1
Write each of the following using correct algebraic notation, simplified where possible.
(2)
(Total for Question 1 is 2 marks)
Pearson Edexcel GCSE Maths · Topic A
Expressions, equations, graphs, sequences, functions and algebraic proof. Use the references below to find real questions on Pearson's site. Then practise with the original printable pack.
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26 original questions written in the style of the real papers. Attempt one on paper, then reveal the mark scheme and award yourself the marks. Marks you award are saved in this browser against that question.
1
Write each of the following using correct algebraic notation, simplified where possible.
(2)
(Total for Question 1 is 2 marks)
2
You are given the formulae v = u + at and s = ut + ½at². In this question u = 6, a = −3 and t = 4.
(a)
(2)
(b)
(2)
(Total for Question 2 is 4 marks)
3
Here are four statements. A: 5y + 2 B: V = IR C: 3(x − 2) = 3x − 6 D: 2x + 7 = 15
(2)
(Total for Question 3 is 2 marks)
4
A is the point (−4, 5) and B is the point (2, −3). M is the midpoint of the line segment AB.
(a)
(2)
(b)
(1)
(Total for Question 4 is 3 marks)
5
The graph of y = k^x, where k > 0, passes through the point (2, 49).
(a)
(2)
(b)
(1)
(Total for Question 5 is 3 marks)
6
The distance-time graph for Sara's cycle ride is made of three straight sections: from (0 min, 0 km) up to (30 min, 12 km); a horizontal section from (30 min, 12 km) to (45 min, 12 km); then a straight section from (45 min, 12 km) down to (90 min, 0 km).
(a)
(1)
(b)
(2)
(Total for Question 6 is 3 marks)
7
A car starts from rest. On a velocity-time graph, its motion is a straight line from (0 s, 0 m/s) to (8 s, 20 m/s). After that the car travels at a constant 20 m/s for a further 12 seconds.
(a)
(2)
(b)
(3)
(Total for Question 7 is 5 marks)
8
A sequence has first term 5. The term-to-term rule is 'multiply by 2 and then subtract 3'.
(2)
(Total for Question 8 is 2 marks)
9
This question is about manipulating algebraic expressions.
(a)
(2)
(b)
(2)
(Total for Question 9 is 4 marks)
10
Simplify each of the following. Write each answer as a single power or term where possible.
(a)
(1)
(b)
(1)
(c)
(1)
(Total for Question 10 is 3 marks)
11
The sizes of the three angles of a triangle, in degrees, are x + 20, 2x and 3x − 20.
(a)
(3)
(b)
(1)
(c)
(1)
(Total for Question 11 is 5 marks)
12
Solve the quadratic equation by factorising.
(3)
(Total for Question 12 is 3 marks)
13
Solve the equation.
(3)
(Total for Question 13 is 3 marks)
14
A is the point (1, 4) and B is the point (4, 13).
(a)
(2)
(b)
(2)
(Total for Question 14 is 4 marks)
15
This question is about a linear inequality.
(a)
(2)
(b)
(1)
(Total for Question 15 is 3 marks)
16
Prove, using algebra, that the sum of any three consecutive integers is always a multiple of 3.
(3)
(Total for Question 16 is 3 marks)
17
Prove that the sum of the squares of any two consecutive integers is always an odd number.
(3)
(Total for Question 17 is 3 marks)
18
You are given the formula y = 3x − 7.
(2)
(Total for Question 18 is 2 marks)
19
A student is sketching the graph of the straight line with equation y = 2x − 3.
(a)
(1)
(b)
(2)
(Total for Question 19 is 3 marks)
20
Simplify t⁹ ÷ t⁴.
(1)
(Total for Question 20 is 1 mark)
21
Solve these equations.
(a)
(2)
(b)
(2)
(Total for Question 21 is 4 marks)
22
Here are the first four terms of an arithmetic sequence: 5, 8, 11, 14
(a)
(2)
(b)
(1)
(c)
(2)
(Total for Question 22 is 5 marks)
23
This question is about number sequences.
(a)
(1)
(b)
(1)
(c)
(1)
(Total for Question 23 is 3 marks)
24
A rectangle has length (x + 4) cm and width x cm. The perimeter of the rectangle is 28 cm.
(a)
(3)
(b)
(2)
(Total for Question 24 is 5 marks)
25
A taxi company works out the cost, £C, of a journey of m miles using the formula C = 3 + 2m.
(a)
(2)
(b)
(2)
(Total for Question 25 is 4 marks)
26
A bag contains n red counters and 4 blue counters. Two counters are taken at random without replacement. The probability that both counters are blue is 1/6.
(5)
(Total for Question 26 is 5 marks)
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