29

### Question 8. How many millilitres in 1.3 litres?

There are 1000 millilitres in a litre.

1300 ml

### Question 9. What is the difference between the product of 4 and 5 and the sum of 6 and 2?

Product means "multiply". Sum means "add". Difference means "subtract"

12 or −12

### Question 10. Solve 4x − 2.1 = 14.09

Add 2.1 to both sides of the equation then divide both sides by 4.

4.0475

### Question 11. What is 0.42 as a fraction in its simplest form?

How many hundredths are there in 0.42?
Now simplify.

21/50

### Question 12. What is the total order of symmetry of a kite?

Total order of symmetry = NUMBER of AXES of SYMMETRY plus the ORDER of ROTATIONAL SYMMETRY.

Total order of symmetry = 1 + 1 = 2

### Question 13. A clock loses 15 minutes every day. What is this loss as a percentage (to 2 s.f.) ?

How many minutes in a day?

Percentage Loss = [15/(24 x 60)] x 100
= 1% (to 2 s.f.)

### Question 14. A meal for 4 people uses 2 eggs. How many eggs are needed if the meal is to be made for 6 people ?

How many eggs would ONE person need?

Three eggs

### Question 15. What is the order of rotational symmetry of a regular pentagon?

Draw a 5 sided regular polygon and see how many times you can rotate it onto itself!

5

### Question 16. What is the image of the point (3,2) after a reflection in the y-axis followed by a quarter turn (90°) rotation about the point (0,0)?

Draw a set of x-axis and y-axis and mark the point (3,2) then carry out each of the changes.

(−2, −3)

### Question 17. How many square centimetres is the surface area of a cube of side 2 cm ?

Find the area of one face of the cube. Now work out how many faces a cube has.

24 cm2

### Question 18. Write 9.4 x 10−1 as an ordinary number.

For a NEGATIVE index move the decimal point to the LEFT.

0.94

### Question 19. What is the direction SE as a bearing ?

Remember that NORTH is 0° and direction is measured CLOCKWISE.

135°

### Question 20. Write the fraction 77/1000 as a decimal?

The THOUSANDTHS column is the third one to the right of the decimal point.

0.077

### Question 21. Expand (4x − 2)(3x − 1)?

Multiply 4x by 3x then
4x by −1

12x2 −10x +2

### Question 22. Expand (4x − 1)2?

Expand (4x − 1)(4x − 1)

16x2 −8x +1

### Question 23. What is 6% of 20?

Multiply 20 by 0.06
(This is the DECIMAL form of 6%)

20 x 0.06 = 1.2

### Question 24. How many one litre cans of paint would you need to buy to paint a solid cuboid of dimensions 40cm by 80 cm by 60 cm with four coats of paint if each can of paint covers 30 000 cm2?

Find the area of each of the six faces of the cuboid.

Three cans of paint would be needed.

### Question 25. Simplify 3a x 4b x 2c

Multipy numbers first and then the variables.

24abc

### Question 26. Which is the largest solution for the inequation 3x < 11 if x is a member of the set W

Divide both sides of the inequation by 3 first.

x < 3.666666666666
i.e. 3

### Question 27. What name is given to the line AB? This term is also used in music.

Chord

### Question 28. A barometer indicates a pressure of 760 mm of mercury. What is this height in centimetres ?

There are 10 mm in 1 cm

76 cm

### Question 29. Calculate Brackets. Exponents. Multiplication and division. Addition and subtraction

2

### Question 30. Calculate (0.2)3

Do NOT multiply 0.2 by 3 !!!!

0.008

### Question 31. What is the value of 2 −2 ?

You could use your calculator...or...you could use the laws of indices.

0.25

### Question 32. Express 6 as a percentage of 30.

Write 6 out of 30 as a fraction i.e. 6/30
and now change to a percentage by multiplying by...

20%

### Question 33. If x = −3, what is the value of 3x2

Remember that when you square a negative number you get a positive number.

27

### Question 34. If a * b means 2a + b, what is the value of 3 * 2 ?

Substitute 3 into a and 2 into b and then work it out!

8

### Question 35. Calculate (5.2 x 10−12) x (6.5 x 109) Leave the answer in standard form to 3 decimal places.

On the calculator use the EXP button after typing 5.2 to enter numbers in standard form.

3.380 x 10−2

### Question 36. One litre of water weighs 1000 grams. What is the weight in grams of four millilitres of water?

How many millilitres in a litre?

4

### Question 37. Is 22/7 a rational number? Yes or no?

A rational number is one which can be written as a fraction.

Yes!

### Question 38. If a = 4 and b = −3, what is the value of 2ab ?

Substitute the numbers and then multiply the three things together.

−24

### Question 39. Solve the equation Turn both sides of the equation upside down.

x = 9

### Question 40. What is the least possible area for a rectangle whose sides have been measured at 15 m and 3.5 m ?

The minimum value for a measurement of 15 m is 14.5 m

50.025m2

### Question 41. What is the reciprocal of 3.5 ?

There is a reciprocal button on your calculator (1/x or x−1 OR If you are finding the reciprocal of a fraction −turn it upside down.

0.29 (to 2 decimal places)

### Question 42. Two coins are tossed at the same time.What is the probability that a head and a tail come up ?

There are 4 possibilities when two coins are tossed. HH,TT,HT,TH

0.5

### Question 43. Solve 2x - 3 = 7

Add three to both sides and then divide both sides by 2.

x = 5

### Question 44. Calculate 13 − 4 x 32

Do EXPONENTS first !!!!

−23

### Question 45. What is the value of 3x0 ?

What is the value of anything to the power of 0? (And the answer is not 0)

3

### Question 46. Approximately what is the volume of the Earth in km3 ? (Leave answer as a normal number to 3 significant figures.)

The volume of a sphere (assume the Earth is spherical) is V = 4/3 1r3

1080 000 000 000 km3

### Question 47. Express 167% as a decimal.

167% means 167/100

1.67

### Question 48. Increase \$48.00 by one third of its value.

To find one third of anything divide it by 3

\$64

### Question 49. Express 75 as a percentage of 300.

Calculate 75 ÷ 300 and then multiply by 100

25%

### Question 50. Give the formula for the surface area of a cube of length L.

How many faces does a cube have? The area of each face will be the same.

6L2

### Question 51. What is the square root of 0.16? (try to work it out without your calculator)

The positioning of the decimal point is crucial. Check your answer by multiplying it by itself.

0.4

8 x 9 = 72

### Question 53. A square has a perimeter of 64 cm. How many square centimetres in its area ?

If the perimeter of a square is 64, how long is each of its equal sides?

256 cm2

### Question 54. Each interior angle of a regular polygon is 144°.What is the sum of its exterior angles?

The interior angle and the exterior angle are the only two angles on the same straight line, so what do they add up to?

360°

### Question 55. How many sides has a rhombus?

A rhombus is a quadrilateral with all sides equal in length and opposite sides are parallel.

4

### Question 56. Evaluate (find the value of) 7 ⁺ − 8 ⁺ 5

Watch the negative!

4

### Question 57. If a house costs \$250 000 including GST at 12.5%, how much is it without GST (to the nearest cent)?

Multiply by 100 and divide by 112.5 i.e. Multiply by 8/9

\$222,222.22

### Question 58. Decrease a salary of \$150,000 by 20%

Multiply the amount by 0.8 (100 - 20)/100

\$120,000

### Question 59. Find x Use the rule that begins "The exterior angle of a triangle equals the sum of..."

25°

### Question 60. If a = 6, b = 2 and c = 3 evaluate a2bc

Work out a2 first

216

### Question 61. Write twelve thousandths as a decimal.

Which is the thousandths column?

0.012

Draw a diagram!

15 metres

### Question 63. Calculate 23 − 4 x 2 + 23

BEDMAS! Multiply before adding and subtracting.

23

### Question 64. How many milligrams in three and a half kilograms?

There are 1000 grams in 1 kilogram and 1000 milligrams in a gram.

3 500 000 g

Remember BEDMAS

17

### Question 66. WWhat is the complement of an angle of 46°?

An angle and its complement add up to 90°

44°

### Question 67. Which is bigger? The mean of 6, 5, 6, 3 OR The median of 6, 5, 6, 3

Mean is average.
Median is middle mark.

The median is the bigger.

### Question 68. My share of a Lotto jackpot is \$420. There are 7 other people in the syndicate. How much did we win altogether?

Read the question carefully. How many people are there altogether?

\$3360

### Question 69. How many minutes are there between 1.33 am and 2.17 pm on the same day?

Remember these are TIMES and not DECIMAL numbers. (There are 60 minutes in an hour!)

764 minutes

### Question 70. \$42 is shared between two people in the ratio 3:4 Jane gets the smallest share. How many dollars does she get?

How many "parts" are there altogether?

\$18

### Question 71. Two 380 g weights are added to a 600 g weight. Express the total weight in kilograms?

There are 1000 grams in a kilogram.

1.36 kg

### Question 72. How many sides has a regular polygon with exterior angles of 36°?

The EXTERIOR angles of ANY polygon add up to 360°

360/36 = 10
Therefore there are 10 sides.

### Question 73. What is 2.8% of 30?

To find 2.8% of a quantity multiply it by 0.028

30 x 0.028 = 0.84

### Question 74. The equation for a triangle containing parallel lines gives
6 . x = 9 . 4 for this triangle. The dot means "multiply")

x = 6

### Question 75. If it takes 5 hours to drive 450 km, what speed is this in metres/minute?

To change km/hr to metres/min multiply by 1000 and then divide by 60.

1500 metres/minute

### Question 76. If it takes 5 hours to drive 450 km, what speed is this in metres/minute?

To change km/hr to metres/min multiply by 1000 and then divide by 60.

1500 metres/minute

### Question 77. If a car travels 274 km in 6 hours, what is its speed in km/hr (to nearest whole number)?

Speed equals distance divided by time.

46 km/hr

### Question 78. Fully factorise 10x2− 80x + 70

Is there a COMMON factor?

10(x2 − 8x + 7)
= 10(x − 7)(x − 1)

### Question 79. What is the next prime number after 41?

Prime numbers have only themselves and 1 as factors.

43

### Question 80. How many m2 are there in 2.5 ha?

A hectare (ha) is a square with sides of 100m.

25000 m2

### Question 81. Calculate 2.19 (Give answer correct to 5 sig. fig.)

A calculator with an exponent button such as xy will obviously be of great value here!

794.28

### Question 82. What is the percentage increase if \$220 is increased to \$242?

%increase = amount of increase × 100 / original amount × 100

22 x 100 /220 = 10%

### Question 83. How many two digit numbers can be made using the digits 1, 2 and 3?

How many ways can you fill the first digit and how many ways can you fill the second digit? Remember both digits can be the same.

There are 9 ways from 11 through to 33

### Question 84. Evaluate −(2x)0

ANYTHING to the power of zero is 1 but be careful with the negative sign.

−1

### Question 85. What is the size of angle B ? Use corresponding angles but be careful!

B = 118°

### Question 86. What is 55% of 210?

Multiply by 0.55 to find 55%

115.5

### Question 87. \$360 is divided among 3 friends in the ratio 3:4:5 What is the biggest share?

How many parts are there altogether?

\$150

### Question 88. Calculate (100 − (100 − (100 − (100 + 100))))2

Start from the inside brackets first.

10 000

### Question 89. What is the size of angle PRS if PR = PQ? What do you know about the base angles of an isosceles triangle?

110°

### Question 90. Solve the equation 6 = 2x + 4

Subtract 4 from both sides and then divide both sides by 2

x = 1

### Question 91. How many vertices has a cube?

The vertices are the corners of the cube.

A cube has 8 vertices.

### Question 92. What is the mode of {6, 8, 7, 5, 5} ?

The mode of a set of numbers is the most common number.

The mode is 5

### Question 93. How many g in 2.137 kg?

There are 1000g in 1kg

2137 grams

### Question 94. What is the ratio of the surface area to volume of a cuboid of sides 5 cm by 6 cm by 7 cm? (Leave answer in simplest form)

When working out the surface area of the cuboid remember there are 6 faces to consider.

107 : 105

### Question 95. What is the y-intercept of the graph of y = 3x − 1?

If the equation is written in the form y = mx + c
the c stands for the y = intercept.

y-intercept = −1

### Question 96. A cake contains 12% sugar. How many grams of sugar are there in a 6 kg cake ?

To find 12% of a quantity multiply it by 0.12. Remember there are 1000 g in 1 kg

720 grams of sugar

### Question 97. How many kilometres in 800 cm ?

There are 100 centimetres in a metre and 1000 metres in a kilometre. So there's not going to be much of a kilometre in the answer!

0.008 km

### Question 98. Which is the bigger? 300 tonnes or 30 000 kg

There are 1000 kg in a tonne

300 tonnes is much heavier!

### Question 99. 100 sheets of paper are stacked on top of each other. The stack is 1.8 cm high. What is the thickness (in mm)of each piece of paper ?

There are 10 mm in 1 cm

Each piece of paper is 0.18 mm thick.

### Question 100. True or false? (0.2)4 = 0.16

You don't even need to get your calculator out for this one.

False
(0.2)4= 0.0016

Remember BEDMAS

5x

### Question 102. Write 8.35 correct to one decimal place.

Start counting the decimal places from the decimal point

8.4

### Question 103. What is the order of rotational symmetry of a rhombus?

Rotational symmetry is the number of times a shape maps onto itself when rotated about its middle.

2

### Question 104. Simplify 3p x 5w x 2c

Multiply the numbers first and then the variables (leave variables in alphabetical order).

30cpw/p>

### Question 105. What is the gradient of the graph of the function 4x + y = 2?

Rearrange the equation into the form y = mx + c
The gradient is the value of m.

### Question 106. If x = 0, what is the value of x2 + 5x − 3?

Replace each x with 0 and work out the value of the expression.

−3

Draw a diagram!

(3, −2)

4 + 3p

### Question 109. Solve the equation 2n − 13 = 11?

Add 13 to both sides and then divide both sides by 2.

n = 12

### Question 110. How many different ways can a total of 8 be obtained when two 6-sided dice are thrown?

Remember a 5 followed by a 3 is different from a 3 followed by a 5.

5 ways
(5, 3), (3, 5), (2. 6), (6, 2), (4, 4)

### Question 111. What is the probability that a day of the week, chosen at random, begins with a T or an S?

Write the answer as a fraction with a denominator of 7

4/7

### Question 112. What is the area of the triangle? Area of triangle = 0.5 x base x height

Area = 15 m2

### Question 113. How many cans of paint would you need to paint a solid cuboid of dimensions 30 by 80 by 60 cm with three coats of paint, if each can covers 90 000 cm2?

Remember a cuboid has 6 faces

One can

### Question 114. What is the value of x? The angle at the centre of a circle equals twice the angle at the circumference.

110°

### Question 115. What name is given to an equal sided and equiangular quadrilateral?

Choose from rhombus, square, parallelogram, kite or rectangle

Square

### Question 116. Write 8.37 x 10-2 as a decimal number

Move the decimal point two places to the ...

0.0837

### Question 117. Calculate (4.2 x 10−12) x (3.5 x 109)

Use the EXP button on your calculator to enter the two standard form numbers.

1.47 x 10−2

### Question 118. How many sides of equal length does a scalene triangle have?

An equilateral triangle has 3 equal sides, an isosceles triangle has 2 equal sides and a scalene triangle has...

...no equal sides.

### Question 119. What are the limits of accuracy of a measurement (x) of 0.5 m ?

Cover a range of half of the smallest unit on either side of the measurement.
i.e 0.05 m

0.45 ≤ x < 0.55

### Question 120. How many axes of symmetry has a rectangle?

Axes of symmetry are mirror lines drawn through the shape.

Only 2 (the diagonals are not axes of symmetry)

### Question 121. A clock gains 15 minutes every week. What is this gain as a percentage (to 2 significant figures)?

% gain = amount of gain/original amount x 100

0.15

### Question 122. Write 5/6 as a decimal correct to 3 decimal places.

Use calculator to divide 5 by 6 then round off.

0.833

### Question 123. The length of a rectangle is three times its width. If its perimeter is 24 cm what is its area?

Draw a diagram. Let the width be x. Form an equation.

27 cm2

### Question 124. How many axes of symmetry has an isosceles trapezium?

An isosceles trapezium is a trapezium (one pair of parallel sides) and the two other sides are of equal length.

One axis of symmetry

### Question 125. Is 43 a prime number?

Does it have any factors apart from 43 and 1?

Yes, it is a prime number as are 41 and 47.

### Question 126. Find a positive solution to the equation a(a + 4) = 45

This is a quadratic equation.Expand the bracket and then subtract 45 from both sides of the equation. THEN you can solve the quadratic equation by factorising.

a = 5

### Question 127. What is a speed of 60 km/hr in m/s?

Multiply by 1000 to change it to metres .. .then divide by 60 x 60 to change the hours to seconds.

17 m/s

### Question 128. 143 seconds + 397 seconds is equal to how many minutes?

Add the two numbers and then divide by 60 to change to minutes.

9 minutes

### Question 129. If a bike costs \$400 including GST at 12.5%, how much is it without GST (to nearest cent) ?

Multiply by 8 and divide by 9 (i.e. 100/112.5)

\$355.56

1 Ha = 10 000 m2

32 500 m2

### Question 131. Solve 3(2x + 5) = 0

Expand the brackets first and then find x on its own

x = −2.5

### Question 132. Simplify a + a x 5a

Remember that BEDMAS applies to algebra too.

a + 5a2

### Question 133. Calculate 2.18 (give answer correct to 5 significant figures)

Use the xy or similar button on your calculator.

378.23

### Question 134. Give the bearing equivalent to the compass direction of West

North is a bearing of 000°

270°

### Question 135. Find the value of 4x2 if x = −2

REMEMBER a (negative number)2 is equal to a positive number.

16

### Question 136. What is the mean of {6, 7, 7, 5, 5} ?

The MEAN is the AVERAGE. Add all of the numbers together and then divide by how many numbers there are.

Mean = 6

### Question 137.   Calculate (5 − (5 − (5 + (5 +5))))

Start from the innermost brackets.

15

### Question 138.   How many axes of symmetry does a rhombus have?

Axes of symmetry are mirror lines.

A rhombus has NO axes of symmetry

### Question 139. What is the ratio of the surface area to volume of a cube of side 5 cm? (Leave answer in simplest form)

Work out the surface area and volume of each and then simplify the ratio

6:5

### Question 140. Solve the equation 4x − 13 + 7x = 31

Combine the x terms and then add 13 to both sides of the equation

x = 4

### Question 141. Which points are INVARIANT under a reflection in the x-axis?

Invariant means that they do not move.

The x-axis itself is invariant. (The line y = 0)

### Question 142. A car uses 20 litres of petrol to travel 175 km. How many kilometres does it travel on 13 litres of petrol?

Divide by 20 to find out how far it would travel on ONE litre. Then multiply by ...

113.75 km on 13 litres of petrol.

### Question 143. Which is the smallest: Eleven twentieths, thirteen twenty - fifths or fifty three hundredths?

Change them all to hundredths

Thirteen twenty - fifths

### Question 144. Calculate 3 + 4 x 2 − 6

Remember BEDMAS. Multiply before Adding or Subtracting

5

### Question 145. Write 0.0879 correct to two decimal places.

Decimal places start at the decimal point.

0.09

### Question 146. How many hours are there in a week?

How many hours in a day? How many days in a week?

168 hours

### Question 147. Solve 5(x - 4) = 2(x + 5)

Expand the brackets and then take x terms to one side and numbers to other.

x = 10

### Question 148. How many minutes are there between 5.45 pm and 7.23 pm on the same day?

Remember there are 60 minutes in an hour.

98 minutes

### Question 149.  How many edges has a square-based pyramid?

Edges are where two faces meet.

8 edges

### Question 150. What is the second largest prime number between 10 and 20?

Prime numbers have only themselves and 1 as factors.

19

### Question 151. The triangles are equilateral. What is the shaded area ? Does the left hand vertex of the smaller triangle BISECT the base of the larger triangle?

Shaded area = 0.75 x 15.6 cm2 =11.7 cm2

### Question 152. How many multiples of 3 are there between 30 and 40?

Multiples of 3 are numbers such as 24, 27, 30 etc.

There are 3 multiples of three 33, 36 and 39

### Question 153. If 10 books cost \$80.60 What would 6 books cost?

Find the cost of ONE book first by dividing, and then...

Six books would cost \$48.36

### Question 154.  How many edges does a cube have?

An edge is where two faces meet.

A cube has 12 edges.

### Question 155.  What is the highest common factor of 100 and 108?

List all of the factors of each number and then find the largest. (A FACTOR is a number that divides into another without a remainder.)

H.C.F is 4

### Question 156.  What is the median of {16, 18, 17, 15, 15}?

The median is the middle score when they are arranged in order.

The median is 16

### Question 157.  16 grams = ....... mg

The prefix m means one thousandth

16 000

### Question 158.  How many degrees do the exterior angles of a hexagon add up to?

The EXTERIOR angles of any polygon always add up to ...

...360°

### Question 159.  To dig a tunnel 0.5 km long, 4 m wide and 4 m high (rectangular), how much earth, in cubic metres would have to be removed ?

Change the km into m

8000 m3

### Question 160.  Find x if 3x = 7 - 4x

Add 4x to both sides of the equation.

x = 1

1 Ha = 10000 m2

52 000

### Question 162.   To dig a rectangular-shaped tunnel 2 km long, 5 m wide and 5 m high, how much earth, in cubic metres would have to be removed?

Don't forget to change the 5 km into metres first!

50 000 m3

### Question 163. What is the lowest common multiple of 12 and 10 ?

Write out the multiples of 10 and 12 and find the lowest common one

60

### Question 164. How many vertical planes ? There are two horizontal planes. How many vertical ones?

There are 4 vertical planes.

### Question 165. Factorise x2 + 2x − 3

One of the factors is (x + 3)

(x + 3)(x − 1)

### Question 166. How many degrees do the two smallest angles of a right-angled isosceles triangle add up to?

One of the angles in the triangle is 90°

90°

### Question 167. How many centimetres in 8 kilometres?

There are: 100 centimetres in 1 metre and 1000 metres in 1 kilometre

There are 800 000 cm in 8 kilometres.

### Question 168.   Simplify 5p − (3 − p)

What effect does the negative sign OUTSIDE the bracket have on the negative sign INSIDE the bracket?

5p − (3 − p) = 5p − 3 + p = 6p − 3

22

### Question 170.  What is the value of x ? Use a combination of corresponding angles and angles on a straight line.

x = 48°

### Question 171. Expand (2x + 3)(x − 7)

There should be three terms in the final answer.

2x2 − 11x − 21

### Question 172. Solve 2(x + 3) − 3(x − 2) = 3(2 − x) ?

You'd better expand the brackets first and then take all of the x terms to one side and all of the numbers to the other.

x = -3

### Question 173.   Two of the interior angles of a cyclic quadrilateral are 103° and 21°. What are the other two angles?

The interior opposite angles of a cyclic quadrilateral add up to 180°

77° and 159°

### Question 174. For what two angles between 0° and 360° is the tangent ratio undefined?

Think of where the dotted lines are on the tangent graph ( the asymptotes)

90° and 270°

### Question 175. If a straight line has a gradient of 2, what is the gradient of its perpendicular bisector?

It will be flatter (a smaller number) and it will be a negative gradient.

- 0.5

### Question 176.  What is the upper quartile of the numbers. 3, 4, 6, 1, 2, 5, 6, 3, 9, 5, 6, 2, 4, 3?

Arrange them in order then split the numbers into 4 equal sets.

Upper quartile is 6

### Question 177.  What is the size of the exterior angles of a regular octagon?

Each outside angle is 360/(number of sides)

45°

### Question 178. Simplify 6p = 2(p − 3)

Expand the brackets first.

p = −1.5

### Question 179.  Evaluate 4 − 2 − 32

Remember that when you minus a negative it is equivalent to adding a positive. Strange but true!

−7

### Question 180. What is the size of each interior angle of a regular hexagon?

The sum of the exterior angles of any polygon is 360° and in a hexagon there are 6 of them. The interior angle plus the exterior angle add to 180°.

120°

### Question 181. True or false? −42 + −4 x −5 = −26 −4

Apply the BEDMAS rule.

FALSE! The left hand side comes out to be −22 and the right hand side is −30

### Question 182.  The size of each exterior angle of a regular polygon is 24 degrees. How many sides does the polygon have?

The exterior angles of ALL polygons always add up to 360°

The polygon has 360/24 = 15 sides

### Question 183. Factorise 3x2 + 6x

Look for the common factor

3x(x + 2)

### Question 184.  A 0.405 kg can of pears costs \$1.20, while a 125 g can of the same fruit costs \$0.40. Which is better value?

By division, work out the cost of 1 g of pears for each can.

The 0.405 kg can is better value.

### Question 185.  Two students toss a coin at the same time. What is the probability that neither of the coins comes up heads?

If neither of the coins is a head, what must they both be!

P(Tail,Tail) = 0.5 x 0.5 = 0.25

### Question 186.  Bill spends two thirds of his money at the movies and a half of what is left on his lunch. What fraction of his money remains?

When he spends two thirds, what fraction is left?

1/6

### Question 187.  Find the value of x The exterior angle of a triangle equals the sum of the two interior opposite angles.

x = 97°

### Question 188.  Find the two solutions to the equation x2 + 4x - 5 = 0

Factorise it first!

x = -5 or +1

### Question 189. Change 245 000 cm3 into m3

There are 100 x 100 x 100 cubic cemtimetres in a cubic metre.

0.245 m3

### Question 190. The mean of a golfer's first 5 rounds of the season is 73 strokes. How many strokes would she need on her next round to bring her average down to 72?

What total is needed on 6 rounds to average 72?

She would need a round of 67 strokes!

### Question 191. Give the largest number that is a multiple of 3 and also a factor of 18?

List the factors of 18 and list the multiples of 3. Then find the biggest!

18

### Question 192. Find x How many x are there? What is the total number of degrees in a quadriltateral?

9x = 360, x = 40
The biggest angle is 3x = 120°

### Question 193. Solve the equation (x + 2)2 = 9? (There are two solutions)

There are two ways. EITHER...take the square root of both sides first. (Remember plus AND minus 3!) OR...expand the brackets, re-arrange and then re-factorise.

x = -5 or 1

### Question 194. The length of the sides of a square are 12.5 cm. Between what limits do the length of its perimeter lie?

Limits of accuracy lie within half a unit either side of the measurement.

The perimeter would lie between 49.8 cm and 50.2 cm

### Question 195. The probability of passing an examination is estimated at 0.45. If 600 people sit the examination how many would you expect to pass?

Expected value = Number of people x Probability of passing

270 would be expected to pass.

### Question 196. Use your calculator to calculate 34.45 x 106 + 6.85 x 107Give the answer in standard form.

To enter a number in standard form into your calculator use the EXP button.

1.0295 x 108

### Question 197. In a triangle there are three angles A, B and C . A is half the size of B and B is twice the size of C.How big is the largest angle in the triangle?

Which is the biggest angle?

90°

### Question 198. Factorise 4x2 − 49

This looks like the "difference of two squares" i.e. Two brackets

(2x + 7)(2x − 7)

### Question 199. Write 3.502 kg in g?

There are 1000 grams in 1 kilogram.

3.502 kg = 3502 g

### Question 200. What is the mean of the following amounts: \$2.37, \$4.56, \$2.34 and \$7.65?

To get the mean of four amounts of money, add the four amounts together and then divide by 4.

Mean = \$4.23