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## Purple questions are about STATISTICS

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### Question 1. How many sides does an octagon have?

A pentagon has 5 sides and an octagon has more!

A octagon has 8 sides.

### Question 2. Calculate 3 x 102 + 4 x 102

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

300 + 400 = 700
= 7.0 x 102

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

Work out the expression inside the bracket first.

49

### Question 4. What is the sum of the interior angles of an isosceles triangle?

All triangles have the same number of degrees.

180°

4

Remember BEDMAS

12

### Question 7. List the prime numbers between 10 and 20.

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

11, 13 ,17 and 19

### Question 8. How many millimetres in 2.3 cm?

There are 10 millimetres in a centimetre.

23 mm

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

Product means "multiply"
Difference means "subtract"

3 or −3

### Question 10. Solve 3x − 2 = 13

Add 2 to both sides of the equation.

x = 5

### Question 11. What is 0.96 as a fraction in its simplest form?

How many hundredths are there in 0.96?

24/25

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

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

Total order of symmetry = 2 + 2 = 4

### Question 13. A clock loses 25 minutes every week. What is this loss as a percentage (to 2 s.f.)?

How many minutes in a week?

Percentage Loss
=[25/(24 x 60 x 7)] x 100
= 0.25% (to 2 s.f.)

### Question 14. A meal for 4 people uses 3 eggs. About how many eggs are needed if the meal is to be made for 11 people? How many eggs would ONE person need?

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

Draw a 6-sided regular polygon and see how many times you can rotate it onto itself!

6

### Question 16. What is the image of the point (3,2) after a reflection in the y-axis followed by a half turn (180°) rotation about the point (0,0)?

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

(3, −2)

### Question 17. How many square centimetres is the surface area of a cube of side 3 cm ?

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

54

### Question 18. Write 505.7 x 10−2 as an ordinary number.

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

5.057

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

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

270°

### Question 20. Write the fraction 27/50 as a decimal?

Change the denominator to 100

0.54

### Question 21. Expand (6x − 1)(2x − 3)

Multiply 6x by 2x then 6x by −3 etc.

12x2 − 20x + 3

### Question 22. Expand 2(x − 1)2

Multiply x by 2x then x by −1 etc. then multiply everything by 2

2x2 − 4x + 2

### Question 23. What is 30% of 210?

Multiply 210 by 0.30 (this is the DECIMAL form of 30%).

210 x 0.3 = 63

### Question 24. How many one litre cans of paint would you need to buy to paint a solid cuboid of dimensions 30 cm by 50 cm by 20 cm with three coats of paint if each can of paint covers 10 000 cm2?

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

Two cans of paint would be needed. (18 600 cm2)

### Question 25. Simplify 5a x 3b x 2a

Multipy numbers first and then the variables.

30a2b

### Question 26. Which is the solution for the inequation 3x < −15

Divide both sides of the inequation by 3 first.

x < −5
e.g. −6

### Question 27. What name is given to the area above the line AB? Begins with "s"

The area above chord AB is a SEGMENT.

### Question 28. A barometer indicates a pressure of 772 mm of mercury. What is this height in metres ?

There are 1000 mm in 1 m

0.772 m

Use BEDMAS

−1

Exponents FIRST

4.32

### Question 31. What is the value of 23?

You should not need to use your calculator!

8

### Question 32. Express 8 as a percentage of 40.

Write 8 out of 40 as a fraction i.e. 8/40
and now change to a percentage by multiplying by...

20%

### Question 33. If x = −2, what is the value of 2x2?

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

8

### Question 34. If a * b means 2a + ab, what is the value of 4 * 3?

Substitute 4 into a and 3 into b and then work it out!

20

### Question 35. Calculate (3 x 104) x (4 x 105) Leave the answer in standard form.

On the calculator use the EXP button after typing 3 to enter numbers in standard form.

1.2 x 1010

### Question 36. One tonne of water weighs 1000 kilograms. What is the weight in kilograms of a quarter of a tonne of water?

What is a quarter as a decimal.

250 kg

### Question 37. Is 2.5 an integer? Yes or no?

No clues!

No!
Integers are ... −2, −1, 0, 1, 2 ...

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

Substitute the numbers and then multiply the three things together.

12

### 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 3 m and 4 m?

The minimum value for a measurement of 3 m is 2.5 m.

8.75 m2

### Question 41. What is the reciprocal of 4?

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.

0.25

### Question 42.Two coins are tossed at the same time. What is the probability that two heads come up?

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

0.25

### Question 43. Solve 2x + 4 = 9

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

x = 2.5

### Question 44. Calculate 13 − 4 x −2

Do the MULTIPLYING first!!!!

21

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

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

1

### Question 46. What is the volume of the cube with a side length of 4 cm in cm3?

The volume of a cube is l3

64 cm3

33% means 33/100

0.33

### Question 48. Increase \$75.00 by one third of its value.

To find one third of anything divide it by 3

\$100

### Question 49. Express 35 as a percentage of 700.

Calculate 35 ÷ 700 and then multiply by 100

5%

### Question 50. Give the formula for the surface area of a cylinder of length L in terms of its diameter D, including both ends.

The surface area of a cylinder is 2πrl.
The area of each end is πr2
Diameter D = 2r ### Question 51. What is the square root of 0.04? (try to work it out without your calculator)

The positioning of the decimal point is crucial.

0.2

64 + 81 = 145

### Question 53. A square has a perimeter of 36 cm. How many square centimetres in its area ?

"If the perimeter of a square is 36, how long are each of its equal sides?"

81 cm2

### Question 54. Each exterior angle of a regular polygon is 20°. How many sides does this polygon have?

What do the exterior angles of any polygon add up to?

18

4

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

A negative plus a negative gives a bigger negative!

−18

### Question 57. If a house costs \$500,000 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

\$444,444.44

### Question 58. Decrease a salary of \$250,000 by 9%

Multiply the amount by 0.91 (100 - 9)/100

\$227,500

### Question 59. Find x in the diagram 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 2a2bc

Work out a2 first

432

### Question 61. What is the reciprocal of 4?

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.

0.017

### Question 62. The length of a netball court is twice its width. If its perimeter is 150 metres how far is it from the centre spot to the sideline?

Draw a diagram and let the length be 2x and the width be x

12.5 metres

### Question 63. The area of a banner is 6 m2. What is the area of the banner in cm2

1 m2 = 10 000 cm2

60,000 cm2

### Question 64. How many metres in 3.05 km?

There are 1000 metres in 1 kilometre.

3050 metres

Remember BEDMAS

−17

### Question 66. What is the supplement of an angle of 146°

An angle and its supplement add up to 180°

34°

### Question 67. What is the median 12 cm, 5 cm, 9 cm and 3cm?

Arrange in order and find the middle one.

7 cm

### Question 68. My share of a Lotto jackpot of \$30. There are 10 other people in the syndicate. How much did we win altogether?

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

\$330

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

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

1484 minutes

### Question 70. \$72 is shared between three people in the ratio 3 : 4 : 2. Jane gets the smallest share. How many dollars does she get?

How many "parts" are there altogether?

\$16

### Question 71. Three 380 g weights are added to two 600 g weight. Express the total weight in kilograms.

There are 1000 grams in a kilogram.

2.34 kg

### Question 72. How many sides does a regular polygon with exterior angles of 20° have?

The EXTERIOR angles of ANY polygon add up to 360°.

360/20 = 18
Therefore there are 18 sides.

### Question 73. What is 18% of 50?

To find 18% of a quantity multiply it by 0.18

9

### Question 74. One of the exterior angles of a triangle is 79° and one of the interior angles is 48°. What is the size of each of the other two interior angles?

The interior angles of a triangle add up to 180°

101° and 31°

### Question 75. If it takes 9 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.

833 metres/minute (to 3 s.f.)

### Question 76. If a car travels 1000 km in 12 hours, what is its speed in km/hr (to nearest whole number)?

Speed equals distance divided by time.

83 km/hr

### Question 77. What is the reciprocal of 0.8?

Use a calculator (1/x or x−1 button) or turn 4/5 upside down!

1.25

### Question 78. Fully factorise x2 − 8x − 20

Which two numbers multiply to −20 and add to −8?

(x + 2)(x − 10)

### Question 79. What is the next prime number after 53?

Prime numbers have only themselves and 1 as factors.

59

### Question 80. How many m2 are there in 4.5 ha?

A hectare is a square with sides of 100 m.

45 000 m2

### Question 81. Calculate 3.15 (Give answer correct to 4 sig. fig.)

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

286.3

### Question 82. What is the percentage increase if \$200 is increased to \$250?

% increase =
amount of increase x 100
original amount

50 x 100 / 200 = 25%

### Question 83. How many two digit numbers can be made using the digits 1, 2, 3 and 4?

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.

4 x 4 = 16 numbers
from 11 to 14
from 21 to 24
from 31 to 34
from 41 to 44

### Question 84. Evaluate (−2x)2

(negative) x (negative) = positive

4x2

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

B = 118°

45% means 0.45

85.5

### Question 87. \$720 is divided among 3 friends in the ratio 3:4:5. What is the biggest share?

How many parts are there altogether?

\$300

### Question 88. Calculate (10 + (10 + (10 + (10 + 10))))2

Start from the inside brackets.

2500

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

70°

### Question 90. Solve the equation 16 = 2x − 4

Add 4 to both sides and then divide both sides by 2.

x = 10

### Question 91. How many vertices does a cuboid have?

The vertices are the corners of the cuboid.

A cuboid has 8 vertices.

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

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

The mode is 5.

### Question 93. How many kg in 21 300 g?

There are 1000g in 1kg

21.3 kg

### Question 94. What is volume of a cuboid of sides 5 m by 65 cm by 7 cm?

Care with the units!

2 275 000 cm3
or
2.275 m3

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

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

### Question 96. A cake contains 17% sugar. How many grams of sugar are there in a 4 kg cake ?

To find 17% of a quantity multiply it by 0.17. Remember there are 1000 g in 1 kg

680 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 kilometere in the answer!

0.008 km

### Question 98. Which is the bigger? 30 kilograms or 3 000 000 mg

There are 1000 mg in 1 g and 1000 g in 1 kg

30 kilograms is much heavier!

### Question 99. A blanket covers an area of 6 m2. What is this area in cm2?

There are 10 000 cm2 in 1 m2

60 000 cm2

### Question 100. True or false? (0.2)2 = 0.4

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

False
(0.2)2 = 0.04

### Question 101. Simplify 8x + (x − 6x)

Remember BEDMAS (Brackets first)

3x

### Question 102. Write 8.36 correct to one significant figure.

Start counting at the first non-zero digit.

8

### Question 103. How many axis of symmetry does a rhombus have?

Axes of symmetry are mirror lines.

2

### Question 104. Simplify 3p x 5p

Multiply the numbers first and then the variables.

15p2

### Question 105. What is the gradient of the graph of the function y = 2x + 3?

For the function y = mx + c
The gradient is the value of m

### Question 106. If x = 1, what is the value of 2x2 + 5x?

Replace each x with 1 and work out the value of the expression

7

Draw a diagram!

(−3, 2)

10 − p

### Question 109. Solve the equation 4n − 10 = 20?

Add 10 to both sides and then divide both sides by 4.

n = 7.5

### Question 110. How many different ways can a total of 4 be obtained when two 6-sided dice are thrown?

Remember a 3 followed by a 1 is a different from a 1 followed by a 3.

3 ways
(1, 3), (3, 1), (2, 2)

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

Write the answer as a fraction with a denominator of 7

2/7

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

Area = 15 m2

### Question 113. What is the volume of a cuboid of dimensions 3 m by 80 cm by 60 cm in m2?

Watch out for the units?

1.44 m3

### Question 114. What is the value of x, when 6x = 3x + 12?

Get the x terms to one side of the equation.

x = 4

### Question 115. What name is given to an equiangular three sided polygon with equal length sides?

It must be a triangle of some sort!

An equilateral triangle

### Question 116. Write 8.37 x 102 as a decimal number

Move the decimal point two places to the ...

837

### Question 117. Calculate (4.2 x 103) x (3.5 x 102)

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

1.47 x 106

### 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 is 345.6 in standard form?

Write the number as a number between 1 and 10 multiplied by a power of 10

3.456 x 102

### Question 120. How many axes of symmetry does a parallelogram have?

Axes of symmetry are mirror lines drawn through the shape.

Zero!
(the diagonals are not axes of symmetry)