1Question 1
3 marks
Solve x² − 5x + 6 = 0. (3 marks)
Model answer
(x − 2)(x − 3) = 0 So x − 2 = 0 or x − 3 = 0 x = 2 or x = 3
Mark scheme
- Correct factors (x − 2)(x − 3), or an equivalent pair1 mark
- x = 21 mark
- x = 31 mark
WASSCE SHS
WASSCE Core Mathematics: Quadratic equations
A quadratic equation has the unknown squared, and no higher power. It can have two solutions, one solution, or none among the real numbers.
The idea
The standard form is ax² + bx + c = 0, with a not equal to zero. If the left side factorises into two brackets, set each bracket equal to zero and solve the two linear equations. That works cleanly when the numbers are integers. Check by expanding the brackets: you should get back the original quadratic. A solution that does not satisfy the original equation is a slip in a sign.
When factorising is awkward, the quadratic formula gives the solutions from a, b and c. You still begin by arranging the equation into standard form, because a sign error in c changes both answers. A word problem becomes a quadratic only after you define the unknown and write the sentence as an equation. The final line should answer the sentence. If a length comes out negative, reject it and say why. A length cannot be negative.
What earns the marks
Method and accuracy are separate. Expanding to check is not required unless the question asks, but a sign error in a bracket is a method error and it usually spoils both roots. Give both solutions. x = 2 alone, when the equation also has x = 3, is incomplete. Reject a result that the original story cannot use, and write the rejection. That sentence is often a mark.
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 x² − 4x − 5 = 0. (3 marks)
Model answer
(x − 5)(x + 1) = 0 x = 5 or x = −1
Mark scheme
- Factors (x − 5)(x + 1)1 mark
- x = 51 mark
- x = −11 mark
3Question 3
4 marks
The square of a positive number is 20 more than the number. Find the number. (4 marks)
Model answer
Let the number be n. n² = n + 20 n² − n − 20 = 0 (n − 5)(n + 4) = 0 n = 5 or n = −4 The number is positive, so n = 5.
Mark scheme
- Equation n² = n + 20, or equivalent1 mark
- Rearranged to n² − n − 20 = 0 and factorised1 mark
- Both roots 5 and −4 found1 mark
- Rejects −4 and states n = 5 because the number is positive1 mark
Practise Core Mathematics with Anna
More questions on this topic are inside GLearn, marked as you answer, with the reason written out. The first ones need no account.
Practise Core Mathematics free