Revision questions for the Mid-term break

These are the questions you should try to work through over the mid-term break. Attempt as much of it as you can after revising the related chapters.
If you get stuck, check here over the course of next week, as I may post some tips for each section.
In the classes after the mid-term break, we will cover as much ground as possible and hopefully resolve any issues that you got stuck on.

I will add some help in blue text like this for some of the questions over the next few days.
I have now finished adding my notes - you can add a comment here if you need more help.

Paper 1
Question 1 - Arithmetic
Page 135 q4, 5 (In q4b, put all money amounts into either euro or cent.In q4c, remember the way we laid out these questions - you need to navigate backwards from the net tax, adding pack tax credits etc.)

Question 2,3 - Algebra
Page 22 q2 (In part b and c you should tidy up the equations with fractions by multiplying across by the number under the line. In the evaluation questions, write on the page e.g. 2(-2)² - 3(-2)(1/3) before you go to your calculator.
Page 40 q6 (part a: find LCM of the denominators. Part b: remember that (x-2)² = (x-2)(x-2). Part c: remember that if say x=2 is a root of the equation, it means that if you sub x=2 in to the equation it will balance. There will be only 1 unknown which you can solve.)
Page 156 q3, 7 (Part b: Use the rules on page 140 to work out how to write 1/27 as 3 to the power of something. A clue is that 3³=27. Also note that 3²=9. Write both sides of the equation as 3 to the power of something and then equate the powers.)

Question 4 - Complex Numbers
Page 78 q6 (For all these questions, you need to revise argand diagrams, complex conjugates, modulus and division of complex numbers. For part b see the top of page 76 for a similar question.)

Question 6,7,8 - Functions and Calculus
Page 281 q 6 (For part bi) the coordinates of a and b are both going to be (something, 0) as they are both on the x-axis, or y = 0. So if you solve the equation x² +2x -3 = 0 you will get the two values of x. c is on the Y-axis, so this means that x=0. Sub this value of x in to x² +2x -3 and you will get the output value y. Part iii is like a repeat of part i with =0 replaced by = -3. Remember that you can only solve quadratic equations with = 0 on the right hand side so you need to rearrange it before solving.)
Page 306 q2, 4 and 5(a) (For q2, you need to use the quotient rule for ii and iii. In iii you can write as a single fraction, but you can't simplify the top of the fraction. First principles is coming up on the mock exam, worth 20 marks, so practice a few of these. Make sure you always check your answer f(x) =x² -4x so f'(x) = 2x -4. For part c, you need to get the 1st derivative and set up an equation with this = 2. Note you are asked for the point on the curve, so this means you have to give an (x,y) pair and you can find y by subbing x into the original function. Turning point occurs where slope = 0, check your notes on the shape of a function (wine-glass upsidedown or right way up) to work out if it is a max or a min.)


Paper 2
Question 1 - Perimeter area and volume
Page 175 q14 (Remember the relationship between the radius, the height and the slant height of a cone - a right angle triangle. For the last part of the question, you need to set up an equation: vol of cylinder = 5 × vol of cone. Leave both volumes in terms of π.)
Page 184 q5, page 185 q7 (Straightforward Simpson's Rule questions, the second one has an unknown as one of the heights.)
Page 189 q5 (Part b works out exactly if you use π = 22/7)

Question 2 and 3 - Coordinate Geometry of Line and Circle
Page 58 q5, 13 (For q5: remember that the corners of a parallelogram are always given either clockwise or anti-clockwise in order. Try drawing a rough sketch and solve using translations. For q 13 you check if a point is on a line by subbing. The word "verify" means that the point is on the line. To find the equation of the image of a line you have to find the two points on the line, find the slope (*) and plug values into y -y1 = m(x - x1).
(*) Note that the slope won't change under translation so that step isn't necessary.)
Page 61 q1 (Remember how to calculate the slopes of perpendicular lines - invert and change sign. For part c, find the distance between a and b. Then set up an equation with the distance formula subbed in for a(1,6) and c(2,y) on the left hand side and the distance between a and b on the right hand side. To solve this equation, your first step will be to square both sides before re-arranging it as ...x² ...x....a number =0 and solving.)
Page 208 q3 (Very straightforward circles question if you revise the chapter. You prove if a point is on a circle exactly the same way that you prove a point is on a line - by subbing in (x,y).) To prove the last part, you need to find the equation of the line that the 2 points (centres of the circles) are on .... slope, y-y1= m(x-x1) etc.)

Question 6 - Probability
Page 239 q2 (Revise the notation. Large brackets with e.g. 5 on top and 2 below means "5 choose 2" - in other words how many ways can you choose 2 people from a group of 5. The answer is (5×4)/(2×1) and you can work this out using the nCr button on your calculator.)
Page 256 q6 (Part b could be solved with a sample space B1 B2 G1 G2. If you write the sample space correctly (should have 24 rows) then you can just count the number of cases where the 2 girls are in the middle and express P(2 girls in middle)=this number/24. For part c, this is like the one we did in class. If the number has to be bigger than 9000 then there is only 1 option for the first position, 4 left for the second position etc. If the number must be even then there are 3 options for the last position. Remember to always start with the most restricted positions.)

Question 7 - Statistics
Page 105 q2 (Note the means are different, but the two sets of data are equally "spread out". Make a table with the values in the first column, the difference between it and the mean in the next column, this value squared next and so on. Follow the steps on the previous page.)
Page 110 q7 (For the median, you have to imagine the data written out long (i.e. not in a frequency distribution. It would be 2 2 2 3 3 3 3 5 6 6 and the median value would be the middle value. When drawing the ogive in part b, be sure to put the frequency (i.e. number of students) on the vertical axis. If there are 40 students, then the last entry in the cumulative frequency table should be 40. The median student will be the 20th student, lower quartile will be the 10th student and upper quartile will be the 30th student. Find these students on the vertical axis and then draw lines across to your curve and down to read the corresponding marks on the horizontal axis. Remember the interquartile range is a number (not an upper and lower number as in the range of a periodic function.))

Question 11 - Linear Programming
Page 396 q3, 6 (For both of these, use points to find slope, then use slope and one point to find equation of the line, then use a test point to decide the direction of the inequality).
Page 414 q6 (For part b, your first inequality has to do with "number of people the chalet types can accomodate. Don't forget that x is the number of type A that the builder is going to build - so if he builds 10 of them then they can accommodate 6x or 6%times;10 = 60 people. When graphing don't forget to shade in the appropriate region, taking the two implicit inequalities x ≥ 0 and y ≥0 into account. For part ii, you need to work out the intersection point of the two diagonal lines on your graph using simultaneous equations and then maximise the expression you create using the additional information you're given about rent.)