1. Main Grid 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. To access a particular question from the main grid click on the question number. To get the solution for a question press the space bar. To access the formula sheet press the button To begin click on Main Grid button. PRESS F5 TO START F

2. Topic Units 1, 2 & 3 2002 III Significant Figs Scientific Notation % Calculations 10 Volumes of Solids 6 Linear Relationships 2 Multiplying out Factorising 4 Circles: arcs, sectors, symmetry, chords 4 Trigonometry Sine Cosine Rules Area of triangle 1 8 Simultaneous Equations 2 Graphs, Charts Tables Cumulative Freq Dotplot Boxplot 5 fig summary 5 Statistics: Standard Deviation Cumulative Freq Diag Line of Best Fit Probability 13 Algebraic Fractions Change of Subject Surds & Indices 799 1111 Quadratic Functions Graphs, Formula 5 7 Trigonometry Graphs Equations, Identity 3 63 612 Formulae List START Page

3. This is the formula that we use

4. Main Grid 2002 Paper 1 Solution ScoresFreqCum Freq 7022 7135 7238 73311 74213 75215 76116 (b) Prob (<72) =

5. Main Grid Solution m = 5 / 2 c = 5 Equation:y = 5 / 2 x + 5

6. Main Grid Solution 2 nd Quadrant: (180° – 60°) = 120° 3 rd Quadrant:(180° + 60°) = 240°

7. Main Grid Solution

8. Main Grid Solution 4 5 4 1 4 3 2 2 4 6 2 3 4 4 1 3 1 2 3 1 1

9. Main Grid 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 = 11 th 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.

10. Main Grid Solution (a) (1, -16) (b) x = 1 x = 1 Graph crosses x axis when y = 0 (x – 1) 2 – 16 = 0 x 2 – 2x + 1 – 16 = 0 x 2 – 2x – 15 = 0 (x + 3)(x - 5) = 0 x = -3 and x = 5 So AB = 5 + 3 = 8 units

11. Main Grid Solution (a) (b)

12. Main Grid Solution 2002 P2

13. Main Grid Solution Sub into equ 1 3x – (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)

14. Main Grid Solution

15. Main Grid (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.

16. Main Grid Solution

17. Main Grid 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°

18. Main Grid Solution = 3y(y – 2) = (y + 3)(y – 2)

19. Main Grid Solution

20. Main Grid Vol required = vol of whole cone – vol of bottom cone Vol = ( ⅓ x π x 8 2 x 32) - ( ⅓ x π x 5 2 x 20) = 2143.57 – 523.333 = 1620.24 = 2000 cm³ (1 sig fig) Watch for radius!

21. Main Grid Solution

22. Main Grid Solution

23. Main Grid Total height of pole = 21.7 + 1.6 = 23.3m B 33° 122° T A 80m a B 51.38m Opp 1.6m 33° SOH CAH TOA

24. Main Grid Solution Pythagoras a² = c² – b² =2.5² – 1.5² a = √4 = 2m 2.5m 1.5m a 2.5m d d = 2.5 – 2 = 0.5m

25. Main Grid Solution Newtown’s Population In 2yrs = 50 000 x 1.052 = 55 125 In 3yrs = 50 000 x 1.05³ = 57 881 Coaltown’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

26. Main Grid Solution Swop sides

27. Main Grid Solution

28. Main Grid (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 2 nd quad: t = 180 – 30 = 150 t is in seconds, so height is 12.5m after 30s and 150s