Algebra — IGCSE Mathematics - International (0607) questions by topic
Algebra is the biggest topic on the page: simplifying algebraic fractions, expanding triple brackets, rearranging a formula for safe office occupancy, and setting up simultaneous equations from a growth model all fall under this heading, spanning single-step manipulation to multi-stage problems.
Find, complete, show, calculate and work out lead the command words, worth anywhere from 1 to 19 marks, reflecting 75 real questions drawn from 2025 papers. Because a single slip in expanding brackets can cascade through a long question, practise each stage of simplification separately, then submit your working for instant marking so a sign error or missed term is caught on that line rather than at the final answer.
May–June 2025, Paper 11
Write down all the integer values of x that satisfy this inequality. -3 <= x < 2
Answer this question and get it marked →Solve the simultaneous equations. 2x + 3y = 5 3x - 5y = 17
Answer this question and get it marked →May–June 2025, Paper 12
These are the first four terms of a sequence. 2 5 10 17 Find the next two terms of the sequence.
Answer this question and get it marked →These are 4 graphs, A, B, C and D. Complete the following sentence. The equation y = 2x + 3 is represented by graph ......
Answer this question and get it marked →May–June 2025, Paper 13
These are the first 5 terms of a sequence. 2 6 10 14 18 Write down the next term in this sequence.
Answer this question and get it marked →T = 3x - 4y Find the value of T when x = 5 and y = -2.
Answer this question and get it marked →Write 60 as a product of its prime factors.
Answer this question and get it marked →May–June 2025, Paper 21
P = 2^3 x 3^a x 5^b x 7 Q = 2 x 3^5 x 7^c The highest common factor (HCF) of P and Q is 2 x 3^4 x 7. The lowest common multiple (LCM) of P and Q is 2^3 x 3^5 x 5^2 x 7. Find the…
Answer this question and get it marked →These are the first 5 terms of a sequence. 1 7 17 31 49 Find the next term of the sequence.
Answer this question and get it marked →Expand and simplify. (x - 4)(2x + 1)(x + 2)
Answer this question and get it marked →y is inversely proportional to x^3. y = 1 when x = 2. Find y in terms of x.
Answer this question and get it marked →May–June 2025, Paper 22
Expand and simplify. 5(2x - 1) - 3(3 + 4x)
Answer this question and get it marked →Find the lowest common multiple (LCM) of these expressions. 2x^3 y^4 3x^2 z^3 4y^2 z
Answer this question and get it marked →Find the next term and the nth term in the sequence. 12, 14, 16, 18, 20, ....
Answer this question and get it marked →Apples cost $2.50 per kilogram. The total cost of x kg of apples and y kg of pears is $10. Find the cost of 1 kg of pears. Give your answer in terms of x and y.
Answer this question and get it marked →May–June 2025, Paper 23
The cost of a bar of chocolate is $c. The cost of a packet of sweets is $p. The total cost of 5 bars of chocolate and 2 packets of sweets is $13. The total cost of 7 bars of…
Answer this question and get it marked →y^(2k) x y^3 = 1/y Find the value of k.
Answer this question and get it marked →Rearrange 4y - 3x = 1 - py to write y in terms of p and x.
Answer this question and get it marked →Solve. Give each answer as an exact value. 2^x = 5
Answer this question and get it marked →These are the first 5 terms of a sequence. 3 6 12 24 48 Find the next term of the sequence.
Answer this question and get it marked →Write as a single fraction in its simplest form. 2 - 3/(x - 2)
Answer this question and get it marked →May–June 2025, Paper 31
These are the first 4 terms of a sequence. 5 11 17 23 Write down the rule for continuing this sequence.
Answer this question and get it marked →The equation of line L is 3y − x = 12. Rearrange 3y − x = 12 to make y the subject.
Answer this question and get it marked →May–June 2025, Paper 32
A = (1/2)(x + 2y) Find the value of A when x = 7.23 and y = 2.16.
Answer this question and get it marked →May–June 2025, Paper 33
A company uses this formula to work out the number of people who can safely work in an office. N = (L × W) / 15 L is the length of the office in metres. W is the width of the…
Answer this question and get it marked →May–June 2025, Paper 41
s = (u + v)/2 × t Find s when u = 4.3, v = 9.5 and t = 8.5 .
Answer this question and get it marked →Pierre drives from town P to town Q and then to town R. The distance from P to Q is 112 km. The distance from Q to R is 87 km. The average speed from P to Q is x km/h. The average…
Answer this question and get it marked →May–June 2025, Paper 42
A = (1/2)(x + y)h Find the value of A when x = 7, y = 12.5 and h = 6.
Answer this question and get it marked →y varies inversely as the square root of (x - 1). y = 1 when x = 5. Find y in terms of x.
Answer this question and get it marked →May–June 2025, Paper 43
w is proportional to sqrt(x + 1). When x = 3, w = 8. Find x when w = 20.
Answer this question and get it marked →Priya buys pieces of fruit. The pieces of fruit are apples and oranges. The price of 1 apple is x cents. The price of 1 orange is (x + 10) cents. Priya spends 420 cents on apples.…
Answer this question and get it marked →Simplify. (3x - 5) / (3xy - 3x - 5y + 5)
Answer this question and get it marked →May–June 2025, Paper 51
The sequence is 5, 6, 7, 8. Complete the statements. Product of inside pair 6 x .......... = 42 Product of outside pair 5 x .......... = 40 Product difference 42 - 40 = 2
Answer this question and get it marked →Each sequence in this question has 4 terms. In these sequences the increase is more than 1. Complete the table. Sequence Increase Product of inside pair Product of outside pair…
Answer this question and get it marked →Find the sequence that has a product difference of 578 and a last term of 100. .......... , .......... , .......... , 100
Answer this question and get it marked →May–June 2025, Paper 52
Write down the core integer and the shell integers for the sequence 5 6 7 8 9 10 11 12 13.
Answer this question and get it marked →Calculate C and S for the exponential sequence 2 6 18 54 162.
Answer this question and get it marked →Calculate C and S for the sequence of 3 consecutive terms in the Fibonacci sequence formed by the 2nd, 3rd and 4th terms. 1 2 3
Answer this question and get it marked →Complete the table. (The first row, 17 18 19, has common difference d = 1 and F = 1. In the third row, 14 20 ..., and in the fourth row, 20 ... 40, the missing last/middle terms…
Answer this question and get it marked →May–June 2025, Paper 53
In this investigation you will look at the numbers in a pyramid of numbers. The numbers are placed in order in rows. Each row has one more number than the row above. The pyramid…
Answer this question and get it marked →The numbers at the end of the rows of the number pyramid make this sequence: 1, 3, 6, 10, 15, ... Complete the statement. This is the sequence of ........................ numbers.
Answer this question and get it marked →To find a number in the pyramid add its position in the row to the last number in the row above. For example, N(6, 4) = 15 + 4 = 19, since the last number in row 5 is 15 and the…
Answer this question and get it marked →Numbers in the pyramid can be joined to make a diamond, written D(a, b, c, d) with the four numbers in order from smallest to largest. The width is c - b (the difference between…
Answer this question and get it marked →May–June 2025, Paper 61
The sequences in this question have 4 terms. Complete the table. Sequence Increase Product of inside pair Product of outside pair Product difference --- --- --- --- --- 1, 2, 3, 4…
Answer this question and get it marked →A sequence has 3 terms. The multiplication of the inside pair is the middle number squared. Example for the sequence 1, 2, 3: product of inside pair 2 x 2 = 2^2 = 4; product of…
Answer this question and get it marked →May–June 2025, Paper 62
Write down the core integer and the shell integers for the sequence 5 7 9 11 13 15 17 19 21.
Answer this question and get it marked →Write down a linear sequence with 5 terms. .......... , .......... , .......... , .......... , ..........
Answer this question and get it marked →The general linear sequence has 1st term a and common difference d. So the first 3 terms of this sequence are a, a+d, a+2d. Write the 7th term of the general linear sequence in…
Answer this question and get it marked →Complete the table. Linear sequence with common difference d - 1st term Middle term Last term Number of terms n F --- --- --- --- --- a a+d a+2d ( )^2 a a+2d 5 ( )^2 a 7 ( )^2 a…
Answer this question and get it marked →A linear sequence has n terms. The common difference is d. F = 100d^2 Find the number of terms in the sequence.
Answer this question and get it marked →The best release angle A is approximately 45 degrees. This angle gives the greatest horizontal distance that the hammer travels after release. An Olympic athlete uses the best…
Answer this question and get it marked →May–June 2025, Paper 63
In this investigation you will look at the numbers in a pyramid of numbers. The numbers are placed in order in rows. Each row has one more number than the row above. (Row 1…
Answer this question and get it marked →To find a number in the pyramid add its position in the row to the last number in the row above. Example: N(6, 4) is in row 6. The last number in row 5 is 15. N(6, 4) is in…
Answer this question and get it marked →Numbers in the pyramid can be joined to make a diamond. The four numbers are always written in order from smallest to largest. A diamond D(a, b, c, d) has a width equal to the…
Answer this question and get it marked →Irene uses this model for the length of a kingfish: L = ax^2 + bx + 2. Use the lengths at age 10 years (L = 94) and at age 20 years (L = 122) to write two equations in terms of a…
Answer this question and get it marked →Other IGCSE Mathematics - International topics
- Number (70)
- Statistics (21)
- Geometry (20)
- Mensuration (18)
- Functions (14)
- Trigonometry (14)
- Coordinate geometry (8)
- Vectors and transformations (8)
- Sets (6)
- Probability (5)