y = (1)/(x). Work out the value of y when x = 4.

Write down the equation: y = (1)/(x) Substitute x = 4: y = (1)/(4) Work out the division: y = 1 ÷ 4 = 0.25 Answer: y = 0.25

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 = x^3

. Work out the value of

y

when

x = 3

Worked solution

Write down the equation
$y = x^3$
The equation is the rule that turns each value of x into a value of y.
Substitute $x = 3$
$y = (3)^3$
Replace every x with 3. Keep the brackets so that the power is worked out before the adding and subtracting.
Work out the value of y
$y = 27$
$3$ cubed means $3 \times 3 \times 3$ , which is $27$ .

Answer

y = 27

Question 2

1 markeasy

y = x^3

. Work out the value of

y

when

x = -2

Worked solution

Write down the equation
$y = x^3$
The equation is the rule that turns each value of x into a value of y.
Substitute $x = -2$
$y = (-2)^3$
Replace every x with -2. Keep the brackets round the negative number: cubing a negative number gives a negative answer.
Work out the value of y
$y = -8$
$-2$ cubed means $-2 \times -2 \times -2$ , which is $-8$ .

Answer

y = -8

Question 3

2 markseasy

A student is completing a table of values for

y = x^3 - 2x

. Work out the value of

y

when

x = 2

Worked solution

Write down the equation
$y = x^3 - 2x$
The equation is the rule that turns each value of x into a value of y.
Substitute $x = 2$
$y = (2)^3 - 2(2)$
Replace every x with 2. Keep the brackets so that the power is worked out before the adding and subtracting.
Work out the value of y
$y = 8 - 4 = 4$
Work out each part first: $(2)^3 = 8$ , $-2(2) = -4$ . Combining them gives $y = 4$ .

Answer

y = 4

Question 4

2 markseasy

y = x^3 + 1

. Work out the value of

y

when

x = -1

Worked solution

Write down the equation
$y = x^3 + 1$
The equation is the rule that turns each value of x into a value of y.
Substitute $x = -1$
$y = (-1)^3 + 1$
Replace every x with -1. Keep the brackets round the negative number: cubing a negative number gives a negative answer.
Work out the value of y
$y = -1 + 1 = 0$
Work out each part first: $(-1)^3 = -1$ . Combining them gives $y = 0$ .

Answer

y = 0

Question 5

1 markeasy

y = \frac{1}{x}

. Work out the value of

y

when

x = 4

Worked solution

Write down the equation
$y = \frac{1}{x}$
y is found by dividing 1 by x.
Substitute $x = 4$
$y = \frac{1}{4}$
Replace x with 4 in the denominator.
Work out the division
$y = 1 \div 4 = 0.25$
$1$ divided by $4$ is $0.25$ . Both numbers have the same sign, so the answer is positive.

Answer

y = 0.25

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