Write a formula for the perimeter P of a regular pentagon with side length s.
(1)
2
Write a formula for the total cost C, in pounds, of buying n rulers at 0.65 pounds each.
(1)
3
Write a formula for the area A of a triangle with base b and height h.
(1)
4
Use the formula S = 3h + 2. Find S when h = 5.
(1)
5
Use the formula S = 3h + 2. Find S when h = -3.
(1)
6
A train travels at a constant speed. Distance d in kilometres is given by d = 80t, where t is time in hours. How far does the train travel in 2.5 hours?
(2)
7
Using d = 80t, how long does it take the train to travel 360 km? Give your answer in hours.
(2)
8
The formula for average speed v in m/s is v = s / t. A cyclist covers 300 m in 40 s. Find the average speed in m/s.
(2)
9
Using s = vt, a skater travels at 3 m/s for 25 s. Find the distance covered in metres.
(2)
10
The formula A = 4x + 9 is used. Given A = 25, find x.
(1)
11
Using A = 4x + 9, given A = -3, find x.
(1)
12
The volume of a prism is given by V = (1/2) b h l. Rearrange the formula to make l the subject.
(2)
13
Using l = 2V / (bh), find l when V = 60, b = 5 and h = 4.
(2)
14
Write a formula for this rule, using the same letter throughout: multiply a number n by 7, then add 5. Call the result R.
(1)
15
Write a formula for this rule: add 6 to a number p, then divide the result by 2. Call the result S.
(1)
16
Substitute negative and fractional values into formulae. Use C = 4t - 5.
(a)Find C when t = -2.(1)
(b)Find C when t = 1/2.(1)
17
A parking garage charges a fixed entry fee of 200 pence plus 8 pence per minute parked, using the formula C = 200 + 8m. Find the cost of parking for 45 minutes, giving your final answer in pounds.
(3)
18
Using C = 200 + 8m, a customer pays 560 pence in total to park. Work out how many minutes they parked for.
(3)
19
A delivery charge is M = 4(a - b) + 3b, where a is distance in miles and b is a discount in pounds. Simplify M in terms of a and b, then find M when a = 5 and b = 2.
(3)
20
A gym charges a joining fee of 30 pounds plus a monthly fee of m pounds, giving total cost after n months as T = 30 + mn.
(a)Given m = 22, find the total cost after 6 months.(2)
(b)A member has paid 250 pounds in total after 10 months. Find m.(2)
21
Stretch: A large square and a similar small square have sides in ratio n:1. Area scales as the square of the linear scale factor, so the large square's area Al = k times the small square's area As.
(a)Write k in terms of n.(1)
(b)Find Al when As = 5 and n = 4.(3)
Mark scheme · KS3.M-A12D Writing and Using Formulae: Fluency and Exam Drill
Question 1
B1 P = 5s oe
Answer: P = 5s
Question 2
B1 C = 0.65n oe
Answer: C = 0.65n
Question 3
B1 A = (1/2)bh oe
Answer: A = (1/2)bh
Question 4
B1 17 cao
Answer: 17
Question 5
B1 -7 cao
Answer: -7
Question 6
M1 substitutes t = 2.5
A1 200 cao
Answer: 200 km
Question 7
M1 sets up 360 = 80t
A1 4.5 cao
Answer: 4.5 hours
Question 8
M1 substitutes s = 300, t = 40
A1 7.5 cao
Answer: 7.5 m/s
Question 9
M1 substitutes v = 3, t = 25
A1 75 cao
Answer: 75 m
Question 10
B1 x = 4 cao
Answer: 4
Question 11
B1 x = -3 cao
Answer: -3
Question 12
M1 multiplies both sides by 2, 2V = bhl
A1 l = 2V / (bh) cao
Answer: l = 2V / (bh)
Question 13
M1 substitutes V = 60, b = 5, h = 4
A1 6 cao
Answer: 6
Question 14
B1 R = 7n + 5 oe
Answer: R = 7n + 5
Question 15
B1 S = (p + 6) / 2 oe
Answer: S = (p + 6) / 2
Question 16
(a) B1 -13 cao
(a) Answer: -13
(b) B1 -3 cao
(b) Answer: -3
Question 17
M1 substitutes m = 45
A1 560 pence
B1 converts to 5.60 pounds (ft their pence value)
Answer: 5.60 pounds (560 pence)
Question 18
M1 sets up 560 = 200 + 8m
M1 correct rearrangement, e.g. 8m = 360
A1 45 cao
Answer: 45 minutes
Question 19
M1 expands the bracket, 4a - 4b + 3b
A1 M = 4a - b cao
B1 18 cao (ft their simplified formula)
Answer: M = 4a - b; value 18 when a = 5, b = 2
Question 20
(a) M1 substitutes m = 22, n = 6
(a) A1 162 cao
(a) Answer: 162 pounds
(b) M1 sets up 250 = 30 + 10m and subtracts 30
(b) A1 22 cao
(b) Answer: 22 pounds
Question 21
(a) B1 k = n2 cao
(a) Answer: k = n2
(b) M1 substitutes n = 4 into k = n2 to get k = 16