Math Exam Prep: Calculations and Ratios

Exam Preparation Information

• Exam preparation courses for CSEC Chemistry, Physics, and ADMS are in progress.
• The preparation course lasts for approximately four months.
• Interested students can contact Terry via WhatsApp to inquire.
• Terry's students have achieved high rankings, including a fourth-place in CSEC Chemistry in 2024.
• Another student placed ninth in CSEC Mathematics.

Question 1 Part A: Calculation

• The term "of" indicates multiplication in the context of the question.
• 2/3 multiplied by (1/8 + 5/2 divided by 1/9)
• The result is 207/12 or other equivalent improper fractions

Question 1 Part B: Standard Form

• 314.2 minus (26082 divided by 521.64)
• Result of the calculation is 313.7.
• To convert to standard form, the decimal point is shifted two places to the left and the answer becomes 3.137 x 10^2

Question 1 Part C: Ratios

• Juice case packing problem with apple, orange, and pineapple juices in a 2:5:1 ratio respectively.
• There are 24 boxes of juice in each case.
• To find the number of pineapple boxes, you calculate 1/8 of the total boxes in a case (24).
• There are three boxes of pineapple juice in each case.

Problem with Question 1 Part C: Profit Calculation

• The profit from pineapple juice boxes is given, and the price per box is $3.34.
• The question asks to show that the cost price is $2.35, and percentage profit should be calculable.
• Crucially, the number of cases Jim packed is missing.
• This missing data prevents solving the for-profit percentage, which equals (profit / cost price) * 100.

Question 2 Part A: Factorization

• Factorize x^2 - 49.
• Recognize the expression as the difference of two squares.
• Results in (x + 7)(x - 7).

Question 2 Part B: Quadratic Factorization

• Factorize x^2 + 2x - 35.
• Results in (x + 7)(x - 5).

Question 2 Part C: Simplification

• Simplify the expression (x^2 - 49) / (x^2 + 2x - 35).
• Use the factorized forms from previous questions: (x + 7)(x - 7) / (x + 7)(x - 5).
• Simplify to (x - 7) / (x - 5).

Question 2 Part D: Subject of the Formula

• Rearrange the formula S = K - m^2 to make m the subject.
• m = sqrt(K - S).

Question 2 Part E: Inequalities

• Lisa has $56 to buy red and green balloons, with no more than 70 balloons total.
• X represents red balloons costing $0.75 each, and Y represents green balloons costing $0.50 each.
• Lisa buys more green than red balloons, with at least 15 red balloons.
• Inequality 1: 0.75X + 0.50Y <= 56 (total cost).
• Inequality 2: X + Y <= 70 (total balloons).
• Inequality 3: Y > X (more green than red).
• Inequality 4: 0.75X + 0.50Y = 15 (at least 15 red).

Question 2 Part F: Proportionality

• Y varies inversely proportional to x - 2.
• This is expressed as Y = k / (x - 2), where k is a constant.
• When X is 11, Y is 9, so 9 = k / (11 - 2) = k / 9.
• Solving for k gives k = 81, making the equation Y = 81 / (x - 2).
• To find Y when X is 29, substitute X, giving Y = 81 / (29 - 2) = 81 / 27 = 3.

Question 3 Part A: Regular Hexagon Angles

• Angle sum of interior angles = (n-2) * 180 degrees.
• Each interior angle of a regular hexagon is 120 degrees.

Question 3 Part B: Calculating Angles

• Angle LWX calculation: Determine angle ZWQ, which is part of triangle ZWQ, an isoceles triangle
• Angle ZWQ is determine as being 30', so angle LWX can be calculated and is 60'.

Question 3 Part C: Construction Explanation

• Constructing a lampost location on a field diagram involves: Construct a 30* angle at point S
• It also involves locating L on the perpendicular bisector of UR.
• The intersection of both lines determine the location of the point L.

Question 4 Part A: Midpoint Formula

• Midpoint formula is ((x1+x2)/2, (y1+y2)/2)
• Use formula to determine midpoint with points C(-5,6) and D(7,2), which becomes (1,4)

Question 4 Part B: Gradient Formula

• Gradient formula is (y2-y1)/(x2-x1)
• Use formula to determine gradient with points C(-5,6) and D(7,2), which becomes -1/3

Question 4 Part C: Perpendicular Bisector

• If the equations are perpendicular gradients become the negative reciprocal.
• New point becomes y=3x+c, sub in coordinates
• Solution is Y=3x+1

Question 4 Part D: Line Equation

• Parallel lines have the same gradient
• The Equation of the line is y = -1/3x + 1

Question 5 Part A Table and Frequency

• To find the mean of a data set you need to create a new calculation (XF) or X*Frequency.
• You then need to take the sum of XF dividied by sum of F
• Sum of XF = Sigma XF
• Sum of Frequency = Sigma F
• Solution is Sum of XF / Sum of F therefore 300 / 40 = 7.5

Question 5 Part B Table Mode and Median

• To calculate Mode, you need to fidn which value had the highest frequency
• In this scenario the Modal Mark is 6
• Medians need the average of 2 values to be determined, as there is no exact middle.
• The 20th student received a score of 7
• The 21st student received a score of 8
• Average the 2 and result is 7.5

Question 5 Part C Pie Chart Frequency

• Frequency over total number of values * 360 = frequency angle.
• angle = frequency pie chart answer.
• Solution is 81*.

Question 5 Part D Dice Probability

• Dice have six faces, so 1/6 is probability of landing on any one number, assuming it is a fair value.
• The word 'fair' means the possibility of each outcome is 1/6
• Not getting a 2 results in landing on 5 possible values therefore 5/6 is solution.

Question 5 Part E Dice Probability

• Probability to get both values that is calculate, multiple the 2 possibilities together.
• Results the probability of 1 is 3/6.
• With multiplication the solution becomes 1/4

Question 5 Part F Dice Estimate

• The probability of an event occurring has to be accounted for with the total number of occurrence.
• To calculate you take the total number of occurrence over dice value times number of trials
• Results in 72 * (1/6) = 12 estimate for die falling to a 3.

Question 5 Part G Sample Space Diagram

• Table is a sample space table for the number produced from the dice, with the multiple recorded.
• If either a value is 2 or 3, the probability is required.
• Results in 12 options to win
• Total Number of outcomes is 36
• Simplify to 1/3.

Question 6 Part A Sector Length Proof

• There is information on the formula sheet for calculating length.
• Arc = Theta / 360 * 2 * pi *r
• Pi value will need to be approximated to determine solution.
• Results in approximately 80 degrees.

Question 6 Part B Area Enclosed by the Wire

• Formula sheet provides information on the formula, and with the correct calculation 226 centimeter squared, can be determined.
• Use: Theta / 360 * Pi *r^2
• Using 80/360 results in 22

Question 7 Part A Table and Shapes

• Need to determine a pattern to calculate pattern N
• In figure four, there are 14 dots.
• Figure 4, there are 29 lines

Question 7 Part B Calculations and Formula

• With lines if you jump to each level you add 3 on each round. To make forurmla use the constant, in this case 3 and say 3n since its times by the factor. To justify say in the first trial when n=1. Since 3 * 1 doesn't equal 5, you need to add 2, therefore the solution is 3n + 2
• Follow the same technique for lines
• Line formula solution 7n + 1

Question 7 Part C Table Completion

• You can apply the formula in the previous to work out solutions, you may also be able to extend the factor.
• Use formula to work out solution of 134.

Question 7 Part D Value Determination

• N=21
• Dots for each Value= 65

Question 8 Part A Functions and Calculations

• You are given a function for f(X) and asked to evaluate for -2
• Answer is 5/3

Question 8 Part B Expression and Substitutions

• FG requires G to be placed with F as a substitute value with X
• Correct substitution is required, with solution of (16/3x) / (4-x)

Question 8 Part C Matrix Substitution

• First take equation Y = 1/3x over (x-1)
• Second flip x and y
• Third cross multiply and change for Y, Y(1-x)*= 1+z0

Question 9 Part A Geometry Explanation

• Two angles in similar are equal, as there are two tangent lines in parallel.

Question 9 Part B Angle Value Determination

• Calculation 180*(2xX- 18 = Y

Question 9 Part C Geometry Bearing

• Place bearing value on diagram, and establish a triangle.
• To detemrine values sign/cos/tan will needed to be used.
• Result is Sin/ Tan/ Cos/ to work out solution

Question 10 Part A Vectors

• MN is a vector equation calculation
• Calculate to point and then work out

Question 10 Part B Diagram Description

• LMA vector is divided by the ratio of 1 and 2

Question 10 Part C

• Lengths/ AB length and relationship.
• To prove result multiple factor and apply all possible equations.