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This presentation contains Intermediate 2 past paper questions complete with solutions for the year 2002.

The questions are sorted into topics based on the specific outcomes for the Intermediate 2 course.

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F

Topic Units 1, 2 & 32002

I II

Significant FigsScientific Notation

% Calculations 10

Volumes of Solids 6

Linear Relationships 2

Multiplying out Factorising 4

Circles: arcs, sectors, symmetry, chords 4

TrigonometrySine Cosine RulesArea of triangle

1 8

Simultaneous Equations 2

Graphs, Charts TablesCumulative FreqDotplot Boxplot5 fig summary

5

Statistics:Standard Deviation Cumulative Freq Diag Line of Best Fit Probability

1 3

Algebraic Fractions Change of SubjectSurds & Indices

7 9 11

Quadratic FunctionsGraphs, Formula 5 7

Trigonometry GraphsEquations, Identity 3 6 12

For

mul

ae L

ist

ST

AR

T P

age

This is the formula that we use

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2002 Paper 1

Solution

Scores Freq Cum Freq

70 2 2

71 3 5

72 3 8

73 3 11

74 2 13

75 2 15

76 1 16

(b) Prob (<72) = 16

5

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Solution

m = 5/2 c = 5

Equation: y = 5/2 x + 5

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2nd Quadrant: (180° – 60°) = 120°

3rd Quadrant: (180° + 60°) = 240°

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313

31234

)14)(3(

23

223

2

xxx

xxxxx

xxx

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4 5 4 1 4 3 2 2 4 6 2

3 4 4 1 3 1 2 3 1 1

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1 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 4 4 5 6

Position of median = (21 + 1) ÷ 2 = 11th No.

Q1 = (1 + 2)÷2 = 1.5

Q2 (median) = 3

Q3 = 4

5 (a)

(b)

No. of Cinema Visits

No. of football matches

(c) The median for football matches is greater (5 > 3) so on average more matches attended than going to cinema.

IQR is greater for football matches (6 > 2.5) so more

variation in attendance.

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(a) (1, -16)

(b) x = 1

x = 1

Graph crosses x axis when y = 0

(x – 1)2 – 16 = 0

x2 – 2x + 1 – 16 = 0

x2 – 2x – 15 = 0

(x + 3)(x - 5) = 0

x = -3 and x = 5

So AB = 5 + 3 = 8 units

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5

5253

5259

5245

(a) (b)

2

22

2

1

1

11

x

xx

x

x

xx

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2

0

8.5437

651001202

1

2

1

m

Sin

abSinCArea

2002 P2

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Sub into equ 13x – (2 x -1) = 11 3x + 2 = 11 3x = 11 – 2 3x = 9 x = 3

3x – 2y = 11 (eq1) x2

2x + 5y = 1 (eq2) x3

6x – 4y = 22

6x + 15y = 3

subtract -4y – 15y = 22 – 3

-19y = 19

y = -1

Check with eq2 2x + 5y = 1 2 x 3 + 5 x -1= 6 – 5= 1 √

Solution (3, -1)

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(b) Mean price is the same so on average milk prices in

local stores and supermarkets are similar.

Standard deviation of the local stores is much higher than the supermarkets, 17.7 > 10.5, so there is more variation in their prices.

49.10 110 5

550

16

3197432524

32524597975897066

319746

191844

6

)438(

)(

736

438 )(

438597975897066

2222222

22

s

x

n

x

n

xxMean

x

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Circumference of complete ‘circle’ = ∏ x D

= 3.14 x 40

= 125.6 cm

Fraction of circle

pendulum swings thru = 28.6 ÷ 125.6

= 0.227707

Angle pendulum swings thru = 0.227707 x 360°

= 81.97°

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= 3y(y – 2)

= (y + 3)(y – 2)

3) (y

3y

2)– 3)(y (y

2)– 3y(y

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Vol required = vol of whole cone – vol of bottom cone

Vol = (⅓ x π x 82 x 32) - (⅓ x π x 52 x 20)

= 2143.57 – 523.333

= 1620.24

= 2000 cm³ (1 sig fig)

Watch for radius!

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1d.p. to1.8-or 3.0

1.78-or 28.04

173

4

173

4

)8(93

22

)124()3(3

1 3 2

0132

2

2

or

x

cba

xx

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m

hOpp

7.21

Sin2538.51

Sin380

0

Total height of pole = 21.7 + 1.6

= 23.3m

mSin

Sin

SinSin

aSinT

t

SinA

a

38.51122

3380a

Sin3308aSin122

multiply) (cross 122

80

33

122)2533(180T Angle 0

B33°

122°

T

A 80m

a

B

51.38mOpp

1.6m33°

SOH CAH TOA

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Solution

Pythagoras

a² = c² – b²

=2.5² – 1.5²

a = √4 = 2m

2.5m

1.5m

a

2.5m

2.5m

d

d = 2.5 – 2

= 0.5m

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Solution

Newtown’s Population

In 2yrs = 50 000 x 1.052 = 55 125

In 3yrs = 50 000 x 1.05³ = 57 881Coaltown’s Population

In 2yrs = 108 000 x 0.82 = 69 120

In 3yrs = 108 000 x 0.8³ = 55 296

In 3 yrs time Newtown’s population will be greater. i.e. 57 881 > 55 296

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x

x

xx

3

3

26

26

2

2

2

1

2

3

2

1

2

3

Swop sides

3

2t– r p

2t– r 3p

r 2t 3p

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(a) H = 10 + 5Sin10° = 10.87m

(b) H = 12.5m

10 + 5Sint° = 12.5

5Sint° = 2.5

Sint° = 2.5 ÷ 5 = 0.5

Sine positive in quadrant 1 and 2

Acute angle: t = sin-1(0.5) = 30

2nd quad: t = 180 – 30 = 150

t is in seconds, so height is 12.5m

after 30s and 150s