Substitution into formulae

Work out the value of 2(a 2 + 3 a) when a = 4

d represents the number of days to complete a job.

w represents the number of workers needed.

Assume the job needs completing in 20 days.

How many workers are needed?

In fact, the job needs completing in fewer than 20 days.

What does this mean about the number of workers that are needed? Tick one box.

Which of these values of x gives the greatest value of y ? Circle your answer.

Expand and simplify fully (x + 2)(2 x + 3)(3 x + 4)

Use your answer from part (a) to work out 102 × 203 × 304

Work out the value of x² + 7x when x = –4

Rearrange y = w – 1 to make w the subject.

Simplify fully 4(a + 2) + a

A window cleaner uses this formula.

C = cost, in £, for the customer W = number of windows to be cleaned

How much does it cost for 6 windows to be cleaned?

The cost for another customer was £24

Show why this cost must be incorrect.

Here is a table of values for the equation y = 3 x + 1

Draw the graph of y = 3 x + 1 for values of x from 1 to 4

Work out the value of y when x = 2.5

y =

A graph passes through the points (3, 15) and (7, w)

Assume that the equation of the graph has the form y = x² + c

Work out the value of w that this would give.

w =

In fact, the graph is a straight line.

What does this mean about the actual value of w ?

Tick one box.

Multiplying y by 6 gives the same result as adding 15 to y

Write this as an equation.

Show that the value of y is not 4

d = g² – 2h

Work out the value of d when g = 15 and h = 63

Rearrange m = n + k to make n the subject.

n =

Work out the value of T when P = 4 and W = 2

Work out the value of P when T = – 40 and W = 10

P =

In a game,

an ordinary fair six-sided dice is rolled

the fair spinner shown is spun.

The score is the dice number substituted into the spinner expression.

Complete the table to show all of the possible scores.

A player wins the game if their score is 10 or more. Work out the probability that they win the game.

The game is played 711 times. Estimate the number of games that are won.

In a game,

an ordinary fair six-sided dice is rolled

the fair spinner shown is spun.

The score is the dice number substituted into the spinner expression.

Complete the table to show all of the possible scores.

A player wins the game if their score is 10 or more. Work out the probability that they win the game.

The game is played 711 times. Estimate the number of games that are won.

Complete the table of values for y = x² + 2x

Draw the graph of y = x² + 2x for values of x from –3 to 1

Complete the table of values for y = x² + 2x

Draw the graph of y = x² + 2x for values of x from –3 to 1

The graph shows the values of D and E for 2 D 6

Choose one point on the graph and state if Sunil’s equation is correct for that point.

G is directly proportional to the square root of H. G: H = 3: 2 when H = 16 Work out G: H when H = 100

A graph has the equation y = x² + px + r where p and r are constants. The graph passes through the points (0, 4), (1, 3) and (8, w) Work out the value of w.

Work out the value of 3 r + 4 t when r = 13 and t = – 2

To travel to a festival, a group of people will hire a minibus. This formula has all costs in £

With 12 people in the group, the cost of the minibus will be £567 Work out the cost per person.

With 15 people in the group, they will hire a different minibus. The cost per person will be £50 Work out the cost of this minibus.

Circle the point that is on the line 4 x + y = 7

(2, 1) (2, – 1) (1, 2) (– 1, 2)

Write down the coordinates of the y-intercept of the line y = 3 x + 8

Work out the gradient of the line 2 y = 10 x

Work out the value of a² – 4a when a = 10

This formula converts temperature in degrees Fahrenheit (F) to kelvin (K)

A pottery oven is heated to 2192 degrees Fahrenheit. Work out this temperature in kelvin.

Circle the expression that has the smallest value when x = 4

Circle the expression that has the largest value when a –1

Here is a formula.

Work out T when n = 5

Why is T always positive when n is negative?

a = 7 and b = 2 Work out the value of – a

Here is an inflated swimming ring with dimensions in centimetres.

The volume of the ring, V cm³, is given by

Work out the volume when a = 20 and b = 30 Give your answer to 3 significant figures.