Nyansapc

SHS Core Mathematics · Year 1

Algebraic Expressions and Factorisation practice questions

Number patterns and algebraic expressions, the four operations on algebraic expressions, factorisation, perfect squares and the difference of two squares, and operations on simple algebraic fractions.

27 questions in this topic: 6 recall, 13 applying skills and concepts and 8 strategic thinking. Every one carries a written explanation.

Sample questions

5 of 27 questions in this topic. Sign up to answer them and see the explanations.

  1. Question 1Skills & concepts

    For the expression 3/(x−1), the value of x that makes the expression undefined is found by

    • asetting the denominator x − 1 equal to zero, giving x = 1
    • bsetting the numerator equal to zero
    • csetting the whole fraction equal to 1
    • dthere is no such value since 3 is never zero
  2. Question 2Strategic thinking

    To factorise 3x² + 7x + 4 by splitting the middle term, you need two numbers whose product is ac = 3 × 4 = 12 and whose sum is b = 7. These numbers are

    • a3 and 4
    • b1 and 12
    • c2 and 6
    • d7 and 12
  3. Question 3Recall

    To factorise 4x + 4by, the correct first step is to

    • aidentify the highest common factor, 4, and factor it out to get 4(x + by)
    • bdivide every term by x
    • cexpand the expression further before factorising
    • dtreat 4x and 4by as unrelated and leave the expression as is
  4. Question 4Recall

    A perfect square is defined as

    • aan integer that can be expressed as the square of another integer, e.g. 16 = 4²
    • bany even number
    • cany number with a square root that is irrational
    • da negative number that equals the square of another integer
  5. Question 5Skills & concepts

    To simplify 1/x − 3/x², the first correct step is to

    • arewrite 1/x with the LCM denominator x², giving x/x², then subtract to get (x − 3)/x²
    • bsubtract the numerators directly to get −2/x
    • ccross-multiply the two fractions as though solving an equation
    • dadd the two denominators together first

Answer these and 22 more on Algebraic Expressions and Factorisation

Free account. Instant marking, a written explanation for every question.

Start practising free

More Core Mathematics Year 1 topics

All Core Mathematics topics