1Question 1
3 marks
Solve 4x − 7 = 13. (3 marks)
Model answer
4x = 13 + 7 4x = 20 x = 5
Mark scheme
- Adds 7 to both sides, or an equivalent first move1 mark
- 4x = 201 mark
- x = 51 mark
BECE JHS
BECE Mathematics: Linear equations
A linear equation has the unknown to the power one. You isolate it by doing the same operation to both sides.
The idea
An equation is a balance. Whatever you add, subtract, multiply or divide on one side, you do on the other, and the two sides stay equal. Collect the terms that contain the unknown on one side and the numbers on the other. If a bracket is in the way, expand it first. If the unknown is in a fraction, multiply through by the denominator.
Check the answer by substituting it back into the original equation. If both sides agree, the solution is right. A linear equation in one unknown has one solution. Two different unknowns need two equations, which is a later skill. Show each line of working. A correct final number with no working often loses the method marks.
What earns the marks
Award method marks for a correct first step even when the arithmetic later slips. The last mark is for the value, with the unknown named. A candidate who writes 5, and never says x = 5, can lose that mark. Substituting back is good practice. It is not usually a marked line unless the question asks for a check.
Practice questions
These are practice questions in the style of the paper, with a model answer and a mark scheme. They are not a promise of what your paper will ask.
2Question 2
3 marks
Solve 3(x + 2) = 21. (3 marks)
Model answer
3x + 6 = 21 3x = 15 x = 5
Mark scheme
- Expands the bracket to 3x + 6, or divides both sides by 3 first to get x + 2 = 71 mark
- Reaches 3x = 15, or x + 2 = 71 mark
- x = 51 mark
3Question 3
4 marks
The sum of a number and 9 is three times the number. Find the number. (4 marks)
Model answer
Let the number be n. n + 9 = 3n 9 = 2n n = 4.5 Check: 4.5 + 9 = 13.5, and 3 × 4.5 = 13.5.
Mark scheme
- Defines the unknown in a sentence or a line1 mark
- Writes n + 9 = 3n, or an equivalent equation1 mark
- Collects terms correctly, for example 9 = 2n1 mark
- n = 4.5 or 9/21 mark
Practise Mathematics with Kevin
More questions on this topic are inside GLearn, marked as you answer, with the reason written out. The first ones need no account.
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