Thankfully, there is no real GCSE in algebra. But if there was, would you pass?

1. Which of the below options is a simplified version of this expression?
a – 67a – 67a + 10Starting with 4a – (3a + 6) you first simplify by removing the brackets, to get 4a – 3a – 6. Subtracting 3a from 4a gives the final answer: a – 6.

2. When a = 3 and b = 2, which of the following expressions has the lowest value?
b/a is equal to two thirds, a – b is 1 and ab is 6.

3. There are two values of w for which the below equation is true. Someone tells you the values are w = 1 and w = 1. Are they right?
Yes, that person must be very good at maths.No, they're lying.w = 1 works, but if you set w as 1 the above expression works out as 2. The two correct values are 1 and 2.

4. Solve this inequality:
x > 5x < 5x > 3x < 3The expression simplifies to 3x > 15, so x > 5.

5. Solve the following equation:
y = 6y = 7y = 88y = 64, so y = 8.

6. Which of the following expressions is equivalent to this expression?
x² + y²2x + y²2x + 2y²x + x = 2x and y * y = y² so the full expression is 2x + y².

7. Which of these sequences is a geometric progression?
1, 2, 3, 41, 2, 3, 51, 2, 3, 61, 2, 4, 8In a geometric progression each number is multiplied by the same common factor to get the next term. In the sequence 1, 2, 4, 8 the common factor is 2.

8. Which of the below options describes a line that is parallel to this one:
y = x + 10y = 2x – 5y = 10x + 2The number before the x is the gradient of the line, so y = 2x – 5 is parallel to y = 2x + 10.

9. What are the two solutions to this equation?
Write your answer in the format x, x.
For the equation to be true, either x – 4 = 0 or x + 8 = 0.

10. Is the following statement true or false?
TrueFalsex could also be 4.

11. Which of these numbers appears in both of these sequences?
235The 2nd term in both sequences is 5.

12. Solve these simultaneous equations:
x=1, y=2x=2, y=2x=2, y=4If you substitue y=2x into the first equation you get 5x=10, so you know x=2. Then just put that into y=2x to get y=4.
Kelly Oakes is science editor for BuzzFeed and is based in London.
Contact Kelly Oakes at kelly.oakes@buzzfeed.com.
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