Iteration Worked Solutions — GCSE Maths

Fully worked, step-by-step solutions to GCSE Iteration questions. See exactly how to solve problems on substitution, evaluating f(x), sign of f(x), iterative formula.

substitutionevaluating f(x)sign of f(x)iterative formularoundingsign change
GCSE Higher70 questionsStep-by-step solutions
Question 1
1 markeasy
f(x)=x3−2x−5f(x) = x^3 - 2x - 5. Work out the value of f(2)f(2).

Worked solution

  1. Substitute the value into the function

    f(2)=23−2×2−5f(2) = 2^{3} - 2 \times 2 - 5

    Replace every xx in f(x)f(x) with 22.

  2. Work out each term

    f(2)=8−4−5f(2) = 8 - 4 - 5

    Deal with the powers first, then the multiplications, then add and subtract.

  3. State the value

    f(2)=−1f(2) = -1

    So f(2)f(2) is -1, which is negative.

Answer
f(2)=−1f(2) = -1
Question 2
1 markeasy
f(x)=x3−2x−5f(x) = x^3 - 2x - 5. Work out the value of f(3)f(3).

Worked solution

  1. Substitute the value into the function

    f(3)=33−2×3−5f(3) = 3^{3} - 2 \times 3 - 5

    Replace every xx in f(x)f(x) with 33.

  2. Work out each term

    f(3)=27−6−5f(3) = 27 - 6 - 5

    Deal with the powers first, then the multiplications, then add and subtract.

  3. State the value

    f(3)=16f(3) = 16

    So f(3)f(3) is 16, which is positive.

Answer
f(3)=16f(3) = 16
Question 3
1 markeasy
f(x)=x3+x−5f(x) = x^3 + x - 5. Work out the value of f(1)f(1).

Worked solution

  1. Substitute the value into the function

    f(1)=13+1−5f(1) = 1^{3} + 1 - 5

    Replace every xx in f(x)f(x) with 11.

  2. Work out each term

    f(1)=1+1−5f(1) = 1 + 1 - 5

    Deal with the powers first, then the multiplications, then add and subtract.

  3. State the value

    f(1)=−3f(1) = -3

    So f(1)f(1) is -3, which is negative.

Answer
f(1)=−3f(1) = -3
Question 4
1 markeasy
f(x)=x2−4x−3f(x) = x^2 - 4x - 3. Work out the value of f(5)f(5).

Worked solution

  1. Substitute the value into the function

    f(5)=52−4×5−3f(5) = 5^{2} - 4 \times 5 - 3

    Replace every xx in f(x)f(x) with 55.

  2. Work out each term

    f(5)=25−20−3f(5) = 25 - 20 - 3

    Deal with the powers first, then the multiplications, then add and subtract.

  3. State the value

    f(5)=2f(5) = 2

    So f(5)f(5) is 2, which is positive.

Answer
f(5)=2f(5) = 2
Question 5
1 markeasy
f(x)=x3+x+3f(x) = x^3 + x + 3. Work out the value of f(−2)f(-2).

Worked solution

  1. Substitute the value into the function

    f((−2))=(−2)3+(−2)+3f((-2)) = (-2)^{3} + (-2) + 3

    Replace every xx in f(x)f(x) with −2-2.

  2. Work out each term

    f((−2))=−8−2+3f((-2)) = -8 - 2 + 3

    Deal with the powers first, then the multiplications, then add and subtract.

  3. State the value

    f((−2))=−7f((-2)) = -7

    So f(−2)f(-2) is -7, which is negative.

Answer
f((−2))=−7f((-2)) = -7

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