Cubic and reciprocal graphs Worked Solutions — GCSE Maths

Fully worked, step-by-step solutions to GCSE Cubic and reciprocal graphs questions. See exactly how to solve problems on table of values, cubing a number, cubing a negative number, substitution.

table of valuescubing a numbercubing a negative numbersubstitutioncubic graphreciprocal graph
GCSE Foundation70 questionsStep-by-step solutions
Question 1
1 markeasy
The table shows values of y=x3y = x^3. Work out the value of yy when x=3x = 3.

Worked solution

  1. Write down the equation

    y=x3y = x^3

    The equation is the rule that turns each value of x into a value of y.

  2. Substitute x=3x = 3

    y=(3)3y = (3)^3

    Replace every x with 3. Keep the brackets so that the power is worked out before the adding and subtracting.

  3. Work out the value of y

    y=27y = 27

    3 cubed means 3 × 3 × 3, which is 27.

Answer
y=27y = 27
Question 2
1 markeasy
y=x3y = x^3. Work out the value of yy when x=−2x = -2.

Worked solution

  1. Write down the equation

    y=x3y = x^3

    The equation is the rule that turns each value of x into a value of y.

  2. Substitute x=−2x = -2

    y=(−2)3y = (-2)^3

    Replace every x with -2. Keep the brackets round the negative number: cubing a negative number gives a negative answer.

  3. Work out the value of y

    y=−8y = -8

    -2 cubed means -2 × -2 × -2, which is -8.

Answer
y=−8y = -8
Question 3
2 markseasy
A student is completing a table of values for y=x3−2xy = x^3 - 2x. Work out the value of yy when x=2x = 2.

Worked solution

  1. Write down the equation

    y=x3−2xy = x^3 - 2x

    The equation is the rule that turns each value of x into a value of y.

  2. Substitute x=2x = 2

    y=(2)3−2(2)y = (2)^3 - 2(2)

    Replace every x with 2. Keep the brackets so that the power is worked out before the adding and subtracting.

  3. Work out the value of y

    y=8−4=4y = 8 - 4 = 4

    Work out each part first: (2)3=8(2)^3 = 8, −2(2)=−4-2(2) = -4. Combining them gives y=4y = 4.

Answer
y=4y = 4
Question 4
2 markseasy
y=x3+1y = x^3 + 1. Work out the value of yy when x=−1x = -1.

Worked solution

  1. Write down the equation

    y=x3+1y = x^3 + 1

    The equation is the rule that turns each value of x into a value of y.

  2. Substitute x=−1x = -1

    y=(−1)3+1y = (-1)^3 + 1

    Replace every x with -1. Keep the brackets round the negative number: cubing a negative number gives a negative answer.

  3. Work out the value of y

    y=−1+1=0y = -1 + 1 = 0

    Work out each part first: (−1)3=−1(-1)^3 = -1. Combining them gives y=0y = 0.

Answer
y=0y = 0
Question 5
1 markeasy
y=1xy = \frac{1}{x}. Work out the value of yy when x=4x = 4.

Worked solution

  1. Write down the equation

    y=1xy = \frac{1}{x}

    y is found by dividing 1 by x.

  2. Substitute x=4x = 4

    y=14y = \frac{1}{4}

    Replace x with 4 in the denominator.

  3. Work out the division

    y=1÷4=0.25y = 1 \div 4 = 0.25

    1 divided by 4 is 0.25. Both numbers have the same sign, so the answer is positive.

Answer
y=0.25y = 0.25

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