Review thinkmath 2A chapter 2-4

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Review Chapter 2-4

Chapter 2

  1. Given that y is an integer, -3 < y ≤ 2.7, and y ≠ 0, write down all the possible values of y.

  2. It is given that z ≥ 41.5.

    1. Write down the least possible value of z if z is:
      1. an integer
      2. a prime number
      3. a perfect square
    2. Suggest a possible value of z for which z is a factor of 1260 and z is an even number.

  3. Solve the inequality 7 - (1/3)x ≥ 5 and represent the solution on a number line.

  4. A smartphone costs $750. Form an inequality and solve it to find the maximum number of smartphones that a company can buy with a budget of $25,000.

  5. Consecutive Even Numbers: Let the numbers be z, z+2, z+4. If the inequality z+(z+2)+(z+4)>120 is given, find the smallest even number z that satisfies this condition and calculate the product of these numbers.

Chapter 3

  1. Without factorising 9y2-y-20, give reasons why it is not equivalent to 3(3y+4)(y-5).

  2. A polynomial in x can be written as:

    Polynomial = quotient × divisor + remainder.

    Find the polynomial when the quotient is 3x2+2x-5, the divisor is 2x+3, and the remainder is 4.

  3. Factorise completely the expression 8a2b-16ab2+24b3.

  4. Factorise completely 12ax+21a-8bx-14b.

  5. Given that x2+y2=9 and xy=5, find the value of (x-y)2.

  6. n is a positive integer.

    Show that, for all n, (7n+3)2-(7n-3)2 is a multiple of 84.

chapter 4

  1. Expand and Simplify: Expand and simplify the expression (4m+3n)2.

  2. Factorization: Factorize the expression 50x2-80xy+32y2 completely.

  3. Express in Specific Form: Express 64a2-96ab+36b2 in the form b/4(pa+qb)2, where b, p, and q are integers.

  4. Algebraic Identity Application: Given that u2-v2=45 and u-v=9, find the value of (u+v)2.

    1. Expand and simplify (5p-8)2.
    2. Rearrange s=ut+1/2at2 to make a the subject.
    3. Write 3/(x-5)-6/(2x+1) as a single fraction in its simplest form.
    4. Find the greatest rational value of x that satisfies the inequality 7(4-5x)/3 ≥ -8.

  6. The diagram shows a rectangular sheet of paper ABCD.

    AB = (11x+6y-12) mm, BC = (3x+7y+7) mm, CD = (18y-5x) mm and AD = (10y-2) mm.

    A B C D (11x+6y-12) mm (3x+7y+7) mm (18y-5x) mm (10y-2) mm

    Find the perimeter and area of the rectangle.

Quiz 1









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