Edexcel GCSE Maths
Topic questions Pure mathematics Substitution into formulae
40 questions · 160 marks · about 3 hours
Complete the table of values for y = x2 + x – 4
| x | –3 | –2 | –1 | 0 | 1 | 2 |
| y | 2 | –4 |
On the grid, draw the graph of y = x2 + x – 4 for values of x from –3 to 2
Write down the coordinates of the turning point of the graph of y = x2 + x – 4
Complete the table of values for y = x2 + x – 4
| x | –3 | –2 | –1 | 0 | 1 | 2 |
| y | 2 | –4 |
On the grid, draw the graph of y = x2 + x – 4 for values of x from –3 to 2
Write down the coordinates of the turning point of the graph of y = x2 + x – 4
Here is a rule to work out the cost of buying a number of floorboards. Cost = £55 × number of floorboards Toby buys a number of floorboards. The cost is £330 Work out the number of floorboards Toby buys.
Complete the table of values for y = x2 – 2x – 3
| x | –2 | –1 | 0 | 1 | 2 | 3 | 4 |
| y | 0 | –3 |
On the grid, draw the graph of y = x2 – 2x – 3 for values of x from –2 to 4
Complete the table of values for y = x2 – 2x – 3
| x | –2 | –1 | 0 | 1 | 2 | 3 | 4 |
| y | 0 | –3 |
On the grid, draw the graph of y = x2 – 2x – 3 for values of x from –2 to 4
Simplify 2c
3d
T = x + 2y x = 3 and y = – 4
Work out the value of T.
The number of hours, H, that some machines take to make 5000 bottles is given by H 
where n is the number of machines. On Monday, 6 machines made 5000 bottles. On Tuesday, 9 machines made 5000 bottles. The machines took more time to make the bottles on Monday than on Tuesday. How much more time?
Complete the table of values for y = x2 – x
| x | –2 | –1 | 0 | 1 | 2 | 3 |
| y | 6 | 0 | 2 |
On the grid, draw the graph of y = x2 – x for values of x from –2 to 3
Use your graph to find estimates for the solutions of the equation x2 – x = 4
The number of hours, H, that some machines take to make 5000 bottles is given by H where n is the number of machines. On Monday, 6 machines made 5000 bottles. On Tuesday, 9 machines made 5000 bottles. The machines took more time to make the bottles on Monday than on Tuesday. How much more time?
w = 40 – t2
Calculate the value of w when t = –5
Make h the subject of the formula.
P = 2g + 4h
Work out the value of P when g = 3 and h = 5
Work out the value of g when P = 38 and h = 3
V = 3r – q
Work out the value of V when r = –3 and q = 2
Complete the table of values for y = x2 – x – 2
| x | −2 | −1 | 0 | 1 | 2 | 3 |
| y | 4 | −2 |
On the grid, draw the graph of y = x2 – x – 2 for values of x from −2 to 3
Complete the table of values for y = 6x − x3
| x | −3 | −2 | −1 | 0 | 1 | 2 | 3 |
| y | 9 | 4 | −9 |
On the grid, draw the graph of y = 6x − x3 for values of x from −3 to 3
Safiya wants to hire a van. She uses this rule to work out the cost of hiring a van for a number of days.
Safiya is going to hire the van for 7 days. Work out the cost.
y = 6x − 5 Work out the value of y when x = 4
Complete the table of values for y = x2 − 3x + 1
| x | −1 | 0 | 1 | 2 | 3 | 4 |
| y | 1 | −1 |
On the grid, draw the graph of y = x2 − 3x + 1 for values of x from −1 to 4
Using your graph, find estimates for the solutions of the equation x2 − 3x + 1 = 0
T = 4m2 − 11
Work out the value of T when m = − 3
Make p the subject of the formula d = 3p + 4
T = 4m2 − 11
Work out the value of T when m = − 3
Make p the subject of the formula d = 3p + 4
ABCD is a kite.
AB = (4x – 2) cm Jasper says that x could be 0.5
Explain why Jasper cannot be correct.
AD = 3AB The kite has a perimeter of 64 cm.
Find the value of x.
Complete the table of values for y = x2 – 2x + 2
| x | –2 | –1 | 0 | 1 | 2 | 3 | 4 |
| y | 10 | 2 | 5 |
On the grid, draw the graph of y = x2 – 2x + 2 for values of x from –2 to 4
Use your graph to find estimates of the solutions of the equation x2 – 2x + 2 = 4
Complete the table of values for y = x2 – 2x + 2
| x | –2 | –1 | 0 | 1 | 2 | 3 | 4 |
| y | 10 | 2 | 5 |
On the grid, draw the graph of y = x2 – 2x + 2 for values of x from –2 to 4
Use your graph to find estimates of the solutions of the equation x2 – 2x + 2 = 4
T = 3x + 4y
Work out the value of T when x = 5 and y = –7
Work out the value of y when T = 38 and x = 6
Complete the table of values for y = 5 – x3
On the grid below, draw the graph of y = 5 – x3 for values of x from –2 to 2
Complete the table of values for y = 5 – x3
On the grid below, draw the graph of y = 5 – x3 for values of x from –2 to 2
w = 4 u + 3
Find the value of w when u = 8
Complete the table of values for y = 4 x – 6
On the grid, draw the graph of y = 4x – 6 for values of x 
P = 7 r + 3 q Work out the value of P when r = 5 and q = –4
You can use this rule to work out the total hire charge, in pounds (£), for hiring a 3D printer for a number of weeks.
Mia wants to hire a 3D printer for 4 weeks.
Work out the total hire charge.
Zahir hires a 3D printer. The total hire charge is £680
For how many weeks does Zahir hire the 3D printer?
g = 9 h = 4
Work out the value of 2 g + 3 h
Work out a value of v.
Work out a value of v.
Here is a sketch of a curve.
The equation of the curve is y = x2 + ax + b where a and b are integers.
The points (0, −5) and (5, 0) lie on the curve.
Find the coordinates of the turning point of the curve.
Complete this table of values for y = x2 + x – 4
| x | –3 | –2 | –1 | 0 | 1 | 2 | 3 |
| y | –2 |  | –2 |
On the grid, draw the graph of y = x2 + x – 4 for values of x from –3 to 3
Use the graph to estimate a solution to x2 + x – 4 = 0
P = 4 x + 3 y
x
y = – 2
Work out the value of P.
Expand 4 e (e + 2)
Solve 3(m – 4) = 21
Complete the table of values for y = x2 – x – 6
| x | –3 | –2 | –1 | 0 | 1 | 2 | 3 |
| y | 6 | – 6 |
On the grid, draw the graph of y = x2 – x – 6 for values of x from –3 to 3
Use your graph to find estimates of the solutions to the equation x2 – x – 6 = –2
Complete the table of values for y = x2 – x – 6
| x | –3 | –2 | –1 | 0 | 1 | 2 | 3 |
| y | 6 | – 6 |
On the grid, draw the graph of y = x2 – x – 6 for values of x from –3 to 3
Use your graph to find estimates of the solutions to the equation x2 – x – 6 = –2
w = 5.6
10–5 d = 1.4
10–4
Work out the value of T. Give your answer in standard form correct to 3 significant figures.
w is increased by 10% d is increased by 5%
Lottie says, “The value of T will increase because both w and d are increased.”
Lottie is wrong. Explain why.
The table shows some values of x and y that satisfy the equation y = acos x
+ b
| x | 0 | 30 | 60 | 90 | 120 | 150 | 180 |
| y | 3 | 1 + 3 | 2 | 1 | 0 | 1 – 3 | –1 |
Find the value of y when x = 45
v = u + at
Work out the value of v.
T = 4 v + 3
Work out the value of T when v = 2
Make v the subject of the formula T = 4 v + 3
Memes
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