Write an expression. Multiply a number, k, by 5, then subtract 3.
(1)
3
Write an expression. Divide a number, q, by 6, then add 9.
(1)
4
Simplify 4a + 7a.
(1)
5
x = 3 and y = 6.
(a)Find the value of 4x + 2y.(1)
(b)Find the value of x2 - y.(1)
6
Simplify 5x + 3y + 4x + 2y.
(2)
7
Simplify 7a - 9 - 3a + 5.
(2)
8
Simplify 12c - 12c.
(1)
9
Expand 4(x + 5).
(2)
10
Expand 3(2y - 4).
(2)
11
Expand -3(2a + 5).
(2)
12
Factorise fully 8x + 12.
(1)
13
Factorise fully 15y - 20.
(1)
14
A taxi firm charges a call-out fee of 3 pounds plus 2 pounds for every mile travelled.
(a)Write a formula for the total cost C, in pounds, of a journey of m miles.(1)
(b)Find C when m = 7.(2)
15
Priya has (2x + 5) pens and gives away (x - 3) pens.
(a)Write an expression, in its simplest form, for the number of pens she has left.(2)
(b)Find the number of pens left when x = 6.(1)
16
A rectangle has length (3x - 2) cm and width (x + 4) cm.
(a)Write an expression, in its simplest form, for the perimeter of the rectangle.(2)
(b)Given that x = 5, find the numerical perimeter of the rectangle in cm.(2)
17
The cost of hiring a bike is given by the formula H = 6d + 15, where H is the cost in pounds and d is the number of days.
(a)Work out the cost of hiring a bike for 4 days.(2)
(b)A customer pays 63 pounds to hire a bike. Work out how many days they hired it for.(2)
18
Simplify fully 5(2x + 3) - 2(x - 4). Then use your simplified expression to find its value when x = -3.
(4)
19
A number x is doubled and then 7 is added. This expression is then multiplied by 3. Write down, in its simplest form, an expression for the result. Then evaluate your expression when x = 5.
(3)
Mark scheme · KS3.M-A1D Algebra: Expressions and Formulae: Fluency and Exam Drill
Question 1
B1 t + 8 oe
Answer: t + 8
Question 2
B1 5k - 3 oe
Answer: 5k - 3
Question 3
B1 q/6 + 9 oe
Answer: q/6 + 9
Question 4
B1 11a cao
Answer: 11a
Question 5
(a) B1 24 cao
(a) Answer: 24
(b) B1 3 cao
(b) Answer: 3
Question 6
M1 collects x terms or y terms correctly
A1 9x + 5y cao
Answer: 9x + 5y
Question 7
M1 collects a terms or number terms correctly
A1 4a - 4 cao
Answer: 4a - 4
Question 8
B1 0 cao
Answer: 0
Question 9
M1 multiplies both terms by 4
A1 4x + 20 cao
Answer: 4x + 20
Question 10
M1 multiplies both terms by 3
A1 6y - 12 cao
Answer: 6y - 12
Question 11
M1 multiplies both terms by -3
A1 -6a - 15 cao
Answer: -6a - 15
Question 12
B1 4(2x + 3) cao
Answer: 4(2x + 3)
Question 13
B1 5(3y - 4) cao
Answer: 5(3y - 4)
Question 14
(a) B1 C = 2m + 3 oe
(a) Answer: C = 2m + 3
(b) M1 substitutes m = 7 into their formula
(b) A1 17 cao
(b) Answer: 17
Question 15
(a) M1 removes the bracket correctly, e.g. 2x + 5 - x + 3
(a) A1 x + 8 cao
(a) Answer: x + 8
(b) B1 14 cao (ft their simplified expression)
(b) Answer: 14
Question 16
(a) M1 adds the four sides or doubles the sum of length and width
(a) A1 8x + 4 cao
(a) Answer: 8x + 4
(b) M1 substitutes x = 5 into their perimeter expression