1. Problem: A pie chart shows the family's monthly expenditure with angles for each category. (a) Find the percentage spent on Food. (b) Given total expenditure 4500, find amount spent on Rent. 2. Problem: A class of 40 students' favorite subjects are given. Calculate angles for a pie chart. 3. Problem: A student’s weekly study time distribution is given in percentages. (a) Convert percentages to degrees. (b) Calculate hours spent on Mathematics if total study time is 30 hours. 4. Problem: Given functions $y=x^2+2x-3$ and $y=-x+1$. (a) Graph both functions. (b) Find points of intersection. (c) Write solutions of the equation $x^2+2x-3=-x+1$. 5. Problem: Height of a ball $h=-t^2+6t+2$. (a) Complete table for $t=0,1,2,3,4,5$. (b) Plot height vs time. (c) From graph find: (i) Maximum height. (ii) Time ball hits ground. 6. Problem: Survey of 60 students' favorite fruits. (a) Draw vertical bar graph. (b) Find most preferred fruit. (c) Find percentage choosing Apple. 7. Problem: Number of boys and girls in SHS 3 classes. (a) Draw double bar graph. (b) Find class with greatest gender difference. (c) Find total students. 8. Problem: Marks of 30 students. (a) Group marks into intervals of width 5. (b) Construct frequency table. (c) Draw histogram. (d) State modal class. --- ### Solutions 1. 1. Total angle in pie chart is $360^\circ$. 2. Percentage for Food = $\frac{120}{360} \times 100 = 33.33\%$. 3. Amount spent on Rent = $\frac{90}{360} \times 4500 = 1125$. 2. 1. Total students = 40. 2. Angle for each subject = $\frac{\text{number of students}}{40} \times 360$. 3. Mathematics: $\frac{10}{40} \times 360 = 90^\circ$. 4. English: $\frac{8}{40} \times 360 = 72^\circ$. 5. Science: $\frac{12}{40} \times 360 = 108^\circ$. 6. Social Studies: $\frac{6}{40} \times 360 = 54^\circ$. 7. ICT: $\frac{4}{40} \times 360 = 36^\circ$. 3. (a) 1. Convert percentages to degrees: multiply by 3.6. 2. Science: $25\% \times 3.6 = 90^\circ$. 3. Mathematics: $35\% \times 3.6 = 126^\circ$. 4. English: $20\% \times 3.6 = 72^\circ$. 5. Other subjects: $20\% \times 3.6 = 72^\circ$. (b) Hours on Mathematics = $35\% \times 30 = 10.5$ hours. 4. (a) Graph $y=x^2+2x-3$ (a parabola) and $y=-x+1$ (a line). (b) Find intersection by solving $x^2+2x-3 = -x+1$. (c) Rearrange: $x^2+3x-4=0$. Solve quadratic: $$x=\frac{-3 \pm \sqrt{3^2 - 4\times1\times(-4)}}{2} = \frac{-3 \pm \sqrt{9+16}}{2} = \frac{-3 \pm 5}{2}$$ Solutions: $x=1$ or $x=-4$. Find $y$ values: For $x=1$, $y=-1+1=0$. For $x=-4$, $y=4+1=5$. Points of intersection: $(1,0)$ and $(-4,5)$. 5. (a) Calculate $h$ for $t=0,1,2,3,4,5$: $t=0$: $h=0+0+2=2$ $t=1$: $h=-1+6+2=7$ $t=2$: $h=-4+12+2=10$ $t=3$: $h=-9+18+2=11$ $t=4$: $h=-16+24+2=10$ $t=5$: $h=-25+30+2=7$ (b) Plot points $(t,h)$. (c)(i) Maximum height is $11$ meters at $t=3$ seconds. (c)(ii) Ball hits ground when $h=0$: Solve $-t^2+6t+2=0$. Multiply by -1: $t^2 -6t -2=0$. Use quadratic formula: $$t=\frac{6 \pm \sqrt{36 + 8}}{2} = \frac{6 \pm \sqrt{44}}{2} = \frac{6 \pm 2\sqrt{11}}{2} = 3 \pm \sqrt{11}$$ Approximate: $t=3 - 3.316$ (negative, discard), $t=3 + 3.316 = 6.316$ seconds. Ball hits ground at approximately $6.32$ seconds. 6. (a) Vertical bar graph with fruits on x-axis and number of students on y-axis. (b) Most preferred fruit is Mango with 22 students. (c) Percentage choosing Apple = $\frac{10}{60} \times 100 = 16.67\%$. 7. (a) Double bar graph with classes on x-axis, bars for boys and girls. (b) Differences: 3A: $|20-18|=2$ 3B: $|15-22|=7$ 3C: $|19-17|=2$ 3D: $|12-20|=8$ Greatest difference in 3D. (c) Total students = sum all boys and girls = $(20+18)+(15+22)+(19+17)+(12+20)=38+37+36+32=143$. 8. (a) Class intervals: 10-14, 15-19, 20-24, 25-29, 30-34, 35-39, 40-44. (b) Frequency table: 10-14: 3 (12,14,13) 15-19: 6 (17,15,19,18,16) 20-24: 5 (20,23,21,22,24) 25-29: 5 (25,28,27,26,29) 30-34: 4 (30,32,31,33) 35-39: 5 (35,38,34,39,37) 40-44: 2 (40,42,41) (c) Histogram bars heights correspond to frequencies above. (d) Modal class is 15-19 and 25-29 and 35-39 (all with frequency 5), so multiple modal classes. --- Final answers summarized: 1(a) 33.33%, (b) 1125 2(a) Angles: Math 90°, English 72°, Science 108°, Social Studies 54°, ICT 36° 3(a) Degrees: Science 90°, Math 126°, English 72°, Others 72°; (b) Math hours 10.5 4(b) Intersection points: (1,0) and (-4,5) 5(c)(i) Max height 11m at t=3s; (ii) hits ground at ~6.32s 6(b) Most preferred: Mango; (c) Apple 16.67% 7(b) Greatest difference in 3D; (c) Total students 143 8(d) Modal classes: 15-19, 25-29, 35-39