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A.C.T. MATH LIST

New York State

Scoring Key and Answers, but No Solutions

Ireland  Part 1   2 

Scoring Key and Solutions

Study the solutions.

 

 

The following list is helpful in finding ways to get higher marks. Remember: You don't have to know everything on the list. But each day you can add one more item to your memory.

(By the way, are you getting enough memory-building omega-3?)

 

Arithmetic

  • Find Compound Interest.
  • Find the cost price when given the percentage profit or discount.
  • Be able to work out a person's take home pay if given their gross pay, tax free allowance and tax rates.
  • Handle numbers written in scientific notation.
  • Calculate % of error.
  • Deal with ratios.

 

Algebra

  • Solve an inequality.
  • Write a given expression in index form, and solve an index equation.

  • Make good attempts at solving:

    Simultaneous equations: equations of the form 3x + 4 y = 10, and 5x – 7y = 3.

    Quadratic Equations: for example,  x2 + 3x +2 = 0 either by factoring or using this formula:

  

        Simultaneous equations of different degrees: 

        3x + 4 y = 10, and x2 – y2 = 3.

        Cubic equations: x3 + 2x2 + 3x +9

 

More Algebra

  • Use the factor  theorem.
  • Answer questions using the graph of a quadratic function. Or given a quadratic function, find the coefficients of x and the independent term.

 

Complex Numbers

  • Add, subtract, multiply, divide complex numbers, find the modulus and the conjugate.
  • Must be able to solve a Quadratic Equation which has complex roots, (use the roots formula and don't forget that i = .
  • Must be able to plot complex numbers on a graph. The vertical axis is i, the horizontal real.
  • Must be able to solve linear equations involving complex numbers.

 

Number Sequences  

  • Memorize the formulas for the Tn and Sn of an arithmetic progression, and be able to find a and d using simultaneous equations.
  • Remember that T2 - T1 = T3 - T2 = d.
  • Be able to find a or d if given Sn and d or a.
  • Memorize the formulas for Tn and Sn of a geometric progression.
  • Remember that in geometric progressions T2/T1 = T3/T2 = the common ratio r.
  • Be able to find a and r if given two terms of a geometric progression. (This is one of the easiest questions on Paper 1.)

 

Periodic Functions

  • This can be a time-consuming question and should be saved for the second hour. 
  • Be able to find the period and range when given the graph of a function.
  • Be able to find the Max and Min.
  • Graphs: Be able to sketch the graph of the cubic function in part (b) for certain values of x. You will use the results of part (b) to help you draw your graph.

 

Calculus

  • Be able to use the product rule, the quotient rule, and the chain rules for differentiation. The product and quotient formulas are on page 42 of the blue Tables booklet given to you with the exam.
  • Be able to deal with problems involving distance, speed, and time using differentiation.

 

Functions

  • Be able to find f(x) given different values for x.
  • Be able to solve equations of the form f(x) = a.
  • Be able to sketch the graphs of functions with unusual curves such as f(x) = 1/(x + 3).