Simplify each expression by collecting like terms.
(a)3a + 5a(1)
(b)7b - 2b(1)
(c)4c + 3c - c(1)
(Total for Question 1 is 3 marks)
2
Simplify each expression.
(a)t x t(1)
(b)5 x n x 2(1)
(c)y x y x y(1)
(Total for Question 2 is 3 marks)
3
x = 4 and y = 3. Work out the value of each expression.
(a)x + y(1)
(b)2x - y(1)
(c)xy(1)
(d)x2(1)
(Total for Question 3 is 4 marks)
4
a = -3 and b = 5. Work out the value of each expression.
(a)a + b(1)
(b)b - a(1)
(c)ab(1)
(d)a2(1)
(Total for Question 4 is 4 marks)
5
Write an expression for each statement. Use n or m for the unknown number as shown.
(a)5 more than n(1)
(b)double m, then subtract 3(1)
(c)the cost, in pounds, of x pens at 20p each(1)
(Total for Question 5 is 3 marks)
6
Solve each equation.
(a)x + 7 = 12(1)
(b)y - 4 = 9(1)
(c)3m = 18(1)
(d)n/4 = 6(1)
(Total for Question 6 is 4 marks)
7
Solve each equation, showing your working.
(a)2x + 3 = 11(2)
(b)5y - 4 = 16(2)
(c)3n + 7 = 1(2)
(Total for Question 7 is 6 marks)
8
Expand each expression.
(a)3(x + 4)(1)
(b)5(2y - 3)(1)
(c)-2(m + 6)(1)
(Total for Question 8 is 3 marks)
9
Expand and simplify 3(x + 2) + 2(x - 5).
(Total for Question 9 is 2 marks)
10
Solve 4(x + 3) = 24.
(Total for Question 10 is 2 marks)
11
Here is a number sequence: 3, 7, 11, 15, ...
(a)Write down the next two terms of the sequence.(2)
(b)Describe the term-to-term rule for the sequence.(1)
(c)Calculate the 10th term of the sequence.(2)
(Total for Question 11 is 5 marks)
12
Here is a number sequence: 2, 5, 8, 11, ...
(a)Find an expression, in terms of n, for the nth term of the sequence.(2)
(b)Use your expression to find the 20th term of the sequence.(1)
(c)Show that 100 is not a term in this sequence.(2)
(Total for Question 12 is 5 marks)
13
Solve 5x - 3 = 2x + 12.
(Total for Question 13 is 2 marks)
14
Answer the following inequality questions.
(a)Solve x + 4 < 9.(1)
(b)Solve 3x ≥ 15.(1)
(c)List all the integer values of x that satisfy -2 < x ≤ 3.(2)
(Total for Question 14 is 4 marks)
15
Factorise each expression fully.
(a)6x + 9(1)
(b)4y - 12(1)
(c)10m + 15n(1)
(Total for Question 15 is 3 marks)
16
Priya thinks of a number. She multiplies it by 3, then adds 8. Her result is 29. Let n be Priya's number.
(a)Write down an equation in n to represent this information.(1)
(b)Solve your equation to find n.(2)
(Total for Question 16 is 3 marks)
17
A rectangle has length (x + 5) cm and width (x - 2) cm. The perimeter of the rectangle is 26 cm.
Diagram NOT accurately drawn
(a)Show that 4x + 6 = 26.(2)
(b)Solve the equation to find the value of x.(2)
(c)Find the length and the width of the rectangle.(2)
(Total for Question 17 is 6 marks)
18
Solve (2x - 1)/3 = 5.
(Total for Question 18 is 2 marks)
19
Solve 4(x + 2) = 2(3x - 1).
(Total for Question 19 is 2 marks)
20
A pattern is made from squares. Pattern 1 has 4 squares, pattern 2 has 7 squares and pattern 3 has 10 squares. The number of squares increases by 3 for each new pattern.
(a)Calculate the number of squares in pattern 5.(1)
(b)Find an expression, in terms of n, for the number of squares in pattern n.(2)
(c)A pattern in the sequence has 61 squares. Calculate which pattern number this is.(2)
(Total for Question 20 is 5 marks)
21
Solve 5 - 2x > 1.
(Total for Question 21 is 2 marks)
22
The sum of three consecutive integers is 84. Let the smallest of the three integers be n.
(a)Write an expression, in terms of n, for the sum of the three consecutive integers.(1)
(b)Form and solve an equation to find the value of n.(2)